Enhancing Antenna Design Through Simulation Software

An antenna model is a representation of a real-world antenna in a computer program. This type of model should not be confused with a scale model, which is sometimes built to measure the radiation characteristics of a larger physically-sized, identical antenna. Due to the mathematical complexity involved in modeling, computer software is often programmed to predict and analyze antenna performance.

Computer simulation in the industry is used to overcome challenges and drive innovation in the product creation and development processes. A computer model offers the advantage of being easily modified, redesigned, broken, destroyed, and rebuilt multiple times without wasting materials. Therefore, the design process can achieve a significant reduction in the cost of building successive physical models with the aid of simulation software.

AN-SOF is a comprehensive simulation software suite for antenna modeling and design. It facilitates the design of various wire antennas, such as dipoles, monopoles, yagis, log-periodic arrays, helices, spirals, loops, horns, fractals, phased arrays, and many other antenna types. Additionally, AN-SOF supports the modeling of feeding systems using transmission lines, allowing for a detailed analysis of antenna configurations. The software is capable of simulating antennas positioned above lossy ground planes or broadcast antennas above radial wire ground screens.

Moreover, AN-SOF’s calculation method has been expanded to include single-layer microstrip patch antennas and the computation of radiated emissions from Printed Circuit Boards (PCBs). Consequently, AN-SOF can be effectively utilized for Electromagnetic Compatibility (EMC) Applications. The software accommodates passive circuits with lumped impedances and non-radiated networks, enabling a comprehensive analysis of antenna systems.

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In the realm of antenna applications, AN-SOF proves invaluable as it empowers users to achieve the following:

• Design superior antennas.
• Predict and optimize antenna performance.
• Fine-tune antenna parameters for optimal results.
• Account for environmental effects on antenna performance.
• Employ script-based optimization to refine designs.
• Gain valuable insights into antenna behavior.
• Experiment multiple times prior to physically building the antenna model.
• Deepen understanding of antennas and their properties.
• Facilitate knowledge sharing and collaboration with colleagues.

Embrace the excitement of this fascinating field with AN-SOF at your disposal!

With AN-SOF, the possibilities for antenna analysis and optimization are extensive, providing a comprehensive toolkit for antenna design and performance evaluation.

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AN-SOF enables us to perform a wide range of tasks, including:

• Describing the antenna’s geometry accurately.
• Selecting appropriate construction materials.
• Specifying the environmental and ground conditions.
• Determining the antenna’s height above the ground.
• Analyzing the radiation pattern and front-to-back ratio.
• Plotting directivity and gain.
• Evaluating impedance and SWR (Standing Wave Ratio).
• Predicting bandwidth.
• Obtaining numerous additional parameters and plots.

The structure’s geometry can be easily drawn in AN-SOF using the mouse, menus, and user-friendly dialog windows. Wires are drawn in a 3D space, where tools are available to zoom, move, and rotate the structure.

To plot the results from a simulation, a suite of integrated applications allows us to display graphs: AN-XY Chart, AN-Smith, AN-Polar, and AN-3D Pattern. These tools can also be executed independently for subsequent graphic processing.

Introduction to AN-SOF: Antenna Simulation Essentials

AN-SOF performs computations of electric currents flowing on metallic structures, including antennas in transmitting and receiving modes, as well as scatterers. A scatterer refers to any object capable of reflecting and/or diffracting radiofrequency waves. For instance, wave scattering analysis can be conducted on the surface of an aircraft to determine optimal antenna placement, on a parabolic reflector to examine gain in relation to the reflector shape, or on a car’s chassis to predict interference effects.

The Method of Moments (MoM) stands as one of the most widely validated techniques for antenna simulation. AN-SOF incorporates an enhanced and advanced version of this method called the Conformal Method of Moments (CMoM) with Exact Kernel, which addresses various challenges associated with traditional MoM approaches and achieves unparalleled accuracy.

Interested in learning more about the CMoM implementation in AN-SOF? Read this article >.

According to the MoM, any metallic structure can be represented using conductive wires, as illustrated in Fig. 1. These wires are subdivided into small segments, which assume the shape of cylindrical tubes. To obtain accurate results, the length of each wire segment should be comparatively short compared to the wavelength, as depicted in Fig. 2. However, this concern can be alleviated during the initial simulation since AN-SOF automatically handles the segmentation of wires.

The flow of electric currents within the structure can be achieved by introducing a voltage generator at a specific location operating at a given frequency. Current generators can also serve as the excitation source, alongside plane waves impinging on the structure from distant sources. Once the geometry, materials, and sources of the structure are defined, the computation can be executed to determine the currents flowing through the wire segments. Generally, these electric currents exhibit varying intensities along and across the structure, collectively referred to as a current distribution. Fig. 3 showcases an example of the current distribution on a log-periodic antenna.

In the subsequent phase of the simulation process, the electromagnetic field radiated by the current distribution can be calculated. However, the current distribution itself provides valuable insights into the behavior of the structure, particularly when a frequency sweep is conducted. In the case of antennas, the feed point impedance can be analyzed as a function of frequency to assess the bandwidth. The Voltage Standing Wave Ratio (VSWR) can be plotted on a Smith chart for better interpretation of the results, as demonstrated in Fig. 4. The electric and magnetic fields in the proximity of the structure, known as the near-field zone, can be obtained and visualized as a color map, with intensities often resembling temperature maps used in weather forecasts, as shown in Fig. 5.

In the far-field zone, situated several wavelengths away from the structure, the magnetic field becomes proportional to the electric field. As a result, the electric field intensities are commonly used to analyze the results. This region is depicted in polar diagrams, as illustrated in Fig. 6, where the radiated field is represented as a function of direction. A more comprehensive representation can be achieved by plotting a 3D pattern, where radiation lobes can be superimposed onto the structure’s geometry, providing enhanced visualization of its directional properties, as exemplified in Fig. 7.

AN-SOF stands out as the easiest-to-use software tool for simulating antennas, particularly those that can be modeled using conductive wires. Are you ready to embark on your first simulation? Let’s get started!

Performing the First Simulation with AN-SOF

Several example files are included in the AN-SOF installation directory, located within a folder named “Examples”. When opening a file with the extension “.emm”, the wire structure will be displayed on the screen. To run the calculation, click on the Run ALL button on the toolbar. The main results can be plotted by clicking on the following buttons: Plot Current Distribution, Far-Field 3D Plot, and Far-Field Polar 1 Slice.

As a first experience using AN-SOF, let’s simulate a standard half-wave dipole, which is one of the simplest antennas that can be modeled. A dipole is a straight wire that is fed at its center. When the wire’s cross-section is circular, it is referred to as a cylindrical antenna. Since the wire is typically made of a highly conductive material, it can be considered a perfect conductor with zero resistivity. Therefore, we will model a cylindrical antenna with zero resistivity in this example. Follow the steps below to perform this simulation.

Step 1: Setup

The first step is to set the operating frequency. Navigate to the Setup tab in the AN-SOF main window. Within the Frequency panel, there are three options to choose from. Select Single and enter the operating frequency for the antenna (see Fig. 8). In this case, the frequency is given in megahertz (MHz), and lengths are measured in meters (m). If desired, you can change the unit system for frequencies and lengths by going to Tools > Preferences. Please note that for a frequency of 300 MHz, the wavelength is approximately 1 meter (0.999308 m).

Step 2: Draw

Once the operating frequency has been set, you can draw the antenna geometry on the Workspace tab. The workspace is where the wire structure is visualized, representing a 3D space that allows zooming, rotation, and movement.

In AN-SOF, a straight wire is referred to as a Line. To draw a line, go to the main menu and select Draw > Line. This will open the Draw dialog box. In the Line tab, you can set the coordinates of two distinct points.

For this example, we will create a line along the z-axis that is 0.5 meters long, corresponding to half a wavelength at 300 MHz. Figure 9 illustrates the chosen starting point of the line at (X1, Y1, Z1) = (0, 0, -0.25) m, and the ending point at (X2, Y2, Z2) = (0, 0, 0.25) m. Next, switch to the Attributes tab (see Fig. 10). To ensure accurate results, the line should be divided into segments that are relatively short compared to the wavelength. Generally, a segment length equal to or less than one-tenth of a wavelength is considered short. AN-SOF suggests a minimum number of segments to achieve reliable results automatically. If you require higher resolution, you can increase the number of segments.

In this case, the line will be divided into 17 segments, and the wire cross-section will be circular with a radius of 5 millimeters. On the Materials tab (refer to Fig. 11), you can set the wire’s resistivity to zero.

The next step is to feed the dipole. Right-click on the wire and select the Source/Load command from the pop-up menu that appears. A toolbar with a slider will be displayed at the bottom of the screen. Move the slider to the segment located at the center of the wire. Then, click the Add Source button. Add a voltage source with an amplitude of 1 Volt and a phase of zero (see Fig. 12).

Step 3: Run

To run the calculation, go to Run > Run Currents in the main menu. Once the calculations are completed, proceed to Run > Run Far-Field in the main menu. This will calculate the current distribution on the dipole antenna and the radiated field.

AN-SOF provides integrated graphical tools for result visualization. Right-click on the wire and select Plot Currents from the displayed pop-up menu. A plot showing the current distribution in amplitude along the dipole antenna will be displayed (refer to Fig. 13). Since a half-wave dipole has been drawn, the resulting current distribution resembles a semi-cycle approaching a sine function.

You can obtain several parameters from the perspective of the voltage source connected to the antenna terminals. Right-click on the wire and select List Currents from the pop-up menu. Move the slider to the position of the voltage source and click on the Input List button. This will display the input impedance of the dipole antenna, along with many other parameters (see Fig. 14).

Alternatively, you can obtain the input impedance by simply clicking on the List Input Impedances (Zin) button in the main toolbar. To represent the radiation pattern in a 3D plot, navigate to Results > Plot Far-Field Pattern > 3D Plot in the main menu. The normalized radiation pattern will be displayed in the AN-3D Pattern application. A color bar-scale indicates the field intensities over the radiation lobes. Additionally, you can plot the directivity, gain, and electric field patterns by accessing the Plot menu in AN-3D Pattern. In the case of a half-wave dipole, it exhibits omnidirectional characteristics in the plane perpendicular to the dipole axis (xy-plane) (refer to Fig. 15).

As you have just experienced, a simulation consists of three simple steps. We hope you have enjoyed this example. For additional step-by-step examples, please visit our section titled Examples > Step by Step.

Summary

The key advantages of AN-SOF can be summarized as follows:

• AN-SOF is antenna modeling and design software that offers fast and user-friendly input and output graphical interfaces.

• AN-SOF employs the Conformal Method of Moments with Exact Kernel, resulting in enhanced accuracy and speed.

• AN-SOF provides an extended frequency range, enabling simulations from extremely low frequencies (such as 60 Hz circuits) to microwave antennas.

Simulating a wire structure involves a three-step procedure:

1. Setup: Set frequencies, environment, and desired results.

2. Draw: Draw the geometry, specify materials, and add sources.

3. Run: Perform the calculation and visualize the results.

At the beginning of the simulation, you can choose a convenient unit system for frequencies and lengths. This choice can be adjusted later by accessing Tools > Preferences. For instance, wire lengths are typically measured in meters (m) or feet (ft) for frequencies below 100 MHz, while millimeters (mm) or inches (in) are commonly used for higher frequencies.

Features and Capabilities

AN-SOF is a comprehensive software tool for the modeling and simulation of antenna systems and radiating structures in general.

AN-SOF is intended for solving problems in the following areas:

• Modeling and design of wire antennas.
• Antennas above a lossy ground plane.
• Broadcast antennas over radial wire ground screens.
• Single layer microstrip patch antennas.
• Radiated emissions from printed circuit boards (PCBs).
• Electromagnetic Compatibility (EMC) applications.
• Passive circuits, transmission lines, and non-radiating networks.

AN-SOF is based on an improved version of the so-called Method of Moments (MoM) for wire structures. Metallic objects like antennas can be modeled by a set of conductive wires and wire grids, as it is illustrated in Fig. 1. In the MoM formulation, the wires composing the structure are divided into segments that must be short compared to the wavelength. If a source is placed at a given location on the structure, an electric current will be forced to flow on the segments. The induced current on each individual segment is the first quantity calculated by AN-SOF.

Once the current distribution has been obtained, the radiated electromagnetic field can be computed in the far- and near-field zones. Input parameters at the position of the source or generator can also be obtained, such as the input impedance, input power, standing wave ratio (SWR), reflection coefficient, transmission loss, etc.

The modeling of the structure can be performed by means of the AN-SOF specific 3D CAD interface. Electromagnetic fields, currents, voltages, input impedances, consumed and radiated powers, directivity, gain and many more parameters can be computed in a frequency sweep and plotted in 2D and 3D graphical representations.

In the case of curved antennas like loops, helices, and spirals, the MoM in AN-SOF has been improved to accurately account for the wire’s exact curvature. Traditional calculations often use straight-line segments to approximate curved antennas, resulting in many discontinuous wire junctions. This linear approximation can be inefficient in terms of computer memory and the number of calculations required, as it necessitates multiple straight segments to mimic the smooth curvature of wires. To address this issue, AN-SOF uses curved segments that precisely follow the contours of curved antennas. This innovative technique is known as the Conformal Method of Moments (CMoM).

As an example, Fig. 2 shows the different approaches to a circular disc obtained by means of the MoM and CMoM methods. Both methods are available in AN-SOF since the MoM is a special case of the more general CMoM.

In addition to the CMoM capabilities, advanced mathematical techniques have been implemented in the calculation engine making possible simulations from extremely low frequencies (e.g., electric circuits at 50-60 Hz) to very high ones (e.g., microwave antennas above 1 GHz).

In what follows, a summary of the modeling options and the simulation results that can be obtained from AN-SOF is presented.

Modeling of Metallic Structures

Metallic structures can be modeled by combining different types of wires, grids, and surfaces:

Wires

• Linear wire
• Circular arc
• Circular loop
• Helix
• Quadratic wire
• Archimedean spiral
• Logarithmic spiral

Wire Grids and Solid Surfaces

• Patch
• Plate
• Disc
• Flat ring
• Cone
• Truncated cone
• Cylinder
• Sphere
• Paraboloid

1. All types of curved wires can be modeled by means of arced or quadratic segments.
2. Wire grids and solid surfaces can be defined using either curved or straight wire segments. Curved segments follow the exact curvature of discs, rings, cones, cylinders, spheres, and parabolic surfaces. Grids are composed of cylindrical wires that leave holes between them, while solid surfaces are composed of flat wires or strips that cover the surface without leaving holes between them.
3. Tapered wires with stepped radii can be defined.
4. All wires can be loaded or excited at any segment.
5. The structure can also have finite non-zero resistivities (skin effect).
6. Electrical connections of different wires and connections of several wires at one point are possible.
7. Metallic wires in either dielectric or magnetic media can be analyzed.
8. Wires with insulation can be modeled. Dielectric and magnetic coatings are available.
9. The structures can be placed in free space, over a perfectly conducting ground plane or over an imperfect ground plane.
10. Flat strip lines can be defined on a dielectric substrate for modeling planar antennas and printed circuit boards (PCB).
11. Vias in microstrip antennas and printed circuit boards can also be modeled.
12. The wire cross-section can either be Circular, Square, Flat, Elliptical, Rectangular or Triangular.
13. Transmission lines can be connected to the metal structure. There are over 160 cable models available, including two-wire and coaxial cables, with characteristic impedance, velocity factor, and loss parameters adjusted to actual datasheets.
14. The geometry modeling can be performed in suitable unit systems (um, cm, mm, m, in, ft). Different unit systems can also be chosen for inductance (pH, nH, uH, mH, H) and capacitance (pF, nF, uF, mF, F).

Excitation Methods

1. Voltage sources can be placed on the wires, as many as there are segments, with equal or different amplitudes (RMS values) and phases.
2. Current sources (e.g., representing impressed currents) can also be arranged at any segments.
3. The voltage and current sources can have internal impedances.
4. An incident plane wave of arbitrary polarization (linear, circular, or elliptical) and direction of incidence can also be used as the excitation.
5. Hertzian electric and magnetic dipoles can also be modeled and used as the excitation.
6. The antenna input power can be set to obtain the results (current distribution, near and far fields) scaled accordingly.

Frequency options

1. The simulation can either be performed for a single frequency, for frequencies taken from a list or for a frequency sweep.
2. The list of frequencies can either be created inside the program or loaded from a text file. It can also be saved to a txt file.
3. Linear and logarithmic frequency sweeps are possible.
4. A suitable unit system can be selected (Hz, KHz, MHz, GHz).

Data Input

1. 3D CAD tools are implemented for drawing and modifying the structure geometry, including wires, grids, surfaces, discrete generators, and lumped loads.
2. The segmentation of wire geometry can be done automatically or manually.
3. Left-clicking on a wire selects and highlights it. Right-clicking on a wire reveals a pop-up menu with various options.
4. Wire connections are easily established by copying and pasting the endpoints of wires.
5. Special 3D symbols indicate the positions of sources, load elements, and ground points.
6. All dialog boxes validate inputs for accuracy.
7. The program includes mouse-supported functions for rotating, moving, and zooming.
8. Transmission lines can be easily entered into a table, which serves as a library, for later use. A line is highlighted in the graphical interface for easy identification.
9. The program allows you to import geometrical data from text files. It supports three different file formats for importing wires, including the NEC (Numerical Electromagnetics Code) cards. Additionally, it can import DXF files containing 3D LINE entities.
10. The AN-SOF architecture integrates powerful numerical methods to achieve the fastest calculation speed and the most accurate results.

Data Output

1. All computed data is stored in files for subsequent graphical analysis.
2. Input impedances, currents, voltages, VSWR, S₁₁, return and transmission losses, radiated and consumed powers, efficiency, directivity, gain, and other system responses are presented as lists in text format and can be plotted against frequency. A Smith chart is available to represent impedances and admittances, as well as to display the reflection coefficient and VSWR at the selected point on the graph.
3. The current distribution on a selected wire can be plotted in amplitude, phase, real, and imaginary parts against position in a 2D representation. The currents flowing on a structure can also be plotted as a color map on the wires.
4. Radiation and scattering fields are obtained, including power density, directivity and gain patterns, total electric field, linearly and circularly polarized components, axial ratio, and Radar Cross Section (RCS). The surface-wave field can be determined as a function of distance in the case of a real ground with finite conductivity.
5. Near-field components can be calculated in Cartesian, cylindrical, and spherical coordinates. Field intensities can be plotted in 2D and 3D graphical representations and visualized as color maps in the proximity of a structure.
6. A 2D representation of radiated fields is available in Cartesian and polar coordinates. The ARRL-style log scale can be applied to polar diagrams.
7. 3D radiation patterns can be viewed from arbitrary angles with zoom functions, colored mesh and surface representations, and a color bar scale. 3D patterns can be plotted with specially designed lighting and illumination for enhanced visualization of simulation results.
8. Far-field patterns can be separated into theta (vertical) and phi (horizontal) linearly polarized components, as well as right and left circularly polarized components. The axial ratio and the front-to-rear and front-to-back ratios are shown in polar plots and can be displayed as a function of frequency.
9. The frequency spectrum of near- and far-fields can be visualized in a 2D representation for all field components across different frequencies.
10. An average radiated power test, also known as AGT (Average Gain Test), is conducted to verify the accuracy of the simulation.
11. The calculated data can be exported to .csv, .dat, or .txt files for use in other software programs.
12. An embedded transmission line calculator is included to simplify the design of feed lines for transmitting antennas. Actual cable part numbers can be selected from a wide range of manufacturers, thanks to data extracted from cable datasheets and integrated into the calculator.
13. A Bulk Simulation feature enables the automated calculation of multiple files, each with different geometric descriptions, to obtain results based on variable geometric parameters. The results are automatically exported to .csv files for further processing.
14. You can choose suitable unit systems for the plotted results, including current scaling (KA, A, mA, uA), voltage scaling (KV, V, mV, uV), electric field scaling (KV/m, V/m, mV/m, uV/m), magnetic field scaling (KA/m, A/m, mA/m, uA/m), decibel scales, and more.

Integrated graphical tools

AN-SOF has a suite of integrated graphical tools for the convenient visualization of the simulation results. The following applications are installed automatically and used by the main program, AN-SOF:

A friendly 2D chart for plotting two related quantities, Y versus X. Use AN-XY Chart to plot parameters that depend on frequency, such as currents, voltages, impedances, reflection coefficient, VSWR, S₁₁, radiated power, consumed power, directivity, gain, radiation efficiency, radar cross section, field components, axial ratio, and many more. Also plot the current distribution along wires as a function of position, 2D slices of radiation lobes and near fields as a function of distance from an antenna. Choose different units to display results and use the mouse to easily zoom and scroll graphs.

Plot impedance or admittance curves on the Smith chart with this tool. Just click on the graph to get the frequency, impedance, reflection coefficient, VSWR, and S₁₁ that correspond to each point on the curve. Plots can be stored in independent files and opened later for a graphical analysis with AN-Smith.

Plot on a polar diagram the radiation pattern versus the azimuth (horizontal) or zenith (vertical) angles. The maximum, -3dB and minimum radiation levels are shown within the chart as well as the beamwidth and front-to-rear/back ratio. Click on the graph to quickly obtain the values of the radiated field. The represented quantities include power density, directivity, gain, normalized radiation pattern, total electric field, linearly and circularly polarized components, axial ratio, and radar cross section (RCS).

Get a complete view of the radiation properties of a structure by plotting a 3D radiation pattern. AN-3D Pattern implements colored mesh and surface for the clear visualization of radiation lobes, including a color bar-scale indicating the field intensities over the lobes. Quickly rotate, move, and zoom the graph using the mouse. The 3D radiation pattern can be superimposed to the structure geometry to gain more insight into the directional properties of antennas.

The represented quantities include the power density, normalized radiation pattern, directivity, gain, total field, linearly and circularly polarized components, axial ratio, and Radar Cross Section (RCS). Choose between linear or decibel scales. Display near fields as color maps in the proximity of antennas in three different representations: Cartesian, cylindrical and spherical plots. Also plot the current distribution on the structure as a colored intensity map.

Main Window and Menu

When AN-SOF is started, the initial screen contains the following components:

The title bar contains the name of the currently active project (.emm file).

The main menu bar contains the File, Edit, Draw, View, Tools, Run, Results, and Help menus.

The main toolbar contains icons that represent commands.

The tab sheets allow us to quickly switch between pages, from Setup to Plots.

The workspace is the page where the wire structure can be drawn in a 3D space.

The status bar contains information about the number of segments, connections, and ground points.

File Menu

Use the File menu to open, save, close, and print new or existing projects. This menu has the following commands:

New… (Ctrl + N)

Creates a new project.

Open… (Ctrl + O)

Displays the Open dialog box for opening an existing project (.emm file).

Save (Ctrl + S)

Saves the currently active project using its current name.

Save As…

Saves the currently active project using a new name. Also saves a new project using a name specified by the user.

Import Wires

Displays the Import dialog box for importing a list of wires in either AN-SOF (.wre files), NEC, DXF (CAD files) or MM format.

Export Wires

Displays the Export dialog box for exporting wires to a NEC or DXF file.

Copy Workspace

Sends the project workspace to the clipboard as a bitmap image.

Print… (Ctrl + P)

Sends the project workspace to the printer.

Exit (Ctrl + Q) Closes the project that is open and then exits AN-SOF.

Edit Menu

Use the Edit menu commands to edit and handle wires and wire grids. This menu has the following commands:

Undo (Ctrl + Z)

Returns the project to the status before a command was executed.

Source/Load (Ctrl + Ins)

Displays the Source/Load toolbar for exciting or loading the selected wire. This command is enabled when a wire is selected.

Modify (Ctrl + M)

Displays the Modify dialog box for modifying the selected wire or wire grid. This command is enabled when a wire or wire grid is selected.

Wire Color

Displays a Windows(R) dialog box for changing the color of the selected wires. This command is enabled when a wire or group of wires is selected.

Delete (Ctrl + Del)

Deletes the selected wire, wire grid or group of wires with all sources and loads placed on it. This command is enabled when a wire, wire grid or group of wires is selected.

Copy Start Point

Copies the starting point of the selected wire. This point can then be used as the starting point of a second wire, which will be connected to the first one. This command is enabled when a wire is selected.

Copy End Point

Copies the ending point of the selected wire. This point can then be used as the starting point of a second wire, which will be connected to the first one. This command is enabled when a wire is selected.

Start Point to GND

Draws a vertical wire between the start point of the selected wire and the ground plane. This command is shown when a ground plane is included in the model, and it is enabled when a wire is selected.

End Point to GND

Draws a vertical wire between the end point of the selected wire and the ground plane. This command is shown when a ground plane is included in the model, and it is enabled when a wire is selected.

Copy Wires

Displays the Copy Wires dialog box for copying the selected wire or group of wires. The copied wires can then be pasted in a different position. This command is enabled when a wire or group of wires is selected.

Move Wires

Displays the Move Wires dialog box for moving the selected wire or group of wires to a different position. This command is enabled when a wire or group of wires is selected.

Rotate Wires

Displays the Rotate Wires dialog box for rotating the selected wire or group of wires around the chosen axis. This command is enabled when a wire or group of wires is selected.

Scale Wires

Displays the Scale Wires dialog box for scaling the selected wire or group of wires according to the specified scale factor. This command is enabled when a wire or group of wires is selected.

Stack Wires

Displays the Stack Wires dialog box for stacking the selected wire or group of wires along the specified direction and according to the given number of wires in the stack. This command is enabled when a wire or group of wires is selected.

Draw Menu

Use the Draw menu commands to create and draw wires and wire grids. This menu has the following commands:

Line

Opens the Line dialog box for drawing a line or straight wire.

Arc

Opens the Arc dialog box for drawing an arc.

Circle

Opens the Circle dialog box for drawing a circle or circular loop.

Helix

Opens the Helix dialog box for drawing a helix or helical wire.

Quadratic

Opens the Quadratic dialog box for drawing a quadratic wire.

Archimedean Spiral

Opens the Archimedean Spiral dialog box for drawing an Archimedean spiral.

Logarithmic Spiral

Opens the Logarithmic Spiral dialog box for drawing a logarithmic spiral.

Wire Grid

Creates a new wire grid in the workspace. This option has a sub-menu with the following commands:

• Patch: Opens the Draw dialog box for drawing a rectangular grid on the xy-plane.
• Plate: Opens the Draw dialog box for drawing a plate or bilinear surface.
• Disc: Opens the Draw dialog box for drawing a disc.
• Flat Ring: Opens the Draw dialog box for drawing a flat ring or a disc with a hole at its center.
• Cone: Opens the Draw dialog box for drawing a cone.
• Truncated Cone: Opens the Draw dialog box for drawing a truncated cone.
• Cylinder: Opens the Draw dialog box for drawing a cylinder.
• Sphere: Opens the Draw dialog box for drawing a sphere.
• Paraboloid: Opens the Draw dialog box for drawing a parabolic surface.

Tapered Wire

Creates a new tapered wire in workspace. This option has a sub-menu with the same commands as the wire options described above, but each wire can have a stepped radius along its length.

Tabular Input (Ctrl + T)

Opens a table to enter linear wires, sources and loads in spreadsheet format.

View Menu

Use the View menu commands to display or hide different elements of the AN-SOF interface, zoom the wire structure, and view additional information about the project and wires. This menu has the following commands:

Wire Properties… (Ctrl + W)

Displays the Wire Properties dialog box for viewing information about the selected wire. This command is enabled when a wire is selected.

Project Details…

Displays the Project Details dialog box for viewing information about the project that is open.

Zoom In (Ctrl + I)

Increases the size of the view in the workspace (also roll the mouse wheel to zoom).

Zoom Out (Ctrl + K)

Decreases the size of the view in the workspace (also roll the mouse wheel to zoom).

Reset Zoom Scale

Resets the zoom and resizes the view of the structure in the workspace.

Axes (Ctrl + A)

Displays the Axes dialog box for changing the appearance of the axes in the workspace. Press F7 to switch between small and main axes.

X-Y Plane / Y-Z Plane / Z-X Plane

Shows a view of the xy-plane/ yz-plane/ zx-plane parallel to the screen.

Center

Centers the view of the structure in the workspace (double click on the workspace to center the view).

Initial View (Home)

Returns the workspace to the initial view.

Drawing Panel

Displays a panel to the left of the workspace that contains buttons for quicker access to commands for drawing wires and wire grids.

Tools Menu

Use the Tools menu commands to display 3D, polar, rectangular, and Smith charts and to check the wires. This menu has the following commands:

3D Chart

Executes the AN-3D Pattern application for opening 3D plot files (.p3d).

Polar Chart

Executes the AN-Polar application for opening polar plot files (.plr).

Rectangular Chart

Executes the AN-XY Chart application for opening rectangular plot files (.plt).

Smith Chart

Executes the AN-Smith application for opening Smith chart files (.sth).

Check Individual Wires

Checks the segment length, cross-section size and thin-wire ratio of each wire. Wires in warning/error will be highlighted in yellow/red.

Check Wire Spacing

Checks the spacing between wires. Wires in warning/error will be highlighted in yellow/red.

Delete Duplicate Wires

Deletes duplicate or overlapping wires.

Calculator

Executes the Microsoft Windows(R) Calculator application.

Preferences

Displays the Preferences dialog box for setting up the preferred options for unit systems, workspace color, pen width, confirmation questions, etc.

Run Menu

Use the Run menu commands to run the calculations. This menu has the following commands:

Run ALL (F10)

Runs the calculation of the current distribution, far- and near-fields.

Run Currents and Far-Field (F11)

Runs the calculation of the current distribution and far-fields.

Run Currents and Near-Field (F12)

Runs the calculation of the current distribution and near electric and magnetic fields.

Run Currents

Runs the calculation of the current distribution on the wire structure. This command is disabled when the currents are already computed.

Run Far-Field     

Runs the calculation of the far-field generated by the currents flowing on the wire structure. This command is enabled when the currents are already computed.

Run Near E-Field

Runs the calculation of the near electric field generated by the currents flowing on the wire structure. This command is enabled when the currents are already computed.

Run Near H-Field

Runs the calculation of the near magnetic field generated by the currents flowing on the wire structure. This command is enabled when the currents are already computed.

Run Bulk Simulation Opens a dialog box for choosing multiple files in NEC format at the same time. The file extension must be “.nec”. AN-SOF will import these input files and compute the corresponding output results. The results will be saved as CSV files in the same directory as the NEC input files.

Results Menu

Use the Results menu commands to visualize the results from a simulation. This menu has the following commands:

Plot Current Distribution

Executes the AN-3D Pattern application for plotting the current distribution as a colored pattern on the wire structure.

Plot Currents

Executes the AN-XY Chart application for plotting the currents vs. position along the selected wire. This command is enabled when a wire has been selected.

List Currents

Displays the List Currents toolbar for listing the currents vs. frequency at the chosen segment on the selected wire. If the segment has a source on it, the list of input impedances, voltages, and powers as a function of frequency can be shown. This command is enabled when a wire has been selected.

List Input Impedances

Displays a table with the list of input impedances vs. frequency, including reflection coefficient, VSWR, return loss and transmission loss at the antenna terminals.

Plot Far-Field Pattern

This option has a sub-menu with the following commands:

• 3D Plot: Executes the AN-3D Pattern application for plotting a 3D view of the radiation patterns.
• Polar Plot 1 Slice: Displays the Radiation Pattern Cut dialog box for selecting a 2D slice of the 3D far-field pattern. Then, the selected 2D pattern cut will be plotted in polar coordinates by the AN-Polar application.
• Polar Plot 2 Slices: Displays a dialog box for selecting two slices of the 3D far-field pattern. Then, the selected 2D patterns will be plotted in polar coordinates by the AN-Polar application.
• 2D Rectangular Plot: Displays the Radiation Pattern Cut dialog box for selecting a 2D cut of the 3D far-field pattern. Then, the selected 2D pattern cut will be plotted in rectangular coordinates by the AN-XY Chart application.

Plot Far-Field Spectrum

Displays the Select Far-Field Point dialog box for selecting a point in space where the far-field components will be shown versus frequency. Then, the far-field spectrum will be plotted in rectangular coordinates by the AN-XY Chart application.

List Far-Field Pattern

Displays a table showing the total E-field and its components (E-theta, E-phi, E-right, E-left) at the grid of angles theta and phi specified in the Far-Field panel of the Setup tabsheet. This table can be exported as a CSV file.

List Far-Field Spectrum

Displays the Select Far-Field Point dialog box for selecting a point in space where the far-field components will be shown versus frequency. Then, this far-field spectrum will be listed in a table with different columns for the total E-field and the field components: E-theta and E-phi (spherical components) and the right and left polarized components.

Power Budget/RCS

Displays the Power Budget dialog box for listing the total input power, consumed and radiated powers, power densities, efficiency, directivity and gain vs. frequency. In the case of plane wave excitation, the Radar Cross Section (RCS) vs. frequency will be displayed.

Plot Near E-Field Pattern

This option has a sub-menu with the following commands:

• 3D Plot: Executes the AN-3D Pattern application for plotting a 3D view of the near electric field components.
• 2D Plot: Displays the Near-Field Cut dialog box for selecting a 2D cut of the near electric field pattern. Then, the selected 2D pattern cut will be plotted by the AN-XY Chart application.

Plot Near E-Field Spectrum

Displays the Select Near-Field Point dialog box for selecting a point where the near electric field components will be shown versus frequency. Then, this near-field spectrum will be plotted in rectangular coordinates by the AN-XY Chart application.

List Near E-Field Pattern

Displays a table showing the total near E-field and its components at the grid of points specified in the Near-Field panel of the Setup tabsheet. This table can be exported as a CSV file.

List Near E-Field Spectrum

Displays the Select Near-Field Point dialog box for selecting a point where the near electric field components will be shown versus frequency. Then, this near-field spectrum will be listed in a table with different columns for the field components.

Plot Near H-Field Pattern

This option has a sub-menu with the following commands:

• 3D Plot: Executes the AN-3D Pattern application for plotting a 3D view of the near magnetic field components.
• 2D Plot: Displays the Near-Field Cut dialog box for selecting a 2D cut of the near magnetic field pattern. Then, the selected 2D pattern cut will be plotted by the AN-XY Chart application.

Plot Near H-Field Spectrum

Displays the Select Near-Field Point dialog box for selecting a point where the near magnetic field components will be shown versus frequency. Then, the near-field spectrum will be plotted in rectangular coordinates by the AN-XY Chart application.

List Near H-Field Pattern

Displays a table showing the total near H-field and its components at the grid of points specified in the Near-Field panel of the Setup tabsheet. This table can be exported as a CSV file.

List Near H-Field Spectrum

Displays the Select Near-Field Point dialog box for selecting a point where the near magnetic field components will be shown versus frequency. Then, the near-field spectrum will be listed in a table with different columns for the field components.

Help Menu

Use the Help menu to access the user guide, request technical support, activate a license, or view the version of AN-SOF. This menu has the following commands:

User Guide

Displays the AN-SOF user guide in PDF format.

AN-SOF Home Page

Goes to the AN-SOF web page at www.antennasimulator.com in the default web browser.

Knowledge Base

Goes to the knowledge base > where you can search for categorized information.

Email to Tech Support

Executes the default e-mail client to send a technical support request to info@antennasimulator.com.

Chat to Tech Support

Goes to the live chat page in the default web browser.

Activation Key

Executes the AN-Key application to activate a license.

Check for Updates

Goes to the website where the latest AN-SOF releases > are posted.

About AN-SOF

Shows copyright and version information.

Main Toolbar

The main toolbar has the following icons and associated commands:

New (Ctrl + N)

Creates a new project.

Open (Ctrl + O)

Displays the Open dialog box to open an existing project (.emm file).

Save (Ctrl + S)

Saves the currently active project using its current name.

Undo (Ctrl + Z)

Returns the project to the status before a command was executed.

Source/Load (Ctrl + Ins)

Displays the Source/Load toolbar for adding a source or load to the selected wire. This command is enabled when a wire has been selected.

Modify (Ctrl + M)

Displays the Modify dialog box for modifying the selected wire or group of wires. This command is enabled when a wire or group of wires has been selected.

Wire color

Displays a Windows(R) dialog box for changing the color of the selected wire or group of wires. This command is enabled when a wire or group of wires has been selected.

Delete (Ctrl + Del)

Deletes the selected wire, wire grid or group of wires with all sources and loads placed on it. This command is enabled when a wire, wire grid or group of wires has been selected.

Preferences

Displays the Preferences dialog box for setting up the preferred options for unit systems, workspace color, pen width, confirmation questions, etc.

Wire Properties (Ctrl + W)

Displays the Wire Properties dialog box for viewing information about the selected wire. This command is enabled when a wire has been selected.

Project Details

Displays the Project Details dialog box for viewing information about the currently active project.

Select Wire

Enables the selection mode where a wire can be selected individually by left clicking on it.

Selection Box

Enables the selection mode where a group of wires can be selected expanding a box with the mouse (left mouse button pressed).

Draw Line

Enables the drawing mode where a line can be dragged with the mouse (left mouse button pressed). This mode is enabled when the X-Y, Y-Z or Z-X view has been chosen. The coordinates of the starting and ending points of the line will be shown in the status bar.

Rotate around X/Y/Z/3D

Enables the 3D rotation of the view or around the x/y/z-axis by moving the mouse.

Move

Enables the movement of the view by moving the mouse (left mouse button pressed).

Zoom

This allows you to expand a rectangle and select the area of the screen you wish to zoom in on. Additionally, you can use the mouse wheel to adjust the zoom level of the view.

X-Y / Y-Z / Z-X Plane

Shows a view of the xy/yz/zx-plane parallel to the screen.

Center

Centers the view of the structure on the workspace.

Initial View (Home)

Returns the workspace to the initial view.

Run ALL (F10)

Runs the calculation of the current distribution, far- and near-fields.

Run Currents and Far-Field (F11)

Runs the calculation of the current distribution and far-fields.

Run Currents and Near-Field (F12)

Runs the calculation of the current distribution and near-fields.

List Input Impedances

Shows a table with the input impedances vs. frequency. Reflection coefficient, VSWR, return and transmission losses at the antenna terminals are also tabulated.

Plot Current Distribution

Executes the AN-3D Pattern application for plotting the current distribution as a colored pattern on the wire structure.

Far-Field 3D Plot

Executes the AN-3D Pattern application for plotting a 3D view of the radiation pattern.

Far-Field Polar 1 Slice

Displays the Radiation Pattern Cut dialog box for selecting a 2D cut of the 3D far-field pattern. Then, the selected 2D pattern cut will be plotted in a polar chart by the AN-Polar application.

Far-Field Polar 2 Slices

Displays a dialog box for selecting two slices of the 3D far-field pattern. Then, the selected 2D patterns will be plotted in a polar chart by the AN-Polar application.

Far-Field 2D Plot

Displays the Radiation Pattern Cut dialog box for selecting a 2D cut of the 3D far-field pattern. Then, the selected 2D pattern cut will be plotted in rectangular coordinates by the AN-XY Chart application.

Export Results

Opens a dialog box to save the results displayed in the “Results” tab as a CSV file.

User Guide

Opens the user guide file in PDF format.

Preferences

Preferences in AN-SOF allow users to customize the unit system for input and output data, adjust the workspace appearance, and configure various miscellaneous options. To access preferences, navigate to Tools > Preferences from the main menu.

Units

On the Units page of the Preferences dialog box (see Fig. 1), users can select suitable units for frequencies, lengths, wire cross-section, inductances, and capacitances. Apart from standard SI units, options such as inches (in) and feet (ft) are available for lengths and cross-sections.

Workspace

In the Workspace tab (Fig. 2), users can toggle the workspace background color between black and white. Additionally, there are three levels for the pen width used to draw objects on the workspace: Thin, Medium, and Thick. This option applies to axes, wires, and wire grids. Users can also customize the size and color of source symbols and loads. Enabling the Show Segments option displays the segments in the workspace.

Options

In the Options tab, users can check the Show Main Toolbar option to display the toolbar (Fig. 3). Two “Ask before…” questions can be set to avoid mistakes. If the option “Run ALL” also calculates the H-Field is checked, the near H-field will be calculated after clicking on the “Run ALL” button. Users can also choose to close the chart windows after exiting AN-SOF. Additionally, the option “The comma is set as the decimal symbol” should be selected if the comma is used as the decimal separator in the Windows® regional settings. Users can also set the number of significant digits shown in results, although this option does not modify the double precision used in the internal algorithms.

Note

All preferences can be configured at any time, either before or after performing a calculation.

Display Options

The background of the workspace can be white or black. When a white (black) background is chosen, all wires will default to black (white) unless a different color is specified for certain wires. The workspace color can be set by going to Tools > Preferences > Workspace tab. The color of selected wires and wire grids can be changed at any time via Edit > Wire Color in the main menu.

The width of the line used for drawing wires and axes in the workspace can be changed by selecting a Pen Width option in the Workspace tab of the Preferences dialog box. There are three levels: Thin, Medium, and Thick. Figure 1 illustrates the different combinations between the workspace color and pen width that can be obtained.

Viewing 3D Axes

To change the appearance of the X, Y, Z axes in the workspace go to View > Axes (Ctrl + A) in the main menu to display the Axes dialog box, Fig. 2. There are two types of axes, the Small Axes, and the Main Axes. The small axes are displayed in the lower left corner of the workspace, while the main axes are displayed in the center of the screen.

Both positive and negative axes can be displayed. The color of the main axes can be changed by pressing the Color button.

Check the Show Ticks option to add the specified number of ticks to the Main Axes.

Tip

Press F7 to switch between small and main axes.

Zooming the View

To zoom in or out the view of the structure in the workspace, move the mouse wheel. If you are using a laptop touchpad, you can also use two fingers, just like when zooming an image. Alternatively, you can utilize the Zoom In (Ctrl + I) and Zoom Out (Ctrl + K) commands from the View menu.

For a more specific zoom on a particular area of the screen, click on the Zoom button on the toolbar and then select the desired area by expanding a rectangle. To return to the initial view, simply click the Initial View (Home) button on the toolbar.

Rotating the View

To rotate the view of the structure around the desired axis, first press one of these buttons on the toolbar: Rotate around X, Rotate around Y, Rotate around Z, or 3D Rotation.

Then, move the mouse over the screen with the left button pressed.

The view can also be rotated by pressing the following keys:

• F1: Right-handed rotation around the x-axis.

• F2: Left-handed rotation around the x-axis.

• F3: Right-handed rotation around the y-axis.

• F4: Left-handed rotation around the y-axis.

• F5: Right-handed rotation around the z-axis.

• F6: Left-handed rotation around the z-axis.

Moving the View

The view of the structure can be moved in the workspace. First press the Move button on the toolbar and then move the mouse over the screen with the left button pressed.

Tip

Double-click on the workspace to center the view of the structure on the screen.

Introduction

The Method of Moments (MoM) is widely recognized as one of the most reliable techniques for modeling and simulating antennas and radiating systems. However, traditional implementations of MoM suffer from several issues primarily stemming from approximations used in numerical calculations to reduce computational requirements. While these approximations were justified in the 1970s and 1980s due to limited processor speeds and memory capacities, the present-day computing power, even on personal computers, allows for more accurate calculations. The limitations imposed by these approximations in traditional MoM models restrict their validity and applicability.

The fundamental principle of MoM involves representing metal surfaces through wire segments, which is a suitable approximation for many metallic antennas, particularly wire-type antennas like linear antennas, dipoles, monopoles, yagis, log-periodic arrays, quads, antenna arrays of all types, traveling wave antennas, fractals, aperture antennas, and reflectors. It is essential for each wire segment to have a small length and cross-section relative to the wavelength. The MoM seeks to determine the unknown current flowing through each wire segment, as depicted in Fig. 1.

The Thin-Wire Approximation

In the modeling of antennas using cylindrical wire segments, the initial approximation commonly employed is known as the “thin-wire approximation,” as illustrated in Fig. 2. This approximation is based on the following assumptions:

When dealing with a wire segment with a cross-section significantly smaller than the wavelength, assumptions 2, 3, and 4 are reasonably valid and align with experimental observations and theoretical predictions in the quasi-electrostatic regime for metal surfaces. However, assumption 1, regarding the current filament along the wire axis, has sparked debates throughout the history of linear antennas.

Assumption 1 only holds as a limiting case when the wire’s cross-section approaches zero size, such as when the wire has a circular cross-section and its radius tends to zero. This assumption relates to the crucial aspect known as the Kernel of the problem. The Kernel represents the core of the integral equation that the MoM solves to determine the currents flowing along the wires. Instead of employing the “thin-wire Kernel” utilized in traditional MoM, which is based on assumption 1, AN-SOF employs the exact Kernel. In the exact Kernel, it is considered that the current flows on the surface of the wires rather than being confined to a filament along the wire axis.

Eliminating assumption 1 has a significant impact on the accuracy of calculations, particularly in the current distribution near the antenna’s feed point or terminals, where obtaining precise values for input impedance and standing wave ratio (SWR) is crucial. In addition to discarding assumption 1 in AN-SOF, the use of the exact Kernel and curved wire segments helps overcome other issues inherent in traditional MoM, as described below.

Overcoming the 7 Limitations of the Traditional MoM

In AN-SOF, we have departed from the traditional MoM and embraced innovation by implementing a new method called the Conformal Method of Moments (CMoM) with an exact Kernel formulation. This decision stems from the lack of substantial improvements in traditional methods over several decades, despite advancements in computational power. By adopting CMoM with an exact Kernel, we have successfully addressed the main limitations of the traditional MoM, which can be categorized into seven key areas:

Thanks to the Conformal Method of Moments (CMoM) with Exact Kernel, AN-SOF has successfully eliminated these limitations. CMoM employs conformal segments that accurately capture the structure’s contour, enabling an exact representation of geometric details. Conformal segments, resembling curved cylindrical tubes, enable precise modeling of curved wires. By employing the exact Kernel instead of the thin-wire approximation, AN-SOF overcomes limitations associated with bent wires, small wire spacings, and segment lengths. This approach facilitates highly accurate calculations compared to the traditional method.

With the implementation of CMoM and an exact Kernel formulation, AN-SOF achieves enhanced accuracy, reduced computational requirements, and more efficient simulations. The improved method enables AN-SOF to simulate a wide frequency range, spanning from extremely low frequencies (e.g., 60 Hz circuits) to microwave antennas.

AN-SOF stands as the only antenna modeling software that offers a calculation engine based on the Conformal Method of Moments with an Exact Kernel.

The simulation parameters can be set in the Setup tabsheet. This page has the following panels: Frequency, Environment, Far-Field, Near-Field, Excitation, and Settings, Fig. 1.

• In the Frequency panel >, the project operating frequencies can be specified.

• In the Environment panel >, the relative permittivity and permeability of the surrounding medium and the type of ground plane can be set.

• In the Far-Field panel >, the angular ranges for the calculation of the far-field can be set.

• In the Near-Field panel >, the observation points for the calculation of the near-field can be set.

• In the Excitation panel >, the type of excitation for the structure can be set. When discrete sources are chosen as excitation, the total input power can be specified. When an incident field is chosen as excitation, the incoming direction and polarization for the incident wave can be specified.

• In the Settings panel >, additional parameters can be set, such as the reference impedance for VSWR and the accuracy of the calculations.

• On the right side of the Setup page there is a Note panel to write notes associated to the project. These notes will be saved in a text file in the same path as the project file and with the same name as the project.

Go to the Setup tab in the main window and select the Frequency panel.

The Frequency panel has three options: Single, List and Sweep. By choosing one of these options the simulation can either be performed for a single frequency, for frequencies taken from a list or for a frequency sweep.

• If Single is chosen, enter the frequency in the Single Frequency box, as shown in Fig. 1. The wavelength will be shown below the frequency.

• If List is chosen, write the list of frequencies in the Frequency List box, Fig. 2. A list from a text file can be read by pressing the Open button. The frequency list can also be saved to a text file by pressing the Save button.

• If Sweep is selected, it can either be linear or logarithmic. For a linear sweep the start, step and stop frequencies must be set, Fig. 3. For a logarithmic frequency sweep the start, stop and a multiplication factor must be set, Fig. 4.

The frequency unit can be changed going to Tools > Preferences in the main menu and choosing a suitable unit in the Units page of the Preferences dialog box. Refer to Preferences >.

Ground Plane Options

Navigate to the Setup tab in the main window and access the Environment panel. You can adjust the relative permittivity and permeability of the surrounding medium within the Medium box, as shown in Fig. 1.

There are four ground plane options available:

None

When the None ground plane is selected, the simulation will be conducted in free space, with the relative permittivity and permeability values set in the Medium box (see Fig. 1).

Perfect

An infinitely large perfectly electrically conducting (PEC) ground plane will be positioned at the specified height from the xy-plane (“Z Position” in Fig. 2). Consequently, the ground plane will be parallel to the xy-plane. The “Z” position determines the height of the ground plane above the xy-plane, with a negative Z indicating placement below the xy-plane.

When the Perfect option is selected, all wires must be positioned above the perfect ground plane. In simpler terms, all wires must have a Z-coordinate greater than or equal to the specified position. AN-SOF does not verify wires for potential crossings with the PEC ground plane or for placement at the bottom of the plane. Additionally, it does not support horizontal wires lying directly on the ground plane. However, it does allow for connections to be established from wire ends to the ground plane.

Real

A real ground plane, with user-defined conductivity and relative permittivity (relative permeability set to 1), will be situated on the xy-plane at z = 0, as shown in Fig. 3. There are three available options for real ground calculations: Sommerfeld-Wait/Asymptotic, Reflection Coefficients/Asymptotic, and Radial wire ground screen.

All wires must be positioned above the ground plane (z = 0). Horizontal wires placed directly on the ground plane are not supported. However, wire end connections to the ground plane can be established when either the “Sommerfeld-Wait/Asymptotic” or “Radial wire ground screen” options are selected.

The “Reflection Coefficients/Asymptotic” option exclusively permits connections to the ground plane for vertical wires, resulting in perfect zero-Ohm connections. In cases involving horizontal wires, they must be separated by at least one free space wavelength from the ground plane. In such situations, it is essential to verify the validity of the results. AN-SOF does not automatically verify whether these conditions are satisfied within a model.

Real Ground Options

Sommerfeld-Wait/Asymptotic

This option involves calculating the currents flowing through the antenna/wire structure using a model that includes a PEC ground plane and incorporates equivalent loss impedances to address power dissipation in the ground plane, particularly when wires are in close proximity to or connected to the ground. Developed by Prof. James R. Wait, this model is particularly effective for obtaining the input impedance of low-frequency (LF) and medium-frequency (MF) antennas, especially in scenarios where the ground conductivity is high within those frequency bands. Additionally, the finite conductivity and permittivity of the ground are employed to calculate the near-field and far-field radiation from the structure, utilizing the Sommerfeld-Norton asymptotic expressions and Fresnel’s reflection coefficients, respectively.

Connections to the ground are permitted, either at the start or end point of a wire with z = 0, and they are considered imperfect by default. This means that currents flowing between the ground and the grounded wires result in power losses in the ground. However, if you select the “Zero-Ohm connections to ground” option, wire connections to the ground will be treated as perfect, with no power dissipation occurring at the connection point.

Reflection Coefficients/Asymptotic

In this option, the ground parameters have an impact on the current distribution on the antenna or wire structure above the ground. This influence is determined through a generalization of Fresnel’s reflection coefficients, which means that the input impedance of a transmitting antenna is also influenced by the real ground conditions. Moreover, the near and far fields are affected by the finite ground conductivity and its dielectric constant. The near fields are computed using the Sommerfeld-Norton asymptotic expressions, allowing us to calculate the electric and magnetic field as a function of distance from the transmitting antenna. This enables us to observe the attenuation resulting from ground losses. The far-field, on the other hand, is computed using standard Fresnel’s reflection coefficients.

Vertical wire connections to the ground are permitted, but they are treated as lossless connections.

Radial wire ground screen

In this option, a ground screen consisting of buried radial wires will be positioned beneath the ground plane. The screen is centered at the origin of coordinates and features user-specified parameters, including the number of radial wires, wire length (or radius of the circular screen), and wire radius.

The ground screen model influences the current distribution on the antenna/wire structure by calculating the power dissipated in the ground plane-wire screen system. Consequently, the presence of the screen and the finite ground conductivity will impact the input impedance of a transmitting antenna located above the ground screen. Additionally, the finite ground conductivity and permittivity are employed to compute the near- and far-fields radiated from the structure, utilizing the Sommerfeld-Norton expressions and the Fresnel’s reflection coefficients, respectively.

Connections to the ground are permitted, either at the start or end point of a wire with z = 0, and they are considered imperfect by default. This means that currents flowing between the ground and the grounded wires result in power losses in the ground. However, if you select the “Zero-Ohm connections to ground” option, wire connections to the ground will be treated as perfect, with no power dissipation occurring at the connection point.

Substrate

A dielectric substrate, with a user-defined permittivity, will be positioned beneath the xy-plane (z = 0), as shown in Fig. 4. The substrate can either extend infinitely or have finite dimensions in the xy-plane. It is essential to specify the slab thickness, denoted as ‘h,’ along the z-axis. A perfectly electrically conducting (PEC) ground plane will be situated at z = -h, just below the dielectric slab, as illustrated in Fig. 5. To facilitate setting the substrate’s permittivity, choose from a drop-down list with common materials (e.g., FR4, RT/Duroid, Rogers RO slabs).

When the Substrate option is selected, all wires must be positioned on the xy-plane (z = 0). These wires can represent flat traces of planar or patch antennas printed on the dielectric substrate, microstrip lines, or PCB (Printed Circuit Board) traces. The only exception to this rule is for vertical wires, which can be employed to connect wire strips at z = 0 to the PEC ground plane at z = -h. Typically, a voltage or current source is connected to these vertical wires to power the system, whether it’s an antenna or a PCB.

It’s important to note that the PEC ground plane beneath the dielectric substrate cannot be omitted from the model, meaning that ungrounded substrates are not supported with this option. Wires positioned above the xy-plane (with z-coordinates > 0) or below the PEC ground plane of the substrate (with z-coordinates < -h) are not supported. AN-SOF does not automatically verify compliance with these conditions.

The Far-Field Panel

Go to the Setup tab in the main window and select the Far-Field panel, Fig. 1.

The far field can be computed after having calculated the current distribution previously. Thus, the parameters set in the Far-Field panel have no effect in the determination of the currents and can be modified at any time. However, the far field must be recalculated every time these parameters are modified.

There are four options for radiation pattern calculations:

Full 3D

The far field is calculated in angular ranges that cover the entire 3D space, which allows us to obtain 3D radiation lobes. The steps for the Theta (zenith) and Phi (azimuth) angles can be set in the Theta [deg] and Phi [deg] boxes.

Vertical

The far field is calculated at a vertical slice for a given Phi (azimuth) angle. The step for the Theta (zenith) angle can be set in the Theta [deg] box, while the fixed Phi can be set in the Phi [deg] box.

Horizontal

The far field is calculated at a horizontal slice for a given Theta (zenith) angle. The step for the Phi (azimuth) angle can be set in the Phi [deg] box, while the fixed Theta can be set in the Theta [deg] box.

Custom

The far field is calculated for the specified ranges of angles Theta (zenith) and Phi (azimuth). The start, step, and stop values for Theta and Phi can be set in the Theta [deg] and Phi [deg] boxes.

Additionally, the following parameters can be set:

Origin (X0,Y0,Z0)

This can be any point used as a phase reference, its coordinates do not affect the shape of the radiation pattern. The 3D radiation pattern will be plotted centered at this point.

Distance

It is the distance from (X0,Y0,Z0) to an observation point in the far-field region. A normalized far-field pattern can be obtained by setting Distance = 1.

The zenith and azimuth angles, Theta and Phi, are shown in Fig. 2, where it is also shown de Distance R from the structure to an observation point in the far-field zone. These three numbers (R,Theta,Phi) define the spherical coordinates of the far-field point.

Near-Field Panel

Go to the Setup tab in the main window. Then, select the Near-Field panel.

The near field can be computed after having calculated the current distribution previously. Thus, the parameters set in the Near-Field panel have no effect in the determination of the currents and can be set at any time. However, the near field must be recalculated every time these parameters are modified. The Near-Field panel has three options: Cartesian, Cylindrical, and Spherical. By choosing one of these options near-fields can either be calculated in Cartesian, Cylindrical or Spherical coordinates.

Cartesian Coordinates

If the Cartesian option is chosen, the following parameters can be set for near-field calculations, Fig. 1:

Origin (X0,Y0,Z0)

It is the origin of the Cartesian coordinates used to define the observation points where near fields will be calculated.

X

This box is used to set x-coordinates of the observation points where near-fields will be calculated. The start, step and stop x-coordinates must be set. Start and stop x-coordinates are measured from X0.

Y

This box is used to set y-coordinates of the observation points where near-fields will be calculated. The start, step and stop y-coordinates must be set. Start and stop y-coordinates are measured from Y0.

Z

This box is used to set z-coordinates of the observation points where near-fields will be calculated. The start, step and stop z-coordinates must be set. Start and stop z-coordinates are measured from Z0.

Cylindrical Coordinates

If the Cylindrical option is chosen, the following parameters can be set for near-field calculations, Fig. 2:

Origin (X0,Y0,Z0)

It is the origin of the Cylindrical coordinates used to define the observation points where near fields will be calculated.

R

This box is used to set the distances or R-coordinates of the observation points where near-fields will be calculated. The start, step and stop R-coordinates must be set. Start and stop distances or R-coordinates are measured from the origin (X0,Y0,Z0).

Phi

This box is used to set the azimuth angles or phi-coordinates of the observation points where near-fields will be calculated. The start, step and stop phi-coordinates must be set in degrees.

Z

This box is used to set the z-coordinates of the observation points where near-fields will be calculated. The start, step and stop z-coordinates must be set.

Spherical Coordinates

If the Spherical option is chosen, the following parameters can be set for near-field calculations, Fig. 3:

Origin (X0,Y0,Z0)

It is the origin of the Spherical coordinates used to define the observation points where near fields will be calculated.

R

This box is used to set the distances or R-coordinates of the observation points where near-fields will be calculated. The start, step and stop R-coordinates must be set. Start and stop distances or R-coordinates are measured from the origin (X0,Y0,Z0).

Theta

This box is used to set zenith angles or theta-coordinates of the observation points where near-fields will be calculated. The start, step and stop theta-coordinates must be set in degrees.

Phi

This box is used to set azimuth angles or phi-coordinates of the observation points where near-fields will be calculated. The start, step and stop phi-coordinates must be set in degrees.

Excitation Panel

Go to the Setup tab in the main window and select the Excitation panel. There are two types of excitations: Discrete Sources and Incident Field, Fig. 1.

Discrete Sources

The discrete generators placed at the wire structure will be used to calculate the current distribution. The total input power in Watts can be specified, so the voltage/current sources will be adjusted accordingly to achieve the specified input power. If the input power is not specified, then the voltage/current sources will be constant, and the input power will be an output result from calculations.

Incident Field

An incident plane wave will be used as the excitation of the structure. The direction of incidence and polarization of the incoming field can be set in this panel.

The following parameters must be set for the incident wave excitation:

E-Field Major Axis

In the case of linear polarization, it is the amplitude, in Volts per meter (rms value), of the incoming electric field. For an elliptically polarized plane wave, it is the major axis of the polarization ellipse.

Axial Ratio

It is the ratio of the minor axis to the major axis of the polarization ellipse. If the axial ratio is positive (negative) a right-handed (left-handed) ellipse is obtained. If the axial ratio is set to zero, a linearly polarized wave will be obtained.

Phase Reference

It is the phase, in degrees, of the incident plane wave at the origin of coordinates. Its value only shifts all phases in the structure by the same amount.

Gamma

For a linearly polarized wave, it is the polarization angle, in degrees, of the incident electric field measured from the plane of incidence to the direction of the electric field vector, as it is shown in Fig. 2. For an elliptically polarized wave, Gamma is the angle between the plane of incidence and the major ellipse axis.

Theta

It is the zenith angle, in degrees, of the incident direction.

Phi

It is the azimuth angle, in degrees, of the incident direction.

The definition of these parameters is illustrated in Fig. 2.

When the 3D View button is pressed a user interface is enabled in the workspace, where the direction of arrival of the plane wave and its polarization can be specified easily, Fig. 3.

Note

When an incident plane wave is used as excitation, all discrete sources, if any, will not be considered in the simulation.

Go to the Setup tab in the main window and select the Settings panel, Fig. 1.

The accuracy of the integrals involved in the calculations can be set in the Settings panel. The Quadrature Tolerance is the error in the evaluation of interactions between wire segments which are separated by a distance less than the Interaction Distance.

The Interaction Distance is the maximum distance in wavelengths between segments for which an error less than the Quadrature Tolerance is guaranteed in the integrations. The interaction between all wire segments further apart than the Interaction Distance is computed using a third-degree polynomial approximation to the involved integrals, which is more accurate for curved segments than the Hertzian dipole approximation used in the traditional Method of Moments. Therefore, the Interaction Distance could be set to zero for a faster simulation when wire segments are not too close to each other, but results will be less accurate. A convergence test for various values of this parameter is recommended.

For most cases, a quadrature tolerance between 0.1% and 1% and an interaction distance between 0.25 and 1.0 wavelengths will be enough for obtaining accurate results.

In AN-SOF, all calculations are done with double precision. The Matrix Size Threshold allows us to simulate big antenna problems when the size of the structure compromises the available memory space. For instance, by setting the Matrix Size Threshold to 4,000, the set of linear equations associated to the Z-matrix of the antenna system will be computed using single precision for a matrix size bigger than 4,000 x 4,000. This will impact the accuracy of the calculations but will save memory. In practice, the error will be not significant.

The Exact Kernel option allows us to use the exact Kernel for the Electric Field Integral Equation associated to the structure. This option must be chosen when relatively thick wire segments are used to describe the wire structure. If the Exact Kernel option is unchecked, an extended thin-wire approximation will be used for the kernel. If all wire segments are thin enough, then the computation will be a little faster using the extended thin-wire kernel. Refer to The Exact Kernel for further information.

In the Settings panel, the Reference Impedance for VSWR calculations can also be set. A default value of 50 Ohm is set.

Besides, the following options for the type of simulation are available in the Options box:

• If NGF is checked, the Numerical Green’s Function calculation is performed in the simulation, that is, the LU-decomposed matrix of the system is stored in a file in the first simulation. Then, by using the stored information, new simulations are performed faster than the first one. Check this option if you need to change the amplitude values of voltage/current sources frequently.

• If Load Impedances is checked, lumped impedances will be considered in the simulation. With this option all the lumped loads can be disabled or enabled at the same time.

• If Wire Resistivity is checked, the finite resistivity of the wires will be considered in the simulation. Any wire has its own resistivity in [Ohm meter] that can be set when the wire is drawn. This option allows us considering the whole structure as a perfect electric conductor when it is unchecked.

• If Wire Coating is checked, the coating materials of the wires will be considered in the simulation. Any wire has its own coating specified by a dielectric permittivity, magnetic permeability, and thickness, which can be set when the wire is drawn. When this option is unchecked, the wire coating will not be considered in the simulation.

Go to View > Project Details in the main menu to display the Project Details window, where a summary of the project information is shown, Fig. 1. There is also a button on the toolbar to access this window.

The text in the Project Details window can be selected and copied to the clipboard in the usual way (Ctrl+C and Ctrl+V commands).

When a project is saved in AN-SOF, multiple files that share the same name as the project are saved within the same directory. Each file possesses a unique extension that corresponds to its content. These files are the following:

File type	Description
*.emm	Main file with configuration data
*.wre	Geometric description of the wire structure
*.cur	Current distribution
*.phi	E-phi component of the far-field.
*.the	E-theta component of the far-field.
*.pwr	Radiation pattern data
*.nef	Near electric field
*.nhf	Near magnetic field
*.ngf	Numerical Green’s function
*.txt	Notes written by the user

Note

When requesting support, always attach the .emm and .wre files of your project.

Pressing ALT with the underlined letter of a menu item will execute the command associated with the item.

The following keys and associated actions are available:

Key	Action
Home	Return the structure to the initial view
ESC	Unselect a wire
F1	Rotate view around +X axis
F2	Rotate view around -X axis
F3	Rotate view around +Y axis
F4	Rotate view around -Y axis
F5	Rotate view around +Z axis
F6	Rotate view around -Z axis
F7	Show Main/Small axes
F8	Select a wire in order of creation
F9	Select a wire in reverse order of creation
F10	Run ALL
F11	Run currents and far-field
F12	Run currents and near-field
Ctrl + A	Display the Axes dialog box
Ctrl + I	Zoom in
Ctrl + K	Zoom out
Ctrl + M	Modify the selected wire
Ctrl + N	Create a new project
Ctrl + O	Open a project file
Ctrl + P	Print the workspace
Ctrl + Q	Exit AN-SOF
Ctrl + R	Run Currents
Ctrl + S	Save the project
Ctrl + T	Tabular input of linear wires
Ctrl + W	Show properties of the selected wire
Ctrl + Del	Delete the selected wire or group of wires
Ctrl + Ins	Display the Source/Load toolbar

AN-SOF has different types of wires. Each wire type has its own geometrical parameters, attributes and materials that can be set in a specific Draw dialog box. This dialog box allows us drawing a new wire in the workspace.

Choosing Draw in the main menu shows the following commands:

• Line: Displays the Draw dialog box for drawing a linear or straight wire.
• Arc: Displays the Draw dialog box for drawing an arc .
• Circle: Displays the Draw dialog box for drawing a circular loop.
• Helix: Displays the Draw dialog box for drawing a helix or helical wire.
• Quadratic: Displays the Draw dialog box for drawing a quadratic wire.
• Archimedean Spiral: Displays the Draw dialog box for drawing an Archimedean spiral.
• Logarithmic Spiral: Displays the Draw dialog box for drawing a logarithmic spiral.

Menu Options

The commands to draw wires can be accessed from three menus:

• Main menu > Draw.
• Popup menu by right clicking on the workspace.
• Main menu > View > Drawing Panel.

The Attributes page is part of the Draw dialog box for the selected wire type (see Fig. 1). On the Attributes page, you can specify the following attributes:

Number of Segments

Every wire must be divided into a certain number of segments. During the simulation process, AN-SOF needs to determine the unknown current on each segment. When you access the Attributes page, a default Number of Segments is displayed. This default number is calculated based on the wire’s length and the shortest wavelength, but you can modify it as needed.

Note

If you set the Number of Segments to zero, AN-SOF will automatically compute the minimum recommended number of segments for the wire. This calculation assumes 10 segments per wavelength, considering the shortest wavelength in a frequency sweep.

Cross-Section

The Cross-Section of the wire can be chosen from a combo-box. There are six cross-section types available: Circular, Square, Flat, Elliptical, Rectangular, and Triangular. AN-SOF computes an equivalent radius for the five last cases. Infinitesimally thin wires are not allowed, so the cross-section radius must be greater than zero.

The Draw dialog box for any wire type has its own Attributes page with the same features as those described here.

The Materials page belongs to the Draw dialog box of the chosen wire type, Fig. 1.

In the Materials page the following attributes can be specified:

Wire Resistivity

A resistivity in [Ohm meter] can be specified for the wire. The following list of most common metals is available for choosing:

Material (Metals)	Resistivity [Ω m]
Aluminum (Pure)	2.65E-8
Aluminum (6061-T6)	4.01E-8
Aluminum (6063-T832)	3.25E-8
Brass	6.41E-8
Carbon Steel	1.67E-7
Constantan	4.42E-7
Copper	1.74E-8
German Silver	3.33E-7
Germanium	4.55E-7
Gold	2.44E-8
Iron	9.71E-8
Manganin	4.41E-7
Nichrome	1.00E-6
Nickel	6.90E-8
Phosphor Bronze	1.10E-7
Silver	1.59E-8
Solder	1.43E-7
Stainless Steel	9.09E-7
Stainless Steel 302	7.19E-7
Tin	1.14E-7
Tungsten	5.49E-8
Zinc	5.90E-8

The corresponding resistivity value will be automatically displayed for the chosen metal. Choose the Custom option to set a resistivity value if it is not in the list. Choose Perfect (PEC) to set a perfect electrically conducting metal.

The resistivity is used for computing a distributed impedance per unit length along the wire, which considers the skin effect. The equivalent radius for wires of non-circular cross section will be used to compute the impedance per unit length along the wires.

The resistivity of wires is considered in the simulation if the option Wire Resistivity is checked in the Settings panel of the Setup tabsheet.

Wire Coating

Wires can have insulation or coating material. The cross section of a coated wire is circular, so the equivalent radius will be used for wires having a non-circular cross section.  In this case, the material the coating is made of can be set by the following parameters:

• Relative Permittivity: It is the dielectric constant of the coating material relative to the permittivity of vacuum.
• Relative Permeability: It is the magnetic permeability of the coating material relative to the permeability of vacuum.
• Thickness: It is the thickness of the coating shield. It can be set to zero when no coating is used.

The wire coating is considered in the simulation if the option Wire Coating is checked in the Settings panel of the Setup tabsheet.

If wires with non-zero resistivity have been drawn previously and the whole structure must now be considered as a perfect electric conductor, all resistivities can be disabled without modifying the definitions of the wires.

Go to the Setup tabsheet in the main window and select the Settings panel, Fig. 1. If the option Wire Resistivity in this panel is checked, the resistivities are enabled. Uncheck the Wire Resistivity option to disable all of them.

If wires with a coating shield or insulation have been drawn previously and the whole structure must now be considered as composed of bare conductive wires, all coatings can be disabled without modifying the definitions of the wires.

Go to the Setup tabsheet in the main window and select the Settings panel, Fig. 1. If the option Wire Coating in this panel is checked, the coatings are enabled. Uncheck the Wire Coating option to disable all of them.

The wire cross-section can be chosen from a combo-box in the Attributes page of the Draw dialog box for the chosen wire type, Fig. 1.

There are six cross-section types available: Circular, Square, Flat, Elliptical, Rectangular, and Triangular. AN-SOF computes an equivalent radius for the non-circular cross-sections. The equivalent radius is the radius of a circular cross-section that produces the same average electromagnetic fields around the wire and on its surface.

The cross-sections and their equivalent radii are the following:

Circular

A positive and non-zero radius “a” must be set. The equivalent radius is “a”.

Square

A positive and non-zero width “w” must be set. The equivalent radius is 0.59017 w.

Flat

A positive and non-zero width “w” must be set. The equivalent radius is w/4.

Elliptical

The semi-axes “a” and “b” must be positive and non-zero. The equivalent radius is (a + b)/2.

Rectangular

The widths “w” and “t” must be positive and non-zero. The equivalent radius is computed using a polynomial and logarithmic approximation to the solution of an integral equation.

Triangular

A positive and non-zero width “w” must be set. The equivalent radius is 0.42 w.

You can export linear wires from AN-SOF to a text file in NEC format (extension .nec) by navigating to File > Export Wires in the main menu. Linear wires will be saved as GW lines. Additionally, the exported file will include GE (ground connections), GN (ground plane), TL (transmission line), LD (load impedances and wire conductivity), IS (wire insulation), FR (frequency), EX (excitation), EK (exact kernel), and RP (radiation pattern) cards.

Moreover, the exported file can be saved as a Scilab script, with a .sce extension. The exported file will contain programming code that can be adjusted to create a new project, allowing for variations in parameters such as wire lengths and positions, frequencies, and ground conditions.

The Line refers to a linear or straight wire.

Go to Draw > Line in the main menu to display the Draw dialog box for the Line. This dialog box has three pages: Line, Attributes, and Materials, Fig. 1.

The Line page

In the Line page the geometrical parameters for the Line can be set. There are two options: 2 Points and Start – Direction – Length.

The 2 Points option allows us entering the Line by giving two points: “From Point” and “To Point”, as shown in Figs. 1 and 2.

If Start – Direction – Length is chosen, the line will be drawn starting from Start Point, in the direction given by the Theta and Phi angles in spherical coordinates and ending at a point defined by the wire Length measured along that direction, Figs. 3 and 4.

Once the geometrical parameters in the Line page have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.

The Arc refers to a circular arc.

Go to Draw > Arc in the main menu to display the Draw dialog box for the Arc. This dialog box has three pages: Arc, Attributes, and Materials, Fig. 1.

The Arc page

In the Arc page the geometrical parameters for the Arc can be set. There are two options: 3 Points and Start – Center – End.

The 3 Points option allows us entering the Arc by giving three points. An arc starting from Start Point, passing through Second Point and ending at End Point will be drawn on the workspace, Figs. 1 and 2.

If Start – Center – End is chosen, the Arc will be drawn starting from Start Point, with the center given by Center and ending at a point determined by End Point, Figs. 3 and 4. The End Point determines the arc aperture angle and the plane where it will be on, so this point could not coincide with the actual ending point of the arc.

Once the geometrical parameters in the Arc page have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.

The Circle refers to a circular loop.

Go to Draw > Circle in the main menu to display the Draw dialog box for the Circle. This dialog box has four pages: Circle, Orientation, Attributes and Materials.

The Circle page

In the Circle page the geometrical parameters for the Circle can be set. There are two options: Center – Radius – Orientation and 3 Points.

The Center – Radius – Orientation option allows us entering the Circle by giving its Center, Radius, and axis, Figs. 1 and 2. The circle axis can be set in the Orientation page, Fig. 3.

If the 3 Points option is chosen, the Circle will be drawn starting from First Point, passing through Second Point and Third Point, and ending at First Point, Figs. 4 and 5. Thus, the circle starts and ends at the same point. The Orientation page will be invisible when the 3 Points option is chosen.

Once the geometrical parameters in the Circle and Orientation pages have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.

The Orientation page

In the Orientation page the orientation for the Circle can be set. There is a box with two options: Angles and Vector, Fig. 3.

If Angles is selected, the circle axis can be defined by given an orthogonal direction to the rest plane of the circle. Thus, the Theta and Phi angles determine the axis direction in spherical coordinates.

If Vector is selected, the circle axis can be defined by given an orthogonal vector to the rest plane of the circle. Thus, the Nx, Ny, and Nz components of that vector determine the axis direction.

The circle can be rotated around its axis by given the Rotation Angle.

The Helix refers to a helical wire.

Go to Draw > Helix in the main menu to display the Draw dialog box for the Helix. This dialog box has four pages: Helix, Orientation, Attributes and Materials.

The Helix page

In the Helix page the geometrical parameters for the Helix can be set. There are two options: Start – Radius – Pitch – Turns and Start – End – Radius – Turns.

The Start – Radius – Pitch – Turns option allows us entering the Helix by setting its Start Point, Radius, Pitch and Number of turns, Figs. 1 and 2. If Pitch is positive (negative) the helix will be right-handed (left-handed). The helix axis can be set in the Orientation page, Fig. 3.

If Start – End – Radius – Turns is chosen, the helix will be drawn starting from Start Point and ending at End Point, with the given Radius and Number of turns, Figs. 4 and 5. The Number of turns must be an integer number, if it is positive (negative) the helix will be right-handed (left-handed). The orientation of the helix axis is determined by the starting and ending points. The helix can be rotated around its axis by given the Rotation Angle. The Orientation page will be invisible when the Start – End – Radius – Turns option is chosen.

Once the geometrical parameters in the Helix and Orientation pages have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.

The Orientation page

In the Orientation page the orientation for the Helix can be set. There is a box with two options: Angles and Vector, Fig. 3.

If Angles is selected, the helix axis can be defined by given its direction in 3D space. This direction is determined by the Theta and Phi angles in spherical coordinates.

If Vector is selected, the helix axis can be defined by given a vector in the axis direction. Its Nx, Ny, and Nz components define this vector.

The helix can be rotated around its axis by given the Rotation Angle.

The Quadratic refers to a quadratic wire or parabola.

Go to Draw > Quadratic in the main menu to display the Draw dialog box for the Quadratic. This dialog box has three pages: Quadratic, Attributes, and Materials.

The Quadratic page

In the Quadratic page the geometrical parameters for the Quadratic can be set, Fig. 1.

The Quadratic is entered by giving three points. A quadratic curve starting from Start Point, passing through Second Point and ending at End Point will be drawn on the workspace, as shown in Figs. 2.

Once the geometrical parameters in the Quadratic page have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.

The Archimedean Spiral refers to the Archimedes’ spiral with polar equation r(α) = r₀ + p/(2π) α, where r₀ is the starting radius and p is the pitch. For a spiral with an integer number of turns, M, we have α = 2πM at its end point, so r_end = r₀ + pM, the pitch p being the separation between turns. Besides, we have that the pitch equals the constant growth rate of the spiral radius r(α) per turn, that is p = 2πdr/dα.

Go to Draw > Archimedean Spiral in the main menu to display the Draw dialog box for the Archimedean Spiral. This dialog box has three pages: Archimedean Spiral, Attributes, and Materials.

The Archimedean Spiral page

In the Archimedean Spiral page, the geometrical parameters for the Archimedean Spiral can be set, Fig. 1.

The Archimedean spiral is entered by giving the Start Point, Start Radius r₀, Pitch p (positive or negative) and Number of Turns M (complete turns and fractions of a turn can be set). The spiral lies on a plane given by the Orientation Angles Theta and Phi (normal to the plane in spherical coordinates) and can be rotated by setting a Rotation Angle, Fig. 2.

Once the geometrical parameters in the Archimedean Spiral page have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.

The Logarithmic Spiral refers to a spiral with polar equation r(α) = r₀ exp(bα), where r₀ is the starting radius (r at α = 0), b = p/(2πr₀) and p is the starting pitch, that is, the derivative 2πdr/dα at α = 0 (starting growth rate of the spiral radius r(α) per turn). The first two terms of the Taylor expansion r(α) = r₀ + p/(2π) α + r₀(bα)²/2 + … give the polar equation of an Archimedean spiral.

Go to Draw > Logarithmic Spiral in the main menu to display the Draw dialog box for the Logarithmic Spiral. This dialog box has three pages: Logarithmic Spiral, Attributes, and Materials.

The Logarithmic Spiral page

In the Logarithmic Spiral page, the geometrical parameters for the Logarithmic Spiral can be set, Fig. 1.

The logarithmic spiral is entered by giving the Start Point, Start Radius r₀, Start Pitch p (positive or negative) and Number of Turns (complete turns and fractions of a turn can be defined). The spiral lies on a plane given by the Orientation Angles Theta and Phi (normal to the plane in spherical coordinates) and can be rotated by setting a Rotation Angle, Fig. 2.

Once the geometrical parameters in the Logarithmic Spiral page have been set, the Attributes > page can be selected, where the number of segments and cross-section can be set. The wire resistivity and coating can be set in the Materials > page.

A tapered wire is a wire with a variable radius along its length. The cross section of tapered wires is always circular. The radius is varied linearly along the wire and in defined steps, then a wire with a stepped radius is obtained, as shown in Fig. 1.

Go to Draw > Tapered Wire in the main menu and select a wire type for drawing. The wire types available are the same as in the Draw menu. As an example, Fig. 2 shows the Line page of the Draw dialog box when a linear wire is selected.

The wire must be divided into wire portions according to the desired steps in radius, as it is indicated in Fig. 1. Also, each wire portion having a uniform radius must be divided into segments as it is required by the Method of Moments used for the simulation.

The number of wire portions and the number of segments per wire can be set by going to the Attributes tab, Fig. 3. In this page, the Start and End radii can be set. The resistivity for the conductive wire and its coating material can be set in the Materials tab, Fig. 4. In this case, a tapered coating shield can also be set by giving a Start and End thickness.

The wire portions will be displayed in alternating colors for easy identification in the workspace.

Supported Formats

To import wires from an external file into AN-SOF, follow these steps:

1. Navigate to File > Import Wires in the main menu.
2. A sub-menu with four options will be displayed: AN-SOF, NEC, DXF, and MM formats.
3. Note that DXF and MM formats should contain only linear wires in ASCII text format.

AN-SOF Format

Wires can be imported into the AN-SOF workspace from another AN-SOF project. When a project is saved, a corresponding file with a .wre extension is created in the same directory. This file, named after the project, contains the geometrical description of all wires within the project. For details on files generated during project saves, refer to File Formats.

To import wires into your project, navigate to the main menu and select File > Import Wires > AN-SOF Format. Then, choose the specific .wre file you wish to import. You can import multiple .wre files, one at a time, as needed.

NEC Format

There are slight differences between the commands supported by AN-SOF and the standard NEC cards. To maintain compatibility with the NEC format, originally designed for data entry using punch cards, some fields appear repeating, and others must be entered with a zero, having no meaning. Lengths and wire radii are assumed to be in meters. If errors are found while importing a file, an error report will be shown in the Note panel of the Setup tab.

The SY command for symbolic language is not supported. To run simulations with variable geometric parameters, you can write scripts to generate the NEC files and then use the Run Bulk Simulation command (refer to section “12.8 Running a Bulk Simulation”). See examples here >.

GW – Linear Wire

One linear wire per line must be set, beginning with “GW” and ending with an Enter, as follows:

GW Tag Segments X1 Y1 Z1 X2 Y2 Z2 Radius

[Enter]

Tag: Tag number for the linear wire (Tag > 0). The space between “GW” and Tag is optional. A single tab or comma can also be used as a separator between the command name and the first data field.

Segments: Number of segments for the wire. If zero is entered, the minimum recommended number of segments will be computed.

X1 Y1 Z1: Cartesian coordinates of the start point of the linear wire.

X2 Y2 Z2: Cartesian coordinates of the end point of the linear wire.

Radius: Wire radius.

Fields can be separated by up to two spaces, a single tab, a single comma, or a comma and space. Each GW line, including the last one in a set of linear wires to be imported, must end with an Enter (press Enter on the keyboard for a carriage return). The text lines above the GW lines will be ignored, so comments can be added at the beginning of the file.

The following are equivalent examples:

Write comments here

GW 1 12 5.42 0.38 1.262 5.425 -0.378 1.261 0.01[Enter]

GW 2 5 7.45 0 1.122 7.45 0 1.49 0.015[Enter]

GW 3 2 8.3 0.0 1.12 8.37 0.0 1.595 0.01[Enter]

Write comments here

GW1,12,5.42,0.38,1.262,5.425,-0.378,1.261,0.01[Enter]

GW2,5,7.45,0,1.122,7.45,0,1.49,0.015[Enter]

GW3,2,8.3,0.0,1.12,8.37,0.0,1.595,0.01[Enter]

CM and Other Commands

The following commands: CM (comment lines), GH (helical wire), GA (arc), GM (coordinate transformation), GS (scale dimensions), GE (ground connections), GN (real ground parameters), TL (transmission line), LD (load impedances and wire conductivity), IS (insulated wire), FR (frequency), EX (excitation), EK (exact kernel), and RP (radiation pattern), will also be read.

CM lines will be added to the Note panel of the Setup tabsheet after the NEC file is imported. The comment termination card, “CE”, is not needed in AN-SOF. Comments without the CM command at the beginning of the file will be ignored and not imported. The command names—“CM”, “GW”, “GH”, etc.—are reserved words in AN-SOF and are used to recognize the fields between these commands and the final Enter in each text line, so the command names should not be used in comments.

The rest of the AN-SOF commands in NEC format are listed below, where all the indicated fields are mandatory.

GH – Helix

The GH command is used to define a helix in AN-SOF with the following syntax:

GH Tag Segments Spacing Length R R R R Radius

[Enter]

Tag: A positive number representing the tag for the helix. The space between “GH” and the Tag is optional. Note that the helix begins at the origin and develops along the positive z-axis. To adjust the helix’s position or rotation, use the GM command described below. It’s important to mention that the GH command differs in NEC-4.

Segments: The number of segments for the helix. If zero is entered, AN-SOF will compute the minimum recommended number of segments. Unlike NEC, AN-SOF uses conformal segments that precisely follow the helix contour.

Spacing: Spacing between turns.

Length: Total length of the helix. A positive Length value results in a right-handed helix, while a negative Length value produces a left-handed helix. 

R: Radius of the helix (repeated four times).

Radius: Wire radius.

Note: AN-SOF uses conformal segments that exactly follow the helix contour, distinguishing it from NEC.

GA – Arc

The GA command is utilized to define an arc in AN-SOF with the following syntax:

GA Tag Segments R Ang1 Ang2 Radius

[Enter]

Tag: A positive number serving as the tag for the arc. The space between “GA” and the Tag is optional. The arc is situated on the xz-plane, centered at the origin, making the y-axis the axis of the arc. To manipulate the position or rotation of the arc, use the GM command described below.

Segments: The number of segments for the arc. If zero is entered, AN-SOF will compute the minimum recommended number of segments. It’s worth noting that, unlike NEC, AN-SOF uses conformal segments that precisely follow the arc contour.

R: Arc radius.

Ang1: The angle of the first end of the arc measured from the x-axis in a left-handed direction about the y-axis, given in degrees. 

Ang2: The angle of the second end of the arc, measured in degrees.

Radius: Wire radius.

Note: AN-SOF uses conformal segments that exactly follow the arc contour, distinguishing it from NEC.

GM – Coordinate Transformation

The GM command in AN-SOF facilitates coordinate transformations with the following syntax:

GM 0 N rotX rotY rotZ DX DY DZ 0

[Enter]

N: If N is set to 0, it implies that the entire structure above the GM command must undergo rotation and translation based on the specified values for (rotX, rotY, rotZ) and (DX, DY, DZ). The coordinate transformations are applied sequentially in that order. If N is set to 1, it indicates that the structure above the GM command must be copied, and the copy should be moved to a new position (DX, DY, DZ) from the origin. You can use the “GM” command below the “GW,” “GH,” and “GA” commands to rotate, move, and copy linear wires, helices, and arcs as needed.

rotX: Angle of rotation about the X-axis, specified in degrees.

rotY: Angle of rotation about the Y-axis, specified in degrees.

rotZ: Angle of rotation about the Z-axis, specified in degrees.

DX: Translation along the X-axis, moving the structure by an amount DX.

DY: Translation along the Y-axis, moving the structure by an amount DY.

DZ: Translation along the Z-axis, moving the structure by an amount DZ.

GS – Scale Structure Dimensions

The GS command in AN-SOF is used for scaling structure dimensions. The syntax is as follows:

GS 0 0 Scale

[Enter]

Scale: This represents the scaling factor. Applying this command results in the multiplication of all structure dimensions, including wire radii, by the specified scale value.

GE – Ground Connections

The GE command in AN-SOF is used for defining ground connections. The syntax is as follows:

GE Type

[Enter]

Type = 0: No ground plane is present. If a “GE” command is used without specifying a type, it will be interpreted as “GE 0”.

Type = 1: A PEC ground plane is placed at z = 0, and wires ending on the ground plane will be connected to the ground. If a real ground plane has been chosen, Type = 1 indicates that the wire connections to the ground must be considered as zero-Ohm connections.

Type = -1: The wire connections to the ground are imperfect and produce power losses when a real ground plane has been chosen.

GN – Real Ground

The GN command in AN-SOF is used for defining real ground parameters. The syntax is as follows:

GN Type Screen 0 0 Epsilon Sigma Length WireRadius

[Enter]

Type: Type of ground plane.

• Type = -1: Free space simulation; all ground parameters are ignored. “GN -1” can be used in this case.

• Type = 0: Reflection Coefficients/Asymptotic option.

• Type = 1: PEC ground plane at z = 0; other parameters are ignored. “GN 1” can be used in this case.

• Type = 2: Sommerfeld-Wait/Asymptotic option.

Screen: Number of radials in a radial wire ground screen. Set Screen = 0 if no ground screen is present.

Epsilon: Ground plane relative permittivity or dielectric constant.

Sigma: Ground plane conductivity in [S/m].

Length: Length of radial wires if a radial wire ground screen is used. Enter zero if no ground screen is used.

WireRadius: Radius of radial wires if a screen is used. Enter zero if no ground screen is used.

TL – Transmission Line

The TL command in AN-SOF is used to define a transmission line. The syntax is as follows:

TL Tag1 Seg1 Tag2 Seg2 Zc Length Y1r Y1i Y2r Y2i

[Enter]

Tag1: Wire tag number to which the first port of the transmission line connects.

Seg1: Segment number of wire Tag1 to which the first port of the transmission line connects.

Tag2: Wire tag number to which the second port of the transmission line connects.

Seg2: Segment number of wire Tag2 to which the second port of the transmission line connects.

Zc: Characteristic impedance of the transmission line in Ohms. A negative Zc can be entered to set a “crossed” transmission line with a 180° phase reversal relative to the reference directions of the segments. The characteristic impedance of the line is |Zc|.

Length: Length of the transmission line in meters. If Length = 0, the linear distance between the transmission line ports will be considered as the length for the line. To simulate a zero-length transmission line, enter 1E-10.

Y1r: Real part of the shunt admittance across end one of the transmission line [S].

Y1i: Imaginary part of the shunt admittance across end one of the transmission line [S].

Y2r: Real part of the shunt admittance across end two of the transmission line [S].

Y2i: Imaginary part of the shunt admittance across end two of the transmission line [S].

Refer to Adding Transmission Lines for a review of considerations when setting transmission lines, including advanced settings not available with the TL command.

LD – Load Impedance

The LD command in AN-SOF is used to define a load impedance. The syntax is as follows:

LD Type Wire# Seg# Seg# R L C

[Enter]

Type: Type of load. Series RLC loads, fixed impedances R+jX, and wire conductivity can be set.

• Set Type = 0 for a series RLC load.
• Set Type = 4 for a fixed impedance R+jX. The reactance “X” must be entered in the position of “L” (the “C” field will be ignored). The reactance is fixed, so it does not scale with frequency.
• Set Type = 5 and Seg# = 0 to specify a wire conductivity [S/m] in the “R” field for the wire number “Wire#”. Use the command LD 5 0 0 0 R 0 0 to set a conductivity “R [S/m]” on all wires. “LD 5” command for setting wire conductivity must be below all “LD 0” and “LD 4” lines.

Wire#: Wire tag number where the load or conductivity is placed.

Seg#: Segment number where the load is placed. Note that it appears twice due to a NEC convention not used in AN-SOF, so the second Seg# will be ignored. Set Seg# = 0 if a wire conductivity is to be entered.

R: Resistance in Ohms or conductivity in S/m.

L: Inductance in Henries when Type = 0, or reactance in Ohms when Type = 4 (it does not scale with frequency). The “L” field is ignored if R is a conductivity, so a zero can be entered.

C: Capacitance in Farads; if none, enter zero. It is ignored if R is a conductivity, so enter zero.

IS – Insulated Wire

The IS command in AN-SOF is used to define an insulated wire. The syntax is as follows:

IS 0 Wire# 0 0 Epsilon 0 Radius

[Enter]

Wire#: Wire tag number where the insulation or coating will be applied.

Epsilon: Relative permittivity of the dielectric sheath.

Radius: Radius of the insulating sheath. Ensure it is greater than the wire radius.

FR – Frequencies

The FR command in AN-SOF is used to specify frequencies for simulations. The syntax is as follows:

FR Type Num 0 0 Freq Df

[Enter]

Type: Type of frequency sweep. For a linear sweep, set Type = 0; for a logarithmic sweep, set Type = 1.

Num: Number of frequency steps.

Freq: Frequency in MHz or starting frequency in a range.

Df: If Type = 0, it represents the frequency stepping increment in MHz. If Type = 1, it is the multiplication factor for a logarithmic sweep.

EX – Excitation

The EX command in AN-SOF is used to define excitation sources for simulations. The syntax is as follows:

EX Type Wire# Seg# 0 Real Imag

[Enter]

Type: Type of source. Use Type = 0 or 5 (the “5” corresponds to an old source model used in NEC) for a voltage source. Set Type = 6 for a current source. Note that current sources in AN-SOF automatically have a non-zero internal impedance set in parallel with the source (1E6 Ohm).

Wire#: Wire tag number where the source is placed.

Seg#: Segment where the source is located.

Real: Real part of the source voltage or current.

Imag: Imaginary part of the source voltage or current.

EK – Exact Kernel

The EK command in AN-SOF is used to force the use of the Exact Kernel. The syntax is as follows:

EK

[Enter]

This command ensures that the Exact Kernel is utilized, even if this option is disabled. It’s important to note that AN-SOF has the Exact Kernel enabled by default.

RP – Radiation Pattern

The RP command in AN-SOF is used to set the radiation pattern parameters. The syntax is as follows:

RP 0 Ntheta Nphi 1001 Theta Phi Dtheta Dphi R

[Enter]

Ntheta: Number of values of Θ at which the field is to be computed.

Nphi: Number of values of φ at which the field is to be computed.

(Note: The value “1001” is a NEC variable and will be ignored since AN-SOF always computes the average power gain.)

Theta: Initial Θ angle in degrees.

Phi: Initial φ angle in degrees.

Dtheta: Increment for Θ in degrees.

Dphi: Increment for φ in degrees.

R: Radial distance in meters of the field point from the origin. R = 0 is taken as R = 1 m.

DXF Format

The DXF file format is a standard format for storing CAD (Computer Aided Design) geometrical data as ASCII text lines.

Only DXF files containing LINE objects can be imported into AN-SOF. The structure of a LINE entity is as follows, where only the (X,Y,Z) coordinates of the starting and ending points are read:

LINE

8 // Subclass marker. Not read

0 // Thickness (default = 0). Not read

10 // Starting point – 10, 20, 30 are tags – Not read

-0.5000 // X value 

20 // Not read

-0.5000 // Y value  

30 // Not read

1.000 // Z value  

11 // Ending point – 11, 21, 31 are tags – Not read

0.5000 // X value  

21 // Not read

-0.5000 // Y value  

31 // Not read

1.000 // Z value  

0 // Extrusion direction (default = 0) – Not read

Since LINE objects have zero thickness, AN-SOF will set a wire radius equal to 0.5% of the wire length. The LINE coordinates in the DXF file are in meters. AN-SOF will also set the number of segments for each wire according to the operating frequency, so it is recommended to set the frequencies before importing the DXF file. Wire radii and the number of segments can be modified after importing the DXF file using the Modify command > in the main menu.

Download examples of DXF files to import into AN-SOF >

MM Format

One linear wire per line must be defined as follows:

X1,[TAB]Y1,[TAB]Z1,[TAB]X2,[TAB]Y2,[TAB]Z2,[TAB]Radius,[TAB]Segments

[Enter]

X1 Y1 Z1 = Cartesian coordinates of the wire start point.

X2 Y2 Z2 = Cartesian coordinates of the wire end point.

Radius = Wire radius.

Segments = Number of segments.

The last text line must end with an Enter (press Enter in the keyboard for a carriage return).

Example:

5.42,       0.38, 1.262,  5.425, -0.378,                1.261, 0.01,           12

7.45,       0,    1.122,  7.45,  0,                            1.49,  0.015,          5

8.3,         0.0,  1.12,   8.37,  0.0,         1.595, 0.01,           2

[Enter]

In the MM format, automatic segmentation of a wire can be obtained by entering any number equal or less than zero as the number of segments. The units for the coordinates of the start and end points of any wire must be consistent with the length unit chosen in the AN-SOF Preferences dialog box. Also, the wire radius or diameter of any imported wire must be expressed in the unit chosen in the Preferences > dialog box.

Linear wires can be entered and edited in a table using the following steps:

1. Navigate to Draw > Tabular Input (Ctrl + T) in the main menu to display the table (refer to Fig. 5.40).

2. Select the Wires tab and enter values as specified in the column titles. Each row corresponds to a linear wire, and you can input information such as the number of segments (Segs), coordinates of the starting (X1, Y1, Z1) and ending (X2, Y2, Z2) points, wire radius, resistivity, and coating (dielectric insulation). Note that only wires with a circular cross-section can be entered, and transmission lines are not supported in the Tabular Input.

3. Right-click on the table to display a pop-up menu with standard options such as Cut (Ctrl + X), Copy (Ctrl + C), and Paste (Ctrl + V).

4. Single cells can be selected by left-clicking on them or by using the TAB and arrow keys on the keyboard.

5. Rows can be selected by clicking on the row number in the left column (No. column). Use the mouse or the up and down arrows on the keyboard to select a single row. The selected wire (row) is highlighted in red in the workspace. Double-click on a cell to exit row selection mode.

6. Cut (Ctrl + X), Copy (Ctrl + C), and Paste (Ctrl + V) options apply to selected rows. Additionally, you can use Insert (Ins key) and Delete (Del key) options to add or remove rows.

7. The Clear Contents (Ctrl + Del) option in the pop-up menu clears the content of a selected cell or row.

8. Utilize the Sources and Loads tabs to input sources and loads. The Wire No. column specifies the wire on which the source or load is placed.

Ways to Select a Wire

Any wire in the workspace can be selected in three different ways:

1. By clicking on the Select Wire button (arrow icon) on the toolbar and then left clicking on the wire.
2. By right clicking on the wire. In this case, a pop-up menu will be displayed, Fig. 1.
3. By pressing F8 or F9 on the keyboard. In this case, the wires will be selected one by one, forwards or backwards, in the order in which they were created.

A wire is highlighted in light blue when it is selected.

The Pop-Up Menu

Right-clicking on a wire brings up a menu with the following commands:

Source/Load (Ctrl + Ins)

Displays the Source/Load toolbar for exciting or loading the selected wire.

Modify (Ctrl + M)

Displays the Modify dialog box for modifying the selected wire.

Wire Color

Displays a Windows(R) dialog box for changing the color of the selected wire.

Delete (Ctrl + Del)

Deletes the selected wire with all sources and loads placed on it.

Copy Start Point

Copies the start point of the selected wire to connect this point to the start point of another wire.

Copy End Point

Copies the end point of the selected wire to connect this point to the start point of another wire.

Plot Currents

Executes the AN-XY Chart application for plotting the currents vs. position along the selected wire. This command is enabled when the currents are already computed.

List Currents

Displays the List Currents toolbar for listing the currents vs. frequency at the selected wire segment. This command is enabled when the currents are already computed.

Wire Properties (Ctrl + W)

Displays the Wire Properties dialog box where information about the selected wire is shown.

Draw

Contains a sub-menu with the Line, Arc, Circle, Helix, Quadratic, Archimedean Spiral, and Logarithmic Spiral commands to draw these types of wires.

Right-clicking on a wire brings up a menu. Choosing the Modify command from the pop-up menu > shows the Modify dialog box, where the geometrical parameters and attributes of the selected wire can be modified.

The Modify command can also be chosen by first selecting a wire by left clicking on it, and next going to Edit > Modify in the main menu. This option is enabled when the Select Wire button (arrow icon) in the main toolbar is pressed.

When a wire is modified, all sources and loads placed on it are removed. To modify a wire without removing the sources and loads, select the wire using the selection box, as explained in Modifying a group of wires >.

Right-clicking on a wire brings up a menu. Choosing the Delete command from the pop-up menu > deletes the selected wire with all sources and loads placed on it.

The Delete command can also be chosen by first selecting a wire by left clicking on it, and next going to Edit > Delete in the main menu. This option is enabled when the Select Wire button (arrow icon) in the main toolbar is pressed.

AN-SOF allows the simultaneous editing of a group of wires. Click on the Selection Box button on the main toolbar. Left-click on the workspace, drag a box with the mouse, and select multiple wires (Fig. 1). All wires within the selection box will be highlighted in light blue.

Go to Edit > Modify in the main menu to modify the selected wires. The Modify command displays the dialog box shown in Fig. 2, with three tabs: Attributes, Materials, and Sources/Loads. Use the checkboxes to choose the parameters you want to modify. Note that sources and loads will not be removed unless specified in the Sources/Loads tab.

In the Attributes tab, the Segments per Wire and Segments per Wavelength options allow for the mass editing of wire segments. These options are mutually exclusive. “Segments per Wire” sets a fixed number of segments for all selected wires, while “Segments per Wavelength” sets the number of segments for each wire based on its length in wavelengths, considering the shortest wavelength corresponding to the highest frequency set.

Click on the Selection Box button in the main toolbar. Then, left clicking on the workspace a box to select multiple wires can be expanded. The selected group of wires will be highlighted in light blue, Fig. 1.

Go to Edit > Delete in the main menu to delete the selected group of wires. The Delete command can also be executed by pressing Ctrl + Del or the Delete button on the toolbar.

Right clicking on a wire shows a pop-up menu >. Choose the Wire Color command to display a dialog box that allows us to select a color for the wire. This command is enabled when a wire is selected.

The Wire Color command can also be accessed by first pressing the Select Wire button (arrow icon) on the toolbar, then left clicking on the wire to select it, and finally going to Edit > Wire Color in the main menu. The Wire Color command is also available as a button on the toolbar.

The color of a group of wires can be changed by first selecting the wires and next clicking on Edit > Wire Color in the main menu. A group of wires can be selected by expanding a selection box as explained in Modifying a group of wires >.

Right clicking on a wire will display a pop-up menu >, where the Wire Properties command can be selected.

The Wire Properties command can also be accessed by first pressing the Select Wire button (arrow icon) on the toolbar, then left clicking on the wire to select it, and finally going to Edit > Wire Properties in the main menu. The Wire Properties command is also available as a button on the toolbar.

Execute the Wire Properties command to display the Wire Properties dialog box. There are three pages: Geometry, Attributes, and Materials.

The Geometry page

It shows the geometrical properties of the selected wire, Fig. 1, namely,

• Start Point: Coordinates of the start point of the selected wire.
• End Point: Coordinates of the end point of the selected wire.
• Length: Wire length.
• Longest Segment: The length of the longest segment.
• Shortest Segment: The length of the shortest segment.
• Shortest Wavelength (λ): The wavelength related to the highest frequency.
• Length/λ: Wire length in wavelengths. The wavelength corresponds to the highest frequency.
• Longest Segment/λ: Length of the longest wire segment in wavelengths. The wavelength corresponds to the highest frequency.
• Shortest Segment/λ: Length of the shortest wire segment in wavelengths. The wavelength corresponds to the highest frequency.

The Attributes page

It shows the electrical properties of the selected wire, Fig. 2, namely,

• Number of Segments: The number of segments into which the selected wire has been divided.
• Number of Sources: The number of sources placed on the wire.
• Number of Loads: The number of loads placed on the wire.
• Cross-Section: The cross-section type and its dimensions.
• Equivalent Radius: The cross-section equivalent radius >.
• Equivalent Radius/λ: The cross-section equivalent radius as a fraction of the shortest wavelength.
• Thin-Wire ratio: The wire diameter to the shortest segment length ratio. It must be less than 3 when the Exact Kernel option is unchecked in the Settings panel > of the Setup tabsheet. Check the Exact Kernel option to be able to calculate with any value of the thin-wire ratio. For a non-circular cross-section, the wire diameter is two times the equivalent radius of the cross-section.

The Materials page

It shows the properties of the materials the selected wire is made of, Fig. 3, namely,

• Wire Resistivity: The resistivity of the selected wire in [Ohm m]. If the wire is coated, it is the resistivity of the internal conductor.
• Wire Coating: The parameters of the coating shield of the selected wire.
• Relative Permittivity: The permittivity or dielectric constant of the coating material relative to the permittivity of vacuum.
• Relative Permeability: The magnetic permeability of the coating material relative to the permeability of vacuum.
• Thickness: The thickness of the coating shield.

A wire junction is automatically established whenever the coordinates of a wire end are identical to the end coordinates of a wire previously specified. However, two wires will be also connected automatically when their ends are spaced one tenth of the wire radius. Wire junctions must be established to satisfy Kirchhoff’s current law at the connection point.

Figure 1 shows the correct and incorrect ways to connect two wires. To connect the end of wire 1 to a point on another wire 2 that is not another end, you must split wire 2 into two wires. So, three wires will be needed instead of two to make the connection.

Two wires can be connected by copying and pasting their ends. The following procedure will show how to connect the Start Point of a wire #1 to the Start Point of a wire #2.

Procedure for connecting two wires at their ends

1. Right clicking on wire #1 will display a pop-up menu.
2. Choose the Copy Start Point or Copy End Point command from the pop-up menu. This command is also available in the Wire Properties window of the selected wire, Fig. 1.
3. In this example, wire #2 will be a Line. Then, choose Draw/Line in the main menu to display the Draw dialog box for the Line.
4. Press the From Point button to paste the copied point, Fig. 2. Then, complete the definition of wire #2.

By means of this procedure, any number of wires can be connected at the same point.

After drawing the wire structure, we may need to modify the position or size of one wire or a group of them. To modify wires, we must first select them. Click on the Selection Box button on the toolbar and then expand a box using the mouse with the left button pressed. Enclose the wires you want to modify inside the box, Fig. 1.

After selecting the wires, go to the Edit menu, and choose one of these commands:

Move Wires

Displays the “Move Wires” dialog box for moving the selected wire or group of wires to a different position, Fig. 2. A different shift along each coordinate X,Y,Z can be entered.

Rotate Wires

Displays the “Rotate Wires” dialog box for rotating the selected wire or group of wires around the chosen axis, Fig. 3. In addition to the cartesian axes X,Y,Z, the “Custom” option allows to set a rotation axis in spherical coordinates (Theta,Phi). The Rotation Center can also be set in case we want to rotate around a different point from the origin.

Scale Wires

Displays the “Scale Wires” dialog box for scaling the selected wire or group of wires according to the specified scale factor, Fig. 4.

There are two options: Single Factor and Advanced. The “Single Factor” option allows us to set a single scale factor which will be applied to all the point coordinates of the selected wires. The “Advanced” option allows us to set a different scale factor for each point coordinate of the selected wires. The “Advanced” option only applies to lines defined using the “2 Points” option, to arcs defined using the “3 Points” option, and to quadratics.

When drawing a wire structure, it is often necessary to copy wires from one position to another. An antenna array is an example where this situation occurs. To copy wires, we must first select them by first pressing the Selection Box button on the toolbar and then expanding a box using the mouse to enclose the wires we wish to copy, as it is explained in Moving, Rotating and Scaling Wires.

In the Edit menu there are the following commands to copy the selected wires:

Copy Wires

Displays the “Copy Wires” dialog box for copying the selected wire or group of wires. The copied wires can then be pasted in a different position, Fig. 1. An offset in each coordinate X,Y,Z can be entered for the copied wires.

Stack Wires

Displays the “Stack Wires” dialog box for stacking the selected wire or group of wires along the specified direction and according to the given number of elements in the stack, Fig. 2. An “element” in the stack is composed of those wires that have been selected, so an element could be a single wire or a group of wires. The spacing between the elements must also be specified.

The grids are wire frameworks with holes on the surface they depict, whereas the surfaces represent solid metal sheets without holes. The wires of a grid do not overlap but are connected to each other. Wires used in grids or surfaces can be straight or curved.

AN-SOF offers various types of grids and surfaces, each with its unique geometric parameters and attributes that can be configured in dedicated Draw dialog boxes.

To access these options, navigate to Draw > Wire Grid / Solid Surface in the main menu, where you will find the following choices:

• Patch: Opens the Draw dialog box for creating a rectangular patch parallel to the xy-plane.
• Plate: Opens the Draw dialog box for creating a plate or bilinear surface.
• Disc: Opens the Draw dialog box for creating a disc.
• Flat Ring: Opens the Draw dialog box for creating a flat ring, which is a disc with a hole at its center.
• Cone: Opens the Draw dialog box for creating a cone.
• Truncated Cone: Opens the Draw dialog box for creating a truncated cone.
• Cylinder: Opens the Draw dialog box for creating a cylinder.
• Sphere: Opens the Draw dialog box for creating a sphere.
• Paraboloid: Opens the Draw dialog box for creating a paraboloid.

Tip

Go to View > Drawing Panel in the main menu to quickly access the wire grids and solid surfaces.

The Attributes page is part of the Draw dialog box for various wire grids and solid surface types. As shown in Fig. 1, this example illustrates the Attributes page for the Plate, but note that all grids and surfaces share the same Attributes page.

To select between a wire grid or a solid surface, refer to the “Cross-Section” field below. Wire grids consist of wires with a specified circular cross-section, leaving gaps between them, while solid surfaces use flat wires whose width is automatically adjusted to cover the surface without gaps.

On the Attributes page, you can set the following parameters:

Number of Facets

Each grid or surface consists of a specific number of facets. For instance, the plate shown here has a 10×10 arrangement of facets, while the disc here has 6×12 facets. Each facet is a quadrilateral formed by four wires, with each wire divided into segments.

For solid surfaces, the wires are essentially flat strips that cover the entire surface. In the AN-SOF workspace, only the strip axes are displayed. During the simulation process, an unknown current is determined for each wire segment.

You have the flexibility to individually edit any curved or straight wire that comprises a grid or surface. Refer to Modifying a Wire for details on editing individual wires. If you need to make mass edits to the wires that make up a grid or surface, please refer to Modifying a Grid/Surface.

In the case of a Patch, setting the number of facets to 0x0 results in an automatic calculation. The calculation considers 10 segments per wavelength along each side of the patch, with the wavelength corresponding to the highest frequency defined.

Segments per Wire

This parameter determines the number of segments for each wire within the grid/surface. If “Segments per Wire” is set to zero, each wire will be automatically divided into segments, with the calculation based on a default value of 10 segments per wavelength.

Please note that the Patch type does not offer the option to specify “Segments per Wire” since its facets are composed of one-segment wires and the number of facets can be automatically computed by setting 0x0 facets.

Cross-Section

To define a wire grid, choose a Circular cross-section and set the radius of the wires comprising the grid, as shown in Fig. 1 on the left. Wire grids cannot have infinitesimally thin wires, so the cross-section radius “a” must be greater than zero.

To define a solid surface, select either the Flat or Rectangular cross-section for the wires that constitute the surface, as shown in Fig. 1 on the right. These wires are essentially flat strips that completely cover the surface. With the ‘Rectangular’ cross-section option, you can specify the thickness of the solid surface.

A grid or surface can be modified using the procedure described in Modifying a Group of Wires. To select multiple wires, wire grids, or solid surfaces, click on the Selection Box button on the main toolbar. Left-click on the workspace, drag the mouse to create a selection box, and all wires within it will be highlighted in light blue, as shown in Fig. 1.

To apply modifications to the selected wires, go to Edit > Modify (you can also use the shortcut Ctrl + M), or use the Modify button on the toolbar. This command becomes active when you have a group of wires, a wire grid, or a solid surface selected. For details on the dialog window that allows you to modify selected wires, please refer to Modifying a Group of Wires.

If you need to perform actions such as moving, rotating, scaling, copying, or stacking wire grids and solid surfaces, please consult Moving, Rotating and Scaling Wires and Copying and Stacking Wires for more information.

Click on the Selection Box button in the main toolbar. By left-clicking on the workspace and dragging a box with the mouse, you can select a wire grid or a solid surface, as explained in Modifying a Grid/Surface or Modifying a Group of Wires. All wires inside the selection box will be highlighted in light blue.

Go to Edit > Delete (Ctrl + Del) in the main menu to delete the selected grid or surface. There is also a button on the toolbar with the Delete command. This command is enabled when a group of wires, a wire grid, or a solid surface is selected.

Click on the Selection Box button in the main toolbar. By left-clicking on the workspace and dragging a box with the mouse, you can select a wire grid or a solid surface, as explained in Modifying a Grid/Surface or Modifying a Group of Wires. All wires inside the selection box will be highlighted in light blue.

Go to Edit > Wire Color in the main menu to change the color of the selected grid or surface. A dialog window will be opened where a color can be chosen. There is also a button on the toolbar with the Wire Color command. This command is enabled when a group of wires, a wire grid, or a solid surface is selected.

A Patch in AN-SOF represents a solid rectangular conductive surface lying on the xy-plane or a plane parallel to it (z = constant). This structure consists of wires with a flat or rectangular cross-section that cover the entire surface of the patch.

You can use this command to model patch antennas, where the patch is a solid rectangular metal sheet. To do this, you must choose the Substrate option as the ground plane by navigating to the Setup tab > Environment panel > Ground Plane box.

If you need to model a solid rectangular surface or a rectangular wire grid in free space or above a real ground plane, use the Plate command instead of Patch.

To access the Patch command, go to Draw > Wire Grid / Solid Surface > Patch in the main menu. The displayed dialog box consists of three pages: Patch, Attributes, and Materials, detailed in Fig. 1.

The Patch page

On the Patch page, you can configure the geometric parameters for the Patch. To define the Patch, specify the coordinates of two opposite corner points in a plane z = constant, as illustrated in Fig. 2.

Once you’ve configured the geometric parameters on the Patch page, you can proceed to the Attributes page, where you can specify the number of facets for the Patch. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Plate command refers to a plate or bilinear surface.

To access the Plate command, go to Draw > Wire Grid / Solid Surface > Plate in the main menu. The dialog box for the Plate command contains three pages: Plate, Attributes, and Materials, detailed in Fig. 1.

The Plate page

In the Plate page, you can set the geometrical parameters for the Plate. The Plate is defined by specifying the coordinates of its four corner points. In general, a plate or bilinear surface is a non-planar quadrilateral, uniquely defined by its four vertices, as shown in Fig. 2. In some cases, the bilinear surface degenerates into a flat quadrilateral.

After setting the geometrical parameters on the Plate page, you can move on to the Attributes page. Here, you can specify the number of facets for the Plate and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Disc command is used to create a disc or circular surface.

To access this command, go to Draw > Wire Grid / Solid Surface > Disc in the main menu. This action will open the Draw dialog box for the Disc. The dialog box consists of three pages: Disc, Attributes, and Materials, as detailed in Fig. 1.

The Disc page

In the Disc page, you can configure the geometrical parameters for the Disc. Here, you’ll find a combo-box offering two options: Curved segments and Straight segments. Select Curved segments for an exact representation of the disc’s curvature. The Straight segments option provides an approximation using linear wires.

The Disc is defined by specifying the Center coordinates, Radius, and orientation angles, Theta and Phi. These parameters uniquely define a planar disc surface, as illustrated in Fig. 2.

After setting the geometrical parameters on the Disc page, you can move on to the Attributes page. Here, you can specify the number of facets for the Disc and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Flat Ring command creates a disc with a hole at its center.

To access this command, go to Draw > Wire Grid / Solid Surface > Flat Ring in the main menu. This action opens the Draw dialog box for the Flat Ring. The dialog box comprises three pages: Flat Ring, Attributes, and Materials, detailed in Fig. 1.

The Flat Ring page

On the Flat Ring page, you can specify the geometrical parameters for the Flat Ring. Here, you’ll find a combo-box offering two options: Curved segments and Straight segments. Choose Curved segments for an exact representation of the flat ring’s curvature. The Straight segments option provides an approximation using linear wires.

The Flat Ring is defined by providing the Center coordinates, Inner Radius (hole radius), Outer Radius, and orientation angles, Theta and Phi. These parameters uniquely define a planar flat ring surface, as illustrated in Fig. 2.

After setting the geometrical parameters on the Flat Ring page, you can move on to the Attributes page. Here, you can specify the number of facets for the Flat Ring and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Cone command creates a cone-shaped structure.

To access this command, go to Draw > Wire Grid / Solid Surface > Cone in the main menu, which opens the Draw dialog box for the Cone. The dialog box comprises three pages: Cone, Attributes, and Materials, as detailed in Fig. 1.

The Cone page

On the Cone page, you can set the geometrical parameters for the Cone. You’ll find a combo-box with two options: Curved segments and Straight segments. Choose Curved segments for an exact representation of the cone’s curvature, while the Straight segments option provides an approximation using linear wires.

The Cone is defined by specifying the Vertex coordinates, Aperture Angle, Aperture Radius, and orientation angles, Theta and Phi. These parameters uniquely define the cone’s surface, as illustrated in Fig. 2.

After setting the geometrical parameters on the Cone page, you can move on to the Attributes page. Here, you can specify the number of facets for the Cone and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Truncated Cone command creates a truncated cone-shaped structure.

To access this command, go to Draw > Wire Grid / Solid Surface > Truncated Cone in the main menu, which opens the Draw dialog box for the Truncated Cone. The dialog box comprises three pages: Truncated Cone, Attributes, and Materials, as detailed in Fig. 1.

The Truncated Cone page

On the Truncated Cone page, you can set the geometrical parameters for the Truncated Cone. You’ll find a combo-box with two options: Curved segments and Straight segments. Choose Curved segments for an exact representation of the truncated cone’s curvature, while the Straight segments option provides an approximation using linear wires.

The Truncated Cone is defined by specifying the Base Point coordinates, Base Radius, Top Radius, Aperture angle, and orientation angles, Theta and Phi. These parameters uniquely define the truncated cone’s surface, as illustrated in Fig. 2. Depending on its parameters, a truncated cone can take on various shapes, including a cylinder, a cone, a disc, or a flat ring.

After setting the geometrical parameters on the Truncated Cone page, you can move on to the Attributes page. Here, you can specify the number of facets for the Truncated Cone and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Cylinder command creates a cylindrical structure.

To access this command, go to Draw > Wire Grid / Solid Surface > Cylinder in the main menu, which opens the Draw dialog box for the Cylinder. The dialog box comprises three pages: Cylinder, Attributes, and Materials, as detailed in Fig. 1.

The Cylinder page

On the Cylinder page, you can set the geometrical parameters for the Cylinder. You’ll find a combo-box with two options: Curved segments and Straight segments. Choose Curved segments for an exact representation of the cylinder’s curvature, while the Straight segments option provides an approximation using linear wires.

The Cylinder is defined by specifying the Base Point coordinates, Length, Radius, and orientation angles, Theta and Phi. These parameters uniquely define the cylinder’s surface, as illustrated in Fig. 2.

After setting the geometrical parameters on the Cylinder page, you can move on to the Attributes page. Here, you can specify the number of facets for the Cylinder and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Sphere command creates a spherical structure.

To access this command, go to Draw > Wire Grid / Solid Surface > Sphere in the main menu, which opens the Draw dialog box for the Sphere. The dialog box comprises three pages: Sphere, Attributes, and Materials, as detailed in Fig. 1.

The Sphere page

On the Sphere page, you can set the geometrical parameters for the Sphere. You’ll find a combo-box with two options: Curved segments and Straight segments. Choose Curved segments for an exact representation of the sphere’s curvature, while the Straight segments option provides an approximation using linear wires.

The Sphere is defined by specifying the Center coordinates, Radius, and orientation angles, Theta and Phi. These parameters uniquely define the sphere’s surface, as shown in Fig. 2.

After setting the geometrical parameters on the Sphere page, you can move on to the Attributes page. Here, you can specify the number of facets for the Sphere and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

The Paraboloid command creates a paraboloidal structure.

To access this command, go to Draw > Wire Grid / Solid Surface > Paraboloid in the main menu, which opens the Draw dialog box for the Paraboloid. The dialog box comprises three pages: Paraboloid, Attributes, and Materials, as detailed in Fig. 1.

The Paraboloid page

On the Paraboloid page, you can set the geometrical parameters for the Paraboloid. You’ll find a combo-box with two options: Curved segments and Straight segments. Choose Curved segments for an exact representation of the paraboloid’s curvature, while the Straight segments option provides an approximation using linear wires.

The Paraboloid is defined by specifying the Vertex coordinates, Focal Distance, Aperture Radius, and orientation angles, Theta and Phi. These parameters uniquely define the paraboloid’s curved surface, as shown in Fig. 2.

After setting the geometrical parameters on the Paraboloid page, you can move on to the Attributes page. Here, you can specify the number of facets for the Paraboloid and choose whether it should be a wire grid or a solid surface. See Grid/Surface Attributes for additional parameters in the Attributes page and Wire Materials for parameters in the Materials page.

Discrete Sources, Incident Field, and Loads

A structure can be excited by discrete sources or an incident field. Refer to Excitation by an Incident Field > for the second case. Discrete sources can be located on any wire segment and there can be more than one source, as many as there are segments.

A source is used to model the feed point of a transmitting antenna or generator in an electrical circuit. There are two types of sources:

• Voltage sources
• Current sources

Current sources can be used to model impressed currents.

For each source, its amplitude and phase must be set. Internal impedances can also be added to model imperfect sources, which can be series RL, series RC, or R+jX impedances.

Lumped loads can also be added to any wire segment, representing resistors, inductors, capacitors, or fixed impedances. There are three types of loads:

• Series RL impedance (inductive)
• Series RC impedance (capacitive)
• Fixed R+jX impedance (the reactance X does not scale with frequency)

To model a pure resistor, add an inductive impedance with L = 0. The unit of inductance can be pH, nH, uH, mH or H, while that of capacitance can be pF, nF, uF, mF or F. These units can be set going to main menu > Tools > Preferences >.

Tips

• Sources are displayed as a yellow circle in the workspace, while loads are displayed as a green highlighted segment. To change the default colors, go to main menu > Tools > Preferences > Workspace tab.

• Voltage sources have their internal impedance in series, so set a null impedance to model a perfect source.

• Current sources have their internal impedance in parallel, so set a very large impedance (1E6 Ohm) to model a nearly perfect source.

Excitation by Sources

To excite the wire structure with discrete sources, go to the Setup tab > Excitation panel and select the Discrete Sources option, Fig. 1.

If the Set Input Power option is checked, you can set the total input power to the structure. In this case, the amplitudes of the voltage and current sources will be adjusted to achieve the specified input power.

The Source/Load/TL toolbar is used to connect a source, load, or transmission line to a selected wire segment. This toolbar also provides the means to edit sources, loads, and transmission lines.

When you right-click on any part of a wire, a pop-up menu will appear. Click on the Source/Load/TL (Ctrl + Ins) command from the pop-up menu to open the Source/Load/TL toolbar, Fig. 1.

The Source/Load/TL command is also accessible from the main toolbar or by going to the main menu and selecting Edit > Source/Load/TL (Ctrl + Ins). To enable this command, first click on the Select Wire button (the arrow icon) on the main toolbar and then left-click on the wire where you want to place the source or load.

The Source/Load toolbar has the following components:

The Slider

Each position of the slider corresponds to the position of a segment in the selected wire. So, the slider allows us to select a particular segment on the wire. At the right corner of this toolbar, the position of the selected segment is shown. The segment’s position as a percentage of the wire length is also shown. It is measured from the starting point of the wire to the middle point of the selected segment and is defined as follows:

% position = 100 (position / wire length)

The 50% button

The 50% button is used to position the slider in the middle of the wire. Discrete sources and loads are often added at the center of wires, so you can click this button to quickly select the segment at the wire’s center. Please note that the wire must have an odd number of segments for it to have a segment at its center. 

The Add Source button

Click the Add Source button to display a dialog box for adding a source to the selected wire segment, as shown in Fig. 2. This dialog box allows you to set the type of source, its amplitude, phase, and internal impedance.

The Add Load button

Click the Add Load button to display a dialog box for adding a load to the selected wire segment, as shown in Fig. 3. A load can represent either a resistor in series with an inductor (RL), a resistor in series with a capacitor (RC), or a fixed impedance (R+jX) where the reactance X does not scale with frequency.

The Transmission Lines button

Click on the Transmission Lines button to display a dialog box for connecting a transmission line to the selected wire segment. Refer to Adding Transmission Lines for further details.

The Delete button

If the selected segment has a source or a load on it, you can click the Delete button to remove the source or load from the segment.

The Modify button

If the selected segment has a source or a load on it, you can click the Modify button to open the Modify dialog box, allowing you to edit the source or load.

The Exit button

Click the Exit button to close the Source/Load/TL toolbar.

A source can be added to a selected wire segment by means of the following steps:

1. Right click on any part of a wire to display the pop-up menu.
2. Choose the Source/Load/TL command from the pop-up menu to display the Source/Load/TL toolbar.
3. Move the slider to select the desired segment.
4. Click on the Add Source button to display the Add Source dialog box.
5. Set the type of source, its amplitude (rms value), phase and internal impedance. Then, press the OK button.
6. Click on the Exit button to close the Source/Load/TL toolbar.

A source can be edited by means of the following steps:

1. Right click on any part of a wire to display the pop-up menu.
2. Choose the Source/Load/TL command from the pop-up menu to display the Source/Load/TL toolbar.
3. Move the slider to select the segment where the source is placed.
4. Click on the Modify button to display a dialog box where the source can be edited. The source can be deleted by clicking on the Delete button.
5. Click on the Exit button to close the Source/Load/TL toolbar.

A load can be added to a selected wire segment by means of the following steps:

1. Right click on any part of a wire to display the pop-up menu.
2. Choose the Source/Load/TL command from the pop-up menu to display the Source/Load/TL toolbar.
3. Move the slider to select the desired segment.
4. Click on the Add Load button to display the Add Load dialog box.
5. Set the type of load and the values of resistance and inductance or capacitance. Then, press the OK button.
6. Click on the Exit button to close the Source/Load/TL toolbar.

A load can be edited by means of the following steps:

1. Right click on any part of a wire to display the pop-up menu.
2. Choose the Source/Load/TL command from the pop-up menu to display the Source/Load/TL toolbar.
3. Move the slider to select the segment where the load is placed.
4. Click on the Modify button to display a dialog box where the load can be edited. The load can be deleted by clicking on the Delete button.
5. Click on the Exit button to close the Source/Load/TL toolbar.

All the loads can be enabled or disabled at the same time. This option avoids deleting the load impedances when loads must not be considered in a simulation.

Go to Setup tab > Settings panel > in the main window. If the option Load Impedances is checked, the loads are enabled, otherwise they are disabled, Fig. 1.

To choose an incident plane wave as excitation of the structure, go to the Setup tab > Excitation panel > and select the Incident Field option, Fig. 1. When this option is selected, if there are discrete sources on the structure, none will be considered in the simulation.

The following incident field parameters can be set in the Excitation panel > of the Setup tabsheet after clicking on the Incident Field option:

• E-Field Major Axis: Amplitude, in V/m (Volts rms per meter), of the linearly polarized incoming electric field. For elliptical polarization, it is the length of the major ellipse axis.

• Axial Ratio: For an elliptically polarized plane wave, it is the ratio of the minor axis to the major axis of the ellipse. A positive (negative) axial ratio defines a right-handed (left-handed) ellipse. If the axial ratio is set to zero, a linearly polarized plane wave is defined.

• Phase Reference: Phase, in degrees, of the incident plane wave at the origin of coordinates. It can be used to change the phase reference in the calculation. Its value only shifts all phases in the structure by the given amount.

• Gamma: Polarization angle of the incident electric field in degrees. For a linearly polarized wave, Gamma is measured from the plane of incidence to the direction of the electric field vector, Fig. 1. For an elliptically polarized wave, Gamma is the angle between the plane of incidence and the major ellipse axis.

• Theta: Zenith angle of the incident direction in degrees, Fig. 1.

• Phi: Azimuth angle of the incident direction in degrees, Fig. 1.

Note

When an incident plane wave is used as excitation, all discrete sources, if any, will not be considered in the simulation.

The 3D-View interface allows us entering the parameters of the incident field in a graphical way. Follow these steps:

1. Go to the Setup tabsheet and select the Incident Field option in the Excitation panel >.
2. Click on the 3D View button to open the interface and display the Incident Wave dialog box, Fig. 1.
3. Set the Gamma, Theta and Phi angles and press ENTER. You can also use the small arrows to change these angles.
4. Close the Incident Wave dialog box. The angles that have been entered in the dialog box will appear in the Excitation panel, Fig. 2.

A perfectly electric conducting (PEC) ground plane, parallel to the xy-plane, can be added to the model by means of the following procedure:

1. Go to Setup tab > Environment panel >.
2. Select the Perfect option in the Ground Plane box, Fig. 1.
3. Set the ground plane position under the Position label (Z-coordinate).

When the perfect ground is selected, an infinite PEC ground plane will be placed at the specified position, Z, from the xy-plane.

• If Z > 0, the PEC ground plane will be above the xy-plane.

• If Z = 0, the PEC ground plane will be the xy-plane.

• If Z < 0, the PEC ground plane will be below the xy-plane.

A real ground plane, located on the xy-plane (Z = 0), can be added to the model by means of the following procedure:

1. Go to Setup tab > Environment panel >.
2. Select the Real option in the Ground Plane box, Fig. 1.
3. Specify the Real Ground Option: Sommerfeld-Wait/Asymptotic >, Reflection Coefficients/Asymptotic >, or Radial Wire Ground Screen >.
4. Set the ground Permittivity and Conductivity. Also, set the radial length, number of radials and wire radius if a ground screen has been chosen.

To incorporate a dielectric substrate beneath the xy-plane (Z < 0) into the model, follow these steps:

1. Navigate to the Setup tab > Environment panel.

2. In the Ground Plane box, select the Substrate option (see Fig. 1).

3. Choose between an infinite or finite slab in the Substrate Slab Options box.

4. Choose a substrate material from the provided list, or select Custom to specify the substrate’s Permittivity. Set the slab’s Thickness (h) and, if you’ve chosen a finite slab, configure its dimensions along the X and Y axes.

Note that the substrate slab is backed by a PEC ground plane, which runs parallel to the xy-plane at Z = -h, and cannot be removed from the simulation.

A wire will automatically connect to the ground plane when the z coordinate of one of its ends coincides with the position of the ground plane.

• When a PEC ground plane > is chosen, the ground position is specified by the value of Z in the Environment panel > Ground Plane box.
• When a real ground > is chosen, the ground position is Z = 0 (xy-plane).
• When a substrate > is chosen, a PEC ground plane is placed at Z = -h (h: substrate thickness).

Wire connections to the ground plane are shown with 3D symbols, Fig. 1.

WARNING!

All wires must be above the ground plane. Wires that cross the ground plane from one side to the other are not allowed.

To remove the ground plane, do the following:

1. Go to Setup tab > Environment panel >.
2. Choose the None option in the Ground Plane box, Fig. 1.

Once the frequencies, the environment, the geometry of the structure, the excitation, and the points of observation of the radiated field have been set, AN-SOF is ready to execute the calculations. First, the current distribution on the wire segments will be calculated, which allows us to obtain the input impedance when we have a transmitting antenna. Later, the far and near fields can be calculated from the currents in the segments.

The Run ALL (F10) command allows us to run the calculation of the current distribution and the near and far fields sequentially and automatically. Go to main menu > Run > Run ALL to run this command, Fig. 1, or click on the Run ALL button on the toolbar.

If the near field is not required, the calculation can only be run for currents and far fields by clicking on the Run > Run Currents and Far-Field (F11) command. This command is also available on the toolbar.

If the far field is not required, the calculation can only be run for currents and near fields by clicking on the Run > Run Currents and Near-Field (F12) command. This command is also available on the toolbar.

The currents, far and near fields can be computed separately as it is explained in the next articles >.

When the frequencies, the environment, the geometry, and the excitation are set, AN-SOF is ready to compute the currents flowing on the wire segments.

Go to Run > Run Currents in the main menu to run the calculation of the current distribution, Fig. 1.

Tip

When we are modeling a transmitting antenna and we only need the input impedance, this command allows us to save time since the radiated field is not calculated.

Once the current distribution on the structure has been obtained, the far-field in the angular ranges set in the Far-Field panel > of the Setup tabsheet can be computed.

Go to Run > Run Far-Field in the main menu to run the calculation of the far-field, Fig. 1. This command is only enabled when the current distribution has already been calculated.

Tip

To run the calculation of the current distribution and the far field sequentially and automatically, click on the Run Currents and Far-Field (F11) button on the toolbar.

Once the current distribution on the structure has been obtained, the near electric field at those points in space set in the Near-Field panel > of the Setup tabsheet can be computed.

Go to Run > Run Near E-Field in the main menu to run the calculation of the near electric field, Fig. 1. This command is only enabled when the current distribution has already been calculated.

Tips

• To run the calculation of the current distribution and the near fields sequentially and automatically, click on the Run Currents and Near-Field (F12) button on the toolbar. This command also runs the calculation of the near H-Field.

• To avoid the calculation of the H-Field, go to main menu > Tools > Preferences > Options > and uncheck the “Run ALL” also calculates the H-Field option.

Once the current distribution on the structure has been obtained, the near magnetic field at those points in space set in the Near-Field panel > of the Setup tabsheet can be computed.

Go to Run > Run Near H-Field in the main menu to run the calculation of the near magnetic field, Fig. 1. This command is only enabled when the current distribution has already been calculated.

Tips

• To run the calculation of the current distribution and the near fields sequentially and automatically, click on the Run Currents and Near-Field (F12) button on the toolbar. This command also runs the calculation of the near electric field.

• Go to Tools > Preferences > Options > in the main menu and check the “Run ALL” also calculates the H-Field option to enable the calculation of the H-field.

When a calculation is executed using the commands under the Run menu >, the Processing window will be displayed, Fig. 1. There is a button to abort the calculation at any time. Note that you will be prompted to save the project before aborting, as AN-SOF will restart.

There are simulations in which we need to change the excitation of the structure frequently. For example, when we must often adjust the amplitudes of discrete sources or alter the direction of arrival of an incident field. In these cases, we can save a significant amount of time by enabling the NGF (Numerical Green’s Function) option in the Settings panel of the Setup tab, as shown in Fig. 1.

When an NGF calculation is performed, the LU-decomposed matrix of the system is stored in a file after the initial calculation. Subsequently, by reusing this stored matrix, new calculations can be performed more quickly than the initial one.

When transmission lines are included in the model, the NGF option will be automatically enabled.

AN-SOF is capable of importing a sequence of input files to obtain a corresponding sequence of output files, all without requiring any user intervention during the process. The input files must adhere to the NEC format and have a .nec extension. The supported NEC commands for importing wires are described here: Importing Wires.

The output data consists of power budget or RCS (Radar Cross Section), input impedances, far field, and near fields, all provided in CSV format. For each NEC input file, AN-SOF generates an individual project containing .emm and .wre files (see File Formats). This way, each project can be opened separately once the bulk simulation is completed.

To initiate a bulk simulation, navigate to the main menu and choose Run > Run Bulk Simulation. A prompt will appear, asking whether you want to save the changes in the current project, as the bulk simulation requires closing the currently open project. Subsequently, a dialog box will be displayed, allowing you to select a directory and the input .nec files. Upon selecting the desired files and clicking the “Open” button, the bulk simulation will commence, with the input files being imported and computed one after another in alphabetic order.

For instance, if we consider an input file named “InputFile.nec,” the following files will be generated:

Files of the AN-SOF project

InputFile.emm > main file of the project (it can be opened with AN-SOF)

InputFile.wre > geometry data (wires, segments, connections)

InputFile.txt > comments

InputFile.cur > current distribution

InputFile.pwr > input and radiated powers, directivity, gain, etc.

InputFile.the > Theta component of the far field

InputFile.phi > Phi component of the far field

InputFile.nef > near electric field

InputFile.nhf > near magnetic field

Output CSV Files with Results

InputFile_PowerBudget.csv > input and radiated power, efficiency, gain, etc.

InputFile_Zin.csv > input impedances

InputFile_FarFieldX.csv > E-theta and E-phi far field components

InputFile_EFieldX.csv > near electric field components

InputFile_HFieldX.csv > near magnetic field components

where “X” represents the frequency in Hz (e.g., X = 300000000 for a frequency of 300 MHz). Consequently, a FarField, EField, and HField file will be generated for each frequency if a frequency sweep simulation has been configured.

Bulk simulations serve the purpose of automating the calculation process for multiple NEC files, even if they are not directly related, eliminating the need for manual calculations file by file. Conversely, they are also useful for sequentially running calculations on NEC files generated with varying geometric parameters in an antenna. Subsequently, the results can be analyzed by reading data from the generated CSV files.

For instance, you can create a script to generate a sequence of NEC files for a Yagi-Uda antenna, where the spacing between its elements varies. To understand how to accomplish this and read the output data from the CSV files, you can refer to the following link: Element Spacing Simulation Script for Yagi-Uda Antennas.

Commands to Display Results

The output data of a simulation can be listed in tables or displayed in graphs. All results are found under the Results menu >, and are categorized into four groups:

Results related to current distribution

• Run > Plot Current Distribution command.
• Run > Plot Currents command.
• Run > List Currents command.
• Run > List Input Impedances command.

Results related to the far field

• Run > Plot Far-Field Pattern command.
• Run > Plot Far-Field Spectrum command.
• Run > List Far-Field Pattern command.
• Run > List Far-Field Spectrum command.
• Run > Power Budget/RCS command.

Results related to the near E-Field

• Run > Plot Near E-Field Pattern command.
• Run > Plot Near E-Field Spectrum command.
• Run > List Near E-Field Pattern command.
• Run > List Near E-Field Spectrum command.

Results related to the near H-Field

• Run > Plot Near H-Field Pattern command.
• Run > Plot Near H-Field Spectrum command.
• Run > List Near H-Field Pattern command.
• Run > List Near H-Field Spectrum command.

Tip

See the most relevant results for transmitting antennas in the Results tab > of the main window.

Lists and Plots

Listing the currents or input impedances means tabulating them as a function of frequency.

In the case of fields, they can be listed at a given point versus the frequency (Spectrum) or at a given frequency versus the observation point (Pattern).

AN-SOF includes a suite of four tools for plotting results: AN-XY Chart >, AN-Smith >, AN-Polar > and AN-3D Pattern >.

In the AN-SOF main window, you will find a Results tab (see Fig. 1) that displays a table with the primary results for a transmitting antenna, including Input Impedance (Rin + j Xin), VSWR, S₁₁, Directivity, Gain, Efficiency, and the Horizontal (H) and Vertical (V) Front-to-Rear (F/R) and Front-to-Back (F/B) Ratios.

This table is automatically populated only when the structure has been excited by a discrete source and will not be filled when the excitation is an incident wave. The tabulated results persist until a new calculation is performed, allowing you to reference them at any time, even when making changes to the project. To export these results to a CSV file, simply click the Export Results button on the toolbar.

The column headings, from Rin through F/B V, are buttons that you can click to display plots.

Select the Plots tab in the AN-SOF main window to visualize the plots of the main results for a transmitting antenna as a function of frequency, as shown in Fig. 1. These results are obtained from the table in the Results tab.

The left column in the Plots tab presents the real and imaginary parts of the input impedance and VSWR. On the right column are the antenna gain in dBi and the front-to-rear (F/R) and front-to-back (F/B) ratios in dB. These plots are aligned vertically to make it easy to compare.

Use the controls on the right side of the Plots tab to change different aspects of the graphics, including line thickness, visualization of points and marks, scales, axes, and also to choose between VSWR or S₁₁ and horizontal (H) or vertical (V) F/R vs. F/B ratios. Each plot can be maximized by clicking on the “Maximize” checkbox located at its upper right corner.

The input impedance and VSWR/S₁₁ plots can represent the antenna input impedance, the feeder + antenna input impedance, or the tuner input impedance. The tuner and feeder can be configured in their corresponding tabs next to the Results tab. Every time a tuner or feeder parameter is changed, the recalculated results in the Results and Plots tabs can be refreshed by clicking the desired option under the “Zin” box highlighted in Fig. 1 below.

If the Tuner option is chosen to display the plots and results, note that the input impedance of the tuner will be displayed, and if the tuner is connected to a combination of feeder + antenna, the input impedance and VSWR/S₁₁ of the tuner + feeder + antenna system will be displayed.

Go to Results > Plot Current Distribution in the main menu to display a 3D graph of the current distribution on the structure. This command executes the AN-3D Pattern > application where the amplitude of the currents is displayed on the structure using a color scale. Additionally, the currents in phase, real, and imaginary parts can be plotted selecting these options in the Plot menu of AN-3D Pattern, Fig. 1.

A 2D plot of the current distribution along a selected wire can be shown by right clicking on the wire and choosing Plot Currents from the pop-up menu, Fig. 2. The Plot Currents command executes the AN-XY Chart > application, where the current is plotted in amplitude vs. position along the selected wire. The current distribution can also be plotted in phase, real and imaginary parts by choosing these commands under View in the AN-XY Chart main menu.

A wire can also be selected by first clicking on the Select Wire button (arrow icon) on the toolbar and then left clicking on the wire. Once the wire is selected, go to Results > Plot Currents in the main menu to plot the current along that wire. This command is enabled when the current distribution has been calculated.

Tips

• The graph plotted by AN-XY Chart can be zoomed by expanding a box with the left mouse button pressed on the plot.

• Right click on the graph and drag the mouse to move it.

• Left click and expand a rectangle up to return to the original view.

• There are options to change the units of the plotted magnitudes and to export data in the AN-XY Chart main menu.

Right clicking on a wire shows a pop-up menu >. Click on the List Currents command to display the List Currents toolbar, Fig. 1. This toolbar allows us to select a wire segment to see the current flowing through that segment versus frequency. If the segment has a source or load, the list of input impedances, admittances, voltages, powers, reflection coefficient, VSWR, return and transmission losses can also be displayed.

A wire can also be selected by first clicking on the Select Wire button (arrow icon) on the toolbar and then left clicking on the wire. Once the wire is selected, go to Results > List Currents in the main menu. This command is enabled when the current distribution has been calculated.

The List Currents toolbar has the following components:

The Slider

Each position of the slider corresponds to the position of a segment along the selected wire. Thus, the slider allows us selecting the desired wire segment. The position of the selected segment is shown at the right corner of this toolbar. The segment position is shown as a number and as a percentage of the wire length. The percentage position is measured from the starting point of the wire to the middle point of the segment, namely,

% position = 100 (position / wire length)

The 50% button

Moves the slider towards the center of the wire. Note that there must be an odd number of segments for there to be a segment at the midpoint of the wire.

The Current on Segment button

Displays the Current on Segment dialog box, Fig. 2, showing a list of the current in the selected segment versus frequency. Click the Plot button to plot the current in the segment as a function of frequency.

The Input List button

If the selected segment has a source on it, the Input List button will be enabled. Click this button to display the Input List dialog box, Fig. 3, where the list of input impedances, admittances, currents, voltages, and powers is shown. Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency. The input impedance can be plotted in a Smith chart by pressing the Smith button. Click the Export button to save the list in CSV format.

The Source List button

If the selected segment has a source on it, the Source List button will be enabled. Click this button to display the Source List dialog box, Fig. 4, where the list of currents, voltages, and powers in the source internal impedance is shown. Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency. Click the Export button to save the list in CSV format.

The Load List button

If the selected segment has a load on it, the Load List button will be enabled. Click this button to display the Load List dialog box, Fig. 5, where the list of load impedances, currents, voltages, and powers in the segment is shown. Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency. Click the Export button to save the list in CSV format.

The Exit button

Closes the List Currents toolbar.

The following procedure allows us to select a wire segment to tabulate currents versus frequency:

1. Right click on the wire to display the pop-up menu >.
2. Click on the List Currents command to display the List Currents toolbar >.
3. Move the slider and select the desired segment on the wire.
4. Click on the Current on Segment button to display the Current on Segment dialog box, where a list of the currents versus frequency is shown. Currents are shown in amplitude, phase, real and imaginary parts. Click the Plot button to plot the current in the selected segment as a function of frequency.

The following procedure allows us to select a segment that has a source to tabulate input impedance versus frequency:

1. Right click on a wire that has a source to display the pop-up menu.

2. Click on the List Currents command to display the List Currents toolbar.

3. Move the slider and select the segment where the source is placed.

4. Click on the Input List button to display the Input List dialog box, Fig. 13.6, where the list of input impedances, admittances, currents, voltages, powers, reflection coefficient, VSWR, S₁₁ in decibels, return and transmission losses is shown. Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency. Click the Smith button to plot the input impedance in a Smith chart.

Tips

• The reference impedance for reflection calculations (VSWR, S₁₁, and Return Loss) can be set in the Settings panel of the Setup tabsheet.

• When there is a single source on the structure, you can quickly access the input impedance by going to the main menu > Results > List Input Impedances or by clicking on the ‘List Input Impedances’ button on the toolbar.

The Tuner Calculator

AN-SOF features a tuner calculator that enables impedance matching of an antenna input impedance, an antenna with a feeder already connected to its terminals, or a given custom load.

To access the tuner calculator, choose the Tuner tab in the AN-SOF main window (Fig. 1). Here, you can set the tuner parameters on the left side of the window and view the results on the right side. The tuner consists of three components, each of which will be described in the following sections:

• Impedance Matching Network: This component allows the synthesis of an impedance matching network based on the impedance seen at the network output and the desired impedance at the network input. The quality factors of the network, inductors, and capacitors can be adjusted to model real-world scenarios.

• Stray Capacitance: Some networks, particularly high-pass Tee networks, exhibit a parallel stray capacitance at the network output. This capacitance can be specified to account for this effect.

• Impedance Transformer: An impedance transformer can be specified at the network output to transform the input impedance of an antenna, the input impedance of a feeder connected to an antenna, or a custom load entered by the user.

Impedance Matching Network

In the Tuner Parameters box, you can configure the impedance matching network, as shown in Fig. 2.

By expanding the Network Type dropdown menu, you have the following options:

• No Network: Select this option to bypass the matching network, making the network input impedance equal to the impedance at the network output.

• Based on the impedance seen at the network output and the source impedance connected to the network input side, AN-SOF can synthesize the following networks:
  • L – Low-pass
  • L – High-pass
  • PI – Low-pass
  • PI – High-pass
  • T – Low-pass
  • T – High-pass

The network components will be automatically calculated to match the source impedance (R_s + jX_s) connected to the network input side. If the source impedance has a reactance component, jX_s, the network will “absorb” this reactance so that the input impedance of the network plus jX_s will match the real part, R_s, of the source impedance. The same principle applies to the load impedance seen at the network output side. If the network load impedance has an imaginary part, it will be absorbed by the network to synthesize the network components (inductors and capacitors).

Note that a low-pass network could include series capacitors instead of inductors or parallel inductors instead of capacitors, depending on the complex impedances (with real and imaginary parts) being matched. Similarly, a high-pass network might involve series inductors instead of capacitors or parallel capacitors instead of inductors.

You can specify a minimum Q for the network synthesis calculations, as well as the Q for the inductors and capacitors. This allows you to account for component losses to represent real-world components. To model ideal zero-loss components, enter high Q values, such as 1E8.

Stray Capacitance

Stray capacitance, also known as parasitic capacitance, refers to unintended capacitance between two conductors separated by a dielectric or free space. This effect is particularly noticeable at the network output side when a transmission line is connected. AN-SOF allows for the configuration of a feeder composed of a transmission line to feed an antenna, enabling modeling of stray capacitance to accommodate this scenario. While stray capacitance is commonly observed in Tee high-pass networks, it can be added in any case. Typical values range from around 10 pF in HF bands.

Impedance Transformer

In the Tuner Parameters box, an impedance transformer, also known as a “trafo” in RF jargon, can be specified, as shown in Fig. 3.

The transformer allows us to divide a load impedance by a factor, n, making it a 1:n transformer. It’s important to note that this is the impedance transformation factor, not the voltage transformation factor, which is n^-1/2 and is determined by the primary-to-secondary winding relationship of a transformer. A transformer can be used to reduce a high impedance to approach the standard 50 or 75 Ohms used in transmission lines and RF devices. Both the real and imaginary parts of the load impedance will be divided by n.

If n is in the range 0 < n < 1, the transformed impedance will be higher than the load impedance connected to the output side of the transformer. A factor n = 1 can be used to model a 1:1 transformer, also known as an isolation transformer, which is used to transfer voltage from one electrical circuit to another and to isolate a powered device from the power source. The 1:1 ratio transformer has the same input and output voltage and current. It is used to protect secondary circuits and individuals from electrical shocks between energized conductors and earth ground. It also reduces voltage spikes in the power supply line caused by rapid changes in lighting, static electricity, or voltage.

Real-life transformers are manufactured for a specified nominal impedance transformation. The nominal impedance can be entered in the Tuner Transformer box, as well as the transformer insertion loss in decibels. Manufacturers specify a transformer insertion loss relative to a nominal impedance, so it is important to specify the nominal impedance as well. The insertion loss is defined as the power lost inside the transformer, measured in dB relative to the input power. Thus, the output power delivered by the transformer to the load impedance will be lower than the input power due to losses inside the transformer materials (coil conductor losses, magnetic core losses, etc.).

Tuner Frequency and Input Power

The components synthesized in the impedance matching network of the tuner will be automatically calculated for a specified frequency, which can be chosen from a dropdown menu in the Tuner Parameters box, as shown in Fig. 4.

This list of frequencies is taken from the Frequency panel in the Setup tab, where a single frequency, a list of frequencies, or a frequency sweep can be configured. Therefore, to change the list of frequencies available in the Tuner tab, go to the Setup tab and enter the desired frequencies in the Frequency panel. Note that the frequency chosen for the tuner will be its design frequency; thus, the tuner components, inductors, and capacitors will be recalculated if the design frequency changes.

The Input Power to the tuner can also be specified in the Tuner Parameters box. This is the power delivered by the source connected to the input side of the impedance matching network of the tuner. This input power affects the powers calculated in the Results box on the right side of the Tuner tab, as explained below. It is worth mentioning that the tuner input power is not the power delivered to the antenna terminals, which can be set in the Excitation panel of the Setup tab. However, if the tuner is connected to an antenna, we can specify that the tuner output power be delivered to the antenna terminals, as detailed below.

Tuner Source and Load Impedances

The source impedance connected to the tuner input side can be set in real (R_s) and imaginary (X_s) parts, as shown in Fig. 5.

When a non-null source reactance, X_s, is entered, it will be absorbed by the impedance matching network calculations. Thus, the net input impedance of the network, after adding jX_s, will be matched to the real part of the source impedance, R_s. Click on the checkbox next to the “R_s” label to set this resistance as the reference impedance for VSWR calculations. This same resistance will be automatically set in the Settings panel as the “VSWR Ref. Impedance”.

There are three options for the tuner load impedance (R_L + jX_L):

• Antenna Impedance: Select this option to set the antenna input impedance as the tuner load. Note that the antenna impedance varies with frequency, so changing the design frequency for the tuner will trigger a recalculation of the impedance matching network.

• Feeder + Antenna: This option allows us to set the combination of feeder + antenna as the tuner load. In this case, the feeder parameters will be taken from the Feeder tab at the chosen design frequency. Therefore, the load impedance connected at the tuner output is a function of frequency since it is the input impedance to the feeder connected to the antenna.

• Custom Load: This option allows setting a tuner load impedance manually by specifying its real (R_L) and imaginary (X_L) parts. The Tuner tab can be used as an independent impedance matching calculator in this case.

Tuner Results

The results of the calculations based on the configured tuner parameters are displayed in the Results box on the right side of the Tuner tab, as shown in Fig. 6.

The results are categorized into three sections: Network results, input and load impedances, and power results.

Network Results

The network results shown include the resulting network Q and a diagram illustrating the network components, including inductors and capacitors. For inductors, their inductance in Henry and reactance in Ohms will be displayed, while for capacitors, their capacitance in Farads and reactance in Ohms will be shown. The units of inductance and capacitance displayed can be changed to pH, nH, uH, mH, H, or pF, nF, uF, mF, F, respectively, by navigating to the AN-SOF main menu > Tools > Preferences > Units tab.

It’s worth mentioning that the resulting network Q for L-type networks is determined only by the impedances connected to the load and source side of the network. Therefore, the minimum Q specified in the Tuner Parameters box has no effect for L networks.

Tuner Input and Load Impedances

The resulting input impedance to the tuner will be displayed in both real and imaginary parts, along with a polar representation showing its magnitude in Ohms and phase in degrees. If the source impedance, R_s + jX_s, connected to the tuner has a non-null reactance, jXs, this will be absorbed by the impedance matching network. Consequently, the displayed tuner input impedance represents the impedance seen towards the tuner just after R_s, as illustrated in the diagram on the left side of the Tuner tab (Fig. 7).

The load impedance connected to the tuner output terminals will also be shown, which can be the antenna input impedance, a feeder + antenna combination, or a user-entered impedance in the Tuner Parameters box on the left side of the Tuner tab.

For both the tuner input and load impedances, the reflection coefficient (Rho), VSWR, and return loss in dB will be displayed. These values are referred to the reference impedance for VSWR, which has been configured in the Settings panel of the Setup tab.

Powers Delivered and Lost

At the bottom of the Results box, the following powers are calculated:

• Power at Load: This is the power effectively delivered to the tuner load impedance. Note that the tuner consists of the impedance matching network + stray capacitance + transformer sequence. Therefore, the power at the tuner load represents the power delivered at the transformer output terminals. If an antenna impedance is chosen as the tuner load, the “Power at Load” is the power delivered to the antenna terminals. If a feeder + antenna is chosen as the tuner load, the “Power at Load” is the power delivered to the feeder terminals. To apply this power to the antenna model in the Workspace tab, check the checkbox next to the “Power at Load” label.

• Power Lost in Network: This is the total power lost in the network components, including inductors and capacitors, due to the losses related to the specified quality factors, Q. In the impedance matching network, a resistance, R = X/Q, representing component losses, is added in series to the inductor and capacitor reactance, X.

• Power Lost in Tuner Trafo: This is the power lost in the impedance transformer due to the specified insertion loss.

• Total Tuner Loss: This is the sum of the network and transformer losses.

• Radiated Power: If an antenna impedance is set as the tuner load, this is the power effectively radiated by the antenna after discounting losses in the antenna system. If a feeder + antenna is set as the tuner load, this is the power radiated by the antenna after discounting losses in the feeder and the antenna system.

• Antenna Loss: This is the power lost in the antenna structure, considering conductor losses, transmission line losses, if any, and ground plane losses.

• Total Feeder Loss: If a feeder + antenna is chosen as the tuner load, this is the power lost in the feeder system.

• Total System Loss: This is the sum of the power lost in the tuner (network + transformer), antenna (conductors, transmission lines, and ground plane), and feeder (feeding line + transformer), if specified.

The input impedance as a function of frequency can be plotted in a Smith chart by clicking the Smith button in the Input List > dialog box. Follow the procedure described in Listing the Input Impedances > for listing the input impedances versus frequency, and then click the Smith button in the opened dialog box.

Left click on the impedance curve in the Smith chart to see the frequency, input impedance (Zin), reflection coefficient (Rho) and VSWR in a hint message, Fig 1. Go to the AN-Smith main menu > Plot > Admittance to plot the input admittance curve. Go to Edit > Preferences to change the visualization options in AN-Smith.

In this article, you will learn how to add a feed line and transformer to your AN-SOF project. These components are essential for connecting your antenna structure to the external circuitry and impedance matching.

In the case of a transmitting antenna with a single feed port, the feeder used to connect the transmitter to the antenna terminals can be modeled in the Feeder tab, as shown in Fig. 1. The feeder consists of a transmission line, or feed line, and an impedance transformer.

Setting the Impedance Transformer

The transformer, also known as trafo, can represent a balun or unun that connects directly to the antenna terminals to divide its input impedance by a factor, n. In the Feeder Transformer box, three parameters can be specified:

Impedance Factor 1:n

Here, “n” is the factor by which the antenna input impedance will be divided. For example, if we have a folded half-wave dipole, which typically has an input impedance on the order of 300 Ohms, we can set n = 4 to get 300/4 = 75 Ohms of input impedance after the transformer (i.e., a 1:4 balun). If the input impedance is complex, both its real and imaginary parts will be divided by n.

If the transformation factor is in the range 0 < n < 1, the transformer input impedance will be greater than the antenna impedance. By setting n = 1, we can represent a 1:1 transformer, also known as a common-mode choke or line isolator, used to transform a balanced or symmetrical antenna to an unbalanced feed line.

Note that “n” is the impedance transformer factor, not the voltage transformation factor. In a transformer, which is composed of a primary winding (inductor or coil) and a secondary winding, the voltage transformation factor is n^-1/2.

Nominal Impedance

All actual impedance transformers, whether baluns or ununs, are fabricated for a nominal impedance, for which the manufacturer warranties the transformer performance in terms of bandwidth and insertion loss. So, if a lossy transformer is going to be modeled, we should set its nominal impedance according to the manufacturer’s datasheet.

Insertion Loss

The insertion loss of the transformer can be set in decibels to represent the actual loss given in its datasheet. The insertion loss is defined as the power lost, in decibels, inside the transformer, so that its output power will be lower than its input power due to losses in the transformer materials (coil resistivity, magnetic core losses, etc.).

Note: If no transformer is needed, just set n = 1 and an insertion loss of 0 dB.

Setting Feed Line Parameters

In AN-SOF, various real-life transmission line types are available, each with matched loss parameters adjusted according to the cable datasheets. These cable types are organized by part numbers and include the manufacturer’s name.

For example, entering “RG-8” in the Cable Type option will display this part number for different manufacturers, as shown in Fig. 2. Selecting RG-8 Belden 8237 will reveal a set of K0, K1, and K2 parameters. These constants have been adjusted to match the loss curve as a function of frequency, based on the matched loss vs. frequency table published in the cable datasheet. K0 relates to the DC losses in the transmission line conductors, K1 to the skin effect losses dependent on the square root of frequency, and K2 to dielectric losses increasing linearly with frequency. These losses are then considered in the standard RLGC model of a lossy transmission line.

The nominal values of the cable characteristic impedance Z0 and velocity factor will also be shown for the chosen part number and manufacturer. After selecting the cable type, you can set the operating frequency and input power to the feed line. The frequency can be chosen from a list that displays the frequencies set in the Setup tab.

Next, you can set the length of the cable, entered according to the length unit used for drawing wires in the workspace. To change the length unit, go to Tools > Preferences in the main menu. As you type the cable length, the length measured in wavelengths (λ) and electrical degrees will be automatically displayed. In fact, all feed line results are calculated automatically by modifying any of the feed line parameters.

You can then choose the load impedance of the feed line. The default option considers the Antenna Impedance as the load impedance of the transmission line, automatically displaying the antenna input impedance at the chosen frequency as the load for the line. However, you can enter any value for the line load impedance by selecting the Custom Load option. This allows you to use the Feed Line tabsheet as an independent calculator for transmission lines.

After specifying the feeder parameters in the left side of the Feeder tab, the following results will be obtained in its right side (Fig. 1):

Characteristic Z0

This is the “true” characteristic impedance of the feed line obtained from the RLGC model via the K0, K1, and K2 constants. The real part of Z0 may differ somewhat from the nominal Z0 depending on frequency and losses in the transmission line. An imaginary part will always appear in Z0 due to non-zero losses. So, note that the true characteristic Z0 will generally differ from the “Nominal Z0” (Z0 in the cable datasheet).

True Velocity Factor

This is the “true” velocity factor obtained from the RLGC model of the transmission line, where the wavenumber (and wavelength inside the line) is affected by losses. The velocity factor will be modified relative to its nominal value accordingly. Therefore, the true velocity factor is a function of frequency and losses in the line.

Matched Loss

Any cable datasheet contains a table of matched loss values expressed in dB/100 feet or dB/100 m as a function of frequency. These values correspond to the attenuation of the line when it is matched (the line has a load impedance equal to Z0). So, the Matched Loss value shown in the Results panel is the attenuation of the line corresponding to the selected frequency.

Total Matched Loss

This is the matched loss that would be obtained for the specified length of the cable. Therefore, the Total Matched Loss equals the Matched Loss (dB/100 feet or dB/100 m) multiplied by the cable length.

At Feeder Input

The input impedance of the feeder (feed line + transformer) will be shown as well as the reflection coefficient (Rho), VSWR, and return loss, all referred to the true characteristic impedance of the feed line. This is the impedance at the feed line end opposite to the end where the load or antenna is connected.

At Feeder Load

The load impedance connected to the feeder (feed line + transformer) will be shown as well as the reflection coefficient (Rho), VSWR, and return loss, all referred to the true characteristic impedance of the feed line. The load impedance will be the antenna input impedance if the Antenna Impedance option was selected as a parameter for the feed line in the left side of the Feeder tab. If a “Custom Load” was selected, then the load impedance will be that entered by the user.

Power at Load

This is the power in Watts consumed at the feeder load impedance or effectively delivered to the antenna terminals. This power will be less than the input power specified as an input parameter for the feed line if the transmission line has losses. The power at the load will be equal to the input power in the case of a lossless transmission line. Check the Power at Load option to automatically set this power as the input power delivered to the antenna terminals. Otherwise, the antenna input power will be that set manually in the Excitation panel of the Setup tab.

Power Lost in Feed Line

This is the power lost along the transmission line in Watts.

Power Lost in Trafo

This is the power lost in the feeder transformer in Watts.

Total Feeder Loss

This is the sum of the powers lost in the feed line and in the transformer.

Radiated Power

This is the power in Watts radiated by the antenna when it is fed using the Power at Load, which is the power effectively delivered to the load impedance of the feeder. The radiated power will be different from the power delivered by the feeder if the antenna itself has its own losses. The radiated power will be shown if the option Antenna Impedance was selected as a load impedance for the feeder in the left side of the Feeder tab.

Antenna Loss

This is the power lost in the antenna structure. It will be shown if the option Antenna Impedance was selected as a load impedance for the feeder in the left side of the Feeder tab.

Antenna Efficiency

This is the ratio of the antenna radiated power to the antenna input power (the power delivered by the feeder). It is expressed as a percentage as it is usual. It will be shown if the option Antenna Impedance was selected as a load impedance for the feeder in the left side of the Feeder tab.

Feeder + Antenna Loss

This is the sum of the powers lost in the feeder (feed line + transformer) and antenna.

In addition to the manufactured cables listed in the Cable Type option, the following custom line options can be chosen, as shown in Fig. 1:

Custom lossless line

This option represents an ideal transmission line with zero losses. Only the nominal Z0 and velocity factor can be specified in this case.

Custom line low-loss model

This option allows the specification of the nominal Z0, velocity factor, and matched loss curve. To define the matched loss curve, two values of attenuation must be entered at two different frequencies, with the second frequency being greater than the first one. AN-SOF will adjust a low-loss model to obtain a curve of attenuation vs. frequency for subsequent calculations. While the real part of the characteristic Z0 will be equal to the nominal Z0 in the low-loss model, which is a good approximation in many cases, especially for higher frequencies, the characteristic impedance will have an imaginary part that depends on the line losses and frequency. The “true” velocity factor is also assumed to be equal to the nominal velocity factor.

Custom line RLGC model

This option represents a transmission line model where losses are accurately considered by adjusting a matched loss curve to the table of attenuation vs. frequency in the cable datasheet. The K0, K1, and K2 constants must be entered in this case. The definition of K0, K1, and K2 considers that the frequency is in Hz and lengths are in meters (SI metric units). This option allows the entry of K0, K1, and K2 obtained from other transmission line calculators.

Follow these steps to select a wire segment that has a load and to tabulate the load impedance versus frequency,

1. Right click on a wire that has a load to display the pop-up menu >.
2. Click on the List Currents command to display the List Currents toolbar >.
3. Move the slider and select the segment where the load is placed.
4. Click on the Load List button to display the Load List dialog box, where the list of currents, voltages, and powers in the load impedance versus frequency is shown. Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency.

Follow these steps to select a wire segment that has a source and to tabulate the source internal impedance versus frequency,

1. Right click on a wire that has a source to display the pop-up menu >.
2. Click on the List Currents command to display the List Currents toolbar >.
3. Move the slider and select the segment where the source is placed.
4. Click on the Source List button to display the Source List dialog box, where the list of currents, voltages, and powers in the internal impedance of the source versus frequency is shown. Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency.

The radiation pattern can be displayed as a 2D rectangular plot by selecting Results > Plot Far-Field Pattern > 2D Rectangular Plot in the main menu. This command will open the Radiation Pattern Cut dialog box (Fig. 1), where you can produce two types of plots:

• Conical plots are obtained with a fixed Theta and variable Phi.

• Vertical plots are obtained with a fixed Phi and variable Theta.

Choose a radiation pattern cut and click the OK button to execute the AN-XY Chart application, Fig. 2, where the radiation pattern is plotted vs. Phi if a conical plot was chosen (for fixed Theta) or vs. Theta if a vertical plot was chosen (for fixed Phi).

In the AN-XY Chart, go to the Plot menu to plot various parameters, including the total E-field, the linearly polarized field components E-theta (vertical) and E-phi (horizontal), the circularly polarized components E-right and E-left, the Axial Ratio, Power Density, Directivity, Gain, and, in the case of plane wave excitation, the Radar Cross Section (RCS).

The absolute value of the Axial Ratio takes on values between 0 and 1, as it is defined as the ratio of the minor axis to the major axis of the polarization ellipse. You can also plot the Axial Ratio in decibels. A circularly polarized field corresponds to an axial ratio of ±1 (or 0 dB), while a field is considered linearly polarized when the axial ratio is zero. A positive (negative) axial ratio corresponds to a right-handed (left-handed) polarized field.

The far-field pattern can also be represented in a 2D polar chart by selecting Results > Plot Far-Field Pattern > Polar Plot 1 Slice in the AN-SOF main menu (refer to Fig. 3). In this case, the chart will display information such as the maximum radiation, beamwidth, and front-to-rear/back ratios.

To plot two slices of a 3D far-field pattern in the same polar chart, go to Results > Plot Far-Field Pattern > Polar Plot 2 Slices in the AN-SOF main menu. A dialog box will appear, allowing you to select the two slices. You can choose from two vertical slices, two conical slices, or vertical-conical combinations (see Fig. 4).

The far-field can be visualized as a 3D plot by selecting Results > Plot Far-Field Pattern > 3D Plot in the main menu. This command will open the AN-3D Pattern application, where the radiation pattern is displayed in a 3D view, showing the radiation lobes.

In addition, you can plot the Power Density, Directivity (numerical and in dBi), Gain (numerical and in dBi), Radiation Pattern (normalized to unity and to 0 dB), total E-field, linearly polarized field components E-theta (vertical) and E-phi (horizontal), as well as circularly polarized components E-right and E-left, by selecting the corresponding commands under the Plot menu in the AN-3D Pattern application (see Fig. 1). If the simulation involves plane wave excitation, the Radar Cross Section (RCS) can be plotted.

You can also plot the Axial Ratio pattern (both dimensionless and in decibels), which is defined as the ratio of the minor to major axis of the polarization ellipse (it equals 0 for a linearly polarized field and 1 for a circularly polarized field).

The 3D graph can be rotated and moved by dragging the mouse with the left button pressed. Move the mouse wheel to zoom the graph. The main menu of AN-3D Pattern has options for changing the units of the magnitudes, showing a color bar, and exporting data.

Note

• If discrete sources were used as the excitation of the structure, the plotted far-field is the total field.

• If an incident plane wave was used as the excitation, the plotted far-field is the scattered field.

To access the Preferences dialog box in the AN-3D Pattern main menu, click on Edit > Preferences (refer to Fig. 2). In this dialog box, you can choose various options for the colored surface and mesh of the radiation lobes (see Fig. 3). Additionally, you can superimpose the wire structure onto the radiation pattern by selecting the Wires option in the ‘Show’ box. You also have control over the graph’s scale and can display the main axes.

Furthermore, to tabulate the far-field pattern for a specific frequency, you can go to Results > List Far-Field Pattern in the AN-SOF main menu.

Far-field frequency spectra are obtained when a simulation is performed by specifying a list of frequencies or conducting a frequency sweep. For each frequency, the far-field is calculated at various directions determined by the zenith (Theta) and azimuth (Phi) angular ranges, and the distance specified in the Far-Field panel of the Setup tabsheet. Therefore, you must select a fixed direction (Theta, Phi) to plot the far-field versus frequency.

Go to Results > Plot Far-Field Spectrum in the main menu to plot the far-field spectrum. This command will display the Select Far-Field Point dialog box (see Fig. 1), where you can select the fixed Theta and Phi angles. After clicking the OK button, the AN-XY Chart application will display the frequency spectrum of the total E-field (refer to Fig. 2).

You can also plot the linearly polarized field components, E-theta and E-phi, as well as the circularly polarized components, E-right and E-left, in amplitude, phase, real, and imaginary parts by selecting these options under the Plot menu in the AN-XY Chart application. Additionally, you can plot the Axial Ratio, defined as the minor to the major axis ratio of the polarization ellipse, as a function of frequency.

The far-field spectrum for a selected far-field point can also be tabulated. To do this, go to Results > List Far-Field Spectrum in the AN-SOF main menu. This action will display the Select Far-Field Point dialog box where you can select fixed values for Phi and Theta. Afterward, a list of the far-field components versus frequency will be shown, and you can plot it by clicking the Plot button (as shown in Fig. 3).

To access the Power Budget dialog box (see Fig. 1), go to Results > Power Budget/RCS in the main menu. The following list of parameters versus frequency is displayed when discrete sources are used for excitation:

• The Input Power column shows the total input power provided by the discrete sources in the structure.

• The Radiated Power column shows the total radiated power from the structure.

• The Structure Loss column shows the total consumed power, representing ohmic losses in the structure.

• The Efficiency column displays the radiated power-to-input power ratio. When the structure is lossless, it results in an efficiency of 100%.

• The Directivity columns display the peak directivity, dimensionless and in decibels (dBi) with reference to an isotropic source.

• The Gain columns display the peak gain, dimensionless and in decibels (dBi) with reference to an isotropic source.

• The Av. EIRP (Effective Isotropic Radiated Power) columns display the average EIRP in Watts and dBW. This value is equal to the Radiated Power.

• The Peak EIRP (Effective Isotropic Radiated Power) columns display the peak EIRP in Watts and dBW.

• The Av. Power Density column is the average power density. This value is calculated averaging the power density over all directions in space.

• The Peak Power Density column is the maximum value of the radiated power density.

• The Theta (max) and Phi (max) columns are the zenith and azimuth angles, respectively, in the direction of maximum radiation.

• The F/R H and F/B H columns are the front-to-rear and front-to-back ratios, respectively, in a horizontal slice of the radiation pattern given by Theta = Theta (max).

• The F/R V and F/B V columns are the front-to-rear and front-to-back ratios, respectively, in a vertical slice of the radiation pattern given by Phi = Phi (max).

• The Error column is the error in the power balance of the system. A necessary, but not sufficient, condition for a model to be valid is that the input power must be equal to the sum of the radiated and lost powers, so the Error is defined as follows:

Error % = 100 x (Input – Lost – Radiated) Power / (Input – Lost) Power

• The Average Gain Test (AGT) column represents a similar indicator to the Error column. To validate a model, AGT should be close to 1, as it is calculated using the formula:

AGT = (Radiated + Lost) Power / Input Power

Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency. Click on the Export button to export the list to a CSV file.

Notes

• A power budget error of about ±10% is permissible from the engineering point of view.

• When a real ground plane is used, the Error column shows the percentage of power lost in the ground due to its finite conductivity.

• When a substrate slab is used, this column shows the percentage of power transferred to the dielectric material in the substrate.

• AGT = 1 means that the power balance is exact. An AGT between 0.99 and 1.01 is comparable to achieving an error of ±1%.

To access the Radar Cross Section dialog box (see Fig. 1), go to Results > Power Budget/RCS in the main menu. The following list of parameters versus frequency is displayed when an incident field is used for excitation:

• The RCS [m²] column shows the Radar Cross Section in square meters.

• The RCS [lambda²] column shows the Radar Cross Section in square wavelengths.

• The RCS [dBsw] column shows the Radar Cross Section in decibels with reference to a square wavelength.

• The Radiated Power column shows the total scattered power from the structure.

• The Structure Loss column shows the total consumed power, representing ohmic losses in the structure.

• The Av. Power Density column displays the average power density scattered from the structure. This value is computed by averaging the scattered power density over all directions in space.

• The Peak Power Density column shows the maximum value of the scattered power density.

• The Theta (max) and Phi (max) columns represent the zenith and azimuth angles, respectively, in the direction of maximum radiation.

Select an item from the list in the upper right corner of the window and then press the Plot button to plot the selected item versus frequency.

The far field patterns and spectra can be tabulated and exported by going to the following commands in the Results menu >:

• List Far-Field Pattern

• List Far-Field Spectrum

A table with the results will be displayed after executing any of these commands, Fig. 1. The tabulated values can be exported to a CSV (Comma Separated Values) file by clicking the Export button.

Two commonly used metrics for quantifying the directional properties of an antenna radiation pattern are the front-to-rear ratio (F/R) and the front-to-back ratio (F/B). Both F/R and F/B are crucial parameters for evaluating antenna performance, especially in applications requiring high directivity and low interference, such as point-to-point communication links and satellite systems.

• F/R is the ratio of the maximum power radiated by the antenna in the forward direction to the maximum power radiated in the backward direction. It indicates the antenna’s directional gain in the forward direction relative to its backward radiation. A high F/R signifies strong forward radiation and low backward radiation.

• F/B is the ratio of the maximum power radiated by the antenna in the forward direction to the power radiated in the opposite direction. It measures the power difference between the front and the directly opposing side of the antenna. A high F/B also implies strong forward radiation and low radiation in the opposite direction.

Both F/R and F/B are typically expressed in decibels (dB).

Metric	Definition
F/R (Worst-case Front-to-Back)	Ratio of maximum forward power to maximum backward power
F/B (180°-Front-to-Back)	Ratio of maximum forward power to power at 180 degrees

Figure 1 illustrates the difference between F/R and F/B, assuming a 360-degree radiation pattern slice.

In summary, the primary distinction between F/R and F/B lies in the direction of backward radiation. F/R compares the maximum forward power to the maximum backward power, while F/B compares the maximum forward power to the power radiated in the opposite direction.

These definitions are applicable to both horizontal (θ = const.) and vertical (φ = const.) radiation patterns in free space. However, the presence of a ground plane introduces complexities. For horizontal patterns, F/R and F/B calculations remain unchanged as the angular range spans 360 degrees. Conversely, for vertical patterns, the angular range is limited to 180 degrees. In this case, F/R is redefined as the front-to-side ratio, comparing the maximum signal to the maximum signal in the opposite quadrant (as depicted in Fig. 2). F/B becomes irrelevant due to the absence of a ‘back’ direction for an infinite ground plane, resulting in a zero value from AN-SOF.

Understanding F/R and F/B is crucial for effective antenna design. The Results tab in the AN-SOF main window presents F/R and F/B values in dB as a function of frequency for both vertical (V) and horizontal (H) radiation pattern slices. The Plots tab offers a visual comparison of F/R and F/B over the frequency range.

Note:

• To ensure proper calculations of F/R and F/B, select the Full 3D, Vertical or Horizontal options in the Far-Field panel.

• Selecting the Custom option in the Far-Field panel will lead to variations in the calculation of F/R and F/B as they will depend on the specific angular ranges that have been configured.

Golden Engineering

Go to Results > Plot Near E-Field Pattern > 3D Plot in the main menu to plot the near electric field as a 3D graph with a color scale. This command executes the AN-3D Pattern application, Fig. 1. Go to Results > Plot Near H-Field Pattern > 3D Plot in the main menu to plot the near magnetic field.

Near-field 3D plots will be shown according to the type of coordinate system that was chosen in the Near-Field panel of the Setup tabsheet: Cartesian, Cylindrical or Spherical. If near-fields were calculated for more than one frequency, a dialog box asking for a fixed frequency will be shown before plotting the near-field pattern.

The near electric field can also be plotted as a 2D rectangular plot by going to Results > Plot Near E-Field Pattern > 2D Plot in the main menu. The near magnetic field can be plotted by going to Results > Plot Near H-Field Pattern > 2D Plot. These commands execute the AN-XY Chart > application, where the total rms electric or magnetic field is plotted in a 2D chart, Fig. 2. A near-field has always three components, which can be plotted individually by going to the Plot menu in the AN-XY Chart.

The near-field patterns for a given frequency can also be tabulated going to Results > List Near E-Field Pattern or Results > List Near H-Field Pattern in the AN-SOF main menu.

Regarding the Near-Field Components

• If Cartesian coordinates have been set in the Near-Field panel of the Setup tabsheet, the E_x, E_y and E_z electric field components and the H_x, H_y and H_z magnetic field components will be calculated in a rectangular grid of points in space with coordinates (x,y,z).

• If Cylindrical coordinates have been set in the Near-Field panel of the Setup tabsheet, the E_r, E_phi and E_z electric field components and the H_r, H_phi and H_z magnetic field components will be calculated in a cylindrical grid of points in space with coordinates (r,phi,z).

• If Spherical coordinates have been set in the Near-Field panel of the Setup tabsheet, the E_r, E_theta and E_phi electric field components and the H_r, H_theta and H_phi magnetic field components will be calculated in a spherical grid of points in space with coordinates (r,theta,phi).

Near-field frequency spectra are obtained when a simulation is performed by specifying a list of frequencies or a frequency sweep. For each frequency, the near-field is calculated at those points specified in the Near-Field panel > of the Setup tabsheet. So, a fixed point in space must be selected to plot the near field versus frequency.

Go to Results > Plot Near E-Field Spectrum or Results > Plot Near H-Field Spectrum in the main menu to plot the near E- or H-field spectrum. These commands display the Select Near-Field Point dialog box, where a fixed observation point can be selected, Figs. 1. The AN-XY Chart > application will show the frequency spectrum of the total near electric or magnetic field, Fig. 2. The field components can be plotted in amplitude, phase, real and imaginary parts by choosing these options under Plot in the  AN-XY Chart main menu.

Near field patterns and spectra can be tabulated and exported by going to the following commands in the Results menu >:

• List Near E-Field Pattern

• List Near E-Field Spectrum

• List Near H-Field Pattern

• List Near H-Field Spectrum

A table with the results will be displayed after executing any of these commands. The tabulated values can be exported to a CSV (Comma Separated Values) file by clicking the Export button.

Adding a transmission line to a model has an impact on the entire calculation, affecting current distribution, input impedance, and near and far fields. AN-SOF allows for the addition of lossy or lossless transmission lines and has a list of preloaded lines with parameters adjusted to the attenuation curves published in the data sheets of real cables. This list of cables includes both two-wire and coaxial transmission lines.

After drawing and segmenting the wire structure that will represent an antenna or an object that will scatter electromagnetic waves, the recommended first step is to create a list of the transmission lines that will be connected to the structure. This is described below.

The ends of a transmission line in AN-SOF are called Port 1 and Port 2 since a line can be considered as a two-port network. Each end or port of a transmission line can be connected to a segment of the wire structure, as Fig. 1 shows. A transmission line is defined by its characteristic impedance, Z0, velocity factor, VF, a loss model or attenuation curve, and shunt admittances, Y1 and Y2, connected across each port. Each transmission line must be connected between two different wire segments (the i-th and j-th segments in Fig. 1 should not be the same segment). In the calculation engine model, a gap is opened in the center of each segment to allow a transmission line to be connected there.

Transmission lines are modeled in an implicit way, meaning that the lines don’t scatter electromagnetic waves in space, but rather interact with the wire structure by establishing boundary conditions on the voltages and currents at the connected segments. Implicit modeling is adequate when the disturbance in the electromagnetic field caused by the physical presence of the transmission line can be neglected, e.g., for twisted-pair lines in most cases. On the other hand, explicit modeling involves drawing the two parallel wires of a two-wire line in the workspace and dividing them into segments, like the rest of the structure. For coaxial lines, a “hybrid” modeling approach can be used, which is explained in Modeling Coaxial Cables.

To add transmission lines, go to the AN-SOF main menu > Draw > Transmission Lines (Ctrl + L). A table will be displayed where a transmission line can be entered on each row. Follow the procedure below to enter the lines:

1. Select a row by clicking on the row number of your choice in the first column labeled ‘No.’, Fig. 2.

2. On the right-hand panel, choose a type of transmission line and double-click on your chosen type. The selected row will be automatically completed, Fig. 3.

3. From type 3 onwards, the parameters correspond to real cable datasheets. If you wish to enter your own parameters, choose types 0, 1, or 2. To edit the value in a cell, double-click on the cell.

Note that in this procedure, the ports of the transmission lines have not been connected to the wire segments yet. This is explained in Connecting Transmission Lines.

The parameters that define a transmission line are:

1) Type: On the right-hand panel of the Transmission Lines window, there is a list of lines with the cable part number and the manufacturer in some cases. The first three types are used to input user-customized lines. The line type simply refers to its position in this list.

2) Z0: Nominal characteristic impedance, in Ohms. If a negative value is entered, the transmission line will be “crossed” with a 180° phase reversal with respect to the reference directions of the segments (the characteristic impedance of the line will of course be |Z0|).

3) VF: Velocity factor (dimensionless). The allowed range is 0 < VF <= 1.

4) Length: Length of the line, in the unit selected in the Preferences window (see Section “3.3 Preferences”). If a length of zero is entered, the length of the transmission line will be equal to the linear distance between the two wire segments connected at the ends of the line.

5) The K0, K1, K2, and K3 columns define the line losses for the so-called RLGC model. These four columns will change to Att. 1, Freq. 1, Att. 2, Freq. 2 when the chosen line model is that of low losses. These cells allow entering the attenuation curve of a real transmission line from its datasheet.

6) Real(Y1) and Imag(Y1) are the real and imaginary parts of the shunt admittance through Port 1 of the transmission line, in Siemens [S].

7) Real(Y2) and Imag(Y2) are the real and imaginary parts of the shunt admittance through Port 2 of the transmission line, in Siemens [S].

A transmission line without shunt admittances (Y1 = Y2 = 0) will always be symmetrical in the sense that if it is connected in reverse, i.e., by swapping ports 1 and 2, the same results will be obtained in a simulation. Ports 1 and 2 are identified so that the locations of the shunt admittances can be distinguished when they are not zero.

If you enlarge or maximize the Transmission Lines window, you will be able to see the columns corresponding to the loss model parameters and shunt admittances, Figs. 4 and 5. Initially, this window only displays cells up to the ‘Length’ column so that the user does not have to worry about the loss parameter values since these are automatically loaded when selecting a line type from the list. Adding an attenuation curve when modeling a cable that is not on the list is explained in Adding a Custom Lossy Line.

If you want to add “custom” transmission lines with your own parameters, you have types 0, 1, and 2 available, Fig. 1, which are explained below.

Type 0: Custom Lossless Line

This is an ideal transmission line with zero losses, so only the nominal Z0 and velocity factor must be specified.

Type 1: Custom line – low loss model

This is a transmission line where the nominal Z0, velocity factor, and matched loss curve can be specified. To define the matched loss curve, two attenuation values must be entered at two different frequencies, with the second frequency being greater than the first. AN-SOF will then adjust a low-loss model to obtain an attenuation vs. frequency curve for subsequent calculations. This is the simplest way to enter parameters from the datasheet of a manufactured real transmission line. Refer to Adding a Custom Lossy Line where it explains how to add the parameters from an attenuation curve published in a datasheet of a real cable.

Type 2: Custom line – RLGC model

This is a transmission line model that considers losses by adjusting a matched loss curve to the table of attenuation vs. frequency in the cable datasheet. The K0, K1, and K2 constants must be entered in this case. The definition of K0, K1, and K2 assumes that the frequency is in Hz and the lengths are in meters (SI metric units). This option allows for the entry of K0, K1, and K2 obtained from third-party transmission line calculators (K3 is an additional constant that is zero for all available cables).

Any transmission lines added through the Transmission Lines command (Ctrl + L) under the Draw menu will remain in the table until the user decides to remove or modify them. During calculations, only transmission lines with both ports connected to respective wire segments will be considered for simulation. Any lines with a single port connected or both ports disconnected will be omitted in the calculations.

To connect a transmission line between two wire segments, follow these steps:

1. Right-click on the first wire to select it and choose the Source / Load / TL (Ctrl + Ins) command from the pop-up menu. This will open a horizontal toolbar with a slider control, Fig. 1.

2. Use the slider to select the specific segment of the first wire to which you want to connect a port of the transmission line.

3. Once you’ve chosen the segment, click on the Transmission Lines button on the horizontal toolbar to open the Transmission Lines table, Fig. 2.

4. Enter an “x” or “X” (without quotes) in the corresponding cell for the port you want to connect to the selected segment (the cells located below the “Port 1” and “Port 2” columns), Fig. 2. You can enter an “X” for all the ports that need to be connected to the same segment as multiple transmission lines can be connected to it. Finally, close the Transmission Lines window.

5. Select the second wire and repeat steps 1-4 to connect the second port of the transmission line to another segment, Fig. 3. The transmission lines with both ports connected will be graphically displayed as shown in Fig. 4.

While performing this procedure, you have the option to add more transmission lines directly in the “Transmission Lines” dialog window. This saves you from having to follow the steps outlined in Adding Transmission Lines. The advantage of adding transmission lines here is that you can edit the connections of the lines in the “Port 1” and “Port 2” columns. However, with the Draw > Transmission Lines (Ctrl + L) command, you can quickly edit the lines (Z0, VF, length, etc.) if you don’t need to change the port connections.

A port that is already connected to a segment will show the status as “Connected,” while if it is not connected to any segment, it will display the status as “FREE”. When we are on a selected segment, a connected port will show the status as “Here,” which refers to the port being connected specifically to that selected segment.

To disconnect a port from a segment, enter the word “FREE” (without quotes, in uppercase) in the corresponding cell instead of an “X”. This allows you to use the “X” and “FREE” commands to easily connect and disconnect ports on a selected segment.

The transmission lines that have both ports connected to segments are displayed as straight dashed lines in orange color in the workspace, Fig. 4. An arrow will indicate the direction of the line, which goes from port 1 to 2. Since the length of a line is another parameter that is entered, such as its characteristic impedance and velocity factor, the length of the line in the workspace may not represent the configured or “real” length of the line.

If you select a row by clicking on the row number in the Transmission Lines table, the corresponding line will be highlighted in red in the workspace (if it has both ports connected to segments), Fig. 5. This way, you can visually identify which line you are editing.

IMPORTANT Information

• A transmission line with only one port connected to a wire segment will not be considered in the calculations. Instead, it exists as a row within the table, which can be used as a library of lines to select from and connect to the wire structure. Therefore, when a port is FREE, it does not mean that the corresponding end of the transmission line is open circuited, but rather that this line will simply be omitted in the simulation. It is sufficient for only one port to be FREE for the line to be omitted. If you need to connect a line with an open or short-circuited end, please refer to Open and Short-Circuited Lines for detailed instructions.

• A voltage or current source can be connected to any segment where one or more transmission line ports are connected. In this case, the sources will always be “ideal”, i.e., with zero/infinite internal impedance (zero for voltage sources and infinite for current sources), unlike in an ordinary segment without a port connected, where sources may have non-zero/finite internal impedance (in AN-SOF, current sources should always have a finite internal impedance because this impedance is connected in parallel with the current source).

• In each segment, only transmission line ports or a load impedance are allowed, but not both. If a port is connected to a segment where a load impedance already exists, this impedance will be eliminated, and vice versa. If you need to connect a load impedance in series with the port of a transmission line, connect the impedance in an adjacent segment to the port.

• When there are transmission lines in the model, the NGF (Numerical Green’s Function) option will be automatically enabled in the Settings panel of the Setup tabsheet. This way, calculations will be performed faster in the next simulation if only the parameters of the transmission lines are modified while the wire structure remains unchanged.

• It is recommended to connect transmission lines after drawing and segmenting the wire structure. If the number of segments changes, the lines may become disconnected and need to be manually reconnected using the procedure described in this section.

• To ensure a smooth calculation process, AN-SOF will verify the correct connections between the transmission lines and the wire segments. If AN-SOF detects any errors, it will promptly remove the faulty connection by setting the corresponding port to FREE state.

Due to the model used in the calculation engine, the transmission lines that are considered to exist in the simulation are those that have both ports connected to wire segments. Therefore, if you want to have an open-circuited line connected to a certain segment, the opposite port must also be connected to another wire segment. Create a short wire with only one segment that is no longer than 1% of the wavelength (its radius can be one-tenth of its length) and connect it to the open circuit transmission line port. This short wire should be disconnected from the rest of the structure, and the shunt admittance of the port it’s connected to should be zero, Fig. 1.

On the other hand, if you need a transmission line with a short-circuited port, connect that port to any other segment and set a shunt admittance at that end that is very large, for example, 1E6 [S]. At this end, you could connect a short wire segment created for this purpose, as is done for an open-circuited line, Fig. 2.

When creating short wires to connect open or short circuit transmission line ports, it is advisable to move these wires away from the rest of the structure to minimize interaction with it. Enter the length of the transmission line as indicated in Adding Transmission Lines. Remember that the length of the line is not necessarily related to the actual distance between the segments where it is connected.

The Transmission Lines table has a pop-up menu with keyboard shortcuts, Fig. 1. To access this menu for editing cells and rows, right-click on the table. The available commands are:

1. Standard Cut (Ctrl + X), Copy (Ctrl + C), and Paste (Ctrl + V) options are available for cells. A single cell can be selected by left clicking on it or by using the TAB and arrow keys on the keyboard.

2. To select a row, click on the row number in the left column (the “No.” column). Use the mouse or the up and down arrow keys on the keyboard to select a single row. Double-click on a single cell to exit row selection mode.

3. Cut (Ctrl + X), Copy (Ctrl + C), and Paste (Ctrl + V) options also apply to a selected row. In addition, Insert (Ins key) and Delete (Del key) options can be used to add or remove rows.

4. The Clear Contents (Ctrl + Del) command clears the content of a selected cell or row.

5. The Move Rows (Ctrl + M) command allows you to enter a mode where rows can be moved up or down to order them as desired. To exit this mode, click Move Rows (Ctrl + M) again.

6. The Update Ports (Ctrl + U) command checks and updates the status of the transmission line ports. Use this command to verify that the lines have their ports connected to wire segments when you have made any modifications to the segmentation or geometry of the wires where there are transmission line ports.

Coaxial transmission lines can be modeled implicitly as explained in the previous articles. To define a coaxial cable, one needs to know its characteristic impedance (Z0), velocity factor (VF), length, parameters that model losses (K0, K1, K2, etc.), and the shunt admittances at each end (Y1 and Y2). Furthermore, each end or port of the line must be connected to the center of a wire segment. In this implicit model, the electromagnetic interaction between the coaxial cable shield and the wire structure is neglected, and the line ends impose boundary conditions on the voltage and current in the connected segments. However, in certain scenarios, a current can be induced that flows through the outside of the coaxial cable shield, and this current cannot be neglected. To address this, a hybrid model is used, which is explained in detail below.

In the hybrid model, the internal behavior of a coaxial cable is implicitly modeled using its parameters such as Z0, VF, length, etc. On the other hand, the outer shield is modeled by adding a wire that must be divided into segments like the rest of the structure, Fig. 1. This additional wire considers the current induced outside the coaxial cable shield.

The wire representing the shield should be connected between two ends of the segments where the cable is connected, Fig. 2. Unlike transmission lines that connect in the center of the segments, wires are connected at their ends. Hence, the additional wire representing the shield will be a segment offset from the actual position of the cable. This is not a significant concern since the segments should be small compared to the wavelength.

Please be reminded that to connect one wire to another and connect the ends of the coaxial cable shield, you will need to manually divide the wires involved, as explained in Connecting Wires.

To simulate the dielectric coating of actual coaxial cables, an outer insulation can be added to the wire representing the shield, and its thickness can be input as well.

AN-SOF provides parameters for modeling the losses of more than 160 types of transmission lines. These parameters have been obtained by adjusting the loss model to the attenuation curves published by manufacturers. In case a particular type of cable is not listed or if the manufacturer has updated the parameters, a custom transmission line can be created using the following procedure:

1. Open the Transmission Lines window by going to the main menu > Draw > Transmission Lines (Ctrl + L) or follow the procedure in Connecting Transmission Lines to open this window by selecting a wire.

2. Select a row from the table by clicking on the row number (under the first column labeled No.).

3. In the panel on the right, double-click the Custom line low loss model option.

4. All manufacturers publish the nominal characteristic impedance, Z0, and the velocity factor, VF. Enter these values as well as the length of the line. If you enter “0” in the length cell, the linear distance between the ends of the cable will be calculated.

5. Manufacturers also publish an attenuation table as a function of frequency. Here is an example for the Belden 8237 cable, type RG-8/U:

6. In the cells corresponding to Att. 1, Freq. 1, Att. 2, and Freq. 2, enter the values from the attenuation table so that the simulation frequency range is included between Freq. 1 and Freq. 2. For example, if you are running a calculation between 150 and 170 MHz, enter Att. 1 = 1.9 dB/100 ft, Freq. 1 = 100 MHz, Att. 2 = 2.8 dB/100 ft, Freq. 2 = 200 MHz, as indicated in the table for the Belden 8237 cable, Fig. 1.

Be careful with the units of attenuation and frequency, as they will be displayed in the units chosen in the Preferences window. Go to main menu > Tools > Preferences > Units tab to change the units for frequency and length.

In the directory where AN-SOF was installed there is a folder called “Examples” which contains many examples of antennas and wire structures. The default directory is

C:\AN-SOF X\Examples

where X is the AN-SOF version.

You can also download the examples from here >.

We constantly upload files with examples on our website. You will find downloadable examples on our Resources and Blog pages.

At the bottom of our website there are Categories and a Search bar to facilitate the search for information.

We also invite you to subscribe to our Newsletter here > and to follow us on our social media channels.

From this link you can download 5 examples of antenna models that have less than 50 segments, so the calculations can be run with the trial version of AN-SOF:

• 2 Element Quad
• 2 Element Delta Loop
• HF Skeleton Slot
• Inverted V
• 5 Element Yagi-Uda

A center-fed cylindrical antenna is the simplest example that we can simulate. It consists of a straight wire with a source at its center and becomes a half-wave dipole when the frequency is such that the length of the antenna is half the wavelength. Follow the steps below to model this antenna.

Step 1 | Setup

Go to Tools > Preferences > in the main menu for selecting suitable units for frequencies and lengths. In this example, frequencies will be measured in MHz and lengths in mm. Then, go to the Setup tabsheet. In the Frequency panel choose Sweep and fill the Frequency Sweep box as shown in Fig. 1. Make sure None is selected in Environment panel > Ground Plane box and Discrete Sources is selected in the Excitation panel.

Step 2 | Draw

Right click on the workspace and choose Line from the displayed pop-up menu >. The Draw dialog box for the Line will be shown. Fill the Line and Attributes pages as shown in Figs. 2 and 3. A straight wire with 17 segments and 5 mm in radius will be drawn in the workspace. Right click on the wire and choose the Source/Load command from the pop-up menu. Follow the procedure described in Adding Sources > and put a voltage source in segment number 9 (at the wire center). The source voltage is 1 (0º) V. The center-fed cylindrical antenna in the workspace is shown in Fig. 4.

Step 3 | Run

Click on the Run Currents and Far-Field (F11) button on the toolbar. After the calculations are complete, right click on the wire and choose Plot Currents from the displayed pop-up menu and select the desired frequency. The current distribution along the wire will be plotted, Fig. 5. Follow the procedures described in Displaying Results > for obtaining other parameters of interest.

As an example, the current distribution in amplitude and phase, the input impedance vs. frequency, the gain, and E-field patterns at 100 MHz are shown in the following figures. Note that the antenna length is half a wavelength at 100 MHz, so the current distribution approaches a semi cycle of a sine function, as expected for a half-wave dipole.

After learning how to simulate a Cylindrical Antenna >, we are ready to build a dipole array. A 3-element Yagi-Uda antenna, consisting of a reflector, a driven element, and a director, is shown in Fig. 1, where the coordinates of the wire ends are indicated in meters.

Step 1 | Setup

Go to the Setup tabsheet and set an operating frequency of 300 MHz in the Frequency panel. None must be selected in Environment panel > Ground Plane box and Discrete Sources in the Excitation panel.

Step 2 | Draw

Follow the procedure described in Cylindrical Antenna > to draw one wire at a time. Set the coordinates of the ends of the wires indicated in Fig. 1. Set 15 segments for each wire and a radius of 5 mm. Then, right click on the driven element, select the Source/Load command, and connect a voltage source at the middle segment. Refer to Adding Sources >.

Step 3 | Run

Click on the Run Currents and Far-Field (F11) button on the toolbar. Fig. 2 shows the table in the Results tabsheet, where a peak gain of 8.9 dBi is obtained. This can also be seen in the gain pattern of the Yagi-Uda array shown in Fig. 3. Click on the Far-Field 3D Plot button on the toolbar to plot the 3D radiation pattern.

A monopole is a vertical element connected to a ground plane and with the feed point at its base. In this example we will simulate a radio mast on an imperfect ground, which is used for broadcasting in the LF and MF bands.

Step 1 | Setup

Go to the Setup tabsheet and set an operating frequency of 3 MHz in the Frequency panel. Then, go to the Environment panel > Ground Plane box and select Real, Fig. 1. Select Radial wire ground screen and the Poor ground options. Note that the soil conductivity will automatically be set to 0.001 S/m and the permittivity (dielectric constant) to 5.

Finally, set the number of radials, their length and radius as shown in Fig. 1. In radio masts it is customary to use a constant input power as a reference, for example 1 kW. Go to the Excitation panel, select Discrete Sources, Set Input Power and enter 1,000 W, Fig. 2.

Step 2 | Draw

Right click on the workspace and select Line from the displayed pop-up menu >. Specify a vertical wire 25 m in height (1/4 of a wavelength at 3 MHz) and with a triangular cross section as shown in Fig. 3. Although the recommended minimum number of segments is 3, we will divide the wire into 10 segments to obtain greater resolution in the current distribution. Note that the wire will be automatically connected to the ground at the origin (0,0,0).

Right click on the wire, select the Source/Load command from the pop-up menu and put a voltage source on the first segment, so the source will be connected to the base of the mast. Refer to Adding Sources >.

Step 3 | Run

Click on the Run Currents and Far-Field (F11) button on the toolbar. After the calculations are complete, click on the Far-Field 3D Plot button on the toolbar to display the radiation pattern. Choose Radiation Pattern under the Plot menu in AN-3D Pattern to plot the normalized radiation pattern (dimensionless). Then, choose the Radiation Pattern [dB] option to see the pattern in decibel scale. Note that the far field has a null on the xy-plane due to the losses in the ground plane, Fig. 4.

The antenna efficiency is the radiated to the input power ratio. Go to the Results tabsheet to see the input impedance, VSWR, Directivity, Gain, and Efficiency, Fig. 5. Note that the efficiency is low and therefore the gain too since most of the input power is lost to the ground. In this example we have chosen a Poor soil. Try different soils and increasing the number of radial wires and their length to improve the antenna efficiency.

The helix is a good example where we need curved segments to describe the geometry of the antenna. When the length of the helix is of the order of or greater than the wavelength, it can work in the so-called “axial mode”. To do this, we need to add a ground plane as a reflector.

Step 1 | Setup

Go to the Setup tabsheet and set an operating frequency of 100 MHz in the Frequency panel. Then, go to Environment panel > Ground Plane box, select Perfect, and set the ground plane position at Z = 0 (xy-plane), Fig. 1. Make sure the Discrete Sources option is selected in the Excitation panel.

Step 2 | Draw

Go to the Workspace tab, right click on the screen, and select Helix from the displayed pop-up menu >. The Draw dialog box for the Helix will be shown, Fig. 2. The helix will start above the ground plane, at the point (0,0,0.3) m, and run along the Z axis. We will then add a vertical wire that will connect the helix to the ground plane and where we will place the source.

The recommended helix dimensions for the axial mode can be obtained from any antenna book. Here we will set the helix radius, pitch (spacing between turns), and number of turns shown in Fig. 2. In the Attributes tab, we will leave the recommended number of segments of 103. The wire cross-section will be circular with 3 mm in radius

After drawing the helix, right click on the helix and choose the Start Point to GND command from the pop-up menu. The Draw dialog box for a Line will be displayed, where the coordinates of the ends of the wire are already set to connect the helix to the ground plane, Fig. 3. Set up 2 segments and a radius of 3 mm for this vertical wire. Finally, right click on the vertical wire, choose the Source/Load command, and connect a voltage source to the segment that is closest to the ground plane. Refer to Adding Sources > to add the source.

Step 3 | Run

Click on the Run Currents and Far-Field (F11) button on the toolbar. After the calculations are complete, click on the Far-Field 3D Plot button on the toolbar to display the radiation pattern, Fig. 4(a). The main lobe is on the axis of the helix, hence the name “axial mode”.

Because the helix is right-handed, the radiated field is circularly polarized, and the right-handed component predominates. Go to the AN-3D Pattern Plot menu and choose E-right or E-left to see the difference between both components, Figs. 4(b) and 4(c). To make the comparison between the color scales meaningful, go to Edit > Preferences in AN-3D Pattern and set the maximum of E-left to the same value as the maximum of E-right.

To draw a left-handed helix, specify a negative number of turns. Repeat the calculations and compare the E-right and E-left components.

This step-by-step guide empowers you to simulate circular loop antennas in AN-SOF. We’ll configure the software, define loop geometry, and explore how its size relative to wavelength affects radiation patterns and input resistance. Gain valuable insights into this fundamental antenna type!

This article provides a step-by-step guide to modeling a circular loop antenna using AN-SOF software. Circular loops are a common antenna type, and their analysis requires curved segments within the simulation environment. The guide will detail the configuration process, including defining the loop geometry, setting up the frequency sweep, incorporating a voltage source, and analyzing the key parameters like radiation pattern and input resistance. This guide is valuable for RF engineers, ham radio enthusiasts, students, and antenna design professionals seeking to utilize AN-SOF for circular loop antenna simulations.

1. Specifying the Simulation Setup

This section outlines the initial setup steps required to model a circular loop antenna in AN-SOF. We’ll configure a frequency sweep to analyze the antenna’s behavior across a specified range.

Frequency Sweep:

1. Navigate to the Setup tab and select Sweep within the Frequency panel.
2. Choose Lin for a linear frequency sweep. This allows for evenly spaced data points across the desired range.
3. Define the sweep parameters:
   • Start frequency: 3 MHz
   • Step: 1 MHz (adjust as needed based on desired resolution)
   • Stop frequency: 30 MHz

These settings establish a linear sweep from 3 MHz to 30 MHz with 1 MHz increments between each data point (as shown in Fig. 1).

Additional Settings:

• Environment: Ensure that None is selected in the Ground Plane box within the Environment panel. This removes any ground plane influence from the simulation, which might not be relevant for a free-space loop antenna.
• Excitation: In the Excitation panel, verify that Discrete Sources is selected. This indicates that we’ll define a lumped source (voltage or current) to excite the antenna later in the modeling process.

By following these steps, we’ve established the foundation for our loop antenna simulation by configuring the frequency sweep and essential simulation settings in AN-SOF. The next section will delve into defining the geometry of the circular loop itself.

2. Defining the Circular Loop Geometry

This section focuses on creating the circular loop geometry within the AN-SOF workspace:

1. Access the Draw Menu: Navigate to the Workspace tab. Right-click on an empty area within the workspace and select Circle from the pop-up menu.
2. Specify Loop Parameters: The Draw dialog box for the circle will appear (Fig. 2). Define the following parameters for your loop antenna using the provided tabs:
   • Center: (Cx, Cy, Cz) = (0, 0, 0) (Circle tab)
   • Radius: 0.5 meters (Circle tab)
   • Segments: 8 (Attributes tab)
   • Cross-section type: Circular (Attributes tab)
   • Cross-section radius: 5 millimeters (Attributes tab)

Segment Selection: The number of segments used to discretize the loop circumference is crucial for accurate simulation results. While 8 segments are a reasonable starting point, a convergence study might be necessary to ensure sufficient accuracy, especially for electrically large loops. As a rule of thumb, aim for 10-20 segments per wavelength at the highest frequency of interest.

Electrical Size Considerations: It’s important to consider the loop’s electrical size relative to the wavelength. At 30 MHz (the highest frequency in your sweep), the wavelength (λ) is indeed 10 meters, and the loop’s circumference (0.314λ) is close to one-third of a wavelength. This suggests the loop might not be electrically small at the high end of the frequency range. This characteristic will affect the antenna input impedance and radiation pattern.

Assigning the Excitation Source:

1. Right-click on the circular loop within the AN-SOF workspace.
2. From the pop-up menu, select Source/Load.
3. Choose to add a voltage source and position it at the first segment of the loop.

For detailed instructions on source placement and parameter definition, refer to the AN-SOF documentation’s ‘Adding Sources‘ section.

3. Running the Simulation and Analyzing Results

This section guides you through initiating the simulation process and analyzing the obtained results in AN-SOF:

1. Run Simulation: Locate the Run Currents and Far-Field (F11) button on the toolbar and click it. This initiates the simulation, calculating the current distribution on the loop and its far-field radiation pattern across the defined frequency sweep.
2. Visualizing the Radiation Pattern: Once the simulation is complete, click the Far-Field 3D Plot button on the toolbar. This will display the radiation pattern of the loop antenna in a 3D format (AN-3D Pattern application similar to Fig. 3).
3. Frequency-Dependent Analysis: The AN-3D Pattern toolbar offers functionalities to explore the radiation pattern’s behavior at different frequencies within the sweep range.
   • Frequency selection dropdown menu: This menu allows you to directly choose a specific frequency point to view its corresponding radiation pattern.
   • Frequency navigation buttons: Utilize the up and down arrow buttons on the toolbar to navigate through the calculated frequencies and observe the dynamic changes in the radiation pattern. As expected for a circular loop antenna, the pattern should exhibit a doughnut-like shape at lower frequencies.
4. Input Resistance Analysis: Navigate to the Results tab within AN-SOF. Here, you should observe a very low input resistance value, likely around 0.000195 Ohm at 3 MHz.
5. Comparison with Theoretical Radiation Resistance: The well-known formula for the radiation resistance, R_r, of an electrically small loop antenna is R_r = 31,200 (A/λ²)². Applying this formula with the loop’s area (A) and the wavelength (λ) at 3 MHz, you obtain a theoretical value of R_r ≈ 0.000192 Ohm. The close agreement between the simulated and theoretical values at 3 MHz demonstrates that the loop behaves according to the small loop antenna model at lower frequencies within the sweep range.

Important Note:

It’s important to remember that the formula used for radiation resistance applies to electrically small loops. As mentioned earlier, the chosen loop dimensions might not be electrically small across the entire frequency sweep (especially at 30 MHz). This will lead to deviations between the theoretical and simulated results at higher frequencies.

Figure 3 illustrates the frequency dependence of the loop antenna’s 3D radiation pattern. Subfigures (a), (b), and (c) depict the patterns at 3 MHz, 15 MHz, and 30 MHz, respectively.

By following these steps, you’ve successfully run the simulation, analyzed the radiation pattern, and compared the input resistance with theoretical expectations.

Two-wire transmission lines can be modeled explicitly in AN-SOF. In this example, the line will have a single wire but there will be a ground plane below it, so we have the mirror image of the wire as the return of the line.

Step 1 | Setup

Go to the Setup tab and select Single in the Frequency panel >. Set a frequency of 100 MHz. Then, go to the Environment panel > and set a perfect ground plane at Z = 0, Fig. 1.

Step 2 | Draw

Go to the Workspace tab, right click on the screen, and select Line from the pop-up menu >. Draw a horizontal line with the coordinates indicated in Fig. 2. Next, connect the ends of the line to the ground plane by drawing two vertical wires. You can right click on the line and select the commands Start point to GND and End point to GND to connect the ends to ground.

Set 40 segments for the horizontal wire and 1 segment for each of the vertical wires. Note that dimensions in Fig. 1 are in millimeters. To change the unit of length, go to Tools menu > Preferences > Units tab >.

Right click on the vertical wire at (0,0,0), select Source/Load from the displayed pop-up menu and put a 1 Volt voltage source on it. Refer to Adding Sources > to add the voltage source.

Step 3 | Run

Go to the Run menu and click on Run Currents. Since we are only interested in the current distribution and the input impedance, it is not necessary to calculate the radiated field (you can do it to check that it is practically negligible). Click on the Zin (List Input Impedances) button on the toolbar to display a table where the input impedance is shown as a function of frequency, Fig. 3. Refer to Listing Input Impedances >.

The impedance obtained is practically reactive, j512 Ohm. The small real part is the radiation resistance, since the line radiates a small amount of power, which is negligible but not zero.

This is a short-circuited line. Now right click on the vertical wire at (0,500,0) mm and select Delete from the pop-up menu to remove it. You will get an open-circuited line in this way. Rerun the calculations with the Run Currents command in the Run menu. The input impedance will now be -j105 Ohm.

Summarizing, we have,

• Z_in (short-circuited line) = j512 Ohm.
• Z_in (open-circuited line) = -j105 Ohm.

According to transmission line theory, the characteristic impedance can be calculated as the geometric mean of the short-circuit and open-circuit line input impedances, hence

On the other hand, the expression for the characteristic impedance of a line above a ground plane is given by:

where a is the wire cross-section radius and h is the line height above the ground plane. As we can see, the agreement between the characteristic impedance obtained from AN-SOF and that from theory is quite good. The difference is since the theory neglects the radiation of the line, and the logarithmic formula is an approximation that is valid when h >> a.

The ability of AN-SOF to simulate at extremely low frequencies can be demonstrated with a model of an RLC circuit that will resonate at only 800 Hz, so the wavelength is 375 km!

Step 1 | Setup

Go to Tools > Preferences > in the main menu and select Hz, mm, mH and uF as the units for frequency, length, inductance, and capacitance, respectively. Then, go to the Setup tab and select Sweep in the Frequency panel >. Choose Lin for a linear sweep and set the Start, Step, and Stop frequencies. The frequency sweep will start at 600 Hz and end at 1,000 Hz, incrementing by 10 Hz for each calculation, Fig. 1. In the Environment panel >, set a perfect ground plane at Z = 0.

Step 2 | Draw

Go to the Workspace tab, right click on the screen, and select Line from the pop-up menu >. Draw the three wires with the coordinates indicated in Fig. 2 using the Line dialog box. The left vertical wire has 1 segment, the horizontal wire has 1 segment, and the right vertical wire has 2 segments. The wire radius is 0.5 mm.

Right click on the left vertical wire, select the Source/Load command from the pop-up menu and put a 1 Volt voltage source. Then, right click on the horizontal wire, select Source/Load from the pop-up menu and connect a load impedance with R = 10 Ohm. Finally, right click on the right vertical wire, select Source/Load from then pop-up menu and put an inductance L = 20 mH on the first segment and a capacitance C = 2 uF on the second segment. Refer to Adding Sources > and Adding Loads > for adding sources and load impedances.

Step 3 | Run

Go to the Run menu and click on the Run Currents command. Since we are only interested in the input impedance, it is not necessary to calculate the radiated field (you can do it to check that it is practically negligible).

Right click on any of the three wires composing the circuit, select the List Currents command and click on the Current on Segment button of the displayed toolbar >. A table will be shown, where the current is tabulated vs. frequency. Next, press the Plot button to the right of the table to plot the current versus frequency, Fig. 3.

Since this is a series RLC circuit, the current flowing must be the same in all three wires (check this). As can be seen, resonance occurs at a frequency near to 800 Hz. Repeat the calculation for frequencies around 800 Hz, with a step of 1 Hz, and verify that the resonant frequency is 796 Hz. On the other hand, according to circuit theory, the resonance frequency is given by

The agreement between AN-SOF and theory is remarkable!