Tony Golden › AN-SOF Antenna Simulation Software

Simulation results depicting the input impedance of a center-fed half-wave dipole as a function of its length-to-radius ratio.

1Jun, 2023

Linear Antenna Theory: Historical Approximations and Numerical Validation

This article provides a comprehensive review of the theoretical approximations to the current distribution on linear antennas that were analytically derived during the first half of the 20th century. While the advancements in computing and numerical calculation methods have enabled higher precision, the historical theoretical results continue to serve as vital references for validating calculation methods implemented in algorithms. By examining these approximations, researchers can ensure the accuracy and reliability of modern numerical techniques used in antenna analysis and design.

Historical Theoretical Results: Approximations to Current Distribution
Current Distribution Along a Half-Wave Dipole
Validating Numerical Methods: Impedance Convergence
Conclusion
Further Reading

Historical Theoretical Results: Approximations to Current Distribution

In 1956, Ronold W. P. King published his monumental work titled “The Theory of Linear Antennas,” which laid the foundation for understanding linear antennas and became a benchmark for future research. This section explores the significant contributions of King’s work, specifically focusing on the first four approximations to the current distribution on cylindrical antennas derived through an iterative method.

0th-Order Approximation > Perfect Sinusoid for Infinitely Thin Antennas: The 0th-order approximation considers infinitely thin antennas (wire radius = 0) with a delta-gap source (zero gap width between the antenna terminals at the source position). This approximation involves a perfect sinusoidal current distribution.

1st-Order Approximation > Accounting for Finite Radius Effect: The 1st-order approximation incorporates the finite radius effect (wire radius > 0) into the current distribution calculation. In this case, it is necessary to incorporate an additional term to the perfect sinusoidal function in order to obtain the 1st-order current distribution.

2nd-Order Approximation > Controversies Surrounding Finite Gap at the Source: The 2nd-order approximation takes into account the finite gap at the source position, which has historically sparked controversies and debates.

3rd-Order Approximation > Considering Feedline Effect: The 3rd-order approximation considers the feedline effect, which accounts for the boundary conditions at the feeding point resulting from the connection of a transmission line to feed the antenna.

Current Distribution Along a Half-Wave Dipole

To illustrate the aforementioned approximations, this section focuses on the current distribution in amplitude along a center-fed half-wave dipole. Figure 1 provides a graphical representation of the normalized current, i(s), as a function of position in wavelengths, s/λ. It should be noted that the actual current distribution exhibits a sign change in its derivative, ∂i/∂s (the electric charge), at the dipole center due to the excitation source.

Fig. 1: Normalized amplitude current distribution along a center-fed half-wave dipole. The figure illustrates the 0th, 1st, and 2nd order approximations, highlighting the discontinuity of the current derivative at the feed point.

0th-Order Approximation > Perfect Sine Function with Zero Derivative: Figure 1 demonstrates that the 0th-order approximation, representing a wire radius of 0, yields a perfect sine function. Consequently, the derivative at the source position is zero, ∂i/∂s = 0. However, King’s analytical solution results in a finite input impedance of 73.1 + j42.5 Ω, which has been widely accepted and corroborated by other methods.

1st-Order Approximation > Finite Wire Radius and Divergent Input Impedance: The 1st-order approximation considers a finite wire radius and exhibits an infinite derivative, ∂i/∂s = ∞, at the source position. This singularity arises from the zero gap at the antenna terminals and has generated extensive debates throughout the history of linear antennas. As a consequence, the input impedance diverges.

2nd-Order Approximation > Finite Source Gap and Converging Input Impedance: Incorporating a finite source gap, the 2nd-order approximation yields a finite derivative at the source position. As a result, the input impedance converges to a finite value, dependent on the dipole wire thickness and the separation between its feeding terminals.

3rd-Order Approximation > Consideration of Transmission Line Feed: Although not visually distinguishable from the 2nd order on a graph, the 3rd-order approximation accounts for the characteristic impedance of the transmission line at the feed point. This effect, though small, can be accurately calculated using the Method of Moments > with an exact Kernel >.

Validating Numerical Methods: Impedance Convergence

Validating numerical methods is a critical step in ensuring their accuracy, achieved by examining the limiting cases predicted by theory. As demonstrated, the 0th-order input impedance (wire radius = 0) of a center-fed half-wave dipole is determined to be 73.1 + j42.5 Ω. Consequently, this value should serve as a horizontal asymptote for the input impedance when the dipole length-to-radius ratio tends to infinity.

Figure 2 presents simulation results obtained using AN-SOF, which utilizes the Method of Moments with an exact Kernel >. The figures from King’s book illustrate the antenna terminals in detail, where a radial transmission line was considered to account for 3rd-order effects. Notably, the calculated input impedance indeed converges to the theoretical value as predicted.

For a more comprehensive investigation into the impedance convergence of cylindrical antennas, a detailed study on the validation of AN-SOF can be accessed through this link >.

Conclusion

This article has reviewed the historical approximations of current distribution on linear antennas as presented in Ronold W. P. King’s book. The four approximations, namely the 0th, 1st, 2nd, and 3rd-order approximations, have been thoroughly examined. These approximations progressively refine the theoretical model of a cylindrical antenna by considering factors such as the finite wire radius, the finite gap at the feed point, and the incorporation of the connected transmission line.

Moreover, the article has highlighted the importance of numerical validation in establishing the reliability of modern methods. The validation process involved comparing the numerical results to the limiting cases predicted by theory. Through the AN-SOF simulation, which utilizes the Method of Moments with an exact kernel >, the calculated input impedance successfully demonstrated convergence to the theoretical values.

Assessing Antenna Directionality: Front-to-Rear vs. Front-to-Back Ratio

⚠ Are you aware of the importance of calculating the front-to-rear ratio of your antenna? ⚠

✅ It is a crucial factor in determining the directional performance of your antenna system. AN-SOF can display this ratio in various forms, such as in polar radiation patterns, tables, and graphs, as a function of frequency.

✅ Discover the difference between the front-to-rear and front-to-back ratios in this article >.

, antenna design, directional

Wave Matching Coefficient as a function of distance for a 7-element Yagi-Uda antenna.

19May, 2023

Wave Matching Coefficient: Defining the Practical Near-Far Field Boundary

In this article, we explore the concepts of absolute wave impedance and wave matching coefficient (WMC) as practical alternatives to determine a useful boundary between the near and far field regions of an antenna. By utilizing these measures, we gain a better understanding of wave propagation as a function of distance from the source antenna, employing a decibel scale that enables clearer visualization of significant changes in wave impedance. As a general guideline, a WMC value of 20 dB proves to be an appropriate threshold for distinguishing between the near and far field zones. Through examples involving both elementary and large-scale antennas relative to the wavelength, we observe that the 20 dB boundary is consistently located at a distance of λ/3 for elementary antennas, while it takes on an irregular and non-spherical shape for antennas of comparable size or greater than the wavelength.

Introduction
The Traditional Boundary Between Near Field and Far Field
Definitions of Wave Impedance
Absolute Wave Impedance
Wave Matching Coefficient
Examples with a 20 dB Boundary
Conclusions
Further Reading

Introduction

The determination of the far-field region of an antenna has been a topic extensively discussed in books and texts on antennas for nearly a century. However, it continues to spark debates even today. Identifying the regions surrounding an antenna is crucial for various applications, such as near-field measurements in an anechoic chamber to predict the far-field radiation pattern or in electromagnetic compatibility (EMC) to optimize shielding in the near-field region, minimizing interference.

Based on the observation of elementary electric or magnetic dipole fields, three distinct regions can be identified in terms of the distance, r, from the dipole:

1) The reactive near-field region, where terms proportional to 1/r³ predominate.

2) A transition region or Fresnel zone, where terms proportional to 1/r² predominate.

3) The far-field region or Fraunhofer zone, where terms proportional to 1/r predominate.

There is also a two-region model where the reactive near-field and the Fresnel zone are considered as part of the same near-field region. When antennas are more complex than elementary dipoles, it becomes nontrivial to identify the electromagnetic field zones. It is important to note that the definition of a boundary between the near-field and far-field regions is always arbitrary and depends on the acceptable margin of error in practice. There is no sharp edge or discontinuity between these regions; instead, the electromagnetic field initially behaves as a quasi-static field near the radiation source and gradually transforms into a Transverse Electromagnetic (TEM) wave with a spherical wavefront as the distance increases.

The Traditional Boundary Between Near Field and Far Field

In most textbooks, we can find that the far-field region begins at a distance from the antenna given by 2D²/λ, where D is the maximum dimension of the antenna and λ is the wavelength. This boundary between regions works reasonably well for cases of electrically large antennas (D >> λ). However, there are many exceptions to this rule, such as in the case of parabolic antennas where this boundary must be extended twofold. For electrically small antennas (D << λ), the boundary between regions is located at λ/(2π) regardless of the antenna size.

These calculations are based on placing the observation point of the field far enough away so that the antenna remains within a sphere, which, as it expands, approaches a spherical wavefront in the far-field zone. This allows us to develop the phase of the Green’s function of the problem in a Taylor series with respect to distance and retain the first terms. Depending on the number of terms retained, the different field zones will be delimited. For an antenna that is large compared to the wavelength, if we move away to enclose it within a sphere, we may have already moved too far and find ourselves in the far-field region, missing the details of what happens in the near field and where a boundary between both zones could be defined. Hence, these analytical formulas fail in many cases.

Definitions of Wave Impedance

Instead of using a single formula for all cases, which introduces a high level of uncertainty, a more convenient criterion for separating the near-field and far-field regions is to calculate the so-called wave impedance, which is calculated as the ratio of the electric and magnetic fields. Since fields are vectors, we can compute the ratio between their components. For example, when a wave is vertically polarized, at the wavefront, we consider the vertical component of the electric field, E_v, and the horizontal component of the magnetic field, H_h, omitting components in the direction of propagation (which rapidly diminish with distance from the emission source). We define the wave impedance as Z_w = E_v/H_h. This ratio involves two complex quantities with real and imaginary parts, so the wave impedance has both magnitude and phase. By decomposing the wave at the wavefront into its right-handed circular polarization components, E_R and H_R, and left-handed circular polarization components, E_L and H_L, we can define two complex wave impedances: a right-handed impedance, Z_R = E_R/H_R, and a left-handed impedance, Z_L = E_L/H_L.

Regardless of the chosen definition of wave impedance, it will have the following properties:

• Z_w is a function of the distance from the antenna measured in wavelengths, r/λ, and the observation direction, given by two angles (zenith and azimuth) when using spherical coordinates.

• In any chosen direction, as the distance increases (r >> D and r >> λ), Z_w tends to 377 Ω in free space.

Therefore, in the far-field region, the wave impedance approaches the intrinsic impedance of the medium, which is 377 Ω for free space. For an ideal lossless and isotropic medium, the intrinsic impedance is given by Z_i = √(µ/ε), where µ is the magnetic permeability and ε is the dielectric constant. For vacuum, this value is approximately rounded to 377 Ω, often approximated as 120π Ω for convenience, with three significant digits.

Absolute Wave Impedance

The problem with defining wave impedance in terms of components of the E and H vector fields is that we have more than one definition, as we have just seen, and these definitions depend on the chosen coordinate system or frame of reference. A figure that allows us to identify the field regions should satisfy the following conditions:

• It should be calculated based on observables, i.e., quantities that can be measured in practice.

• It should be independent of the frame of reference, i.e., invariant under a coordinate transformation.

• It should be obtainable for any polarization of the field, even when it is unpolarized, as is the case when uncorrelated fields with random phases are summed.

A simple figure that meets these three requirements is what we will call the absolute wave impedance, which is given by the ratio of the root mean square (rms) values of the E(r) and H(r) vector fields,

Z_w(r) = E_rms(r)/H_rms(r), at each point r in space.

These are observables that are independent of the coordinate system. For example, when transforming from Cartesian to spherical coordinates, we have E_rms = |E| = √(|E_x|² + |E_y|² + |E_z|²) = √(|E_r|² + |E_Θ|² + |E_φ|²), where E_x, E_y, E_z, E_r, E_Θ, E_φ are complex components (if working with peak values, they should be multiplied by 1/√(2) to obtain rms values). The same applies to the rms value of the magnetic field, H_rms = |H|.

In general, E_rms and H_rms are invariant under any coordinate transformation. Therefore, Z_w(r) is defined at every point r in space outside the antenna surface because it is a quantity that can be calculated at any point r based on the measured fields, E_rms(r) and H_rms(r). Since this definition disregards the phase, it is also useful for unpolarized waves. Disregarding the phase of the wave impedance is not an issue since we will need to compare it with a real value, equal to 377 Ω (with zero phase), to determine if we are in the far-field zone.

Wave Matching Coefficient

Analogous to the definition of “return loss” used for transmission lines, if 377 Ω were the characteristic impedance of a line, we can define a coefficient in decibels that measures how well the wave impedance is “matched” to the intrinsic impedance of the medium. We will call this coefficient the Wave Matching Coefficient (WMC), given by

where Z_w = E_rms/H_rms is the absolute wave impedance. We will not use the term “return loss” because in the propagation mechanism we are considering, there is no loss or wave returning by reflection to the source that originated it.

As Z_w approaches 377 Ω, the WMC always increases. In a transmission line, a return loss of 20 dB implies that 99% of the power is transmitted and 1% is reflected. Although we don’t have a reflection mechanism here, we could adopt the same tolerance and consider the limit of WMC = 20 dB as the boundary between the near-field and far-field regions. If this limit proves to be too strict or too lenient for a particular practical application, we are free to choose another boundary according to the acceptable tolerance. From an engineering standpoint, we would recommend placing the boundary between the near-field and far-field regions above WMC = 10 dB. In the examples we will consider next, we will use the 20 dB boundary.

Examples with a 20 dB Boundary

Figure 1(a) shows the absolute wave impedance as a function of distance for an elementary electric dipole and an elementary magnetic dipole, while Figure 1(b) shows the corresponding WMC. The direction along which the distance r/λ varies is perpendicular to the axis of the dipoles, where the far-field reaches its maximum value. In both cases, the 20 dB boundary is practically at r/λ = 0.33 ≈ 1/3. Additionally, we could divide the near-field region into two parts, one below the maximum at r/λ = 0.1 and one above.

Wave Impedance and Wave Matching Coefficient for elementary dipoles. — Fig. 1: (a) Absolute wave impedance for elementary electric and magnetic dipoles as a function of distance along the direction of maximum radiation. (b) The corresponding WMC and the separation between the near-field and far-field zones at a threshold of 20 dB.

Figure 2(a) displays the absolute wave impedance for an elementary electric dipole along a direction at 45° from its axis, where the power density drops 3 dB compared to its maximum value, as well as the curve obtained in the previous Figure 1(a) along the direction at 90° from the dipole’s axis. Figure 2(b) shows the corresponding WMC. In this way, we observe the wave impedance and WMC for the directions that define the radiation maximum and the beamwidth of an elementary dipole.

We can observe that the boundary between the near-field and far-field regions moves away from the dipole when observed from a direction other than that of maximum radiation, and a transition zone opens around r/λ = 1/3.

Fig. 2: (a) Absolute wave impedance for an elementary electric dipole as a function of distance along the direction of maximum radiation and the direction where the power density drops by 3 dB. (b) The corresponding WMC and the separation between the near-field and far-field zones at a threshold of 20 dB. A transition zone is opened.

As an example of an antenna with a size of multiple wavelengths, Figure 3 presents the results for a 7-element Yagi-Uda antenna, optimized to provide maximum front-to-back ratio. Figure 3(a) shows the absolute wave impedance in the direction of maximum radiation, perpendicular to the antenna elements, and in the direction where the maximum power density drops by half (-3 dB) and defines the edge of the beamwidth. Figure 3(b) shows the corresponding WMC curves.

In this case, the 20 dB boundary also shifts to a greater distance when the observation direction is different from the direction of maximum radiation, similar to the elementary dipole. Additionally, the transition zone between the near-field and far-field zones is approximately half a wavelength.

We can see that the wave impedance can reach very high values, so representing the WMC provides a more convenient decibel scale for comparing large and small values.

Fig. 3: (a) Absolute wave impedance for a 7-element Yagi-Uda antenna as a function of distance along the direction of maximum radiation and the direction where the power density drops by 3 dB. (b) The corresponding WMC and the separation between the near-field and far-field zones at a threshold of 20 dB. A transition zone of approximately half a wavelength is opened.

Another interesting example of a long-wavelength antenna is the axial mode helical antenna. Figure 4 shows the results for a left-handed helical antenna with a diameter of 0.3λ, a pitch of 0.22λ, and 10 turns, resulting in a total length of 2.2λ from end to end. The helix reflector, which is necessary for it to operate in axial mode (with maximum radiation along the helix axis), has a diameter of 0.95λ.

Figure 4(a) shows the wave impedance along the axis of the helix, from the base, passing through the interior of the helix until it exits. It also shows the wave impedance along a direction corresponding to the -3 dB beamwidth edge. Figure 4(b) shows the corresponding WMC results. Here, too, a displacement of the boundary between the near-field and far-field regions can be observed. However, in this case, the displacement is opposite to the previous cases since the field inside the helix is always “close.” We can see that as we traverse the interior of the helix along its axis, the boundary between the near and far-field zones begins at r/λ = 2.3, which is just a distance of 0.1λ above the top of the helix located at 2.2λ. This is logical since the interior of the helix behaves like a waveguide.

Fig. 4: (a) Absolute wave impedance for a helical antenna in axial mode as a function of distance along the helix axis, passing through its interior, and the direction where the power density drops by 3 dB. (b) The corresponding WMC and the separation between the near-field and far-field zones at a threshold of 20 dB. The near-field zones inside and outside the helix are indicated.

From these examples, we can deduce that the three-dimensional boundary between the near-field and far-field regions does not have a spherical or regular shape around antennas of a size comparable to or larger than the wavelength. The absolute wave impedance, and especially the WMC, allows us to determine where the far-field region begins in each direction of space. We could then choose the farthest boundary resulting from this analysis as the radius of a limiting sphere from which the far-field region begins in all directions.

Conclusions

In this article, we have presented the concepts of absolute wave impedance and Wave Matching Coefficient (WMC) as alternatives for determining a practical boundary between the near and far field regions of an antenna. The WMC, in particular, enables a better visualization of the evolving wave propagation as a function of distance from the originating antenna, providing a decibel scale that enhances the observation of significant variations in wave impedance. As a general guideline, we have observed that a WMC value of 20 dB defines an appropriate threshold for separating the near and far field zones.

Through examples involving elementary antennas and antennas of significant size relative to the wavelength, we have observed that the 20 dB boundary remains at a distance of λ/3 for elementary antennas. However, for antennas of comparable or larger size than the wavelength, the boundary assumes an irregular and non-spherical shape. In this particular case, the radius of a spherical boundary separating the near-field and far-field regions around the antenna will be determined by the maximum distance observed in all angular directions of space where the WMC reaches the 20 dB limit.

AN-SOF 8.20 Passes IEC Validation

The latest version 8.20 of the AN-SOF calculation engine has successfully completed validation for accuracy in accordance with the standard IEC FDIS 62232.

This standard outlines guidelines for calculating radio-frequency field strength and specific absorption rate (SAR) in the vicinity of radiocommunication base stations (RBS) to assess the potential human exposure.

Specifically, the validation of the AN-SOF calculation engine was conducted for the “Antenna with Dipole Radiators” in the aforementioned standard. This significant achievement enhances the reliability of the AN-SOF Antenna Simulator.

Read more >

, antenna arrays, dipole, validation

2May, 2023

Adding Elevated Radials Quickly

24Apr, 2023

Upgrade to AN-SOF 8.20 – Unleash Your Potential

AN-SOF has released its latest version, 8.20, which brings significant enhancements to improve the software’s accessibility and performance.

The new release builds on the improvements made in version 8, with a focus on two key areas. Firstly, it provides an intuitive way to access data, making it easier than ever before to interact with graphs and results. Secondly, the calculation engine has been improved, ensuring greater accuracy and reliability. In addition, math libraries are now embedded in the software, eliminating the need to install external packages.

With AN-SOF version 8.20, users can expect a faster, more powerful, and more accessible experience.

Download FREE Trial >

2Mar, 2023

Modeling a J-Fed 5-Element Collinear Antenna for the 2 m Band

If you’re looking for a high-performing omnidirectional antenna, consider this design. It boasts 5 collinear radiant elements that are connected by phasing coils. The feed point is conveniently located at the base of the antenna on a J dipole. By adjusting the position of the feed point along the J, you can minimize the SWR. At the top end of the antenna, you’ll find a small loop that serves as a tie point, measuring just 1/2″ in diameter. The total length of the antenna is 295″. Each coil features 32 turns and has a diameter of 5/8″.

To accurately model this design, we should use simulation software that is capable of modeling curved wire segments and small, closely-spaced wires. With AN-SOF, you can use the “Helix” object to perfectly model each coil. By using only one segment per turn, this model demonstrates the efficiency of AN-SOF in simulating complex designs.

, antenna arrays, omnidirectional

Interactive User Guide for AN-SOF Antenna Simulation Software.

22Feb, 2023

New Interactive User Guide

16Feb, 2023

AN-SOF 8: Elevating Antenna Simulation to the Next Level

✅ New Plots tab where we can quickly see the input impedance, VSWR, gain, Front-to-Rear, and Front-to-Back ratios as a function of frequency, with various visualization controls (grids, points, markers, etc.).

✅ The different parts of tapered wires are identified with alternating colors to better distinguish the wires of which they are composed.

✅ Click on a column header in the Results tab to display a plot immediately.

✅ New 3D Rotation button on the toolbar to easily rotate the view by moving the mouse.

✅ Combo-boxes now have “memory”. Select the frequency or angles to display polar diagrams and the next time you do so the same values will be pre-loaded.

✅ Users who use the comma as the decimal symbol can now import NEC files that use the period as the decimal separator. Go to Tools > Preferences > Options and check the option “The comma is set as the decimal symbol”.

✅ New Preferences window in AN-Smith to change the display of graphics in the Smith chart (line width, fonts, background, points).

💡 TIP 1: Double-click on the AN-SOF or AN-3D Pattern workspace to center the view in the window.

💡 TIP 2: Check “Show Points” in the Preferences window of AN-Polar to see the points on the radiation pattern lobes.

💡 TIP 3: Check “Equal Scales in 2 Plots” in the Preferences window of AN-XY Chart to display the left and right axes with the same scale.

Enjoy it!

Simulating a multiband dipole with AN-SOF Antenna Modeling Software.

2Feb, 2023

Modeling a Multiband Dipole

Modeling a Loop on Ground (LoG) Antenna with AN-SOF.

11Jan, 2023

A Cardioid Small Loop

The so-called Loop on Ground (LoG) is a small loop antenna with a cardioid-shaped radiation pattern in the horizontal plane, used for reception.
The loop has a 110 Ohm resistor connected to its top, while the antenna terminals are located at the bottom. One of the terminals is connected to ground by a vertical wire, forming a monopole. This is the secret to getting this antenna, despite being small, to be directional.
The image below shows the radiation patterns obtained with and without grounding.

Frequency: 4.5 MHz
Loop diameter: 1 m
Height above ground: 2 m (average real ground)

The segmentation used in the Conformal Method of Moments is observed over the antenna. Very few segments are needed because it is a small antenna in terms of the wavelength.

, directional, loop

Simulating a Log-Periodic antenna with AN-SOF.

31Dec, 2022

Log-Periodic Christmas Tree

At Golden Engineering we are passionate about antenna simulation. On this last day of the year we want to give you our Log-Periodic Christmas Tree made with AN-SOF:

We thank all our clients, users and people who collaborate so that the AN-SOF Antenna Simulator project continues to grow day by day.

Happy New Year!

, antenna arrays, broadband, directional

REQUEST AN-SOF 7.90 TRIAL VERSION >

12Dec, 2022

New Release: AN-SOF 7.90

This version of AN-SOF has new functions and options:

ARRL-style scale in polar plots. Radiation pattern slices in decibels can be displayed on the classic ARRL log scale. This facilitates the comparison between the results obtained from AN-SOF and data published in magazines and in the antenna literature.
Front-to-Rear (worst-case) and Front-to-Back (180-degree) ratios are indicated on polar plots.
Export radiation patterns in MSI Planet format. See how here >.
Improved Preferences window in the AN-XY Chart app, where we can set scales, units, line thickness, points, marks, and grids on rectangular charts.
Visualization of the wire segments in the workspace. Check the “Show Segments” option in the Preferences window to see the segments.

Tip: double click on table items to instantly display plots.

Enjoy AN-SOF!

Modeling a magnetic loop antenna with AN-SOF.

1Dec, 2022

Magnetic loop for 3.5, 7, 14, 21 and 29 MHz

This small transmitting loop antenna is 1 meter high above average ground, so the radiation pattern is not donut-shaped as expected for a small loop in free space. The value of the tuning capacitor is indicated for each resonance frequency.

Large loop: 70 cm in diameter, RG-8 cable.

Small loop: 15 cm in diameter, RG-6 cable. Inductive coupling between the feedline and the large loop, spacing of 2 cm.

The color scale on the loops indicates the current flowing for a reference voltage of 1 V.

Download the project files from this link >.

Go to AN-SOF main menu > Run > Run Bulk Simulation and select the five “.nec” files to run the calculations automatically. You can do it with the trial version of AN-SOF.

, loop, multiband, omnidirectional

Modeling a Quadrifilar Helix (QFH) antenna with AN-SOF.

22Nov, 2022

QFH Antenna for NOAA Satellite Reception

This Quadrifilar Helix (QFH) antenna, also known as QHA, can be used for signal reception from NOAA satellites. These are omnidirectional antennas made up of 4 wires with a helical shape. This design is about 0.14λ in diameter and the length of each helix is 0.4λ. It resonates at 137.5 MHz and has a bandwidth of 6% (SWR < 2). The purpose of the helices is to block surrounding interference.

In free space, the radiation pattern actually points downward when the coaxial cable (the source in the simulation) is connected to the top of the antenna. However, when a real ground plane is added and the antenna is placed 5 meters high, multiple lobes and a more omnidirectional pattern are obtained, as expected.

, helix, omnidirectional

14Nov, 2022

145 MHz Moxon Antenna

Modeling a Biquad UHF antenna with AN-SOF.

7Nov, 2022

Biquad UHF Antenna Array

This 4-element biquad array resonates at 434 MHz. The wires that connect the driven element to the reflector work as a two-wire transmission line that allows us to obtain an input impedance of 50 + j0 Ohm.

It may be noticed that the polar plots are on a log scale. ARRL-style log scaling is coming in the December release of AN-SOF!

Learn more >

, antenna arrays, directional, quad

24Oct, 2022

Broadband Directional Antenna

New version of Antenna Simulation Software: AN-SOF 7.8.

10Oct, 2022

AN-SOF 7.8 is ready!

Quickly view input impedance, VSWR, directivity, gain and efficiency in the new Results tab.
Click the Export Results button on the toolbar to export this data to a spreadsheet.
The wavelength is now displayed in the Frequency panel while entering the operating frequency.
Automatically close all charts when exiting AN-SOF or keep them open to analyze the plots. Go to Tools > Preferences > Options and check “Close charts when exiting AN-SOF”.
A great strength of AN-SOF is the documentation. Explore the new User Guide here >.
Coming soon: our online Knowledge Base!

User Guide for AN-SOF Antenna Simulator.

4Oct, 2022

New AN-SOF User Guide

Simple antenna models designed with the trial version of AN-SOF.

27Sep, 2022

5 Examples with less than 50 Segments

17Sep, 2022

An HF Skeleton Slot Antenna

It is an array of two tightly coupled loops with a bi-directional pattern. Both loops are linked to share a single feed point. This antenna can operate in the 14 to 28 MHz bands with the appropriate impedance matching. It is self-resonant when the perimeter of each loop is around one wavelength. In this example, each loop is 3 x 4.5 m and the resonant frequency is 19.8 MHz.

, directional, loop

1Sep, 2022

17 m Band Spider Delta Loop

These are compact, lightweight antennas that can be used for DX applications. This 2-element array is the simplest we can build to get a directional antenna using delta loops. It is practically resonant with 50 Ohm of input impedance near the band center. This is an example where we need to enable the Exact Kernel option in AN-SOF since we have sharp angles between wires.

, directional, loop

New version of Antenna Simulation Software: AN-SOF 7.20

14Jun, 2022

AN-SOF 7.20 is ready!

9May, 2022

Moxon-Yagi Dual Band VHF/UHF Satellite Antenna

New release of Antenna Simulation Software: AN-SOF 7.10

12Apr, 2022

New Release :: AN-SOF 7.10 ::

AN-SOF 7.10 is now available for download!

Access the input impedance and VSWR easily by going to the Main menu > Results. This avoids selecting the segment where the source is located to access the input impedance.

NEC designs of antennas over real ground can now be imported directly into AN-SOF by means of the GN command. The complete real ground description can also be exported to a NEC file.

The GN command can also be exported to a Scilab .sce file to develop scripts and run bulk simulations.

Modeling a 2-Element Quad Array with AN-SOF.

22Mar, 2022

Script for Modeling 2-Element Quad Array

2-element quad antennas are very popular due to their compact size and gain similar to a more element Yagi. In addition, they can be designed to obtain an input impedance of 50 Ohm.

This design can operate at 27.5 MHz. We have added a script that allows us to plot the gain and front-to-back ratio as a function of element spacing. See this video >.

We can see that both cannot be maximized at the same time, but it is preferable to choose the maximum F/B since the gain changes relatively little.

To create the Scilab script, we started from a basic design in AN-SOF and then exported it as a *.sce file.

Download Model >

Download Script >

, antenna arrays, directional, quad

Modeling an 80 m Spiral Loop with AN-SOF.

9Mar, 2022

An 80 meters DX Antenna: A Spiral Loop

A half-wave dipole would have a length of 40 meters in this band (3.75 MHz), difficult to install at home due to lack of space. Not to mention the complaints from our neighbors.

A spiral loop is attractive for its small size and relative ease of tuning because it is basically an inductor to which a variable capacitor is connected at the feed point to achieve resonance. However, the radiation resistance is extremely small, on the order of milliohms and therefore the efficiency is very low.

Unfortunately any small loss severely affects the antenna efficiency, such as losses in the capacitor, wires, interconnections, solder joints, surrounding objects, ground plane, to name just a few. In fact, this antenna can be tuned and get a wide bandwidth thanks to all the losses. The maximum radiation occurs upwards when the antenna is installed vertical to the ground plane, so some have suggested installing it horizontally. We should emphasize, however, that it is a popular design due to its ease of installation and small size, but we must be careful because high voltages can be expected, especially in the tuning capacitor.

This AN-SOF model consists of a frame of 50 cm on each side (0.00625 of the wavelength) with 7 turns of wire. This is another example where we need to simulate with very short wire segments, very close to each other and bent at right angles.

In these results we can see the effect on the input resistance of adding losses in the ground plane and surrounding objects, such as a wall,

Perfect ground: 4 milliohm
“Cities industrial poor” ground: 1.3 Ohm
“Cities industrial poor” ground + wall: 49 Ohm

This design can be easily transformed into a multi-band antenna by shorting turns of wire, much like a variable inductor, to make it operate on the 40, 30 and 20 meter bands.

, loop, omnidirectional

25Feb, 2022

ISM 433MHz Helical Antenna

Small helical antennas for the 433 MHz ISM band are a good example where we need advanced software that has the ability to model:

curved wires with exact description of the helix contour

very close wires, spaced a fraction of the wire radius

horizontal wires almost touching the ground plane

bent wires at right angles or less

short segments, below 0.001 wavelength

thick wires by means of Exact Kernel instead of thin-wire approximation

AN-SOF includes all these features.

In this example, a perfect ground plane is used to get the input impedance: 48 Ohm, very close to the 50 Ohm of the antenna datasheet. We must subtract 3 dBi from the gain to obtain the gain in free space. It is a simple model, but it coincides very well with reality.

, helix, omnidirectional

20Feb, 2022

Array of Snowflake Quads

Nathan Cohen in the US fractalized the quad loop based on the Minkowski square and invented an array of two elements. The biggest advantage of fractal antennas is that we get a wide bandwidth with a small size.

This simulation shows that we can almost double the bandwidth with a 3-element array. It has a reflector, a driven element, and a director. These are the results for the 20 m band (~ 14 MHz),

Quad size ~ 290 x 290 cm (0.14 x 0.14 of a wavelength)

Element spacing ~ 280 cm

450 KHz bandwidth (VSWR < 2) around 14.5 MHz

6 dBi gain

10 dB F/B

80° beamwidth

Vertical polarization

It has less gain than could be achieved with a 3-element Yagi, but it has a relatively large bandwidth and is a very compact antenna. It does not need a matching circuit and its impedance is 50 Ohm at resonance, so it could be fed directly through a 50 Ohm coax.

, antenna arrays, directional, fractal, quad

New release of Antenna Simulation Software: AN-SOF 7.0

14Feb, 2022

AN-SOF 7.0 is Here!

Run bulk simulations and process multiple input files with just one click. We have chosen the NEC format for the input files as it is a standard adopted by many users. Forget about running the simulations one by one, run them all at once.

Import a single input file as a bulk simulation and get all the output data in one step. All computed parameters are saved as CSV files (power budget, gain, input impedance, VSWR, far and near fields, etc.).

Export AN-SOF designs to Scilab format (*.sce files) and easily develop scripts that generate multiple descriptions with variable geometric parameters.

And last but not least, in this link > you will find the model of a Yagi-Uda antenna with variable element spacing. Follow the instructions therein and run the scripts to get the gain of a 3-element Yagi antenna as a function of the element spacing.

Enjoy!

Plotting Level Curves with AN-SOF and Scilab.

17Dec, 2021

Scilab Script for Plotting Level Curves

New release of Antenna Simulation Software: AN-SOF 6.40

29Nov, 2021

New Release :: AN-SOF 6.40 ::

We can highlight the following improvements:

Tabular input of linear wires as well as sources and loads. AN-SOF has many tools to make drawing wires an easier task. However, for those who prefer to enter wires in spreadsheet format we have added a tabular entry.

List of recently open projects in the File menu. Access the last projects you have been working on much faster going to main menu > File > List of recently open projects.

Zoom in and out by rotating the mouse wheel (or using the touchpad in a laptop with two fingers). You can continue to zoom by first clicking on the magnifying glass icon and then moving the mouse, but using the mouse wheel is more direct.

10Oct, 2021

How to Export Data and Plots

Did you know that AN-SOF data can be exported to Excel?

It is important to be able to export data so we can write reports and share our progress with colleagues. Simulation results can be exported to CSV (Comma Separated Values) files, where data are saved in tabular format. CSV files can then be opened with a spreadsheet program, such as Microsoft Excel or Google Sheets.

We will find the “Export” button next to the following tables:

Select a wire in AN-SOF, go to Main menu > Results > List Currents. Move the slider to choose a segment and click on the Current on Segment button or Input List button (it is enabled if there is a source there). A table of current/input impedance vs. frequency will be shown.
Go to Main menu > Results > Power Budget/RCS to display the table of input power, radiated power, directivity, gain and efficiency.
The far-field can be tabulated as a function of the direction (far-field pattern) for a chosen frequency or as a function of frequency for a selected direction (theta,phi). Go to Main menu > Results > List Far-Field Pattern for the first option or Results > List Far-Field Spectrum for the second one.
Regarding the near field, we can say the same as in 3). Go to Main menu > Results > List Near E-Field (H-Field) Pattern or Results > List Near E-Field (H-Field) Spectrum.

Regarding plots, after plotting some result in AN-XY Chart, AN-Polar or AN-Smith, go to the main menu of any of these applications > File > Export to export a CSV file.

In addition, there is a Copy Plot (Ctrl+C) command in the Edit menu of these applications. This option is called Copy Workspace in the File menu of AN-SOF. It sends the graphic to the clipboard as a bitmap, which can then be pasted elsewhere (Ctrl+V), e.g. in Microsoft Word, Power Point or their Google-equivalents, in an image editor, in an email body, etc.

New release of Antenna Simulation Software: AN-SOF 6.20

20Sep, 2021

New Release :: AN-SOF 6.20 ::

Radiation patterns plotted in AN-Polar can now be exported as *.ant files. The *.ant format can then be imported into the Radio Mobile propagation software. See the format description here: http://www.g3tvu.co.uk/Antenna_Plots.htm. Versions 1 and 3 are implemented in AN-SOF 6.20.

See how to export radiation patterns from AN-SOF to Radio Mobile here: https://antennasimulator.com/downloadpro/Export_from_AN-SOF_to_Radio_Mobile.pdf. For 1 slice polar plot, an azimuth pattern must be chosen (theta = const). For 2 slices polar plot, slice 1 must be azimuthal (theta = const) and slice 2 must be zenithal (phi = const). The Full 3D option must be selected in AN-SOF Configure tab > Far-Field panel.

Exportation of linear wires in DXF format has been added. DXF files can then be read by Autodesk viewer at https://www.autodesk.com/viewers/all-viewers/compare

Detecting errors in a model with AN-SOF.

6Sep, 2021

How to Detect Errors in a Model

To discover errors in the wire structure we can use the following functions in the AN-SOF main menu > Tools option:

Check Individual Wires: It will be checked that the length of each segment and its radius are short compared to the wavelength. If the Exact Kernel is not set in Setup tab > Settings, then the segment diameter/length ratio will also be checked (the so-called thin-wire ratio).
Check Wire Spacing: It will be checked that each wire does not overlap with the others. Two wires can be as close as their radii allow, without overlapping.
Delete Duplicate Wires: It will be checked that each wire is unique, in other words, that an identical wire has not been superimposed on it. Duplicate wires will be automatically deleted.

Those wires in error will be highlighted in red and those in warning in yellow.

Keep in mind that we can still run a simulation with wires in warning if we check the validity of the model using an Average Gain Test (AGT). On the other hand, at a point where several wires are connected, slight overlaps may occur that do not generate errors in the results since Kirchhoff’s current law is fulfilled there.

Adjusting the Color Bar in a 3D Radiation Pattern Plot.

20Aug, 2021

Adjusting the Color Bar in AN-3D Pattern

It is important to have control over the scales of the graphs for a better presentation and interpretation of the results. We can adjust the maximum and minimum values of the color bar in AN-3D Pattern to obtain increments in multiples of 5 or the value we want.

Go to the AN-3D Pattern main menu > Edit > Preferences and set the Max and Min values of the color scale.

12Aug, 2021

Setting the Radiation Pattern Center

From the far field point of view, the whole structure of an antenna and its surroundings is reduced to a single point at the origin (X,Y,Z) = (0,0,0). So the standard practice of superimposing the 3D radiation pattern to the antenna structure is just a means to facilitate the interpretation of the directional characteristics of an antenna.

For this reason, you can move the phase origin of the 3D radiation pattern to the desired point in order to get a better view of the antenna orientation versus its radiation pattern. Go to the Setup tab > Far Field > Origin and set the X0, Y0, Z0 coordinates of the radiation pattern center (see Section “4.3 Far-Fields” in AN-SOF user’s guide).

11Aug, 2021

How to Merge Projects

Wires can be imported into AN-SOF from another AN-SOF project, so wire structures of different projects can be merged in a single project.

When a project is saved, a file having extension .wre will also be saved. This file contains the geometrical description of the wires. To import wires to a project, go to File menu > Import Wires > AN-SOF Format and just find and select the .wre file that you want to import.

For instance, this feature allows us to analyze the electromagnetic response of an antenna and its supporting structure separately, and then to combine them in a new project to analyze the response of the whole structure.

11Aug, 2021

On the Modeling of Radio Masts

Radiating towers or radio masts can be modeled in AN-SOF with a high degree of detail, as shown in this figure. Since we already know the omnidirectional shape of the radiation pattern, what interests us is to calculate electric field values at ground level for a given input power. Go to Setup tab > Near Field panel and set the desired coordinate system (Cartesian or Cylindrical: Z = 0, Spherical: theta = 90°). Go to the Excitation panel to set the input power (it is customary to set 1,000 W). To increase the conductivity of the soil and therefore the radiation efficiency, we can use a radial wire ground screen.

Regarding the feeding point, we can put a source at the position of the base insulator if the feedline will be connected there in the real life antenna. In this way, we will obtain the input impedance of the antenna, which we can then post-process (e.g. tuning house + transmission line coming from the transmitter).

To speed up the simulation, we could use a simplified model, which consists of a single vertical wire with a triangular cross section. The radiation pattern will be the same as before, but we must be careful at the feeding point.

The base of the tower in the detailed model forms a short transmission line to the source position at the tower center. In the simplified model, we can offset the source from the center a distance equal to the half width of the tower to simulate the short transmission line effect.

, monopole, omnidirectional, tips & tricks

H-field calculation option in the AN-SOF Preferences window.

10Aug, 2021

H-Field Option in Preferences

We see that most of the time we are interested in calculating only the E-field in antenna projects when we are talking about the near field. For this reason, we have added an option to enable or disable the automatic calculation of the H-field when we click on the “Run ALL” (F10) button. Go to Tools > Preferences > Options tab.

If we are only interested in the near field and we don’t want to waste time calculating the far field, we can click on the “Run Currents and Near-Field” (F12) button.

In the “Simulate” menu we also have the options: “Run Far-Field”, “Run Near E-Field” and “Run Near H-Field” to calculate each field separately.

9Aug, 2021

How to Speed Up a Simulation

There is always a trade-off between speed and accuracy. However, we often need to prioritize speed in the first simulations of an antenna model. Here are some tips to speed up the calculations.

Start with the minimum number of segments (10 segments per wavelength). AN-SOF sets the minimum number if you write “0” (zero) as the number of segments on any wire. In a wire grid, use one segment per cell side if the electrical size of each cell is < 10% of the wavelength.
Set the Quadrature Tolerance between 5% and 10% in Setup tab > Settings panel. This parameter only has an appreciable effect when there are parallel wires very close to each other (about two wire radii apart).
Go to Setup tab > Settings and set Interaction Distance = 0. It also only affects parallel wires that are very close to each other.
To calculate the gain, directivity and efficiency usually it is enough to set a spatial resolution of 5 or 10 deg in the far-field. Setup tab > Far-Field panel > Theta Step = 5 and Phi Step = 10 deg.
Last but not least, just calculate what you really need. The “Run ALL” option will calculate everything, currents, far and near fields. If you only need the currents and the far-field, click on “Run Currents and Far-Field (F11)”. If you are only interested in the input impedance, go to Run > Run Currents in the main menu.

The example in this figure shows that we can run a simulation more than 3 times faster, especially by setting the Interaction Distance to zero. You will find the “car.emm” project in the Examples folder which is installed together with AN-SOF.