Enhancing Antenna Design Through Simulation Software

An antenna model represents a real-world antenna within a computer program. It is important not to confuse this type of model with a scale model, which is sometimes constructed to measure the radiation characteristics of a larger, physically identical antenna. Due to the mathematical complexity involved in modeling, specialized software is often used to predict and analyze antenna performance.

Computer simulation plays a critical role in overcoming challenges and driving innovation throughout the product development lifecycle. A computer model offers significant advantages, including the ability to modify, redesign, break, destroy, and rebuild designs multiple times without wasting physical materials. By leveraging simulation software, engineers can significantly reduce the costs associated with building successive physical prototypes, streamlining the design process.

AN-SOF is a comprehensive simulation software suite designed for antenna modeling and optimization. It supports the design of a wide range of wire antennas, including dipoles, monopoles, Yagis, log-periodic arrays, helices, spirals, loops, horns, fractals, phased arrays, and many other types. Additionally, AN-SOF enables detailed modeling of feeding systems using transmission lines, allowing users to analyze complex antenna configurations with precision. The software can simulate antennas positioned above lossy ground planes or broadcast antennas above radial wire ground screens, providing realistic and accurate results.

Furthermore, AN-SOF’s calculation capabilities have been extended to include single-layer microstrip patch antennas and the computation of radiated emissions from Printed Circuit Boards (PCBs). As a result, AN-SOF is a powerful tool for Electromagnetic Compatibility (EMC) applications. The software also supports passive circuits with lumped impedances and non-radiating networks, enabling comprehensive analysis of antenna systems.

Note

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.

With AN-SOF at your disposal, you can explore the exciting possibilities of antenna analysis and optimization. The software provides an extensive toolkit for designing, evaluating, and enhancing antenna performance, empowering engineers and enthusiasts alike to push the boundaries of innovation.

Note

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.

Drawing the geometry of structures in AN-SOF is intuitive and user-friendly. Wires can be created in a 3D space using the mouse, menus, and easy-to-navigate dialog windows. Tools are available to zoom, move, and rotate the structure, ensuring precise control over the design process.

To visualize simulation results, AN-SOF integrates seamlessly with a suite of specialized applications: AN-XY Chart, AN-Smith, AN-Polar, and AN-3D Pattern. These tools allow users to display graphs and analyze data effectively. They can also be executed independently for further graphic processing, offering flexibility and convenience for advanced users.

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:

• Overcoming 7 Limitations in Antenna Design: Introducing AN-SOF’s Conformal Method of Moments

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!

Explore Our Pre-Computed Examples in the Models Tab

AN-SOF includes a collection of pre-calculated models that enable users to quickly load example projects directly into the interface. These models are organized into categories for easy navigation, making this feature especially useful for users exploring example designs and learning key antenna concepts.

In the Models tab, you’ll find quick-access buttons for opening example models (see Fig. 8). Each model displays a 3D radiation pattern and includes a PDF guide with informational resources. Since all models are pre-calculated, they can be opened and explored using the AN-SOF Trial version.

The total number of segments used in each model is displayed after the “|” symbol on each button label in the Models tab, as well as in the Status Bar at the bottom of the AN-SOF window. This total includes:

• Wire segments
• Wire-to-wire junctions
• Wire-to-ground connections (labeled as “GNDs”)

Note:

The AN-SOF Trial version supports models with up to 50 total segments. If you modify an example model and exceed this limit, you’ll need an active license for the AN-SOF PRO Edition to run additional simulations.

To explore the example models, simply click the buttons in the Models tab. On the right side of the screen, you can use the options “Open PDF Document” and “Show Radiation Pattern” to toggle the display of the PDF guide or the radiation pattern plot as needed.

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. 9). 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 10 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. 11). 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. 12), 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. 13).

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. 14). 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. 15).

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. 16).

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 starts, the main window displays several key components that form the core of the user interface (Fig. 1):

• Title Bar – Displays the name of the currently active project file (.emm format).
• Main Menu Bar – Provides access to the primary menus: File, Edit, Draw, View, Tools, Run, Results, and Help.
• Toolbar – Contains icons for quick access to commonly used commands and tools.
• Tab Sheets – Allow users to switch between different stages of the workflow, from Setup to Plots, with a single click.
• Workspace – The central 3D canvas where wire structures are drawn and visualized.
• Status Bar – Displays real-time information, such as the number of segments, wire-to-wire junctions, and wire-to-ground connections (GNDs).

File Menu

The File menu provides commands for managing AN-SOF projects, including creating, opening, saving, importing, and exporting files. The available commands are:

• New… (Ctrl + N)
  Creates a new project from scratch.
• Open… (Ctrl + O)
  Opens an existing project file (.emm) using the standard Open dialog.
• Save (Ctrl + S)
  Saves the current project under its existing name.
• Save As…
  Saves the current project with a new name. If the project is new, this command prompts the user to assign a name and location.
• Import Wires
  Opens a dialog to import wire data from various formats, including AN-SOF (.wre), NEC (.nec), and MM format (.txt).
• Export Wires
  Allows exporting the wire geometry to several formats:
  • NEC (*.nec)
  • DXF (*.dxf)
  • Scilab script (*.sce)
  • MATLAB/Octave script (*.m)
• Copy Workspace
  Copies the current workspace view to the clipboard as a bitmap image.
• Recent Files List
  Displays up to ten recently opened project files for quick access. Use “Empty Recent Files List” to clear the history.
• Exit (Ctrl + Q)
  Closes the current project and exits AN-SOF.

Edit Menu

The Edit menu provides tools for modifying, organizing, and managing wires in your project. The available commands include:

• Undo (Ctrl + Z)
  Reverts the project to the previous state before the last command was executed.
• Redo (Ctrl + Y)
  Reapplies the last undone action, restoring the project to the state before Undo was used.
• Source / Load / TL (Ctrl + Ins)
  Opens the Source/Load/TL toolbar, allowing you to add sources, loads, or connect transmission line (TL) ports to a selected wire segment. This command is enabled when a single wire is selected.
• Modify (Ctrl + M)
  Opens the Modify dialog box for editing properties of the selected wire(s). Available when one or more wires are selected.
• Wire Color
  Opens a standard color selection dialog to change the color of the selected wire(s). Enabled when one or more wires are selected.
• Delete (Ctrl + Del)
  Deletes the selected wire(s), including any attached sources or loads. Enabled when one or more wires are selected.
• Copy Start Point
  Copies the start point coordinates of the selected wire. This point can be used as the start of a new wire, enabling direct connection. Enabled when a wire is selected.
• Copy End Point
  Copies the end point coordinates of the selected wire for use as the starting point of a new, connected wire. Enabled when a wire is selected.
• Start Point to GND
  Draws a vertical wire from the start point of the selected wire down to the ground plane. This command is available only when a ground plane is defined in the model and a wire is selected.
• End Point to GND
  Draws a vertical wire from the end point of the selected wire down to the ground plane. Like the previous command, it is available when a ground plane exists and a wire is selected.
• Move Wires… (Ctrl + Alt + M)
  Opens the Move Wires dialog to reposition the selected wires. Enabled when at least one wire is selected.
• Rotate Wires… (Ctrl + Alt + R)
  Opens the Rotate Wires dialog to rotate selected wires around a specified axis. Enabled when at least one wire is selected.
• Scale Wires… (Ctrl + Alt + S)
  Opens the Scale Wires dialog to apply a scaling factor to the selected wires. Enabled when at least one wire is selected.
• Copy Wires…
  Opens the Copy Wires dialog to duplicate the selected wires, with options to apply translation or rotation to the copies. Enabled when at least one wire is selected.
• Stack Wires…
  Opens the Stack Wires dialog to generate multiple copies of the selected wires arranged along a specified direction. Enabled when at least one wire is selected.

Draw Menu

The Draw menu provides tools for creating a wide variety of wire geometries and wire grids. These commands allow users to model antenna elements with precision and flexibility. The available options include:

• Line
  Opens the Line dialog box to draw a straight wire between two defined endpoints.
• Arc
  Opens the Arc dialog to draw a circular arc segment.
• Circle
  Opens the Circle dialog to draw a complete circular loop.
• Helix
  Opens the Helix dialog to create a helical wire, often used in axial-mode antennas.
• Quadratic
  Opens the Quadratic dialog to draw a curved wire defined by a quadratic function.
• Archimedean Spiral
  Opens the Archimedean Spiral dialog to draw a spiral with uniform spacing between turns.
• Logarithmic Spiral
  Opens the Logarithmic Spiral dialog to create a spiral with exponentially increasing spacing—ideal for frequency-independent antenna designs.

Wire Grid / Solid Surface

This option creates a wire grid or a discretized surface geometry. It includes the following sub-commands:

• Patch – Draws a rectangular mesh on the xy-plane.
• Plate – Creates a bilinear surface or flat panel.
• Disc – Draws a flat circular disc.
• Flat Ring – Draws a ring-shaped disc with a central hole.
• Cone – Creates a conical surface structure.
• Truncated Cone – Draws a cone with a flat top (cut-off cone).
• Cylinder – Draws a cylindrical surface.
• Sphere – Creates a spherical grid or surface.
• Paraboloid – Draws a parabolic reflector surface.

Tapered Wire

This option allows drawing wires with stepped-radius profiles, useful for simulating tapered elements such as monopoles or matching sections. Each command mirrors the standard wire options above (e.g., Line, Arc, Helix), but with the ability to assign different radii along the length.

• Tabular Input (Ctrl + T)
  Opens a spreadsheet-style table for entering linear wires, sources, loads, and transmission lines numerically—ideal for precise control and batch input.
• Transmission Lines (Ctrl + L)
  Opens a dedicated table to define transmission lines by specifying their characteristic impedance, velocity factor, length, and loss parameters.

View Menu

The View menu provides options to control the display of interface elements, adjust zoom levels, and access additional project and wire information. Use these commands to customize your workspace and enhance your modeling experience:

• Wire Properties… (Ctrl + W)
  Opens the Wire Properties dialog, showing detailed information about the selected wire. This command is available when a wire is selected.
• Project Details…
  Opens the Project Details dialog, displaying a summary of the current project, including the number of segments, wires, sources, and loads.
• Zoom In (Ctrl + I)
  Magnifies the view within the workspace. You can also zoom in by scrolling the mouse wheel backward.
• Zoom Out (Ctrl + K)
  Reduces the view scale in the workspace. You can also zoom out by scrolling the mouse wheel forward.
• Reset Zoom Scale
  Resets the zoom level and resizes the workspace to fit the entire structure.
• Axes… (Ctrl + A)
  Opens the Axes dialog to adjust the appearance of the coordinate axes. Press F7 to toggle between the small axes (shown in the lower-left corner) and the main axes (centered in the workspace).
• X-Y Plane / Y-Z Plane / Z-X Plane
  Switches the view to align the selected plane (XY, YZ, or ZX) parallel to the screen, offering easier modeling and inspection from different perspectives.
• Center
  Centers the view on the structure in the workspace without altering the zoom level.
• Initial View (Home)
  Resets the workspace to the default orientation and zoom level.
• Drawing Panel
  Displays a panel on the left side of the workspace with quick-access buttons for drawing wires, wire grids/solid surfaces, and tapered wires.

Tools Menu

The Tools menu provides access to plotting tools, wire checking utilities, and other helpful features for project analysis and customization. The commands available in this menu include:

• 3D Chart
  Launches the AN-3D Pattern application to open and view 3D radiation pattern files (.p3d).
• Polar Chart
  Launches the AN-Polar application for displaying polar radiation patterns from .plr files.
• Rectangular Chart
  Launches the AN-XY Chart application to view rectangular (Cartesian) plots from .plt files.
• Smith Chart
  Launches the AN-Smith application to display impedance or reflection coefficient data from .sth files using a Smith chart.
• Check Individual Wires
  Verifies the segment length, cross-sectional size, and thin-wire ratio for each wire. Wires that fall outside acceptable ranges are highlighted in yellow (warning) or red (error).
• Check Wire Spacing
  Analyzes the spacing between adjacent wires to ensure they are sufficiently separated. Wires with spacing issues are also highlighted in yellow or red.
• Delete Duplicate Wires
  Automatically detects and removes duplicate or overlapping wires from the project.
• RF Calculators
  Opens a webpage with a collection of online tools for calculating antenna parameters, propagation metrics, component values, and unit conversions.
• Calculator
  Launches the built-in Microsoft Windows® Calculator for quick arithmetic operations.
• Preferences…
  Opens the Preferences dialog box, where users can configure unit systems, workspace appearance, pen width, confirmation prompts, and other interface settings.

Run Menu

The Run menu provides commands to execute the simulation of currents and electromagnetic fields. These options allow users to selectively perform calculations depending on their analysis needs:

• Run Currents and Far-Field (F10)
  Calculates the current distribution on the wire structure, from which input impedance and VSWR are derived, along with the far-field radiation pattern, used to compute radiation efficiency, gain, and front-to-back ratio.
• Run Currents and Near-Field (F11)
  Calculates the current distribution and the near electric and magnetic fields around the antenna structure.
• Run ALL (F12)
  Executes a complete simulation including currents, far-field, and near-field calculations in a single step.
• Run Currents (Ctrl + R)
  Calculates only the current distribution on the wire structure.
  This is useful when interested solely in input parameters (impedance, reflection coefficient, VSWR), avoiding the time cost of field computations.
  Note: This command is disabled when the currents have already been computed.
• Run Far-Field
  Calculates the far-field radiation pattern based on previously computed currents.
  Enabled only after the current distribution has been calculated.
• Run Near E-Field
  Computes the near electric field generated by the current distribution.
  Requires prior current calculation.
• Run Near H-Field
  Computes the near magnetic field generated by the current distribution.
  Requires prior current calculation.
• Run Bulk Simulation
  Opens a dialog to select multiple input files in NEC format (.nec). AN-SOF will import each file, run the simulation, and export the results as CSV files to the same directory. This is ideal for batch processing multiple designs.

Results Menu

The Results menu provides a set of commands for visualizing and exporting simulation results. These include current distributions, field patterns, power metrics, and spectral data. The available commands are as follows:

Plot Current Distribution

Launches the AN-3D Pattern application to visualize the current distribution as a color pattern mapped onto the wire structure.

Plot Currents

Opens the AN-XY Chart to plot the magnitude and phase of currents versus position along a selected wire. This command is enabled only when a wire is selected.

List Currents…

Displays the List Currents toolbar to show current values versus frequency at a specific segment on a selected wire. If the segment includes a source, additional data such as input impedance, voltage, and power versus frequency will also be available. This command is enabled only when a wire is selected.

Export Currents

Exports the current distribution along a wire to a CSV file, including position and frequency-dependent data. Enabled only when a wire is selected.

List Input Impedances…

Shows a table of input impedances versus frequency, including associated parameters such as reflection coefficient, VSWR, return loss, and transmission loss at the antenna terminals.

Plot Far-Field Pattern

Opens a sub-menu with commands for plotting the radiation pattern in various formats:

• 3D Plot: Launches AN-3D Pattern to visualize the full 3D far-field radiation pattern.
• Polar Plot 1 Slice: Opens a dialog to select a single 2D slice of the far-field pattern, displayed in polar coordinates using AN-Polar.
• Polar Plot 2 Slices: Allows selection of two 2D slices of the far-field pattern, displayed in polar coordinates using AN-Polar.
• 2D Rectangular Plot: Allows selection of a 2D slice of the far-field pattern, displayed in rectangular (Cartesian) coordinates using AN-XY Chart.

Plot Far-Field Spectrum

Opens a dialog to select a point in space where far-field components will be analyzed across frequency. The spectrum is displayed using AN-XY Chart.

List Far-Field Pattern

Displays a table of the total electric field and its components (E-theta, E-phi, right-hand and left-hand circular polarization) at the theta–phi angular grid defined in the Far-Field panel. The data can be exported as a CSV file.

List Far-Field Spectrum

Opens a dialog to select a spatial point where the far-field components will be listed versus frequency. The table includes the total E-field and its components: E-theta, E-phi, right-hand and left-hand polarized components. The data can be exported as a CSV file.

Power Budget / RCS

Displays the Power Budget dialog showing total input power, radiated and consumed power, power density, efficiency, directivity, and gain as functions of frequency. For simulations with plane wave excitation, the Radar Cross Section (RCS) versus frequency is shown.

Plot Near E-Field Pattern

Opens a sub-menu for near-field electric field visualization:

• 3D Plot: Launches AN-3D Pattern to show a 3D visualization of near E-field components.
• 2D Plot: Opens the Near-Field Cut dialog for selecting and plotting a 2D cut using AN-XY Chart.

Plot Near E-Field Spectrum

Opens a dialog to select a spatial point and plots the frequency response of the near E-field components using AN-XY Chart.

List Near E-Field Pattern

Displays a table of the total near electric field and its components at the grid defined in the Near-Field panel. The data can be exported as a CSV file.

List Near E-Field Spectrum

Opens a dialog to select a point in space and displays the near E-field spectrum in table format, including the individual field components versus frequency. The data can be exported as a CSV file.

Following these commands, similar options are available for Near H-Field and Power Density data. To compute power density, both the near E-field and H-field must have been previously calculated, as power density is obtained from the vector (cross) product of these fields at each spatial point.

Help Menu

Use the Help menu to access the user guide, technical support, license activation, and version information. This menu includes:

• User Guide
  Opens the AN-SOF User Guide in PDF format.
• AN-SOF Home Page
  Opens the official website at www.antennasimulator.com in your default browser.
• Knowledge Base
  Opens the Knowledge Base where you can search categorized help articles and how-to guides.
• Email to Tech Support
  Launches your default email client to send a support request to info@antennasimulator.com.
• Chat to Tech Support
  Opens the live chat support page in your default browser.
• Activate AN-SOF
  Runs the AN-Key application, which shows your PC’s serial number and allows you to enter an activation key to license the software.
• Check for Updates
  Opens the webpage with the latest AN-SOF software releases.
• About AN-SOF…
  Displays version number, license, and copyright.

Main Toolbar

The main toolbar provides quick access to essential commands, many of which are also found in the main menu. In addition, it includes extra tools not available in the menu.

One such group consists of 3D View Controls, which help users interact with the 3D workspace (see Fig. 2):

3D View Controls

• Select Wire (arrow icon)
  Activates selection mode. Click a wire to select it. To select multiple wires, hold Ctrl and click each one. Selected wires are highlighted in light blue. To deselect, Ctrl + click again, or double-click in the workspace or press ESC to clear all selections.
• Selection Box
  Allows selecting multiple wires by dragging a box with the left mouse button:
  • Drag from top to bottom to select only wires fully enclosed.
  • Drag from bottom to top to select any wires that intersect the box.
  • Previously selected wires will be deselected if included again.
  • Double-click the workspace or press ESC to deselect all.
• Rotate around X/Y/Z
  Rotates the view around the selected axis (X, Y, or Z) by moving the mouse in the workspace.
• 3D Rotation
  Enables free rotation around all axes by moving the mouse in the workspace.
• Move (cross icon)
  Pans the view by dragging the mouse with the left button held down.
• Zoom (magnifying glass icon)
  Lets you zoom into a selected area by dragging a rectangle. After zooming, use the mouse wheel to adjust the zoom level.

Other Toolbar Commands

• Export Results
  Located next to the results-related buttons, this command exports the data in the Results tab to a CSV file.

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

The line width used for drawing wires and axes in the workspace can be adjusted 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 of workspace color and pen width that can be achieved.

Viewing 3D Axes

To customize the appearance of the X, Y, Z axes in the workspace, navigate to View > Axes (Ctrl + A) in the main menu to open the Axes dialog box (see Fig. 2). There are two types of axes:

• Small Axes: Displayed in the lower-left corner of the workspace.
• Main Axes: Displayed at the center of the screen.

Both positive and negative axes can be displayed. The color of the main axes can be changed by clicking the Color button. Check the Show Ticks option to add a 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 of the structure in the workspace:

• Use the mouse wheel.
• On a laptop touchpad, use two fingers (similar to zooming an image).
• Alternatively, use the Zoom In (Ctrl + I) and Zoom Out (Ctrl + K) commands in the View menu.

For a more specific zoom on a particular area, click the Zoom button on the toolbar and drag a rectangle over the desired area. To return to the initial view, click the Initial View (Home) button on the toolbar.

Rotating the View

To rotate the view of the structure around a specific axis:

1. Press one of the following toolbar buttons:

• Rotate around X
• Rotate around Y
• Rotate around Z
• 3D Rotation

2. Move the mouse while holding the left button.

Alternatively, use the following keyboard shortcuts:

• 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

To move the view of the structure in the workspace:

1. Click the Move button on the toolbar.
2. Move the mouse while holding the left button.

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.

Before drawing wires or running a simulation, it’s recommended to configure the simulation parameters in the Setup tab. This tab contains the following panels: Frequency, Environment, Far-Field, Near-Field, Excitation, and Settings (see Fig. 1).

• Frequency panel: Specify the operating frequencies for the project.

• Environment panel: Set the relative permittivity and permeability of the surrounding medium, as well as the ground plane type.

• Far-Field panel: Define the angular ranges for far-field calculations.

• Near-Field panel: Define the observation points for near-field calculations.

• Excitation panel: Choose the excitation type for the structure. If using discrete sources, set the total input power. If using an incident field, define its direction and polarization.

• Settings panel: Set the reference impedance for VSWR and adjust parameters to fine-tune calculation accuracy.

Additionally, a Note panel on the right side of the Setup tab allows you to add project-related notes. These notes are saved in a .txt file in the same folder as the project file, using the same filename.

To define the operating frequencies, go to the Setup tab in the main window and select the Frequency panel. You can choose from three frequency modes: Single, List, or Sweep.

• Single: Enter a single frequency value in the Single Frequency box (see Fig. 1). The corresponding wavelength is displayed automatically below the frequency field.
• List: Enter multiple frequencies in the Frequency List box (Fig. 2). You can import a list from a text file using the Open button, or export the current list using the Save button.
• Sweep: Perform a frequency sweep using either a linear or logarithmic scale.
  • For a linear sweep, specify the start, step, and stop frequencies (Fig. 3).
  • For a logarithmic sweep, enter the start and stop frequencies, along with a multiplication factor (Fig. 4).

To change the frequency unit (e.g., Hz, kHz, MHz, GHz), go to Tools > Preferences in the main menu, and select the desired unit on the Units page of the Preferences dialog box. See Preferences for more details.

Environment and Ground Plane Options

The environment surrounding an antenna or metallic structure can be either free space or include a ground plane. In the case of free space, you can define the relative permittivity (dielectric constant ε_r) and magnetic permeability (µ_r) of the medium, with vacuum corresponding to ε_r = 1 and µ_r = 1.

Three ground plane options are available:

• Perfect Electric Conductor (PEC): An ideal, lossless ground plane.
• Real (Lossy) Ground: A ground plane with user-defined conductivity (σ) and relative permittivity (ε_r). Optionally, a radial ground screen can be added.
• Dielectric Substrate Slab: Used for modeling microstrip lines and printed antennas.

All ground planes lie in the xy-plane. The available environment settings will be described in detail in the sections below.

Configuring the Medium Properties

To configure the medium, navigate to the Setup tab > Environment panel. Use the Medium box (Fig. 1) to set the relative permittivity (ε_r) and permeability (µ_r) of the surrounding medium. When a ground plane is used, these values represent the permittivity and permeability of the medium above the ground.

Note:

The wavelength displayed below the frequency set in the Frequency panel (when the Single option is selected) and the wavelength used internally by AN-SOF for calculations will be adjusted based on the specified permittivity and permeability of the medium. Specifically, these properties cause the wavelength to shorten accordingly relative to the wavelength in a vacuum.

None (Free Space)

Selecting the None option simulates the antenna in free space. The relative permittivity (εᵣ) and permeability (µᵣ) specified in the Medium box (see Fig. 1) define the properties of the surrounding environment.

Perfect (PEC Ground)

Selecting the Perfect option places an infinitely large, perfectly electrically conducting (PEC) ground plane at a specified height relative to the xy-plane (see “Z Position” in Fig. 2). The ground plane remains parallel to the xy-plane, and its position is defined by the Z coordinate: a negative Z places the ground plane below the xy-plane, while a positive value places it above.

When using a perfect ground plane, all wires must be located above it—that is, each wire must have a Z-coordinate greater than or equal to the specified ground plane position. Wires crossing through or lying below the ground plane are not allowed. Additionally, horizontal wires placed directly on the ground plane are unsupported. However, connections from wire ends to the ground plane are permitted.

Real (Lossy Ground)

Selecting the Real option places a lossy ground plane at the xy-plane (z = 0), with user-defined conductivity (σ) and relative permittivity (εᵣ), as shown in Fig. 3. Four modeling methods are available for real ground calculations:

• Sommerfeld–Wait Asymptotic
• Reflection Coefficients
• Radial Wire Ground Screen
• Sommerfeld–Norton

These options are described in the following sections.

All wires must be positioned above the ground plane (z > 0). Horizontal wires directly on the ground plane are not supported.

Wire end connections to the ground are allowed when using either the Sommerfeld–Wait Asymptotic or Radial Wire Ground Screen options.

The Reflection Coefficients and Sommerfeld–Norton models assume perfect (zero-Ohm) wire connections to ground and yield reasonable results only for vertical wires connected to good conducting grounds—not dielectric surfaces. These models are not suitable when vertical wire-to-ground connections are made through dielectric materials.

Real Ground: Sommerfeld – Wait Asymptotic

This option models the antenna/wire currents using a hybrid approach that combines a perfect ground plane with loss impedances to account for power dissipation in the real ground—particularly important when wires are close to or connected to the ground. Developed by Prof. James R. Wait, this model is especially effective for low-frequency (LF) and medium-frequency (MF) antennas, where ground conductivity tends to be high. However, it remains applicable at higher frequencies as long as the ground behaves as a good conductor.

The model uses the ground’s conductivity (σ) and permittivity (εᵣ) to compute both near-field and far-field radiation, applying Norton’s asymptotic approximations to the exact Sommerfeld solution. The far-field results match those predicted by Fresnel reflection coefficients.

Wire connections to ground are supported. If a wire’s starting or ending point is located at z = 0, it will automatically be connected to the ground. These connections are treated as imperfect (lossy) by default, meaning power can be dissipated at the connection point due to current flow. If the Zero-Ohm connections to ground option is enabled, these connections are instead treated as perfect (lossless), though the presence of the lossy ground still influences the overall near and far fields.

In summary, the Sommerfeld – Wait Asymptotic model is appropriate when the ground can be considered a good conductor at the operating frequency and when the structure includes wire-to-ground connections.

Real Ground: Reflection Coefficients

When this option is selected, the ground conductivity (σ) and relative permittivity (εᵣ) influence the current distribution on the antenna or wire structure above the ground. As a result, the input impedance of a transmitting antenna is also affected by real ground conditions. This influence is determined using a generalization of Fresnel’s reflection coefficients, which is theoretically valid when wires are positioned several wavelengths above the ground. In practice, however, good results have been reported for heights between one-quarter and one-half of a wavelength.

Near fields are calculated using Norton’s asymptotic approximations to Sommerfeld’s exact solution, allowing the electric and magnetic fields to be computed as a function of distance from the antenna. This enables analysis of field attenuation due to ground losses. The far field, by contrast, is computed using the standard Fresnel reflection coefficients.

Vertical wire connections to ground may be added when the ground behaves as a good conductor at the operating frequency, even though these connections theoretically violate the height requirement. These wire-to-ground connections are treated as lossless in this model.

In summary, the Reflection Coefficients ground model is best suited for wire structures located several wavelengths above ground, ideally without any wire-to-ground connections. However, if the ground is a good conductor at the operating frequency, vertical wire connections may be included—but results under such conditions should be interpreted with caution.

Real Ground: Radial Wire Ground Screen

When this option is selected, a ground screen made of buried radial wires is placed on the ground plane, which has the specified conductivity (σ) and relative permittivity (εᵣ). The screen is centered at the origin (0,0,0), and its configuration is defined by user-specified parameters: the number of radial wires, their length (or screen radius), and wire radius. These wires are assumed to be laid on the ground surface or buried at a depth less than one soil skin depth.

This model is based on Prof. James R. Wait’s theory for good conducting grounds. It affects the current distribution on the antenna or wire structure by accounting for the power dissipated in the combined ground plane and wire screen system. As a result, both the presence of the screen and the ground properties (conductivity and permittivity) influence the input impedance of a transmitting antenna located above the screen. The same parameters are used to compute the radiated near and far fields using Norton’s asymptotic approximations to Sommerfeld’s solution and Fresnel reflection coefficients, respectively.

Wire-to-ground connections may be defined at wire endpoints located at z = 0. These are treated as imperfect by default, meaning that power is dissipated in the ground-screen system due to currents flowing between the ground and the wires. If the Zero-Ohm connections to ground option is enabled, these connections are treated as perfect, with no power dissipation at the contact point.

In summary, the Radial Wire Ground Screen model is suitable when the ground behaves as a good conductor at the operating frequency and when the structure includes wire-to-ground connections. The screen serves to increase the effective conductivity of the combined ground-screen system, reducing power losses beneath antennas placed above it. Typical use cases include monopole antennas in the form of poles or radiating towers used in broadcasting applications.

Real Ground: Sommerfeld – Norton

Unlike the previous ground models, which apply various approximations to compute the current distribution on wires above a lossy ground plane, the Sommerfeld–Norton model numerically solves Sommerfeld’s exact solution. This enables simulations where the ground does not need to be a good conductor—it may instead be a dielectric medium. To approximate a purely dielectric ground, enter a very low conductivity (e.g., σ = 1E-6 S/m) along with the desired relative permittivity (εᵣ).

Vertical wires can be placed very close to the ground, with a minimum height of one wire radius above ground. Horizontal wires can be simulated as low as 0.005λ above ground. For vertical or horizontal wires at heights below 0.01λ, it is important to increase the accuracy of the calculations. To do this, go to Setup tab > Settings panel and set the Quadrature Tolerance to 0.1%, instead of the default 1% (see Fig. 4).

The near fields are computed from the current distribution using Norton’s asymptotic approximation to Sommerfeld’s solution. This is accurate at distances greater than about one-quarter wavelength from the wire structure, which is sufficient for most practical applications. The far field, in contrast, is calculated using Fresnel reflection coefficients, which yield the correct asymptotic expressions.

Wire-to-ground connections are theoretically not permitted in this model. However, they can be used with caution only for vertical wires, and only if the ground behaves as a good conductor at the operating frequency. In such cases, the model assumes lossless connections and employs specular reflection of the fields to compute the current distribution. These assumptions are valid only when the ground is effectively conductive.

In summary, the Sommerfeld–Norton model is the most accurate among the available ground models, but it comes with certain restrictions. It is recommended for highly dielectric grounds or situations where the ground cannot be considered a good conductor. Horizontal wires must not be placed below 0.005λ above ground. Vertical wires may be connected to ground only when the ground is a good conductor, and the results in such cases should be interpreted with care.

Substrate (Grounded Dielectric Slab)

When this option is selected, a dielectric substrate with user-defined relative permittivity (εᵣ) is placed beneath the xy-plane (z = 0), as shown in Figs. 5 and 6. The slab may extend infinitely or have finite dimensions in the xy-plane, where you can define its width along the X and Y directions. The substrate thickness, denoted as h, must also be specified. A perfectly electrically conducting (PEC) ground plane is located at z = –h, just below the dielectric slab (see Fig. 6). A drop-down list is available to select common substrate materials (e.g., FR4, RT/Duroid, Rogers RO). Note that the dielectric loss tangent cannot be specified—it is assumed to be zero, meaning the substrate is treated as lossless.

When the Substrate option is active:

• All wires must lie horizontally in the xy-plane (z = 0). These wires typically represent traces of printed antennas, microstrip lines, or PCB tracks.
• The only exception is for vertical wires (vias), which may connect traces at z = 0 to the ground plane at z = –h. These are commonly used to feed the structure with voltage or current sources.

Important constraints:

• The PEC ground plane beneath the substrate is mandatory and cannot be omitted. As a result, ungrounded dielectric substrates are not supported.
• Wires above the xy-plane (z > 0) or below the ground plane (z < –h) are not allowed in this model.

The Substrate model is an extension of the Conformal Method of Moments tailored for printed wire structures. It has the following limitations:

Model Limitations

Single-Layer, Lossless Substrate Only

• Only one dielectric layer is supported (multilayer stacks are not).
• The substrate must be lossless (loss tangent is assumed to be zero).
• No holes or cutouts are permitted in the substrate.

Finite-Size Substrate Constraints

• The substrate must be rectangular in shape.
• Traces must be placed at least 5× their width away from the substrate edges.

Ground Plane and Vias

• A PEC ground plane is always present and cannot be disabled.
• Vertical wires (vias) can be added to connect traces to the ground, typically for feeding.

No Slot-Based Designs

• Slot antennas or patches with slots cannot be modeled due to software limitations.

To configure radiation pattern parameters, navigate to the Setup tab in the main window and select the Far-Field panel (Fig. 1).

The far field can be computed after calculating the current distribution. Thus, the parameters set in the Far-Field panel have no effect on 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, allowing you 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 is 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

This represents 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 meter.

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

A frequently asked question is how to displace the center of the radiation pattern in a 3D plot displaying the radiation lobes. The answer lies in setting the Origin (X0, Y0, Z0) in the Far-Field panel. This allows you to adjust the reference point for the radiation pattern, enabling better visualization of the results. For more details, refer to this article:

• How to Adjust the Radiation Pattern Reference Point for Better Visualization

To configure the observation points for the calculation of near fields, navigate to the Setup tab in the main window and select the Near-Field panel.

The near field can be computed after calculating the current distribution. Thus, the parameters set in the Near-Field panel have no effect on the determination of the currents and can be adjusted at any time. However, the near field must be recalculated whenever these parameters are modified.

The Near-Field panel provides three coordinate system options for near-field calculations:

• Cartesian
• Cylindrical
• Spherical

By selecting one of these options, near fields can be calculated in Cartesian, Cylindrical, or Spherical coordinates, depending on your preference or the requirements of your analysis.

Cartesian Coordinates

If the Cartesian option is selected, the following parameters can be configured for near-field calculations (Fig. 1):

Origin (X0, Y0, Z0)

This is the origin of the Cartesian coordinate system used to define the observation points where near fields will be calculated.

X

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

Y

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

Z

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

Cylindrical Coordinates

If the Cylindrical option is selected, the following parameters can be configured for near-field calculations (Fig. 2):

Origin (X0, Y0, Z0)

This is the origin of the cylindrical coordinate system used to define the observation points where near fields will be calculated.

R

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

Phi

This box is used to specify the azimuth angles (phi-coordinates) of the observation points where near fields will be calculated. You must set the start, step, and stop values for the azimuth angles in degrees.

Z

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

Spherical Coordinates

If the Spherical option is selected, the following parameters can be configured for near-field calculations (Fig. 3):

Origin (X0, Y0, Z0)

This is the origin of the spherical coordinate system used to define the observation points where near fields will be calculated.

R

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

Theta

This box is used to specify the zenith angles (theta-coordinates) of the observation points where near fields will be calculated. You must set the start, step, and stop values for the zenith angles in degrees.

Phi

This box is used to specify the azimuth angles (phi-coordinates) of the observation points where near fields will be calculated. You must set the start, step, and stop values for the azimuth angles in degrees.

Near-Field Calculation Workflow

The Cartesian, Cylindrical, and Spherical options described above define a grid of observation points where the near field will be computed. The near electric field (E-field) and near magnetic field (H-field) can be calculated separately, or you can compute them sequentially by clicking Run Currents and Near-Field (F11) in the Run menu or toolbar. This command first calculates the current distribution and then computes the near fields.

Alternatively, the calculation of the current distribution, far-field, and near-field can be executed in a single step by selecting the Run ALL (F12) command in the Run menu.

If the near H-field is not required, you can disable its automatic calculation by turning off the “Run ALL also calculates the H-Field” option. This setting can be found in the Options tab of the Preferences window. To access the Preferences window, click the gear button in the main toolbar or navigate to Tools > Preferences in the main menu.

Accessing Excitation Settings

Navigate to:
Setup tab > Excitation panel
Two excitation types available (Fig. 1):

1. Discrete Sources
2. Incident Field

Discrete Sources

• Purpose: Calculate current distribution using voltage/current sources on wires
• Power Configuration:
  • Specified Input Power: Sources auto-adjust to achieve target power (Watts)
  • Unspecified Power: Sources remain constant; power becomes output result

Incident Field (Plane Wave Excitation)

Define an incident plane wave’s direction and polarization:

Key Parameters

Parameter	Description	Units/Values
E-Field Major Axis	Linear: RMS amplitude (V/m) Elliptical: Major axis of polarization ellipse	V/m
Axial Ratio	Minor/major axis ratio: – Positive: Right-handed ellipse – Negative: Left-handed ellipse – Zero: Linear polarization	Unitless
Phase Reference	Phase shift at coordinate origin	Degrees
Gamma	Linear: Polarization angle from incidence plane Elliptical: Major axis angle from incidence plane	Degrees
Theta	Zenith angle of incidence	Degrees
Phi	Azimuth angle of incidence	Degrees

3D Visualization

Click 3D View (Fig. 3) to interactively set:

• Wave direction
• Polarization state

Note

When an incident plane wave is used as the excitation, any discrete sources present will be ignored during the simulation.

To access advanced simulation options, go to the Setup tab and select the Settings panel. Here, you can:

• Fine-tune the accuracy of the simulation,
• Set the reference impedance for VSWR calculations, and
• Adjust various options that affect the calculation engine.

These settings provide greater control over simulation precision and convergence behavior. See Fig. 1.

Controlling Numerical Precision

The Accuracy section in the Settings panel allows you to control the precision of the simulation and manage memory usage for large models.

• Quadrature Tolerance defines the acceptable numerical error in the evaluation of integrals between wire segments that are closer than the Interaction Distance. This parameter governs the precision of electromagnetic interaction calculations. The default value is 1%.

• Interaction Distance sets the maximum separation (in wavelengths) between segments for which the numerical integration guarantees an error below the Quadrature Tolerance. For segments farther apart than this distance, a third-degree polynomial approximation is used instead of the traditional Hertzian dipole approximation, offering improved accuracy for curved segments. The default value is 0.1λ.

• Matrix Size Threshold determines the maximum size of the impedance matrix (N × N, where N is the number of wire segments) that is computed in double precision. For models with more segments than the set threshold, single precision is used to reduce memory usage. While this may slightly reduce accuracy, it enables the simulation of larger models on systems with limited Windows on-board memory. The default threshold is 4,000.

• Exact Kernel enables the use of the exact formulation of the Electric Field Integral Equation (EFIE), significantly improving accuracy for antennas made with thicker wire segments. When this option is disabled, an extended thin-wire approximation is used. See The Exact Kernel for more information.

VSWR Reference Impedance Configuration

The reference impedance serves as the normalization value for VSWR calculations throughout the simulation. This parameter is particularly important when matching simulation conditions to real-world measurement setups.

Key features:

• Defaults to 50 Ω (standard for most RF systems)
• Commonly adjusted to 75 Ω for television/video applications
• Requires refreshing the results (Ctrl + R) to update all VSWR-dependent data

Simulation Control Options

These global toggles enable efficient comparison of different simulation scenarios without modifying individual element properties. They are especially valuable for parametric studies and troubleshooting.

Option	Technical Implementation	Practical Application
NGF	Stores LU-decomposed impedance matrix after first calculation	Accelerates repeated simulations with varying source excitations
Load Impedances	Master switch for all lumped load elements in the model	Quickly compare loaded vs. unloaded system performance
Wire Resistivity	Toggles Ohmic loss calculation for all conductors	Evaluate conductor loss impact on system efficiency
Wire Coating	Enables/disables dielectric coating effects	Analyze insulation impact on antenna performance

Implementation Note:

These options provide non-destructive alternatives to physically removing/readding model elements when running comparative analyses.

A summary of the project information can be displayed by navigating to View > Project Details in the main menu. This opens the Project Details window (Fig. 1). Alternatively, you can access this window using the dedicated button on the toolbar.

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

The Project Details window provides a comprehensive summary of the following project information:

• Project Name: The name of the project.
• Date and Time: The date and time when the project was last saved.
• Structure: Includes the number of wires, sources, loads, transmission lines, and segment counts.
• Excitation: Indicates whether discrete sources or an incident field are set.
• Frequencies: Displays the frequency range configured for the simulation.
• Medium: Lists the permittivity, permeability, and wavelength (of the upper medium if a ground plane is present).
• Ground Plane: Specifies the type of ground plane and its associated parameters, if applicable.
• Far-Field Parameters: Displays settings related to far-field calculations.
• Near-Field Parameters: Shows settings for near-field calculations.
• Numerical Accuracy: Provides details about the settings employed for numerical accuracy.
• Units: Lists the units used for frequency, length, wire radius, inductance, and capacitance.

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 has a unique extension that corresponds to its specific content.

IMPORTANT: When requesting support, please compress all the project files into a ZIP archive and attach it to your support request email.

These files include:

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

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	Deselect all wires
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/hide main and small axes
F8	Select a wire in order of creation
F9	Select a wire in reverse order of creation
F10	Run current distribution and far-field
F11	Run current distribution and near-field
F12	Run full simulation (all options)
Ctrl + A	Open Axes dialog box
Ctrl + I	Zoom in
Ctrl + K	Zoom out
Ctrl + L	Open Transmission Lines dialog
Ctrl + M	Modify selected wire(s)
Ctrl + N	Create a new project
Ctrl + O	Open an existing project
Ctrl + Q	Exit AN-SOF
Ctrl + R	Run current distribution only
Ctrl + S	Save the project
Ctrl + T	Open tabular input for linear wires
Ctrl + W	Show properties of selected wire
Ctrl + Y	Redo
Ctrl + Z	Undo
Ctrl + Del	Delete selected wire(s)
Ctrl + Ins	Show Source/Load/TL toolbar
Ctrl + Alt + M	Move selected wire(s)
Ctrl + Alt + R	Rotate selected wire(s)
Ctrl + Alt + S	Scale selected wire(s)

AN-SOF provides several wire types for creating antenna geometries. Each wire type has its own geometric parameters, attributes, and material settings, which can be configured through a dedicated Draw dialog box. This dialog box allows you to insert and customize new wires directly in the workspace.

Selecting Draw from the main menu displays the following wire types:

• Line – Opens the dialog box for drawing a straight (linear) wire.
• Arc – Opens the dialog box for drawing a circular arc.
• Circle – Opens the dialog box for drawing a circular loop.
• Helix – Opens the dialog box for drawing a helical wire.
• Quadratic – Opens the dialog box for drawing a wire following a quadratic curve.
• Archimedean Spiral – Opens the dialog box for drawing an Archimedean spiral.
• Logarithmic Spiral – Opens the dialog box for drawing a logarithmic spiral.

Accessing Drawing Commands

The wire drawing tools can be accessed through any of the following:

• Main Menu → Draw
• Right-click Menu – Right-click on the workspace to open the context menu
• Main Menu → View → Drawing Panel (see Fig. 1)

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.

A Line represents a linear (straight) wire in AN-SOF.

Accessing the Line Dialog Box

To open the Line dialog box:

1. Navigate to Draw > Line in the main menu.
2. The dialog box contains three tabs: Line, Attributes, and Materials (see Fig. 1).

Line Tab: Setting Geometrical Parameters

Two options are available for defining the line:

1. 2 Points
   • Define the line by specifying two points:
     • From Point: Starting coordinates (X1, Y1, Z1).
     • To Point: Ending coordinates (X2, Y2, Z2) (see Figs. 1 and 2).
2. Start – Direction – Length
   • Define the line by:
     • Start Point: Initial coordinates.
     • Direction: Spherical angles (Theta, Phi).
     • Wire Length: Total length of the line (see Figs. 3 and 4).

Attributes Tab

• Specify the Number of Segments and Cross-Section properties (refer to Wire Attributes).

Materials Tab

• Set the Resistivity and Coating properties of the wire (refer to Wire Materials).

The “Arc” refers to a circular arc.

To access the “Arc” dialog box for drawing an arc, navigate to Draw > Arc in the main menu. This dialog box contains three pages: Arc, Attributes, and Materials (Fig. 1).

Arc Page

The Arc page allows you to set the geometrical parameters for the arc. Two options are available: 3 Points and Start – Center – End.

The 3 Points option enables you to define the arc by specifying three points: a Start Point, a Second Point, and an End Point. An arc starting from the Start Point, passing through the Second Point, and ending at the End Point will be drawn on the workspace (Figs. 1 and 2).

If Start – Center – End is selected, the arc will be drawn starting from the Start Point, with the center specified by Center and ending at a point determined by the End Point (Figs. 3 and 4). The End Point determines the arc’s aperture angle and the plane in which it lies. Note that the End Point may not coincide with the actual ending point of the arc.

After setting the geometrical parameters on the Arc page, you can select the Attributes page to specify the Number of Segments and Cross-Section. The Materials page allows you to set the wire Resistivity and Coating.

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 wire curved into a circular helical shape.

To access the “Helix” dialog box for drawing a helix, navigate to Draw > Helix in the AN-SOF main menu. This dialog box contains four tabs: Helix, Orientation, Attributes, and Materials.

Helix Page

The Helix page allows you to set the geometrical parameters for the helix. Two options are available: Start – Radius – Pitch – Turns and Start – End – Radius – Turns.

The Start – Radius – Pitch – Turns option enables you to define the helix by specifying its Start Point, Radius, Pitch, and Number of turns, as shown in Figures 1 and 2. The Pitch represents the spacing between turns. A positive (negative) pitch results in a right-handed (left-handed) helix. The Number of turns does not need to be an integer, allowing you to enter fractions of turns. Alternatively, you can enter the Diameter, Pitch Angle, and Wire Length instead of the radius-pitch-number of turns combination. When entering the Radius – Pitch – Turns combination, the Diameter – Pitch Angle – Wire Length set will be automatically calculated, and vice versa. In any case, the helix’s axial height is displayed automatically (calculated from the input data and cannot be entered).

The orientation of the helix axis can be set on the Orientation page (Fig. 3), as described below.

If Start – End – Radius – Turns is selected, the helix will be drawn starting from the Start Point and ending at the End Point, with the specified Radius and Number of turns, as illustrated in Figures 4 and 5. The Number of turns must be an integer, and a positive (negative) value results in a right-handed (left-handed) helix. The orientation of the helix axis is determined by the starting and ending points. The helix can be rotated around its axis by specifying a Rotation Angle. The Orientation page will be hidden when the Start – End – Radius – Turns option is chosen, as the helix axis orientation is already defined by the line connecting its start and end points.

After setting the geometrical parameters on the Helix and Orientation pages, you can select the Attributes page to specify the Number of Segments and Cross-Section. The Materials page allows you to set the wire Resistivity and Coating.

Orientation Page

The Orientation page provides options for setting the helix orientation. A box with two options is available: Angles and Vector (Fig. 3).

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

If Vector is selected, the helix axis can be defined by entering a vector in the axis direction. The N_x, N_y, and N_z components determine this vector.

The helix can be rotated around its axis by specifying a 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 whose radius varies along its length. Because the change in radius occurs in discrete increments, it is also known as a stepped-radius wire. Tapered wires always have a circular cross section, and the radius typically changes linearly in defined steps—resulting in a wire with sections of constant radius, as illustrated in Fig. 1.

To draw a tapered wire, go to Draw > Tapered Wire in the main menu and select a wire type. The available types (e.g., Line, Arc, Circle) are the same as those found under the Draw menu. For example, Fig. 2 shows the Line page of the Draw dialog box when a linear wire type is selected.

The wire must be divided into wire portions based on the desired number of radius steps, as indicated in Fig. 1. Each wire portion with a constant radius should then be subdivided into segments as required by the Method of Moments used in the simulation.

You can define the number of wire portions and the number of segments per portion in the Attributes tab (see Fig. 3). Here, you can also specify the start and end radii of the taper. To set the material properties—including the resistivity of the wire and any coating—use the Materials tab (see Fig. 4). A tapered coating can be specified by assigning start and end thickness values.

In the workspace, wire portions are shown in alternating colors for easier identification.

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 three options will be displayed: AN-SOF, NEC, 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 variables is not supported. To run simulations with variable geometric parameters, you can write a script to sweep those parameters and generate the corresponding NEC files, then use the Run Bulk Simulation feature (see Running a Bulk Simulation).

For optimization tasks, you’ll need an optimizer script and should work with the AN-SOF Engine. Examples of parameter sweeps and optimization scripts are available in the Scripts & Optimizers category.

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.

IMPORTANT: CM lines must always be placed at the beginning of a .nec file and kept separate from other commands.

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.

GB – AN-SOF’s Arc

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

GB Tag Segments Type X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3 Radius

[Enter]

Tag: A positive number serving as the tag for the arc. The space between “GB” and the Tag is optional.

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.

Type: Type of arc. Set Type = 0 for entering three points, and Type = 1 for entering the start point, center, and end point.

X1 Y1 Z1: Cartesian coordinates of the start point of the arc.

X2 Y2 Z2: Cartesian coordinates of the second point of the arc if Type = 0, or the arc center if Type = 1.

X3 Y3 Z3: Cartesian coordinates of the end point of the arc.

Radius: Wire radius.

Note: AN-SOF uses conformal segments that exactly follow the arc contour, distinguishing it from NEC. The “GB” command is exclusive to AN-SOF and cannot be found in any NEC version.

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/parallel/trap RLC loads, fixed impedances R+jX, and wire conductivity can be set.

• Set Type = 0 for a series RLC load.
• Set Type = 1 for a parallel 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, LD 1, LD 4, and LD 6 lines.
• Set Type = 6 for a trap RLC load (series RL + parallel C).

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.

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, a wire can be automatically segmented by specifying any number less than or equal to zero for the segment count. The coordinates of each wire’s start and end points must use the same length unit selected in the Preferences dialog box in AN-SOF. Similarly, the radius of any imported wire must also be expressed in the selected unit.

Linear wires can be entered and edited in a table using the Tabular Input window. To access this feature, navigate to Draw > Tabular Input (Ctrl + T) in the main menu. This opens the Tabular Input window (see Fig. 1), which contains four tabs:

1. Wires:

• Allows you to enter and edit linear wires by specifying their end coordinates, number of segments, wire radius, and materials.

2. Sources:

• Enables you to connect sources to the wires listed in the Wires tab. A source must be connected to a specific wire segment.

3. Loads:

• Allows you to connect loads to the wires listed in the Wires tab. A load must be connected to a specific wire segment.

4. Trans. Lines:

• Enables you to connect transmission lines between two wire segments listed in the Wires tab.

Wires Tab

Select the Wires tab and enter values as specified in the column titles (see Fig. 1). Each row corresponds to a linear wire, and you can input details such as:

• Number of segments (Segs).
• Coordinates of the starting point (X1, Y1, Z1) and ending point (X2, Y2, Z2).
• Wire radius.
• Resistivity.
• Coating (dielectric insulation).

Note: Only wires with a circular cross-section can be entered.

Table Interaction

• Right-click on the table to open a pop-up menu with standard options such as Cut (Ctrl + X), Copy (Ctrl + C), and Paste (Ctrl + V).
• Single cells can be selected by left-clicking on them or by using the TAB and arrow keys on the keyboard.
• Rows can be selected by clicking on the row number in the left column (No. column). Use the mouse or the up/down arrow keys 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.

Row Operations

• Use Cut (Ctrl + X), Copy (Ctrl + C), and Paste (Ctrl + V) to manipulate selected rows.
• Use the Insert (Ins key) and Delete (Del key) options to add or remove rows.
• The Clear Contents (Ctrl + Del) option clears the content of a selected cell or row.
• The Search and Replace (Ctrl + R) option allows for bulk edits to wire end coordinates.

Wire Numbers in the Workspace

While the Tabular Input window is open, wire numbers are displayed in the workspace next to the corresponding wires (see Fig. 2). These numbers indicate the order of the wires in the table.

Note:

• Wires do not have permanent tags in AN-SOF. If a wire is deleted, the numbers will adjust automatically.
• Wire numbers are used solely for identification in the workspace while the Tabular Input window is open.

Sources Tab

Use the Sources tab to enter sources (see Fig. 3).

Entering Source Details

• Type Column: Enter “V” for a voltage source or “I” for a current source.
• Wire No. Column: Specify the wire on which the source is placed. Refer to the wire numbering in the No. column of the Wires tab.
• Position Column: Indicate the segment number where the source is connected. The segment number ranges from 1 to the number of segments (Segs) specified for the wire in the Wires tab.
• Amplitude Column: Enter the amplitude of the source in Volts or Amperes.
• Phase Column: Specify the phase of the source in degrees.

Table Interaction

• Right-click on the table to open a pop-up menu with standard options:
  • Cut (Ctrl + X)
  • Copy (Ctrl + C)
  • Paste (Ctrl + V)
  • Insert (Ins key)
  • Delete (Del key)
  • Clear Contents (Ctrl + Del)

These options function the same way as in the Wires tab, allowing you to manipulate cells and rows.

Loads Tab

Use the Loads tab to enter load impedances (see Fig. 4).

Entering Load Details

• Type Column: Enter one of the following:
  • “L” for an inductor.
  • “C” for a capacitor.
  • “Z” for an impedance (R + jX).
• Wire No. Column: Specify the wire on which the load is placed. Refer to the wire numbering in the No. column of the Wires tab.
• Position Column: Indicate the segment number where the load is connected. The segment number ranges from 1 to the number of segments (Segs) specified for the wire in the Wires tab.
• R Column: Enter the resistance value (R) in Ohms.
• Last Column: Depending on the option entered in the Type column, input one of the following:
  • Inductance (L) in the displayed unit.
  • Capacitance (C) in the displayed unit.
  • Reactance (X) in Ohms.

Table Interaction

• Right-click on the table to open a pop-up menu with standard options:
  • Cut (Ctrl + X)
  • Copy (Ctrl + C)
  • Paste (Ctrl + V)
  • Insert (Ins key)
  • Delete (Del key)
  • Clear Contents (Ctrl + Del)

These options function the same way as in the Wires tab, allowing you to manipulate cells and rows.

Trans. Lines Tab

Use the Trans. Lines tab to enter transmission lines and connect them to wire segments (see Fig. 5).

Entering Transmission Line Details

• Port 1 Columns:
  • Specify the wire segment where Port 1 of the transmission line is connected by entering the Wire No. and Position. Refer to the numbering and number of segments specified for each wire in the Wires tab.
• Port 2 Columns:
  • Similarly, specify the wire segment where Port 2 of the transmission line is connected by entering the Wire No. and Position.
• Additional Columns:
  • Complete the Type, Z0 (characteristic impedance), VF (velocity factor), Length, and other columns as explained in the section Adding Transmission Lines.
  • To simplify the process, select a row and double-click on an option in the right panel, which contains a collection of transmission line types with preloaded parameters.

Table Interaction

• Right-click on the table to open a pop-up menu with standard options:
  • Cut (Ctrl + X)
  • Copy (Ctrl + C)
  • Paste (Ctrl + V)
  • Insert (Ins key)
  • Delete (Del key)
  • Clear Contents (Ctrl + Del)

These options function the same way as in the Wires tab, allowing you to manipulate cells and rows.

Note:

• Entering a zero in Wire No., regardless of the Position entered, disconnects the port from the wire (putting the transmission line port in FREE status).
• Only transmission lines with both ports connected to wire segments will be considered in a simulation.
• Clicking on a row number (first column of the table) in the Trans. Lines tab highlights the transmission line in red in the AN-SOF workspace.

Refresh Button

A Refresh button is located just below the No. cell in all tabs of the Tabular Input window (see Fig. 6). Click the Refresh button to instantly apply changes. This eliminates the need to close and reopen the Tabular Input window to apply modifications.

Ways to Select a Wire

Selecting a wire in the workspace allows you to edit it, visualize its properties, or view simulation results. You can select any wire using one of the following methods:

1. Using the Select Wire Tool: Click the Select Wire button (arrow icon) on the toolbar, and then left-click on the desired wire.
2. Right-Clicking the Wire: Right-click on the wire to open a pop-up menu (see Fig. 1).
3. Using Keyboard Shortcuts: Press F8 or F9 to select wires one by one, either forwards or backwards, in the order they were created.

Double-click on the workspace or press ESC to deselect the wire.

When a wire is selected, it will be highlighted in light blue for easy identification. Once selected, you can:

• Edit the wire.
• View its properties, such as geometrical details, electrical length, number of segments, wire radius, and materials.
• Visualize simulation results, such as current distribution or input impedance (if the wire has a source on one of its segments).

The Pop-Up Menu

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

Source / Load / TL (Ctrl + Ins)

Opens the Source / Load / TL toolbar, allowing you to connect a source, load impedance, or transmission line to a segment of the selected wire.

Modify (Ctrl + M)

Opens the Modify dialog box to edit the selected wire.

Wire Color

Opens a dialog box to change the color of the selected wire.

Delete (Ctrl + Del)

Deletes the selected wire, including all sources and loads placed on it. Transmission line connections will also be removed.

Copy Start Point

Copies the start point of the selected wire, enabling you to connect it to the end of another wire.

Copy End Point

Copies the end point of the selected wire, enabling you to connect it to the end of another wire.

Plot Currents

Opens a chart in the AN-XY Chart application, displaying the current distribution along the selected wire. This option is enabled only after currents have been computed.

List Currents

Opens the List Currents toolbar, allowing you to select a wire segment and tabulate its current versus frequency. This option is enabled only after currents have been computed.

Wire Properties (Ctrl + W)

Opens the Wire Properties dialog box, where you can view the geometry, attributes, and material data of the selected wire.

Draw

Contains a sub-menu with commands to draw various types of wires, including:

• Line
• Arc
• Circle
• Helix
• Quadratic
• Archimedean Spiral
• Logarithmic Spiral

To modify an existing wire, right-click on it and choose Modify from the pop-up menu. This opens the Modify dialog box, where you can adjust the wire’s geometric parameters and attributes.

Alternatively, you can use the Select Wire button (arrow icon) from the main toolbar. After clicking this button, left-click on the wire you wish to modify. Once selected, go to Edit > Modify in the main menu. Note that this option is only enabled when a wire is selected.

Fig. 1 shows how to access the Modify command for a linear wire.

To delete a wire, right-click on it and select Delete from the pop-up menu. This will remove the selected wire from the model. Note that any sources or loads attached to the wire will also be deleted.

Alternatively, you can delete a wire using the Select Wire button (arrow icon) in the main toolbar. Click the button, then left-click on the wire to select it. Once selected, go to Edit > Delete in the main menu. This option is only enabled when a wire is selected.

Fig. 1 shows how to delete a linear wire using these options.

To enable a confirmation prompt before deleting a wire, go to Tools > Preferences > Options and check the option “Ask before deleting wires.”

AN-SOF allows you to simultaneously edit a group of wires. There are three ways to select multiple wires for editing:

1. Using the Selection Box Tool: Drag a rectangular box to select multiple wires.
2. Selecting Wire by Wire: Left-click on individual wires while holding the Ctrl key.
3. Combination of Both Methods: Use a mix of the Selection Box tool and wire-by-wire selection.

Using the Selection Box Tool

1. Click the Selection Box button on the main toolbar.
2. Left-click on the workspace and drag a box to select multiple wires (see Fig. 1).
   • All wires within the selection box will be highlighted in light blue.
   • Dragging the box from top to bottom selects only fully enclosed wires.
   • Dragging the box from bottom to top selects partially enclosed wires as well.
   • Enclosing already selected wires with the selection box will deselect them.
3. To deselect all wires, double-click on the screen or press ESC.

Selecting Wire by Wire

1. Click the Select Wire button (arrow icon) on the main toolbar (Fig. 2).
2. Hold the Ctrl key and left-click on individual wires to select them.
   • To deselect a wire, hold the Ctrl key and click on it again.
3. To deselect all wires, double-click on the screen or press ESC.

Wire Selection Methods – Video Tutorial

Watch the video below to learn how to efficiently select and edit wires in your antenna models. This tutorial demonstrates various selection techniques, including the ‘Select Wire’ and ‘Selection Box’ tools, using Ctrl + Left-Click for multi-selection, and combining these methods to streamline your workflow.

Persistent Wire Selections

Wire selections in AN-SOF persist until you explicitly deselect them—by double-clicking or pressing ESC—making it easier to apply consecutive modifications and run simulations between changes without the need to reselect elements. Even after saving and reopening a project, selected wires remain highlighted, allowing you to seamlessly resume editing exactly where you left off.

AN-SOF also includes Undo/Redo functionality, with up to 10 levels of action history. These options are available via the Edit menu and the main toolbar, or using the shortcuts Ctrl + Z (Undo) and Ctrl + Y (Redo). Together with persistent wire selections, this enables a smooth and efficient iterative workflow, where you can make changes, simulate, and refine your model until the desired outcome is achieved.

This process is illustrated in the video below and the accompanying flowchart (Fig. 3), with a detailed explanation provided beneath the diagram.

Step-by-Step Iterative Workflow

1️⃣ Select Multiple Wires

• Use Ctrl + Left Click, the Selection Box, or both.
• Selected wires are highlighted in light blue.
• To deselect a wire: Ctrl + Left Click on it.
• To deselect all wires: Press ESC or double-click anywhere on the workspace.

2️⃣ Edit the Selection

• Use the Edit menu options: Modify, Move, Rotate, Scale, Copy, Stack.

3️⃣ Run a Simulation

• Press Ctrl + R to calculate input impedance only.
• Press F10 to run the full simulation including far-field results.

4️⃣ Review Results

• Switch to the Results and Plots tabs.

5️⃣ Continue Editing

• Selected wires remain highlighted after simulation.
• Resume scaling, moving, rotating, etc., without reselecting.
• Use Ctrl + Z / Ctrl + Y to undo/redo changes.

🔁 Iterate as Needed

• Edit, simulate, and fine-tune your model continuously until you achieve the desired result.

🆕 Improved View Adjustments

• Panning, rotating, and zooming the view now retain the selection, streamlining the workflow.

Modifying the Selected Wires

Once multiple wires have been selected, navigate to Edit > Modify in the main menu to modify them. The Modify command opens a dialog box (see Fig. 4) with three tabs: Attributes, Materials, and Sources/Loads. Use the checkboxes to specify which parameters you want to modify.

In the Attributes tab, the Segments per Wire and Segments per Wavelength options allow for bulk editing of wire segments. These options are mutually exclusive:

• Segments per Wire sets a fixed number of segments for all selected wires.
• Segments per Wavelength sets the number of segments for each wire based on its length in wavelengths, using the shortest wavelength corresponding to the highest frequency specified.

Entering “0” (zero) in the Segments per Wire field will automatically set the number of segments for each wire based on 10 segments per wavelength.

In the Sources/Loads tab, you can remove sources and loads in bulk by selecting “Delete Sources” or “Delete Loads”.

If you need to manipulate the position or arrangement of selected wires—such as moving, rotating, scaling, copying, or stacking them—rather than editing their attributes like the number of segments, cross-section, or material properties, refer to the following articles:

• Moving, Rotating, and Scaling Wires

• Copying and Stacking Wires

You can delete multiple wires at once by first selecting them using one of the following methods:

• Selection Box – Click and drag a rectangular box around the wires you want to select.
• Wire-by-Wire – Hold down the Ctrl key and left-click on each wire individually.
• Combination – Combine both methods for more flexible selection.

For step-by-step instructions on selecting multiple wires, see the article:

• Selecting and Modifying Multiple Wires

Once the wires are selected, you can delete them using one of the following methods:

• Go to Edit > Delete in the main menu
• Press Ctrl + Del on your keyboard
• Click the Delete button in the toolbar

Fig. 1 shows how to select three wires using the Select Wires tool (arrow icon) and Ctrl + left-click, followed by clicking the Delete button in the toolbar.

To enable a confirmation prompt before deleting wires, go to Tools > Preferences > Options and check the option “Ask before deleting wires.”

To change the color of a wire, right-click on it to bring up the pop-up menu. Select the Wire Color command to open a dialog box where you can choose a color for the wire. This command is enabled only when a wire is selected.

Alternatively, you can access the Wire Color command by:

1. Clicking the Select Wire button (arrow icon) on the toolbar.
2. Left-clicking on the wire to select it.
3. Navigating to Edit > Wire Color in the main menu.

The Wire Color command is also available as a button on the toolbar.

To change the color of a group of wires:

1. Select the wires using the Selection Box or by selecting them individually (as explained in the section Selecting and Modifying Multiple Wires).
2. Navigate to Edit > Wire Color in the main menu.

Right-clicking on a wire displays a pop-up menu, where you can select the Wire Properties command.

Alternatively, you can access the Wire Properties command by:

1. Clicking the Select Wire button (arrow icon) on the toolbar.
2. Left-clicking on the wire to select it.
3. Navigating to Edit > Wire Properties in the main menu.

The Wire Properties command is also available as a button on the toolbar.

Executing the Wire Properties command opens the Wire Properties window, which contains three tabs: Geometry, Attributes, and Materials. This window is designed for viewing wire properties only. To edit a wire, refer to the section Modifying a Wire.

The Geometry Tab

This tab displays the geometrical properties of the selected wire (see Fig. 1), including:

• Start Point: Cartesian coordinates of the wire’s start point.
• End Point: Cartesian coordinates of the wire’s end point.
• Wire Length: Length of the wire.
• Segment Length: Length of a wire segment. For curved wires with non-uniform segments, this is the average segment length.
• Shortest Wavelength (λ): Wavelength corresponding to the highest frequency specified in the Frequency panel.
• Wire Length/λ: Wire length measured in wavelengths (based on the shortest wavelength).
• Segment Length/λ: Length of a wire segment in wavelengths (based on the shortest wavelength).
• Segments Per Wavelength: Number of segments the wire would have if its length were one wavelength. This is the inverse of the segment length measured in wavelengths: 1/(Segment Length/λ).
• Hallen’s Parameter (Ω): A parameter that measures wire thickness, defined as Ω = 2 ln(L/a), where L is the wire length and a is the wire radius.

The Attributes Tab

This tab displays the electrical properties of the selected wire (see Fig. 2), including:

• Number of Segments: Number of segments into which the wire is divided.
• Number of Sources: Number of sources placed on the wire.
• Number of Loads: Number of loads placed on the wire.
• Cross-Section: Type and dimensions of the wire’s cross-section.
• Equivalent Radius: Equivalent radius of the cross-section.
• Equivalent Radius/λ: Equivalent radius as a fraction of the shortest wavelength.
• Thin-Wire Ratio: Ratio of the wire diameter to the segment length. This must be less than 3 when the Exact Kernel option is unchecked in the Settings panel of the Setup tab. If the Exact Kernel option is checked, any value of the thin-wire ratio is allowed. For non-circular cross-sections, the wire diameter is twice the equivalent radius.

The Materials Tab

This tab displays the material properties of the selected wire (see Fig. 3), including:

• Wire Resistivity: Resistivity of the wire in [Ohm·m]. If the wire is coated, this refers to the resistivity of the internal conductor.
• Wire Coating: Parameters of the wire’s coating shield.
• Relative Permittivity: Permittivity (dielectric constant) of the coating material relative to the permittivity of vacuum.
• Relative Permeability: Magnetic permeability of the coating material relative to the permeability of vacuum.
• Thickness: Thickness of the coating shield.

A wire junction is automatically established when the coordinates of a wire end match the end coordinates of a previously added wire. Wire junctions are essential to satisfy Kirchhoff’s current law at the connection point.

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

Connecting Wires by Copying and Pasting Ends

Two wires can be connected by copying and pasting their ends:

1. Right-click on a wire to select it.
2. From the pop-up menu, choose Copy Start Point or Copy End Point to copy the coordinates of the wire end to an internal clipboard.
3. Paste the copied point in the Draw dialog box when adding a new wire by clicking the From Point button, located just above the start point coordinates (X1, Y1, Z1) (see Fig. 2).

Note:

• When a wire is selected in the workspace, it will be highlighted in light blue, and an arrow will appear at the End Point. The opposite end is the Start Point.
• Wire orientation serves as the electrical reference for the phase of the current distribution. However, it does not affect observables such as input impedance (and thus VSWR or S₁₁) or radiation pattern metrics (directivity, gain, efficiency, etc.).

Copying Start and End Points via the Wire Properties Window

The Start and End Points of a wire can also be copied to the AN-SOF internal clipboard for use in a dialog box to draw another wire, using buttons in the Wire Properties window. This procedure is demonstrated in the video below and explained in detail in the following section.

Procedure for Connecting Two Wires at Their Ends

This procedure demonstrates how to connect the Start or End Point of wire #1 to the Start Point of wire #2:

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

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

After drawing the wire structure, you may need to adjust the position, orientation, or size of individual wires or groups of wires. To modify wires, you must first select them.

Selecting Wires

1. Using the Selection Box:
   • Click the Selection Box button on the toolbar.
   • Drag a box using the mouse while holding the left button to enclose the wires you want to modify (see Fig. 1).
     • Dragging the box from top to bottom selects only fully enclosed wires.
     • Dragging the box from bottom to top selects partially enclosed wires as well.
     • Enclosing already selected wires with the selection box will deselect them.
2. Selecting Wire by Wire:
   • Click the Select Wire button (arrow icon) on the toolbar.
   • Hold the Ctrl key and left-click on individual wires to select them.
     • To deselect a wire, hold the Ctrl key and click on it again.
   • To deselect all wires, double-click on the screen or press ESC.

You can also combine the Selection Box method with selecting wires individually.

Transforming Selected Wires

Once the wires are selected, navigate to the Edit menu and choose one of the following commands:

Move Wires

Opens the Move Wires dialog box (see Fig. 2), allowing you to move the selected wire or group of wires to a new position. You can specify the shift along the X, Y, and Z coordinates.

Rotate Wires

Opens the Rotate Wires dialog box (see Fig. 3), enabling you to rotate the selected wire or group of wires around a chosen axis. In addition to the Cartesian axes (X, Y, and Z), the Custom option allows you to define a rotation axis using spherical coordinates (Theta, Phi). You can also set the Rotation Center to rotate around a point other than the origin.

Scale Wires

Opens the Scale Wires dialog box (see Fig. 4), providing the following scaling options:

1. Single Factor:
   • Apply a single scale factor to all point coordinates of the selected wires.
   • Optionally, scale the wire cross-section and coating thickness by the same factor by checking the corresponding boxes.

2. Line Length:
   • Apply scaling only to linear wires.
   • Enter a scale factor and specify an anchored point: the line’s start point (P1) or end point (P2). This allows you to lengthen or shorten the line while keeping one end fixed.

3. Advanced:
   • Apply different scale factors for each Cartesian coordinate (X, Y, and Z).
   • Stretch or contract the selected wires along the direction of one of the Cartesian axes.

Note

Transmission lines fully enclosed by the selection box will be transformed along with the associated wires when using the Move, Rotate, or Scale transformations in the Edit menu. This ensures that transmission lines remain connected to wires selected via the Selection Box.

When drawing a wire structure, it’s often necessary to copy wires from one position to another—for example, when creating an antenna array. To copy wires, first select them using one of the following methods:

1. Click the Selection Box button on the toolbar and drag a box with the mouse to enclose the wires you want to copy (see the Moving, Rotating and Scaling Wires section for details).
2. Hold the Ctrl key and left-click on wires to select them individually.
3. Combine methods 1 and 2 for more flexible selection.

For a full overview of wire selection techniques, see:

• New Tools in AN-SOF: Selecting and Editing Wires in Bulk

In the Edit menu, you will find the following commands for copying the selected wires:

Copy Wires

Opens the Copy Wires dialog box (see Fig. 1), allowing you to copy the selected wire or group of wires.

• Specify the number of copies of the selected group of wires.
• The first copy will be offset from the original wire group based on the entered X, Y, and Z offsets and/or rotated around each axis according to the entered angles.
• Each subsequent copy will be offset and/or rotated relative to the previous copy.

Stack Wires

Opens the Stack Wires dialog box (see Fig. 2), allowing you to stack the selected wire or group of wires along a specified direction.

• Specify the number of elements in the stack. Each “element” consists of the selected wires, which could be a single wire or a group of wires.
• Define the spacing between the elements.

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 in AN-SOF can be excited either by discrete sources or by an incident electromagnetic field. For the latter, refer to Excitation by an Incident Field. Discrete sources can be placed on any wire segment, and multiple sources may be added—up to one per segment if needed.

A source represents the feed point of a transmitting antenna or an electrical generator. There are two types of sources:

• Voltage sources
• Current sources (used to model impressed currents)

For each source, you must define its amplitude and phase. Additionally, you can assign an internal impedance to simulate non-ideal sources. The impedance can take one of the following forms:

• Series RL (inductive)
• Series RC (capacitive)
• Fixed complex impedance (R + jX)

In addition to sources, lumped loads can be inserted into any wire segment to model passive components or matching circuits. Six types of loads are available:

• Series RL impedance (inductive)
• Series RC impedance (capacitive)
• Fixed R + jX impedance (reactance does not scale with frequency)
• Series RLC circuit
• Parallel RLC circuit
• Trap RLC circuit

To model a pure resistor, set an inductive load with L = 0.

Note:

You can set the units for inductance and capacitance in Main Menu > Tools > Preferences. Supported units include:
• Inductance: pH, nH, µH, mH, H
• Capacitance: pF, nF, µF, mF, F

In the 3D workspace:

• Sources are represented by a yellow circle
• Loads are indicated by a green-highlighted wire segment (see Fig. 1)

Tips

• To customize the default colors of sources and loads, go to: Main Menu > Tools > Preferences > Workspace tab.

• To change the size of the source displayed in the workspace, go to Main Menu > Tools > Preferences > Workspace tab, and adjust the Source Size % setting.

• Voltage sources have their internal impedance in series.
  To model an ideal (perfect) voltage source, set the impedance to zero.

• Current sources have their internal impedance in parallel.
  To approximate an ideal current source, use a very high impedance (e.g., 1 MΩ).

Excitation by Sources

To excite the wire structure using discrete sources, go to the Setup tab, open the Excitation panel, and select the Discrete Sources option (see Fig. 2).

If the Set Input Power option is enabled, you can specify the total input power delivered to the structure. In this case, the amplitudes of the voltage and current sources will be automatically adjusted to match the desired input power.

To add a source to a wire segment, first right-click on the desired wire and select “Source / Load / TL (Ctrl + Ins)” from the pop-up menu. A toolbar will appear at the bottom of the screen. Use the slider on this toolbar to select the specific wire segment where you want to place the source.

For more details, see The Source/Load/TL Toolbar.

The Source/Load/TL toolbar is used to connect a source, load, or transmission line to a specific segment of a wire. It also provides tools to edit or remove existing connections.

Accessing the Toolbar

To open this toolbar:

• Right-click on any part of a wire and select Source / Load / TL (Ctrl + Ins) from the pop-up menu (Fig. 1).
• Alternatively, use the main toolbar or go to Edit > Source / Load / TL (Ctrl + Ins) from the main menu. Before using this command, click the Select Wire button (arrow icon on the main toolbar), then left-click the wire where you want to place the source or load.

Toolbar Components

Slider

• The slider lets you choose a specific wire segment.
• Each slider position corresponds to a segment along the selected wire.
• On the right side of the toolbar, you’ll see:
  • The segment number.
  • The segment’s relative position (in %) along the wire, measured from the wire’s starting point to the midpoint of the selected segment:
  Segment Position % = 100 × (segment position / wire length)

50% Button

• Quickly positions the slider at the center of the wire.
• Useful for placing sources or loads at the midpoint.

⚠️ Note: The wire must have an odd number of segments for an exact center segment to exist.

Add Source Button

• Opens a dialog box to add a source to the selected segment (Fig. 2).
• You can specify:
  • Source type
  • Amplitude
  • Phase
  • Internal impedance Zs

• Voltage sources have their internal impedance in series. To model an ideal (perfect) voltage source, set the impedance to zero.
• Current sources have their internal impedance in parallel. To approximate an ideal current source, use a very high impedance (e.g., 1 MΩ = 1E6 Ohm).
• To change the size of the source displayed in the workspace, go to Main Menu > Tools > Preferences > Workspace tab, and adjust the Source Size % setting.
• To customize the default color of sources, go to: Main Menu > Tools > Preferences > Workspace tab.

Add Load Button

• Opens a dialog to add a load to the selected segment (Fig. 3).
• Load types include:
  • Series RL (resistor + inductor)
  • Series RC (resistor + capacitor)
  • Fixed R + jX impedance (non-frequency-dependent reactance)
  • Series or parallel RLC
  • Trap (series RL + parallel C)

• To customize the default color of loads, go to: Main Menu > Tools > Preferences > Workspace tab.

Transmission Lines Button

• Opens a dialog to connect a transmission line to the selected segment.
• See the section Adding Transmission Lines for more information.

Delete Button

• Removes any existing source or load from the selected segment.

Modify Button

• Opens a dialog to edit the source or load on the selected segment.

Exit Button

• Closes the Source/Load/TL toolbar.

To add a source to a specific wire segment, follow these steps:

• Right-click on any part of the wire to open the pop-up menu.
• Select Source / Load / TL (Ctrl + Ins) to open the Source / Load / TL toolbar at the bottom of the screen (Fig. 1).
• Use the slider to choose the wire segment where the source will be placed.
• Click the Add Source button to open the Add Source dialog box (Fig. 2).
• Specify the type of source, its amplitude (rms value), phase, and internal impedance, then click OK.
• Click Exit to close the Source / Load / TL toolbar.

Tips

• To customize the default color of sources, go to: Main Menu > Tools > Preferences > Workspace tab.

• To change the size of the source displayed in the workspace, go to Main Menu > Tools > Preferences > Workspace tab, and adjust the Source Size % setting.

• Voltage sources have their internal impedance in series.
  To model an ideal (perfect) voltage source, set the impedance to zero.

• Current sources have their internal impedance in parallel.
  To approximate an ideal current source, use a very high impedance (e.g., 1 MΩ = 1E6 Ohm).

To edit an existing source on a wire segment, follow these steps:

• Right-click on any part of the wire to open the pop-up menu.
• Select the Source / Load / TL (Ctrl + Ins) command to open the Source/Load/TL toolbar (Fig. 1).
• Use the slider to locate the segment where the source is placed.
• Click the Modify button to open a dialog box where you can edit the source parameters.
  • To remove the source, click the Delete button.
• Click the Exit button to close the Source / Load / TL toolbar.

Tips

• To customize the default color of sources, go to: Main Menu > Tools > Preferences > Workspace tab.

• To change the size of the source displayed in the workspace, go to Main Menu > Tools > Preferences > Workspace tab, and adjust the Source Size % setting.

• Voltage sources have their internal impedance in series.
  To model an ideal (perfect) voltage source, set the impedance to zero.

• Current sources have their internal impedance in parallel.
  To approximate an ideal current source, use a very high impedance (e.g., 1 MΩ = 1E6 Ohm).

To add a load to a selected wire segment, follow these steps:

• Right-click on any part of the wire to display the pop-up menu.
• Select the Source / Load / TL (Ctrl + Ins) command from the menu to open the Source / Load / TL toolbar (Fig. 1) at the bottom of the screen.
• Use the slider on the toolbar to select the desired wire segment.
• Click the Add Load button to open the Add Load dialog box (Fig. 2).
• Specify the load type, along with the required RLC values, then click OK.
• Click the Exit button to close the Source/Load/TL toolbar.

• Load types include (Fig. 2):
  • Series RL (resistor + inductor)
  • Series RC (resistor + capacitor)
  • Fixed R + jX impedance (non-frequency-dependent reactance)
  • Series RLC
  • Parallel RLC
  • Trap (series RL + parallel C)

Tip

• To customize the default color of loads, go to: Main Menu > Tools > Preferences > Workspace tab.

To edit a load on a wire segment, follow these steps:

• Right-click on any part of the wire to open the pop-up menu.
• Select Source / Load / TL (Ctrl +Ins) from the menu to display the Source / Load / TL toolbar.
• Use the slider on the toolbar to select the segment where the load is located.
• Click the Modify button to open the Edit Load dialog box, where you can update the load’s parameters.
• To remove the load, click the Delete button.
• Click the Exit button to close the toolbar.

Tip

• To customize the default color of loads, go to: Main Menu > Tools > Preferences > Workspace tab.

You can enable or disable all loads in the simulation without deleting them. This is useful when you want to temporarily exclude load impedances from the analysis.

1. Go to the Setup tab and locate the Settings panel in the main window.
2. Check or uncheck the Load Impedances option:
   • Checked: Loads are enabled and included in the simulation.
   • Unchecked: Loads are disabled but remain defined in the model.

See Fig. 1 for reference.

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 using the following procedure:

1. Navigate to the Setup tab > Environment panel.
2. Select the Perfect option in the Ground Plane box (see 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 Z-coordinate relative to 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 on the xy-plane.
• If Z < 0, the PEC ground plane will be below the xy-plane.

The ground plane is represented as a square with cross diagonals to visualize its position (see Fig. 2). Note that this is only a symbolic representation, as the ground plane itself is infinite in extent.

A real (i.e., imperfect or lossy) ground plane, located on the xy-plane (Z = 0), can be added to the model using the following procedure:

1. Navigate to the Setup tab > Environment panel.
2. Select the Real option in the Ground Plane box (see Fig. 1).
3. Specify the Real Ground Option:
   • Sommerfeld-Wait Asymptotic
   • Reflection Coefficients
   • Radial Wire Ground Screen
   • Sommerfeld-Norton
4. Set the ground Permittivity and Conductivity. If a Radial Wire Ground Screen is selected, also specify the radial length, number of radials, and wire radius.

The ground plane is represented as a square with cross diagonals to indicate its position (see Fig. 2). Note that this is only a symbolic representation, as the ground plane itself is infinite in extent. When a Radial Wire Ground Screen is selected, the radial wires lying on the ground will be displayed instead of the ground plane symbol (see Fig. 3).

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. Select a substrate material from the provided list, or choose Custom to specify the substrate’s Permittivity. Set the slab’s Thickness (h) and, if a finite slab is selected, configure its dimensions along the X and Y axes.

Note:

The substrate slab is backed by a PEC ground plane, which runs parallel to the xy-plane at Z = -h. This ground plane cannot be removed from the simulation (see Fig. 2).

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

Wire connections to the ground plane are indicated with 3D symbols (see 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, follow these steps:

1. Navigate to the Setup tab > Environment panel.
2. Select the None (free space) option in the Ground Plane box (see Fig. 1).

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

To calculate the current distribution:

• Navigate to Run > Run Currents (Ctrl + R) in the main menu (see Fig. 1).

Tip

• When modeling a transmitting antenna and only the input impedance and VSWR/S₁₁ are needed, the Run Currents (Ctrl + R) command saves time by skipping the calculation of the radiated field.

Once the current distribution on the structure has been calculated, the far-field can be computed within the angular ranges specified in the Far-Field panel of the Setup tab.

To calculate the far-field:

• Navigate to Run > Run Far-Field in the main menu (see Fig. 1).
  • This command is enabled only after the current distribution has been calculated.

Tip

To sequentially and automatically calculate both the current distribution and the far field, click the Run Currents and Far-Field (F10) button on the toolbar.

Once the current distribution on the structure has been calculated, the near electric field can be computed at the points in space specified in the Near-Field panel of the Setup tab.

To calculate the near electric field:

• Navigate to Run > Run Near E-Field in the main menu (see Fig. 1).
  • This command is enabled only after the current distribution has been calculated.

Tips

• To sequentially and automatically calculate both the current distribution and the near fields, click the Run Currents and Near-Field (F11) button on the toolbar. This command also calculates the near H-Field.

• To avoid calculating 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 calculated, the near magnetic field can be computed at the points in space specified in the Near-Field panel of the Setup tab.

To calculate the near magnetic field:

• Navigate to Run > Run Near H-Field in the main menu (see Fig. 1).
  • This command is enabled only after the current distribution has been calculated.

Tips

• To sequentially and automatically calculate both the current distribution and the near fields, click the Run Currents and Near-Field (F11) button on the toolbar. This command also calculates the near E-Field.

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

Once the frequencies, environment, structure geometry, excitation, and far-field observation points have been defined, AN-SOF is ready to perform the calculations. If near-field data is also required, the observation points must first be specified in the Near Field panel. The simulation begins by calculating the current distribution along the wire segments, which also yields the input impedance for a transmitting antenna. The near and far fields are then computed based on these segment currents.

Run ALL (F12) Command

The Run ALL (F12) command allows you to sequentially and automatically calculate the current distribution, far fields, and near fields. To use this command:

1. Navigate to Main Menu > Run > Run ALL (F12) (see Fig. 1).
2. Alternatively, click the Run ALL button on the toolbar.

Alternative Commands

• If the near field is not required, you can calculate only the currents and far fields by clicking Run > Run Currents and Far-Field (F10). This command is also available on the toolbar.
• If the far field is not required, you can calculate only the currents and near fields by clicking Run > Run Currents and Near-Field (F11). This command is also available on the toolbar.

Separate Calculations

The currents, far fields, and near fields can also be computed separately, as explained in the following articles:

• Calculating the Current Distribution
• Calculating the Far Field
• Calculating the Near E-Field
• Calculating the Near H-Field

When a calculation is executed using the commands under the Run menu, the Processing window will be displayed (see Fig. 1). This window includes a button to abort the calculation at any time.

Note:

You will be prompted to save the project before aborting, as AN-SOF will restart after the process is terminated.

In simulations where the excitation of the structure needs to be changed frequently—such as adjusting the amplitudes of discrete sources or altering the direction of arrival of an incident field—the Numerical Green’s Function (NGF) option can save significant computation time. To enable this option, navigate to the Settings panel of the Setup tab, as shown in Fig. 1.

How NGF Works

• During an NGF calculation, the LU-decomposed matrix of the system is stored in a file after the initial computation.
• Subsequent calculations reuse this stored matrix, allowing them to be performed much faster than the initial one.

Automatic NGF Activation

• When transmission lines are included in the model, the NGF option is automatically enabled.

AN-SOF can import a sequence of input files to generate a corresponding sequence of output files, all without requiring 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 in the section: Importing Wires.

Output Data

The output data includes:

• Power Budget or RCS (Radar Cross Section).
• Input Impedances.
• Far Field and Near Fields.

All output data is provided in CSV format. For each NEC input file, AN-SOF generates an individual project containing .emm and .wre files (see File Formats). This allows each project to be opened separately after the bulk simulation is completed.

Initiating a Bulk Simulation

1. Navigate to the main menu and select Run > Run Bulk Simulation.
2. A prompt will appear, asking if you want to save changes in the current project, as the bulk simulation requires closing the currently open project.
3. A dialog box will be displayed, allowing you to select a directory and the input .nec files.
4. After selecting the desired files and clicking the Open button, the bulk simulation will begin. The input files will be imported and computed one after another in alphabetical order.

Generated Files

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

AN-SOF Project Files

• InputFile.emm: Main project file (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, VSWR, S₁₁, etc.
• 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.

Note:

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

Automating Parameter Variations

Bulk simulations automate the calculation process for multiple NEC files, even if they are unrelated, eliminating the need for manual calculations file by file. They are particularly useful for sequentially running calculations on NEC files generated with varying geometric parameters for an antenna. The results can then be analyzed by reading data from the generated CSV files.

For example, 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 learn how to accomplish this and read the output data from the CSV files, refer to the following article: 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

• Results > Plot Current Distribution command.
• Results > Plot Currents command.
• Results > List Currents command.
• Results > Export Currents command.
• Results > List Input Impedances command.

Results related to the far field

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

Results related to the near E-Field

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

Results related to the near H-Field

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

Results related to the Power Density

• Results > Plot Power Density Pattern command.
• Results > Plot Power Density Spectrum command.
• Results > List Power Density Pattern command.
• Results > List Power Density 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.

The Results tab in the AN-SOF main window (see Fig. 1) displays a table with the primary results for a transmitting antenna, including:

• Input Impedance (Z_in = R_in + jX_in)
• VSWR
• S₁₁
• Directivity
• Gain
• Radiation Efficiency
• 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 wire structure is excited by a discrete source. It will not be filled if 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, click the Export Results button on the toolbar (see Fig. 1).

Interactive Column Headers

The column headings, from Rin through F/B V, are interactive buttons. Clicking on them displays rectangular plots, where the data in the column is plotted as a function of frequency.

• Click the “Freq.” column header to display the input impedance (Z_in = R_in + jX_in) in a Smith Chart. By default, this is the input impedance at the antenna feedpoint.
• If the antenna has a feeder and/or tuner connected to its terminals, the impedance seen at the feeder input or tuner input can also be tabulated in the Results tab. These can be plotted against frequency in rectangular or Smith charts by clicking the corresponding column headers.

Plotting Impedance at Different Points

1. Navigate to the Plots tab > “Zin” box (see Fig. 2) and choose between Antenna, Feeder, or Tuner.
2. Go to the Results tab, where R_in, X_in, VSWR, and S₁₁ will be tabulated for the selected option (antenna, feeder, or tuner input).
3. Click the header buttons as indicated in Fig. 1 to plot these results against frequency.

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 derived from the table in the Results tab.

Plot Layout

• Left Column: Displays the real and imaginary parts of the input impedance (Z_in = R_in + jX_in) and the VSWR.
• Right Column: Shows the antenna gain in dBi and the Front-to-Rear (F/R) and Front-to-Back (F/B) ratios in dB.

The plots are aligned vertically to facilitate easy comparison.

Customizing Plots

Use the controls on the right side of the Plots tab to adjust various aspects of the graphics, including:

• Line thickness.
• Visualization of points and marks.
• Scales and axes.
• Selection between VSWR or S₁₁.
• Choice between Horizontal (H) or Vertical (V) F/R and F/B ratios.

Each plot can be maximized by clicking the Maximize checkbox located in its upper-right corner.

Input Impedance and VSWR/S₁₁ Options

The input impedance and VSWR/S₁₁ plots can represent:

• The antenna input impedance.
• The feeder + antenna input impedance.
• The tuner input impedance.

The tuner and feeder can be configured in their corresponding tabs next to the Results tab. Whenever a tuner or feeder parameter is changed, the recalculated results in the Results and Plots tabs can be refreshed by selecting the desired option under the Zin box (highlighted in Fig. 1).

Tuner Option

If the Tuner option is selected:

• The input impedance of the tuner will be displayed.
• 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 currents flowing on a wire can be exported to a CSV (Comma-Separated Values) file. Since the current is calculated at the midpoint of each wire segment, the current distribution is sampled at a finite set of points determined by the number of segments the wire is divided into. Additionally, as the current varies with frequency, there is a unique current distribution along the wire for each frequency.

To export the current distribution as a function of position along a selected wire and as a function of frequency, follow these steps:

1. Click the Select Wire button (arrow icon) in the toolbar.
2. Left-click on the wire to select it (it will be highlighted in light blue).
3. Navigate to the Results menu > Export Currents in the main menu (see Fig. 1).

The complex current (real and imaginary parts) is tabulated based on the position along the wire. Position and frequency units can be configured in the Preferences window.

Note:

• Position is measured from the start point of the selected wire (the end without the arrow when selected).
• The exported CSV file contains the real and imaginary parts of the current as a function of position and frequency, as shown in Fig. 2.

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, 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. It can represent devices such as baluns and ununs — for example, a 1:1 balun for balanced-to-unbalanced conversion without impedance change, a 1:4 balun to match a 200-ohm antenna to a 50-ohm feedline, or a 1:9 unun for matching high-impedance long-wire antennas. This feature is useful for optimizing power transfer and minimizing VSWR in multiband and off-resonance antenna configurations.

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.

Transmit Mode, Duty Cycle, and Time Transmitting

The input power specified is the transmitter’s Peak Envelope Power (PEP). However, when performing RF exposure evaluations, the average power supplied by the transmitter over time is the critical factor. The average power is a fraction of the PEP, determined by the duty cycle (or duty factor) of the selected transmit mode. The transmit mode can be chosen, and the corresponding percentage duty cycle will be displayed, as shown in Fig. 5. To enter a custom duty cycle, select “Custom” as the transmit mode.

It is also important to account for the percentage of time the transmitter remains active within a specific period, such as 6 minutes. For example, if the telegraph mode transmits for only 3 minutes in every 6-minute period, the power considered for RF exposure calculations is reduced by 50%. Therefore, the Time Transmitting parameter can be set as a percentage. Both the duty cycle and the time transmitting percentage will affect the PEP, and an average input power will be calculated accordingly.

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. 6.

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. 7.

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. 8).

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.