This article navigates the intricacies of Skeleton Slot antennas, exploring their sensitivity to geometric parameters and the transformative impact of a simulation-driven methodology. The Skeleton Slot is treated as an array of two loop antennas with a common feed point. We delve into the balance of loop perimeters, conductor radii, and aspect ratios, unraveling their influence on output parameters such as input impedance, VSWR, and gain. We present a script-driven approach to optimize designs, empowering engineers and enthusiasts to craft high-performance Skeleton Slot antennas. Bridging theory and application, the article showcases practical insights, making it an essential resource for anyone seeking to elevate their radio frequency design projects.
Table of Contents
- Geometry of Skeleton Slot and Loop Antennas
- Script for Varying the Loop Aspect Ratio
- Input Impedance, VSWR, and Gain vs. Aspect Ratio
- Sensitivity to the Loop Perimeter Around One Wavelength
- Effect of Changing the Conductor Radius
- Simulation-Driven Design of a Skeleton Slot Antenna
Bill Sykes (call sign G2HCG) is acknowledged as the innovator behind the Skeleton Slot antenna, having successfully deployed it in VHF bands. The inherently versatile Skeleton Slot principle extends its utility to HF communication bands by scaling dimensions based on wavelength, with the physical antenna dimensions remaining practical within the 14-28 MHz bands. Noteworthy advantages of this design include its lightweight nature, ease of construction, low-angle radiation, bi-directional directivity, and the convenience of mounting it as a simple metal framework without the need for insulation.
The nomenclature “Skeleton Slot” is derived from the slot antenna concept. This aperture antenna is crafted by cutting a rectangular hole in a conducting sheet, essentially serving as a “photographic negative” of a dipole, where the slot functions as the radiating element. Reducing the metal sheet until it transforms into a rectangular wire frame results in the formation of the “skeleton slot.”
In our previous article, “A Closer Look at the HF Skeleton Slot Antenna,” we introduced a Skeleton model in AN-SOF and presented the results for the 15m (20 MHz) band. Expanding upon that analysis, this article delves into a comprehensive discussion of the skeleton slot from a general perspective, supported by the theory of loop antennas. This approach complements the insights provided by the inventor in the January 1955 issue of The Short Wave Magazine in the article titled “The Skeleton Slot Aerial System” (Vol. XII, No. 11, pp. 594-598). In that article, the author elucidates the antenna as an array of two closely positioned dipoles. Furthermore, we offer dimensioning guidelines for experimenters keen on venturing into antenna construction.
Geometry of Skeleton Slot and Loop Antennas
In Figure 1, a schematic representation of the Skeleton Slot antenna is presented, highlighting key dimensions:
- L: Length of each loop.
- w: Width of the antenna.
- a: Wire radius.
- p = 2(L + w): Loop perimeter.
- r = L/w: Loop aspect ratio.
The skeleton slot, depicted in Figure 1, functions as a vertical antenna that can be conceptualized as an array comprising two identical, closely coupled loops—a top loop and a bottom loop. These loops share a common feed point located at the antenna’s center, where the feeding transmission line is connected.
In adherence to loop theory, when the loop contour spans approximately half a wavelength, it exhibits an input impedance transitioning from inductive to capacitive. This shift is characterized by high resistance and reactance values, indicative of a resonance akin to that observed in a parallel RLC circuit. Referencing the validation article “Input Impedance and Directivity of Large Circular Loops”, specifically Figure 2, illustrates the input impedance variation concerning the loop circumference measured in wavelengths, C/λ (see Figure 2 below). As the loop circumference approaches one wavelength, the capacitive (negative) reactance decreases in absolute value, reaching resonance similar to a series RLC circuit when the reactance approaches zero. Consequently, the resistance assumes manageable values in practice, approximately around 100 Ohms. The “useful zone” of the loop in practice is identified when C/λ ≈ 1, as shown in Figure 2.
While Figure 2 refers to circular loops, the analogous behavior is applicable to rectangular loops as well. Therefore, the practical utility of the loop is realized when its perimeter, denoted as ‘p,’ approaches one wavelength (p/λ ≈ 1).
A further observation drawn from loops with circumferences comparable to the wavelength is the pronounced sensitivity of reactance to variations in the wire radius. This sensitivity manifests in a logarithmic manner, specifically proportional to ln(C/a), where ‘a’ denotes the wire radius.
Given its configuration, as previously mentioned, the Skeleton Slot antenna can be viewed as comprising two tightly coupled rectangular loops. Consequently, we can anticipate a behavior analogous to that described for loops in general.
Maintaining a constant loop aspect ratio (r = L/w) and conducting numerous calculations while varying the loop perimeter (p = 2(L + w)), we observe that the Skeleton Slot resonates when the loop perimeter is approximately one wavelength (p ≈ λ), aligning with expectations for a single loop. However, it’s crucial to note that this perimeter isn’t precisely equal to one wavelength; its value fluctuates based on the aspect ratio (L/w) and the wire radius compared to the loop perimeter (a/p). While the specific results of these calculations fall beyond the scope of this article, we will concentrate on the behavior of the skeleton slot when the perimeter of each loop approximates one wavelength. In this condition, the antenna approaches self-resonance, obviating the necessity for an impedance matching network at the feed point.
In Sykes’ article, the author employs the aspect ratio of the Skeleton Slot, expressed as 2L/w = 2r, rather than that of each individual loop. Through multiple measurements, the conditions for achieving a self-resonant antenna are outlined as follows:
- An optimal aspect ratio of 3:1, i.e., 2r = 3, leading to r = 3/2 = 1.5 based on our definition.
- The total length of the skeleton must be 2L = 0.56λ, so the loop length is L = 0.28λ.
- The ratio of width to conductor diameter must be 32:1, denoted as w/(2a) = 32.
Given L = 0.28λ and r = L/w = 1.5, the resulting perimeter is calculated as p = 2 (0.28λ + 0.28λ/1.5) = 0.93λ. This closely aligns with our simulation calculations, indicating resonance when the loop perimeter approximates one wavelength. However, it’s essential to note that this resonance condition varies with the ratio of perimeter to conductor radius, denoted as p/a, rather than the ratio w/(2a). Subsequent results, presented in the following sections, illustrate that a thicker conductor necessitates an increased loop perimeter for the antenna to be self-resonant with a given aspect ratio. Conversely, a thinner conductor requires a decreased loop perimeter for the same resonant condition.
Script for Varying the Loop Aspect Ratio
A pivotal inquiry in Skeleton Slot antenna design revolves around determining the optimal aspect ratio. Is there a specific aspect ratio that outperforms others? This section aims to delve into this question, with the pursuit of an “optimal” point focusing on achieving a self-resonant antenna, thereby obviating the need for a matching network. In Sykes’ investigation, a conductor with a radius of 4.76mm (rounded up to 5mm in our study) was employed, corresponding to a 3/16″ radius (3/8″ diameter).
For our exploration, we maintain a fixed conductor radius of 5mm, and we ensure that the perimeter of each loop remains close to one wavelength, as previously discussed. Simulations conducted using AN-SOF are set at a frequency of 20 MHz (15-meter band). Importantly, the conclusions drawn from these simulations hold true for any frequency band, contingent upon scaling the antenna dimensions proportionally with the wavelength. Naturally, the resulting physical dimensions at a given frequency must be practical for constructing the antenna in practice.
To perform calculations with varying geometric parameters, we can leverage the “Run Bulk Simulation” function in AN-SOF in conjunction with a script in Scilab. For those unfamiliar with script programming, a comprehensive tutorial on antenna-related scripts is available in the article “Element Spacing Simulation Script for Yagi-Uda Antennas”, specifically focusing on Yagis with variable element spacing.
Description of Script Elements
Below, the script is provided to generate multiple files in .nec format, where the loop aspect ratio, L/w, is systematically altered while maintaining a fixed perimeter, p. Through multiple simulations, we have determined that the “optimal” p value, rendering the antenna self-resonant for a broad range of L/w ratios, is p = 14.8m at 20 MHz, corresponding to p = 0.99λ.
When the perimeter p is held constant and the loop aspect ratio is varied (r = L/w), the antenna dimensions can be calculated using the following formulas:
- w = 0.5 p/(r+1)
- L = 0.5 p r/(r+1)
To expedite the task, consider creating a Skeleton Slot antenna model in AN-SOF or downloading the model provided in this article. Then, in AN-SOF, navigate to the File menu, select “Export Wires,” choose the file format “.sce,” and save the file. Subsequently, open the .sce file with Scilab and make the modifications as illustrated below:
// Script for AN-SOF Professional // Skeleton Slot Antenna with varying aspect ratio r_min = 1.0; // Min loop aspect ratio r_max = 2.5; // Max loop aspect ratio n = 20; // Number of intervals between r_min and r_max f = 20.0; // Frequency in MHz k = 0.987; // Factor for loop perimeter p = k*299.8/f; // Loop perimeter [m] (299.8/f = wavelength at f MHz) radius = 5; // Wire radius in [mm] S = 11; // Number of segments per wire (it must be odd) for i = 0:n, r = r_min + i*(r_max-r_min)/n; // Loop aspect ratio w = 0.5*p/(r+1); // Loop width L = r*w; // Loop length (total length of skeleton slot = 2L) antenna = [ CM('Skeleton Slot Antenna') CM('Loop length-to-width ratio = ' + string(r)) GW(1, S, 0, -0.5*w, 0, 0, 0.5*w, 0, radius*1e-3) GW(2, S, 0, 0.5*w, -L, 0, -0.5*w, -L, radius*1e-3) GW(3, S, 0, -0.5*w, L, 0, -0.5*w, 0, radius*1e-3) GW(4, S, 0, 0.5*w, 0, 0, 0.5*w, L, radius*1e-3) GW(5, S, 0, -0.5*w, -L, 0, -0.5*w, 0, radius*1e-3) GW(6, S, 0, 0.5*w, 0, 0, 0.5*w, -L, radius*1e-3) GW(7, S, 0, 0.5*w, L, 0, -0.5*w, L, radius*1e-3) GE(0) FR(0, 1, f, 0.0) EX(0, 1, (S+1)/2, 1.4142136, 0) EK() ]; mputl(antenna,'C:/AN-SOF/Skeleton_Ratio' + string(i) + '.nec'); end
This simple script streamlines the process, allowing for efficient exploration of the Skeleton Slot antenna’s behavior under varying loop aspect ratios. This script comprises two main elements:
1. Definition of Constants:
– Fixed values for the extremes of the loop aspect ratio variation range.
– Number of intervals ‘n’ to be calculated (with ‘n+1’ discrete points).
– Loop perimeter ‘p’ and wire radius.
– Numerically adjusted perimeter ‘p’ within 3 significant digits at p = 0.987λ.
2. ‘For’ Loop:
– The script contains a “for” loop where the “antenna” matrix is defined. Each row contains commands (CM, GW, GE, FR, EX, EK) used to describe an antenna in NEC format.
– Each generated .nec file (n+1 files) is named “Skeleton_Ratioi.nec” with i = 0, 1, 2, …, n.
This script is complemented by a second script that reads the results from CSV files and represents them graphically in plots. Additionally, there is a third script that contains the functions associated with NEC commands. To download these three scripts, click on the button provided above.
Running the Scripts in Combination with AN-SOF
Here are the steps to run this script, along with the one displaying graphs with results, in combination with AN-SOF:
1. Download the .zip file containing the three necessary scripts: NECcommands.sce, SkeletonSlot.sce, and SkeletonSlotResults.sce.
2. Unzip the file and save the scripts in a folder to run them from Scilab.
3. Start Scilab and open the scripts.
4. Run NECcommands.sce, which contains functions that write NEC commands.
5. Create a folder C:\AN-SOF and run SkeletonSlot.sce. The n+1 “.nec” files will be saved in this folder.
6. In AN-SOF, go to the menu Run > Run Bulk Simulation, navigate to the C:\AN-SOF folder, and select all the generated .nec files (you can press Ctrl + A). AN-SOF will calculate them one by one, saving the corresponding results in CSV files.
7. Return to Scilab and run the SkeletonSlotResults.sce script. Three graphs will be displayed: the gain, the input impedance, and the VSWR as a function of the loop aspect ratio.
With these scripts, you can obtain results that will be analyzed in the subsequent sections for the input impedance, VSWR, and antenna gain as a function of the loop aspect ratio.
Input Impedance, VSWR, and Gain vs. Aspect Ratio
In Figure 3, the Skeleton Slot input impedance (Rin + jXin) is depicted as a function of the loop aspect ratio, L/w. It’s crucial to note that the loop perimeter remains constant at approximately one wavelength, p ≈ λ, resulting in variable antenna length and width to uphold the constant perimeter. The relative sizes of the Skeleton Slot for three aspect ratios—L/w = 1, 1.8, and 2.5—are illustrated at the bottom of Figure 3. Note that, when L/w = 1, the loops form squares (L = w). These outcomes have been calculated for a conductor radius of 5mm.
The input impedance unveils an intriguing property: commencing at an aspect ratio of 1.7, the antenna maintains self-resonance (Xin = 0) as the aspect ratio increases. The reactance curve (Xin) is notably flat with values that are practically manageable even when the loops form squares (L/w = 1). However, the input resistance, Rin, exhibits a more pronounced variation, initiating at 140 Ohms for L/w = 1 and steadily decreasing to approximately 30 Ohms for L/w = 2.5. The input impedance approaches 50 + j0 Ohms at L/w ≈ 1.8. This suggests an optimal point where the antenna achieves self-resonance without requiring an impedance matching network.
Within the range of L/w spanning from 1.6 to 2, we observe a practical sweet spot with the input resistance falling between 40 and 60 Ohms and the reactance approaching zero. Figure 4 (top) illustrates the Voltage Standing Wave Ratio (VSWR) as a function of the loop aspect ratio, considering a reference impedance of 50 Ohms. The “useful” range for VSWR falls within values of L/w between 1.6 and 2. Additionally, Figure 4 (bottom) showcases the gain of the skeleton slot, demonstrating a monotonic increase with the loop aspect ratio. Opting for L/w = 2 becomes advantageous if the design objective is to maximize gain.
In the subsequent sections, we will delve into an analysis of the skeleton slot’s sensitivity to variations in loop perimeter and conductor radius. This exploration will contribute to the establishment of simulation-driven design guidelines, enabling a more informed and optimized design process.
Sensitivity to the Loop Perimeter Around One Wavelength
With the established optimal loop perimeter for achieving a self-resonant antenna at p = 0.99λ, we explore the impact of a ±1% change in this perimeter. For a frequency of 20 MHz, corresponding to a wavelength of 15 meters, this adjustment would equate to a ±15 cm change in perimeter. Figure 5 (top) illustrates the input impedance as a function of the loop aspect ratio for three different perimeters: 0.99p, 1.00p, 1.01p, where p = 0.99λ.
Notably, the resistive part (Rin) demonstrates minimal variation with changes in perimeter, whereas the reactive part (Xin) undergoes a significant alteration. The sensitivity of the reactive part to changes in p is notably higher. An increase in perimeter results in an augmented reactance (Xin), while a decrease in perimeter leads to a diminished reactance. This observation suggests that the perimeter of the loops can serve as a tuning parameter for the antenna. If, for a given loop aspect ratio L/w, the antenna is not self-resonant (Xin ≠ 0), adjustments can be made by increasing the loop perimeter when Xin < 0 and decreasing it when Xin > 0. Consequently, the antenna can always be tuned to a self-resonant state, provided the ability to adjust its physical dimensions, manipulating both the loop perimeter and aspect ratio.
In the central part of Figure 5, the Voltage Standing Wave Ratio (VSWR) is presented as a function of the loop aspect ratio. The observed variation in VSWR is predominantly attributed to changes in reactance resulting from adjustments in the loop perimeter.
In our model, the antenna is considered in free space without the presence of a ground plane, and no resistivity has been added to the conductors, effectively eliminating power losses. This deliberate choice allows us to isolate the ideal behavior of the skeleton slot and analyze its parameters independently. In an antenna devoid of ohmic losses, the resistive component of its input impedance equals its “radiation resistance.” The gain of a lossless antenna is inversely proportional to the radiation resistance. If this resistance remains insensitive to changes in perimeter, we can anticipate a corresponding insensitivity in gain. This expectation is affirmed in Figure 5 (bottom), where the gain is depicted as a function of the loop aspect ratio for the three distinct values of loop perimeter used in the upper graphs.
Effect of Changing the Conductor Radius
The investigation explores the impact of changing the conductor radius on the input impedance, VSWR, and gain as a function of the loop aspect ratio. It is widely recognized that loops with a circumference close to one wavelength exhibit higher reactance for thinner wire radii. To quantify loop thickness, the loop perimeter to wire radius ratio, p/a, is commonly used. However, since the loop perimeter is held constant in our analysis, we solely vary the radius (a = 5mm) of the example model.
At the top of Figure 6, the input impedance of the Skeleton Slot is depicted as a function of the loop aspect ratio for three different conductor radii: a = 2.5mm, a = 5mm, a = 7.5mm. As observed, reactance increases with a thinner conductor and decreases with a thicker conductor. This observation, combined with insights from Figure 5 in the previous section, leads to the conclusion that the loop perimeter required for a self-resonant antenna is influenced by the wire radius. Given a specific loop wire thickness, p/a, the exact value of p for self-resonance depends on p/a itself, so we can write p(self-resonance) = k(p/a) λ, where k(p/a) is near 1. While it is not within the scope of this study to generate curves illustrating the behavior of the factor k(p/a), simulation tools like AN-SOF allow for a simulation-driven design, a topic to be discussed in the next section.
In the middle of Figure 6, the VSWR behavior is presented, with variations predominantly attributed to changes in input reactance. The bottom graph in Figure 6 illustrates the antenna gain, demonstrating no sensitivity to the wire radius, as expected, since the radiation resistance also remains insensitive to the wire radius, as indicated in the top graph of Figure 6.
Simulation-Driven Design of a Skeleton Slot Antenna
Having established the optimal relationships among the geometric parameters of the Skeleton Slot antenna, conceptualized as two closely coupled loops sharing a feeding point, we can now outline a procedural approach for designing such antennas using simulation tools like AN-SOF.
In practical scenarios, it’s common to have a conductor or wire with a specific diameter. Therefore, our initial step will involve setting the wire radius as a fixed parameter, followed by running simulations with slight variations in the perimeter of each loop, starting with p = λ as a reference. The previously described script can be employed for this purpose, keeping the perimeter constant while adjusting the loop aspect ratio.
Following this, the subsequent step is to identify the loop aspect ratio that maximizes gain within an acceptable VSWR range. To illustrate this procedure, we will present example calculations for HF and VHF, namely for operating frequencies of 14 MHz and 145 MHz, respectively.
HF Skeleton Slot Antenna
We will take as a reference the same example presented in Sykes’ article in “The Short Wave Magazine.” For applications in the HF band, at an operating frequency of 14 MHz, in accordance with the Sykes criterion (loop width to conductor diameter of 32:1), a 4¾-inch wire would be required—an impractical dimension. The author suggests using multiple wires (e.g., 6) to form a circular contour with the desired diameter. However, in our demonstration, we aim to show that achieving a self-resonant antenna with a 3/8″ diameter conductor is indeed feasible.
Figure 7 illustrates the results for input impedance and VSWR obtained from the script with the following input parameters:
f = 14.0; // Frequency in MHz k = 0.987; // Factor for loop perimeter p = k*299.8/f; // Loop perimeter [m] (299.8/f = wavelength at f MHz) radius = (3/16)*25.4; // Wire radius in [mm] S = 7; // Number of segments per wire (it must be odd)
The gain is not displayed since it closely resembles the previously shown results. Figure 7 illustrates that the optimal loop perimeter is maintained with a factor k = 0.987, ensuring the antenna is self-resonant at 14 MHz. The chosen design point is L/w = 1.825, precisely where the VSWR exhibits a dip. Following this, we open the corresponding AN-SOF file (Skeleton_Ratio11.emm) and perform a frequency sweep around the central frequency of 14 MHz.
Figure 8 portrays the VSWR as a function of frequency for the Skeleton Slot with L/w = 1.825. The observation indicates an achieved bandwidth of almost 600 KHz (for VSWR < 2), equivalent to 4.3% in the 14 MHz band. The gain obtained is 5.5 dBi.
If we were to choose L/w = 2.05 and conduct a frequency sweep, we would notice a reduced bandwidth of 500 KHz, signifying that making the skeleton slot slimmer is no longer advantageous, despite yielding slightly higher gain.
VHF Skeleton Slot Antenna
For the operation of the Skeleton Slot at 145 MHz, we maintain the same conductor diameter of 3/8″ (wire radius, a = 3/16″). In this case, by executing the script with the same perimeter factor as the one used before (k = 0.987, with the loop perimeter being p = kλ), we obtain a negative input reactance. As we learned in the previous sections, we will then need to lengthen the loop perimeter to increase the reactance and approach resonance.
Through several calculations (not shown here), we determined that the optimal value is k = 1.03, for which the results are shown in Figure 9. Therefore, a loop perimeter that is 3% longer than a wavelength is necessary in this case to obtain a self-resonant antenna in a wide range of loop aspect ratios. The chosen design point is L/w = 1.9.
f = 145.0; // Frequency in MHz k = 1.03; // Factor for loop perimeter p = k*299.8/f; // Loop perimeter [m] (299.8/f = wavelength at f MHz) radius = (3/16)*25.4; // Wire radius in [mm] S = 7; // Number of segments per wire (it must be odd)
By opening the file corresponding to this aspect ratio (Skeleton_Ratio12.emm for L/w = 1.9) with AN-SOF and performing a frequency sweep around 145 MHz, we obtain the VSWR curve shown in Figure 10. In this case, the obtained bandwidth is 9.5 MHz (for VSWR < 2), which represents 6.6% with respect to the center frequency of 145 MHz. The gain obtained is 5.7 dBi.
With this last example, we believe we have covered the design of Skeleton Slot antennas in a depth that perhaps has not been done before. We complete the information for the designer with a few words about the number of segments, set using the “S” variable in the script. Since each loop has a perimeter of one wavelength, the total number of segments used per wavelength is 4S. Through comparisons with theoretical data for the loops, we have established that about 30 or 40 segments per wavelength are sufficient to reproduce theoretical data. Note that when S = 11 in the Skeleton Slot example for 20 MHz, we have 44 segments per λ, while with S = 7, we have 28 segments per λ. If you have measured data at hand, it is advisable that the number of segments be increased until the simulation model reproduces these experimental data.
In this comprehensive article, we conducted an in-depth study of the Skeleton Slot antenna, emphasizing its applicability across frequency bands by normalizing dimensions to the wavelength. While the theoretical analysis holds true for any frequency, practical construction considerations will be constrained by physical dimensions and installation space available in a specific frequency band.
The Skeleton Slot antenna, conceptualized as an array of two loops with a common feed point, was meticulously examined. We provided a script enabling the alteration of the antenna’s aspect ratio, generating multiple files for bulk simulation in AN-SOF. This facilitated the extraction of input impedance, VSWR, and gain as functions of the aspect ratio. The results highlighted the antenna’s self-resonance when the perimeter of each loop is approximately one wavelength.
We explored how the antenna’s behavior changes with variations in loop perimeter and conductor thickness. The optimal design point for the Skeleton Slot was identified as the loop aspect ratio minimizing VSWR for a given conductor radius. The simulation-driven design methodology can be summarized in the following steps:
- Choose the conductor diameter for constructing the Skeleton Slot.
- Define the operating frequency and determine the optimal perimeter using the provided scripts. The self-resonance loop perimeter is typically around one wavelength.
- Choose the design point by selecting the loop aspect ratio that minimizes VSWR (or maximizes gain, depending on the objective). Conduct a frequency sweep to ascertain the obtained bandwidth.
This simulation-driven design approach is particularly valuable for amateur radio enthusiasts, antenna hobbyists, or RF professionals embarking on projects involving Skeleton Slot antennas. We trust that this article will serve as a valuable resource for those interested in exploring and implementing Skeleton Slot antenna designs.
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We are thrilled to present AN-SOF Version 8.70 🚀. Packed with enhanced functionalities, this release is designed to empower you in the realm of antenna design. We have focused on both Input and Output Data Improvements to refine your experience and offer greater flexibility.
Input Data Improvements:
✅ Solid Surfaces with Thickness: We introduce the capability to model solid surfaces, not just wire grids. These solid surfaces are composed of conductive strips that can have a defined thickness. This enhancement opens the door for more realistic simulations, enabling you to model surfaces that are not infinitesimally thin. While, at present, these solid surfaces may appear as “skeletons” in the AN-SOF workspace, rest assured that we are diligently working on developing an interface to visualize them more realistically.
✅ Material Selection: We’ve added a feature that allows you to select the material of wires, grids, and surfaces from a list of metals. This selection automatically sets the resistivity. We’ve also included a ‘Custom’ option to set the resistivity manually.
✅ Substrate Dielectric Materials: We have integrated a list of dielectric materials into the Substrate ground plane option. Materials like FR4, RT/Duroid, and Rogers RO slabs are now readily available. This means that the permittivity is automatically set for the chosen material, simplifying the design process.
Output Data Improvements:
✅ EIRP Compliance: Compliance with electromagnetic field regulations is paramount. To assist you in this regard, we have added the Average and Peak Effective Isotropic Radiated Power (EIRP) to the Power Budget table. These values are presented in both Watts and dBW, and can be plotted against frequency. This feature enables you to evaluate whether an antenna model adheres to the maximum EIRP limits stipulated by regulations.
✅ AN-3D Pattern Enhancements: Visualizing the 3D radiation pattern lobes just got easier. The AN-3D Pattern app now includes up/down buttons, allowing you to effortlessly resize the antenna relative to the radiation pattern. This feature enhances your ability to grasp the antenna’s directional properties.
✅ Axial Ratio: Recognizing the importance of polarization analysis, we’ve introduced the Axial Ratio in both dB and dimensionless formats. This addition is available in 2D rectangular and polar diagrams, 3D radiation patterns, as well as in graphs depicting the far-field spectrum. The Axial Ratio helps you determine the polarization of the field by providing the minor-to-major axis ratio of the polarization ellipse. Perfect circular polarization is indicated by an Axial Ratio of ±1 (with +1 representing right-handed and -1 representing left-handed polarization), while linear polarization is characterized by an Axial Ratio of 0. Additionally, AN-SOF offers both right and left circular components of the field.
✅ S11 in Decibels: In response to the specific needs of users in microwave frequencies, we’ve added S11 in decibels (representing return loss) to plots and tables. This addition, along with the already available VSWR, offers valuable insights for RF analysis of antenna bandwidth.
We are committed to continuously enhancing your experience and equipping you with the tools necessary for your success 🛠️. Please explore these features, and feel free to reach out with any questions or feedback.
This article presents the calculated results for return loss and gain in the 2.4 GHz band for Wheel antennas. By employing a simplified method to simulate planar antennas on ungrounded dielectric substrates with sufficiently high permittivity, we can accurately replicate the measured data published by the Wheel antenna manufacturer, making it a valuable resource for engineering applications. A summary of the obtained results is provided in Figure 1. Not only is this method straightforward, but it also facilitates the utilization and expansion of cost-effective simulation software tools.
Wheel antennas derive their name from their circular configuration and the presence of spokes akin to a cartwheel. Among wheel antenna designs, solid wheel antennas feature flat metallic traces printed on a singular dielectric substrate. Typically, these substrates are circular and crafted from materials such as FR4. Solid wheel antennas are known for their compact dimensions and frequent application in ISM (industrial, scientific, and medical) frequency bands spanning from approximately 900 to 2400 MHz, primarily within wireless network contexts. In the plane of the wheel, these antennas offer omnidirectional coverage and exhibit horizontal polarization. Moreover, the radiation pattern in the plane perpendicular to the wheel closely resembles that of a magnetic dipole, taking on a distinctive donut-like shape.
This article centers on the examination of a 2.4 GHz wheel antenna manufactured by Kent Electronics (WA5VJB). Our primary objective is to replicate the measured return loss data (S11) for the Big Wheel Rev B antenna variant as provided by the manufacturer, available at this link.
Given the planar nature of wheel antennas, fabricated on an ungrounded dielectric substrate, we can employ a straightforward method for simulating these microstrip antennas. This approach is outlined in the article Simplified Modeling for Microstrip Antennas on Ungrounded Dielectric Substrates: Accuracy Meets Simplicity, which offers a cost-effective means of modeling such antennas. This methodology capitalizes on the capabilities of wire antenna simulation software, such as AN-SOF.
The initial step involves defining the frequency range of interest, which, in this instance, spans from 2.2 to 2.6 GHz. Subsequently, the antenna structure is created within AN-SOF. This process is relatively uncomplicated and entails the addition of Line objects to represent the straight metallic strips and Arc objects to replicate the curved sections of the antenna. This wheel antenna boasts a diameter of approximately 1.5 inches. At the center of this circular structure, the feed point is positioned.
Radiating outward from the antenna’s center, there are spokes that connect to the arcs on the antenna’s periphery, situated above the dielectric substrate. Additionally, there are spokes that return beneath the substrate to close the electrical circuit of the antenna. For the sake of facilitating external connectivity, the manufacturer typically incorporates a coaxial connector at the antenna’s central point, enabling a straightforward connection to a coaxial cable.
AN-SOF, operating on the Conformal Method of Moments, mandates the division of wires into shorter segments relative to the wavelength. In the case of the antenna printed on FR4, which possesses a dielectric constant of 4.6, the applicable wavelength must be that of free space divided by √(4.6) = 2.14. Consequently, for the uppermost frequency within the specified range, 2.6 GHz, the wires have been partitioned into segments measuring 2% of the wavelength within the substrate. This aligns with the same criterion employed for planar dipoles, as detailed in the previously referenced article.
In accordance with the manufacturer’s datasheet, this antenna is tunable through the introduction of a capacitor with an approximate value of 1 pF. This tuning capacitor has been incorporated into the model at the feed point, inserted in series with a voltage source. By configuring a medium characterized by a permittivity of 4.6, as depicted in Figure 2, and initiating the calculations with a Ctrl + R command, we have ascertained that the antenna resonates at 2.43 GHz when equipped with a 0.7 pF capacitor, consistent with the datasheet’s specifications. Consequently, there is no necessity to determine the resonance frequency in free space, as elucidated in the simplified method. This instance exemplifies an alignment between the effective permittivity and the substrate’s permittivity.
Figure 3, included below, presents a photograph of the physical wheel antenna, sourced from the manufacturer’s website, alongside the corresponding AN-SOF model, illustrating the employed segment density.
Comparison with Measured Data
Initiating the input impedance calculation with a Ctrl + R command, within the scrutinized frequency span of 2.2 to 2.6 GHz and employing a medium permittivity of 4.6, we generate the S11 curve presented in Figure 4. This figure also overlays the measured S11 curve, extracted from the manufacturer’s datasheet. It is evident that the agreement between the simulated and measured outcomes is remarkably robust, particularly in the vicinity of the resonance frequency. It is noteworthy that this model’s remarkable accuracy persists despite the simplification that completely disregards the dielectric substrate’s thickness and contour.
To calculate the radiation pattern, we must set the permittivity of the medium (free space) to 1, and then rescale the antenna’s dimensions by a factor of √(4.6) = 2.14. This can be achieved by first clicking on the “Selection Box” button within the AN-SOF toolbar. Subsequently, draw a box around the entire antenna using the mouse and then proceed to Edit > Scale Wires in the main menu. Here, input the scaling factor of 2.14, ensuring that you adjust the wire cross-section accordingly, as depicted in Figure 5. Furthermore, it is necessary to modify the value of the tuning capacitor, reducing it from 0.7 pF to 0.7/2.14 = 0.33 pF.
Once these adjustments are made, the calculation is tailored to the single frequency of 2.43 GHz, since our primary interest lies in the radiation pattern at the resonance frequency. With this configuration, we proceed with the calculations by pressing F11. The outcome, illustrated in Figure 6 (left), portrays the gain pattern in decibels (dBi), which, as anticipated, exhibits near-omnidirectional coverage within the plane of the antenna. Furthermore, the polarization is predominantly horizontal, evident from the dominance of the Eφ (azimuthal) component over the EΘ (zenithal) component of the electric field, as shown in Figure 6 (right). The Eφ component of the electric field reveals that there are three directions with radiation peaks, corresponding to each wheel arch, indicating that the radiation pattern is not perfectly omnidirectional.
The calculated peak gain registers at 2.7 dBi, slightly surpassing the manufacturer’s specification of 2 dBi. It is essential to acknowledge that this computed gain does not account for all potential power losses within the actual antenna, particularly within components such as the coaxial connector and the substrate (incorporating loss tangent). These factors have been omitted in our model, wherein solely a resistivity matching that of aluminum has been introduced for the metal traces.
In this article, we have introduced a simplified method for the modeling of solid wheel antennas, enabling the calculation of their return loss and radiation pattern. We have employed this method to simulate the performance of the Big Wheel Rev B antenna designed for the 2.4 GHz band, as provided by Kent Electronics. The results obtained through AN-SOF simulation have been compared with the measured data furnished by the manufacturer, and a high degree of agreement has been achieved.
This study serves as a clear demonstration of AN-SOF’s efficacy in modeling planar antennas that are printed on ungrounded dielectric substrates, specifically substrates like FR4. The method presented here not only offers simplicity but also demonstrates remarkable accuracy, highlighting its value for antenna engineers and researchers seeking cost-effective, reliable antenna design and analysis tools.
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Since version 8.50, the AN-SOF Antenna Simulator has enabled us to implicitly model transmission lines. This capability allows us to define a transmission line by specifying its characteristic impedance, velocity factor, length, connection ports, and losses. One valuable application of this transmission line modeling technique is in modeling the feeding system of phased arrays. An illustrative example of a versatile phased array that utilizes transmission lines in its feeding system is the four-square array. This configuration consists of four vertical elements, each measuring 1/4-wavelength in height and arranged in a square pattern. It serves as a powerful tool for both radio enthusiasts and professionals seeking a straightforward phased array for controlling the main lobe direction of the antenna radiation pattern.
The figure below illustrates the layout of the four-square array and its corresponding radiation pattern. When treating the four vertical elements as a 4-port network, calculations dictate the addition of an 18 Ohm resistor at the base of each monopole to achieve the desired directional radiation pattern. Additionally, the feeding system of this array involves six transmission lines, meticulously configured for length and interconnections, all detailed in Chapter 8, Section “The Four-Square Array,” found in the 19th edition of the ARRL Antenna Book.
Here are some of the properties that make the four-square array a compelling choice for antenna enthusiasts and professionals:
1) Forward Gain: 3.3 dBi, considering an average ground.
2) Beamwidth: The array offers a 3 dB beamwidth of 100°.
3) Horizontal Front-to-Back Ratio: 20 dB or better over a 130° angular range.
4) Symmetry for Directional Switching: Thanks to its symmetric design, the four-square array allows for directional switching in 90° increments.
By employing the feeding system outlined in this model, the four-square array showcases excellent performance characteristics, with any limitations primarily influenced by environmental factors. Furthermore, the array’s design lends itself to the implementation of a remote switching mechanism, enabling effortless adjustment of the array’s direction as needed.
Whether you’re a ham radio operator, a DXer, or a professional in the field, the four-square array is a fascinating option to consider for your next antenna project.
Simplified Modeling for Microstrip Antennas on Ungrounded Dielectric Substrates: Accuracy Meets Simplicity
In this article, we present a straightforward yet highly accurate model for calculating the input impedance and gain of planar antennas printed on ungrounded dielectric substrates with sufficiently high permittivity. We review existing models based on effective medium theory and introduce a novel approach that, instead of providing analytical formulas for effective permittivity, utilizes simulation software to determine antenna resonance frequencies. This approach leads to improved results compared to established effective medium formulas.
The model’s validity is confirmed through a comparison of simulation results with measured data for planar dipoles printed on FR4 substrates, which feature a standard dielectric constant of 4.5 and a thickness of approximately 1.6 mm—commonly used in practical applications.
“All models are wrong, but some are useful,” a renowned saying attributed to the British statistician George E. P. Box. This statement closely aligns with a fundamental question: to what extent can one simplify a model without compromising its ability to capture what is truly essential? How minimal can a simplified model be while still retaining its “usefulness” despite its inherent inaccuracies?
We delve into this critical question within the context of accounting for the impact of dielectric substrates on planar antennas printed on ungrounded FR4 slabs. In this article, we present an exceptionally simplified method that yields results closely aligned with measurements for the input impedance and gain of planar antennas printed on FR4 dielectric substrates at microwave frequencies.
FR4 is a dielectric material with a standard relative permittivity of 4.5, readily available in the market as flat sheets of various thicknesses, with 1.6 mm being the most common. While these values may vary slightly in practice, the method we discuss is applicable to different variants of this material.
In the realm of microwave bands, antennas printed on dielectric substrates have gained immense popularity, primarily due to their practicality in supporting antenna structures measuring only a few centimeters. However, a pressing issue arises: the dielectric constant’s influence on the effective length of traces and, consequently, the resonance frequency of the antenna. To tackle this challenge, one could opt for full-wave methods, such as the Finite Element Method (FEM), which allow for the discretization of both the metallic antenna components and the dielectric substrate. Yet, this approach demands substantial computational resources, and the available software solutions often come with exorbitant costs.
Figure 1 illustrates the precision attainable with our simplified method, which we will elucidate in the subsequent sections. It presents both simulation and measured results for a planar Yagi-Uda antenna designed for 2.4 GHz applications. The figure encompasses several components: the measured return loss1, a photograph of the actual antenna fabricated on an FR4 epoxy dielectric, and graphs generated through HFSS software. These elements have been extracted from Ref. . The red curve and radiation pattern labeled as “Tony” represent the results obtained after applying our simplified method. Here, it becomes evident that our streamlined approach accurately predicts the resonance frequency and radiation pattern of the planar Yagi-Uda antenna.
Effective Permittivity of Ungrounded Substrates
One of the most straightforward methods one might consider is replacing the dielectric substrate with an infinite medium characterized by an effective permittivity, denoted as εeff. In this approach, the entire antenna resides within this infinite medium. Notably, this method simplifies the model by disregarding the influence of substrate edges and corners, which typically give rise to diffracted waves. The effective permittivity relies on several factors, including the dielectric constant of the substrate, the medium surrounding the substrate (commonly air, treated as free space with a relative permittivity ε0 = 1), the substrate’s thickness, and the dimensions of the printed metal strips—essentially, the geometry of the printed antenna itself.
When a substrate incorporates a ground plane, typically composed of a metal plate, established theories on effective mediums offer closed analytical formulas for calculating the effective permittivity. In such cases, this is feasible because the electric field predominantly concentrates just below the strips. Utilizing techniques like conformal mapping or a transmission line model, researchers can derive closed-form expressions for the capacitance between the strips and the ground plane. Refer to Section “14.2.1 Transmission-Line Model” in Ref.  for further insights. However, when there is no ground plane, computing the effective permittivity becomes significantly more challenging.
In Ref. , researchers explored four analytical methods for estimating the effective permittivity of ungrounded substrates, ultimately concluding that two methods yield acceptable results:
1) Insulated wire approach: This method involves considering an infinitely long circular wire covered by a dielectric sheath with the same thickness as the planar substrate. The key is to calculate the propagation constant within the sheath, denoted as βs, as illustrated in Fig. 2(a). Consequently, the effective permittivity depends solely on the dielectric constant of the sheath and its thickness. Importantly, it does not rely on the length of the strips.
2) Coplanar strips technique: In this method, a conformal mapping transformation is utilized to calculate the effective capacitance between two parallel strips situated within the same plane. From this capacitance, the effective permittivity can be derived. This approach considers the substrate’s permittivity, its thickness, as well as the dimensions (lengths and widths) of the strips, as depicted in Fig. 2(b). The expression for εeff incorporates a factor denoted as K2/K1, which relies on complete elliptic integrals of the first kind. Beyond the mathematical intricacies, it’s intuitive that as the substrate thickness, d, approaches infinity (d → ∞), K2/K1 tends to 1, yielding an effective permittivity equal to the average of the substrate and free space permittivities, εeff(d → ∞) = (1 + εr) / 2. Conversely, when the thickness is zero (d = 0), K2/K1 = 0, and the effective permittivity equals that of free space, εeff(d = 0) = 1. Therefore, the theory of the effective medium produces a permittivity value ranging between 1 and (1 + εr) / 2.
Methods that rely on effective permittivity offer an enticing level of simplicity. However, when applied in practice, they often result in a noticeable shift of the resonance frequency, either toward higher or lower frequencies. This phenomenon was indeed observed and documented in Ref. , where a comparison between simulated results and measurements for a planar dipole printed on an ungrounded FR4 substrate slab demonstrated this effect.
In the realm of microstrip antennas operating at microwave frequencies, it’s quite common for the strip width to closely align with the thickness of the FR4 substrate. In such scenarios, both the “insulated wire” and “coplanar strips” methods typically yield an effective permittivity ranging from approximately 1.5 to 1.8. This specific scenario, where strip width closely matches the substrate thickness, forms the focal point of our discussion in this article. It’s worth noting that for many practical applications, the thickness of the substrate remains a fixed parameter and is not adjustable within our simplified model.
Modeling Method Based on Resonance Frequencies
Unlike the methods described in the previous section, our proposed approach does not rely on analytical formulas to determine the effective permittivity. Instead, it is rooted in simulation techniques, and its application comprises the following steps:
1. Compute the Antenna’s Actual Resonance Frequency
The method we propose is heuristic in nature, rooted in a fundamental observation: in substrates with a permittivity high enough, when the width of the printed metal strips is close to or lower than the substrate thickness (w ≈ d or w ≤ d), the electric field in very close proximity to the strips is predominantly concentrated within the dielectric substrate, rather than in free space (at microwave frequencies). This observation is crucial, as it implies that the propagation constant relevant for calculating the interaction between the strips is approximately βs = 2π √(εr) / λ, where εr represents the relative permittivity of the substrate, and λ denotes the wavelength in free space.
This observation has paramount significance because it suggests that the resonance frequency is primarily determined by εr itself, rather than an effective permittivity (εeff) as assumed in effective medium approaches. Therefore, our initial step involves calculating the resonance frequency of the antenna when it is immersed in an infinite medium with a permittivity equal to that of the substrate. This frequency, denoted as fR(εr), should closely align with the actual resonance frequency of the antenna on the original finite substrate, assuming a high substrate permittivity and either w ≈ d or w ≤ d. Fig. 3(a) illustrates the profile of the original antenna, while Fig. 3(b) depicts the antenna completely surrounded by a dielectric medium with permittivity εr, within which we must ascertain the actual resonance frequency.
2. Calculate the Effective Permittivity and Input Impedance
The radiation resistance of an antenna relies on the far-field radiation it produces, where the propagation constant corresponds to that of free space (β = 2π/λ), rather than the dielectric substrate (βs = 2π √(εr) / λ). In cases where power losses can be neglected, the input resistance of the antenna is, in fact, equal to the radiation resistance. A similar principle applies to the imaginary component of the input impedance, referred to as input reactance, which hinges on the balance between electric and magnetic energies in the vicinity of the antenna, where the dielectric substrate plays a role.
To compute the antenna’s input impedance, we must account for an effective permittivity, one that falls between the permittivity of free space and that of the substrate. Given that, from a radiation perspective, the propagation constant in free space takes precedence, our next step involves calculating the resonance frequency when the antenna exists in free space, devoid of the dielectric substrate, as depicted in Fig. 3(c). We denote this frequency as fR(1), with the “1” signifying the relative permittivity of free space.
It’s crucial to note that, since fR(1) > fR(εr), in order to lower the resonance frequency from fR(1) to fR(εr), we must divide it by the square root of the effective permittivity, i.e. fR(1)/√(εeff) = fR(εr). Consequently, the effective permittivity is calculated as εeff = [ fR(1)/fR(εr) ]2. This value is the permittivity that we will employ to calculate the input impedance, treating the antenna as though it is immersed in an infinite medium with a permittivity of εeff, as illustrated in Fig. 3(d).
3. Rescale the Antenna to Obtain the Far Field
Our final step involves calculating the radiated far field. In the far-field zone, only the free space propagation constant, β = 2π/λ, is relevant. When viewed from a considerable distance, the impact of the substrate on the radiation pattern is essentially a dilation effect on the dimensions of the printed strips, scaled by a factor of √(εeff). Consequently, to create an equivalent antenna in free space without the dielectric substrate, we can increase the size of the antenna by multiplying all its dimensions—both strip lengths and widths—by the scaling factor √(εeff). This results in an antenna of increased size2 surrounded by free space, as illustrated in Fig. 4.
In this context, our primary focus commonly centers on the radiation pattern at the resonance frequency.
Comparisons with Measured Data
In this section, we embark on a comparison between the data generated by the method we’ve elucidated and the measurements obtained for planar dipoles printed on FR4, sourced from Ref. . From this reference, we’ve also extracted results calculated using an effective permittivity corresponding to the “insulated wire” method. This approach allows us to assess the outcomes of our proposed method in comparison to measurements and another method that relies on an effective medium.
For our calculations, we employ the AN-SOF Antenna Simulator, which offers the flexibility to manipulate the permittivity of the medium surrounding the antenna and define flat strips, not restricted to wires with circular cross-sections. The first dipole in our analysis possesses dimensions of L = 93.8 mm in length and w = 2 mm in width, with the dielectric substrate being a standard FR4 characterized by a permittivity of εr = 4.5 and a thickness of d = 1.6 mm. Our frequency range of interest spans from 1 GHz to 1.8 GHz.
To initiate the process, we set the medium’s permittivity to εr = 4.5 in the Setup tab > Environment panel of AN-SOF. We then execute a frequency sweep, stepping through frequencies with a granularity of 0.01 GHz to achieve three significant digits in the resonance frequency. AN-SOF operates on the Conformal Method of Moments, necessitating that the dipole be divided into segments much smaller than the wavelength. In this instance, we employ 25 segments. At the highest frequency of 1.8 GHz, each segment length constitutes approximately 5% of the wavelength within the dielectric medium. It’s important to note that while the wavelength at 1.8 GHz in free space is λ = 166.6 mm, the segments must be small relative to the wavelength within the dielectric medium, which is shorter than the free-space wavelength and can be calculated as λ/√(εr) = 78.5 mm.
After initiating the calculation by pressing Ctrl + R and identifying the point where the imaginary part of the input impedance reaches zero, we obtain a resonance frequency of fR(4.5) = 1.23 GHz. Remarkably, with three significant figures, this result precisely aligns with the resonance frequency of the actual antenna reported by the authors of Ref. . Thus, the error with this level of precision stands at 0%.
The next step involves calculating the resonance frequency of the antenna in free space. To do this, we return to the Setup tab > Environment panel in AN-SOF and set εr = 1. Subsequently, we rerun the frequency sweep without needing to alter the number of segments for the dipole. As the wavelength nearly doubles when εr = 1, each segment now spans approximately 2% of λ. The computed resonance frequency in free space is determined to be fR(1) = 1.51 GHz. Remarkably, this result closely aligns with the reported resonance frequency of the dipole in air, which is 1.5 GHz, as documented in Ref. . The error with this precision is merely 0.67%.
According to our model, the effective permittivity is now calculated as εeff = (1.51/1.23)2 = 1.51. Subsequently, we set εr = 1.51 in the Environment panel of the Setup tab within AN-SOF and initiate the input impedance calculation either by pressing Ctrl + R or through the main menu > Run > Run Currents.
Figure 5 presents a photograph of the actual fabricated antenna, the measured return loss, and the results obtained using the insulated wire method, with all these elements extracted from Ref. . Additionally, we’ve incorporated the curve obtained through AN-SOF3 into the graph of S11 (with a reference impedance of 50 Ohms). Notably, the predictions of the resonance frequency and the mismatch at resonance (the value of S11 at 1.23 GHz) generated by our proposed method closely align with the measured data, surpassing the results of the insulated wire method.
Furthermore, Figure 5 showcases the radiation pattern acquired after rescaling the dipole by multiplying its length L and width w by the factor √(εeff) = √(1.51) = 1.23, followed by conducting calculations in free space while setting εr = 1 in the Environment panel. This analysis yields a donut-shaped radiation pattern with a maximum gain of 1.64, which, to three significant figures, coincides with the theoretical value for a resonant dipole with a length approximately half a wavelength. We can confirm that the effective length of the dipole at 1.23 GHz is 0.47λeff, where λeff = λ/√(εeff).
Now, let’s consider a second dipole, which possesses a length of 72.5 mm and the same width as the previous one, w = 2 mm. This second dipole has been obtained by rescaling the first one in order to achieve a resonance frequency of 1.5 GHz, although in the measurements, as reported by the authors of Ref. , a value of 1.49 GHz was obtained. By following the same procedure as the one outlined earlier, we determined fR(4.5) = 1.50 GHz and fR(1) = 1.94 GHz for the scaled dipole. Consequently, the effective permittivity for this case is calculated as εeff = (1.94/1.50)2 = 1.67. It’s worth noting that to obtain the resonance frequencies for this dipole, we had to employ 51 segments. In each instance, an analysis of result convergence based on the number of segments is imperative.
Figure 6 presents the results for the scaled dipole. We include a photograph of the dipole, the measured S11 curve, and the curve calculated using the insulated wire model, all sourced from Ref. . Additionally, we’ve superimposed the curve obtained by AN-SOF onto the S11 graph. It’s evident that the fit with the measured data is exceptionally satisfactory, surpassing the precision achieved through other methods. The radiation pattern is also depicted, boasting a gain of 1.64, aligning with our expectations.
Recalling the introductory phrase of this article, “All models are wrong, but some are useful,” we have introduced a model here that indeed falls into the category of being “wrong.” It neglects the diffraction of waves at the edges and corners of the dielectric substrate and does not account for substrate thickness, necessitating sufficiently high permittivity and strip widths comparable to or lower than the substrate thickness.
However, it is an exceedingly simple model, arguably one of the simplest conceivable, and it yields valuable results that closely align with measured data. This model leverages the capabilities of simulation software tailored to wire antennas, such as AN-SOF, offering a cost-effective solution for designing microstrip antennas on ungrounded dielectric substrates.
In summary, the construction of the model involves the following steps:
- Determine the antenna’s actual resonance frequency by assuming it is submerged in an infinite medium with the same permittivity as the dielectric substrate, denoted as fR(εr).
- Determine the antenna’s resonance frequency in free space, in the absence of the substrate, denoted as fR(1).
- Calculate the input impedance, from which the return loss (S11) can be derived, by simulating the antenna in an infinite medium with an effective permittivity of εeff = [ fR(1)/fR(εr) ]2. The radiation pattern is obtained by rescaling the antenna in free space, multiplying its dimensions by the factor √(εeff).
The model we’ve introduced considers antenna dimensions, including the lengths and widths of the printed strips, to determine effective permittivity through the resonance frequencies fR(εr) and fR(1). Therefore, the influence of antenna geometry and its dimensions is inherently incorporated into our effective permittivity calculation. In contrast, effective media methods frequently encounter challenges when dealing with complex antenna geometries, and analytical formulas are typically limited to simpler cases, such as the planar dipole. This distinction underscores the accuracy of our method, particularly in determining resonance frequencies for microstrip antennas.
 “High Gain Improved Planar Yagi Uda Antenna for 2.4 GHz Applications and Its Influence on Human Tissues,” by Claudia Constantinescu et al., Appl. Sci. 2023, 13, 6678.
 “Antenna Theory Analysis and Design” by Constantine A. Balanis, 4th Edition, Wiley 2016.
 “A Robust Method of Calculating the Effective Length of a Conductive Strip on an Ungrounded Dielectric Substrate” by M. Kanesan, D. V. Thiel, and S. O’Keefe, Progress In Electromagnetics Research M, Vol. 35, 57–66, 2014.
- In microstrip antennas, it is customary to present the reflection coefficient at the feed port, denoted as S11, rather than the input impedance, as S11 is the more frequently measured parameter. In technical terms, S11 expressed in decibels is often referred to as “return loss.” However, it’s important to clarify that the formal definition of return loss is the negative of S11 in decibels.
- Instead of rescaling the antenna dimensions and reiterating the calculations for obtaining the radiation pattern, a simpler approach is to keep the dimensions constant and adjust the frequency by multiplying it by √(εeff). This method allows us to leverage the calculations already performed in free space to determine the resonance frequency fR(1).
- AN-SOF provides us with the return loss based on its technical definition, which happens to be the negative of S11 when expressed in decibels. To represent S11 as a function of frequency in the graphs, we reversed the sign of the return loss values in decibels obtained from AN-SOF.
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Are you fascinated by antenna design and eager to learn new techniques? Look no further! Our latest video tutorial, Fast Modeling of a Monopole Supported by a Broadcast Tower, is here to take your skills to the next level. 🚀
🔗 In this video, we guide you through the step-by-step process of creating a detailed monopole antenna model, with the added support of a broadcast tower, using the powerful AN-SOF Antenna Simulator. From radial wires to ground plane connections, we’ve got you covered.
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We’re thrilled to introduce AN-SOF version 8.50, a comprehensive update that takes your antenna design and simulation experience to new heights. Let’s explore the remarkable new features:
✅ Transmission Line Models: With over 160 models accurately fitted to real cable datasheets, AN-SOF empowers you to effortlessly model phased arrays and feeding systems with multiple transmission lines. Experience enhanced accuracy while accounting for RF interference caused by coaxial cable shields using our hybrid model.
✅ Enhanced Zoom Functionality: Editing intricate details has never been easier. AN-SOF 8.50 introduces a convenient zoom-in option with the click of a button. Simply access the expansion box through the toolbar’s magnifying glass icon and fine-tune small wires within large structures effortlessly.
✅ Extended Power Budget: Gain valuable insights with the integration of Front-to-Rear (F/R) and Front-To-Back (F/B) ratios into the Power Budget table. Explore F/R and F/B plots as a function of frequency with a simple click on the table headers in the Results tab. You’ll also find this essential data included in the CSV output file during bulk simulations.
✅ Expanded Compatibility: AN-SOF now supports current sources defined via the EX 6 command of NEC-4.2 when importing NEC files. Seamlessly import your preferred NEC files and take full advantage of AN-SOF’s capabilities.
✅ Insulation Integration: Importing NEC files becomes even more versatile with support for wire insulation defined via the IS command. Add insulation to individual wires or the entire setup effortlessly, providing you with greater customization options.
✅ Improved Far-Field Calculation: AN-SOF 8.50 offers enhanced far-field computation, ensuring accurate Directivity and Efficiency calculations for all scenarios. Whether you’ve set a real ground plane or an infinite substrate slab combined with the Vertical, Horizontal, or Custom options in the Far-Field panel setup, rest assured of precise results.
Accelerate your antenna design and simulation prowess with AN-SOF 8.50. Upgrade today and unlock boundless potential for your projects. Don’t miss out – download now!
Introducing AN-SOF 8.50: an exciting update that takes antenna design and simulation to new heights.
Key features of AN-SOF 8.50 include:
✅ Effortless Modeling: With over 160 Transmission Line Models, AN-SOF enables easy modeling of phased arrays and feeding systems while accounting for RF interference generated by coaxial cable shields.
✅ Enhanced Zoom Functionality: Experience seamless editing of small wires with improved zoom functionality, allowing for precise adjustments.
✅ Valuable Insights: Gain valuable insights into your designs with integrated Front-to-Rear and Front-To-Back ratios as a function of frequency in the Power Budget table. This comprehensive analysis empowers you to optimize your antenna’s performance.
✅ Expanded Compatibility: AN-SOF now supports current sources and insulation integration when importing NEC files, providing enhanced compatibility for your projects.
✅ Improved Far-Field Computation: Enjoy precise results with AN-SOF’s advanced far-field computation, ensuring accurate Directivity and Efficiency calculations across various scenarios. Even with real ground planes or infinite substrate slabs, AN-SOF delivers reliable and accurate results.
Whether you’re a beginner or an expert in antenna design and simulation, AN-SOF is the ideal software for you.
If you’re new to antenna simulation, AN-SOF offers a user-friendly interface combined with unparalleled accuracy, allowing you to quickly enter the world of antenna simulation. We recommend starting with our Quick Start Guide, which provides a step-by-step overview of antenna simulation using the Method of Moments.
For experienced users, our comprehensive Knowledge Base provides in-depth descriptions of AN-SOF’s features and functions. Explore numerous examples and articles that validate AN-SOF’s results through comparisons with theoretical and experimental data. Additionally, our blog Antennas and Beyond! offers advanced articles for readers with a more in-depth background.
Furthermore, AN-SOF allows you to program scripts in the language of your choice to generate a sequence of files containing descriptions of an antenna model with variable geometric parameters. You can then run a massive calculation of all these files using the Run Bulk Simulation command. Explore examples of scripts in the language of Scilab, the open-source counterpart of the renowned Matlab, at this link.
Join our vibrant community of antenna modellers and immerse yourself in the exciting world of antenna design and simulation. Count on us to provide comprehensive support for all your projects.
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AN-SOF has incorporated an innovative method based on the James R. Wait theory to accurately compute the ground losses of LF/MF radio masts. The correct calculation of power lost in the ground is crucial for determining the radiation efficiency of monopole antennas. To minimize energy losses, radial wire ground screens are typically installed.
To illustrate the efficacy of this implementation, a simulation has been carried out on an antenna tower 1/4 wavelength in height, placed over an average soil with a conductivity of 0.005 S/m and a dielectric constant of 13. The simulation incorporated 60 buried radials and calculated the E-field at 3 MHz as a function of distance for an antenna input power of 1 kW.
To activate this calculation in AN-SOF for LF and MF band frequencies, users need to select the Sommerfeld-Wait/Asymptotic or Radial wire ground screen options as the real ground plane in the Setup > Environment panel. Here is an article detailing the validation of this model: Enhanced Methodology for Monopoles Above Radial Wire Ground Screens.
Who was James R. Wait?
James R. Wait was a Canadian engineer known for his academic qualifications and prolific contributions to electromagnetic propagation engineering. He was elected as a member of the National Academy of Engineering in 1977 and authored numerous papers and books. Born in Ottawa in 1924, Wait received his BS and MS in engineering physics and his PhD in electrical engineering from the University of Toronto. He held various research positions worldwide and became a professor at the University of Arizona. Those interested in learning more about Wait’s life may refer to the article “James R. Wait—Remarkable Scientist” by Ernest K. Smith, IEEE Transactions on Antennas and Propagation, Vol. 48, No. 9, pages 1278-1286, September 2000″.
AN-SOF Antenna Simulation Software accelerates antenna design by addressing seven limitations encountered in the traditional Method of Moments (MoM). The accompanying image provides a visual representation of the challenges overcome by AN-SOF.
Utilizing a Conformal Method of Moments (CMoM) with an Exact Kernel, AN-SOF overcomes these limitations, enabling accurate modeling and analysis of antennas with complex geometries. This includes high gain antennas with grid reflectors, broadcast towers with elevated radial wires close to the ground, thick dipoles, stepped cylindrical antennas, curved antennas such as helices, spirals, and loops, as well as any design involving curved, short, and closely positioned wires.
By overcoming these limitations, AN-SOF empowers engineers and researchers to design antennas with enhanced accuracy and reliability. The software not only improves the modeling and analysis of complex antenna geometries but also opens up new possibilities for antenna optimization and design across a wide range of applications.
This resource provides a concise introduction to the capabilities of AN-SOF, designed to revolutionize the way you approach antenna design.
What can you expect from the Quick Overview?
✅ An Introduction to AN-SOF: Gain insights into the background, purpose, and features of AN-SOF.
✅ Key Features and Benefits: Delve into the array of tools, functionalities, and simulations that AN-SOF offers.
✅ Unlock New Possibilities: Uncover how AN-SOF breaks away from the limitations of traditional software packages.
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
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.
- 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 >.
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.
For further reading, we highly recommend the book “The Theory of Linear Antennas” by Ronold W. P. King, Harvard University Press, 1956. This seminal work provides a comprehensive understanding of linear antennas and serves as a benchmark for research in the field. In the paper “Currents, Charges, and Near Fields of Cylindrical Antennas” by R.W.P. King and Tai Tsun Wu, Radio Science Journal of Research NBS/USNC-URSI, Vol. 69D, No. 3, pp. 429-446, March 1965, the authors compare the sinusoidal current distribution with measured data and identify the need for an additional term in the model. To delve deeper into the source gap problem, we refer to “The Influence of the Width of The Gap Upon The Theory of Antennas” by L. Infeld, Quarterly of Applied Mathematics, Vol. V, No. 2, pp. 113-132, July 1947. This study provides valuable insights into the effects of gap width on antenna theory.
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⚠ 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 >.
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.
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, Ev, and the horizontal component of the magnetic field, Hh, omitting components in the direction of propagation (which rapidly diminish with distance from the emission source). We define the wave impedance as Zw = Ev/Hh. 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, ER and HR, and left-handed circular polarization components, EL and HL, we can define two complex wave impedances: a right-handed impedance, ZR = ER/HR, and a left-handed impedance, ZL = EL/HL.
Regardless of the chosen definition of wave impedance, it will have the following properties:
• Zw 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), Zw 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 Zi = √(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,
Zw(r) = Erms(r)/Hrms(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 Erms = |E| = √(|Ex|2 + |Ey|2 + |Ez|2) = √(|Er|2 + |EΘ|2 + |Eφ|2), where Ex, Ey, Ez, Er, EΘ, Eφ 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, Hrms = |H|.
In general, Erms and Hrms are invariant under any coordinate transformation. Therefore, Zw(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, Erms(r) and Hrms(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 Zw = Erms/Hrms 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 Zw 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.
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.
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.
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.
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.
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.
The traditional separation between field regions is explained in detail in section “4.4 Region Separation” of the renowned book “Antenna Theory, Analysis and Design” by Constantine A. Balanis, 4th edition, 2016, John Wiley & Sons. For a compelling analysis utilizing wave impedance, refer to “Near Field or Far Field?” by Charles Capps, EDN, Design Feature, Aug. 16, 2001, pp. 95-102. A comprehensive examination can also be found in the paper “Where Does the Far Field of an Antenna Start?” by M. Abdallah, T. Sarkar, M. Salazar-Palma, and V. Monebhurrun, published in IEEE Antennas & Propagation, Vol. 58, Issue 5, Oct. 2016, pp. 115-124.
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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.
Are you seeking to expedite the process of incorporating elevated radial wires into your antenna model created using the AN-SOF Antenna Simulator? Elevate your proficiency in AN-SOF with this instructional video tutorial, spotlighting two efficient methods for swiftly integrating radial wires in a monopole antenna model.
The first method is exceptionally suitable when dealing with a limited number of radial wires. It entails the precise specification of each wire’s parameters using the Start – Direction – Length option. This technique facilitates the step-by-step drawing of radial wires, allowing for rapid adjustments by altering orientation angles in the horizontal plane.
For projects demanding the inclusion of a substantial number of radial wires, the second method shines as the most efficient choice. This approach entails the creation of a disk with a predetermined quantity of radial wires and subsequently eliminating its outline.
Uncover the intricacies of applying these techniques to rapidly incorporate elevated radial wires into your monopole or broadcast tower antenna models within the accompanying video tutorial:
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.
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.
✅ 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.
Presenting a formidable challenge, the creation of an omnidirectional antenna with the capability to function across diverse frequency bands from a singular feed point demands innovative engineering.
The image below illustrates a simulated multiband dipole, which is a composite of five closely spaced parallel dipoles. Converging at the antenna’s center, these dipole extremities meet at a shared feed point. Each dipole spans approximately half a wavelength, yielding resonance frequencies of 3.7, 7.05, 14.2, 18.1, 21.2, and 28.5 MHz. The radiation pattern animation showcases the emergence of a donut-shaped omnidirectional pattern at lower frequencies, evolving into a more intricate lobed pattern as frequencies ascend.
This exemplifies a scenario where the indispensable utility of a simulation tool like AN-SOF comes to the forefront. AN-SOF exhibits an exceptional ability to simulate closely spaced wires, a feat that is often challenging. The remarkable capability of AN-SOF can be attributed to its implementation of a calculation method that triumphantly overcomes the seven key limitations prevalent in traditional methods. These intricacies are thoughtfully detailed in this article, highlighting the innovation driving AN-SOF’s prowess.
The Loop on Ground (LoG) is a small antenna with a cardioid-shaped radiation pattern in the horizontal plane. It is primarily used for reception purposes. The loop consists of a 110 Ω resistor connected at its top, while the antenna terminals are positioned at the bottom. One of the terminals is connected to the ground through a vertical wire, forming a monopole. This clever arrangement enables the antenna to maintain directionality despite its small size.
The accompanying image illustrates the radiation patterns achieved with and without grounding.
Here are the specifications for the antenna configuration:
- Frequency: 4.5 MHz
- Loop diameter: 1 m
- Height above ground: 2 m (average real ground)
Thanks to the application of the Conformal Method of Moments, the LoG antenna model reveals a remarkable feature: it can be accurately represented with only a minimal number of segments. This efficiency is achieved by utilizing curved segments that precisely conform to the loop’s contour. The image provided clearly showcases these curved segments, which enable an effective simulation of the antenna’s behavior. This advantageous characteristic is a result of the antenna’s small size relative to the wavelength.
In conclusion, the Loop on Ground (LoG) antenna is a compact yet directional antenna with a cardioid-shaped radiation pattern. By incorporating a monopole and grounding, this antenna design achieves its distinctive characteristics.
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!
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.
Magnetic loop antennas find extensive application within the realm of amateur radio pursuits. One prevalent design employs a dual loop configuration, wherein a larger loop, equipped with a tuning capacitor at one end, is magnetically linked to a smaller loop positioned inside it. The smaller loop serves as the connection point for the coaxial cable, which feeds the antenna. This antenna’s construction is remarkably straightforward, as it capitalizes on the adaptability of coaxial cable wires for assembly. It is important to emphasize that the interplay between the two loops is rooted in induction rather than physical linkage.
Illustrated in the accompanying image, the simulation delves into an instance where the larger loop, fashioned from RG-8 cable, spans a diameter of 70 cm, while the smaller loop, crafted from RG-6 cable, boasts a 15 cm diameter. Maintaining a separation of 2 cm between the loops at the antenna’s base, the provided diagram outlines the requisite tuning capacitor settings for achieving resonance across five distinct frequencies: 3.5, 7, 14, 21, and 29 MHz.
Sited a meter above a typical ground plane, the antenna showcases a radiation pattern that diverges from the conventional toroidal shape anticipated for a small loop positioned in free space. The color scale displayed on the loops indicates the current intensity corresponding to each resonant frequency.
Facilitating precise simulations of this antenna design, the AN-SOF Antenna Simulator leverages the Conformal Method of Moments featuring curved segments. This enables the meticulous replication of loop contours. A noteworthy attribute of AN-SOF lies in its use of an exact Kernel, which accommodates close proximity of both loops at the antenna’s base.
The simulator further streamlines the calculation process by permitting sequential and automated execution of the antenna’s resonance calculations across the five specified frequencies. This eliminates the need for manual execution of each calculation. To access this feature, navigate to the AN-SOF main menu and select Run Bulk Simulation under the “Run” category. This function allows you to effortlessly run calculations on the five “.nec” files, available for download via the provided button. Importantly, this functionality is available even with the trial version of AN-SOF.
The Quadrifilar Helix (QFH) antenna, also referred to as the QHA, stands as an excellent choice for signal reception from the satellites of the National Oceanic and Atmospheric Administration (NOAA). This antenna configuration boasts omnidirectional capabilities and is composed of four helically wound wires, intertwining to create a helix—an intricate geometric arrangement that imparts distinctive properties to this antenna.
The design depicted in the image below showcases a configuration with a diameter of approximately 0.14 times the wavelength (λ) and helix lengths of 0.4λ. A resonant frequency of 137.5 MHz ensures its optimal functionality, accompanied by a bandwidth spanning 6%, defined by a standing wave ratio (SWR) below 2. This composition serves a dual purpose: enabling efficient signal reception from NOAA satellites while effectively mitigating external interference.
A noteworthy observation emerges when evaluating the antenna’s radiation pattern under varying conditions. In a vacuum environment, the radiation pattern orients downward when the coaxial cable, simulated as a voltage source in simulations, connects to the antenna’s apex. This phenomenon is depicted in the leftward radiation pattern. However, when the QFH antenna is positioned in real-world scenarios, a substantial transformation occurs. Placing the antenna at an elevation of 5 meters and introducing a real ground plane yields an entirely distinct radiation pattern.
The resultant pattern in this real-world configuration displays omnidirectional properties within the azimuth plane. Notably, this pattern showcases multiple lobes concerning elevation angles. The practical application of this radiation pattern is invaluable for effectively capturing signals from a variety of satellite orientations. AN-SOF allows us to accurately model the behavior of these intricate helices, courtesy of the implementation of the Conformal Method of Moments, which utilizes curved segments to faithfully represent the contour of the helices.
In summary, the Quadrifilar Helix (QFH) antenna stands as an ingeniously designed configuration, adeptly capturing signals from NOAA satellites. The configuration of four helically wound wires offers omnidirectional capabilities and robust interference suppression.
The Moxon antenna, or Moxon rectangle, represents a straightforward yet mechanically robust wire antenna meticulously crafted for VHF bands. It owes its name to the renowned radio amateur operator Les Moxon (call sign G6XN). This antenna comprises two folded dipole elements, one of which acts as the driven element, while the other serves as the reflector element. An adjustable gap is deliberately left between these folded dipoles, permitting fine-tuning of the antenna to minimize the VSWR (Voltage Standing Wave Ratio). Consequently, this antenna can be mechanically tuned, negating the necessity for an impedance matching network.
In our article titled “Enhancing Satellite Links: The Moxon-Yagi Dual Band VHF/UHF Antenna,” we introduce a dual-band design optimized for satellite communications. This design amalgamates a 5-element Yagi-Uda array with the Moxon configuration, leveraging the Moxon portion as the excitation point, while the Yagi section is electromagnetically induced for feeding.
In this article, we introduce a modified version of the Moxon antenna featuring two reflector elements, as depicted in the accompanying figure. These reflectors are oriented at an angle of 76° relative to each other. This particular configuration delivers a notable reduction in the beamwidth within the plane of the driven element (the vertical plane denoted as y-z in the figure), resulting in a corresponding increase in gain.
To optimize the performance of this antenna, the gaps have been meticulously adjusted to achieve an input impedance of 47 Ohms precisely at the resonance frequency of 145 MHz, eliminating the need for an external matching network. The key characteristics and outcomes of this antenna design are summarized below:
- Resonance Frequency: 145 MHz
- Input Impedance: 47 Ohms (self-resonant)
- Bandwidth: 7% (VSWR < 2)
- Peak Gain: 6.3 dBi
- Front-to-Back Ratio: 19 dB
- Beamwidth: 130° Horizontal / 80° Vertical
- Polarization: Vertical
As depicted in the figure below, we present the antenna model as simulated using the AN-SOF Antenna Simulator. The three-dimensional radiation pattern is illustrative, showcasing a peak gain of 6.3 dBi. Additionally, the VSWR curve is provided, and it is evident that the resonant frequency of 145 MHz corresponds to the dip in this curve.
Further insight is offered by the polar diagrams at the bottom of the figure, representing the horizontal (on the left) and vertical (on the right) slices of the 3D radiation pattern. These diagrams distinctly show that the vertical pattern is narrower in comparison to the horizontal pattern.
For amateur radio enthusiasts and practitioners, this antenna design serves as an excellent choice when there is a demand for a VHF-frequency directive antenna that is easy to construct, mechanically robust, self-resonant, and delivers outstanding performance.
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!
This is a 4 element broadband directional antenna. More than 50 MHz of bandwidth (SWR < 1.5) around 285 MHz. Gain 7 to 8 dBi. Length 0.52 m and maximum width 0.6 m.
The driven element is shaped like a double arrow and has a folded parasitic element right in front of it.
- 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!
Explore the new AN-SOF User Guide >, where you will find detailed information about its many features, as well as step-by-step examples and tips to help you quickly move forward with your antenna modeling projects.
From this link > you can download 5 examples of antenna models that have less than 50 segments, so the calculations can be run with the trial version of AN-SOF:
- 2 Element Quad
- 2 Element Delta Loop
- HF Skeleton Slot
- Inverted V
- 5 Element Yagi-Uda
In this post, we’re going to dive into the world of HF Skeleton Slot Antennas, a unique array of two tightly coupled loops with a bi-directional pattern.
What is a Skeleton Slot Antenna?
The Skeleton Slot Antenna, believed to originate in the UK post-World War II for TV use, derives its name from the slot antenna. This aperture antenna forms by cutting a rectangular hole in a conducting sheet, effectively acting as a “photographic negative” of a dipole, with the slot serving as the radiating element. Simplifying the design to its bare essentials yields the skeleton slot. For analytical purposes, we can visualize this antenna as two closely interconnected loops sharing a single feed point. The antenna, including its top and bottom loops, as well as simulation results, is shown in the figure below.
This antenna design is known for its bi-directional radiation pattern and is well-suited for high-frequency (HF) bands, specifically within the 14 to 28 MHz range, when appropriately impedance matched. We can observe how the radiation pattern changes within this frequency range, with the gain varying from 4.7 to 6.8 dBi, while the antenna continues to maintain its bidirectionality.
The Key to Self-Resonance
One of the standout features of the Skeleton Slot Antenna is its self-resonant capability. This occurs when the perimeter of each loop is approximately equal to one wavelength at the desired operating frequency, and the ratio between the length and width of each rectangular loop is 3:2. In the example depicted in the figure above, each loop measures 4.5 x 3 meters, resulting in a resonant frequency of 19.8 MHz, as indicated by the dip in the VSWR curve.
Note that the perimeter of each loop is 2 x (4.5 + 3) = 15 meters, which is precisely the wavelength at 20 MHz, very close to the resonant frequency of 19.8 MHz.
In the January 1955 issue of The Shortwave Magazine, there is an article by B. Sykes (G2HCG) titled “The Skeleton Slot Aerial System” (Vol. XII, No. 11, pp. 594-598). In this article, the antenna is described as an array of two dipoles. The author, through experimental findings, concludes that the optimal length of the sides of the entire antenna should be 0.56 times the wavelength (λ), with a total length-to-width ratio of 3:1. These values, applied to each individual loop, result in a perimeter of 2 x (1/2 + 1/3) x 0.56λ = 0.93λ.
However, it’s worth noting that the radiation pattern and input impedance behavior of the antenna correspond more closely to that of a loop-type antenna, composed of two tightly coupled loops in this case. In this configuration, the antenna resonates when its perimeter measures approximately one wavelength. To illustrate this point, you can refer to the article “Input Impedance and Directivity of Large Circular Loops,” which validates AN-SOF results against theory.
Benefits of the HF Skeleton Slot Antenna
1. Bi-Directional Pattern: This antenna’s bi-directional pattern makes it a valuable choice for situations where we need to communicate in two opposite directions simultaneously.
2. Frequency Range: The HF Skeleton Slot Antenna covers a broad frequency range within the HF spectrum, making it versatile for various amateur radio and communication applications.
3. Self-Resonance: Achieving self-resonance simplifies the tuning process and ensures optimal performance at the desired frequency.
In conclusion, the Skeleton Slot Antenna is a remarkable choice for HF communication enthusiasts. Its bi-directional pattern, wide frequency range, and self-resonant capabilities make it a valuable addition to your radio setup.
A balun can be modeled in AN-SOF using an equivalent generator, as the figure below shows. Since voltage sources admit an internal impedance, we can adjust its resistive part to match the antenna input resistance.
Experience versatile communication with this 5-in-1 J-Pole Antenna – your go-to solution for multiband excellence.
J-Pole: A Brief History
The J-pole antenna, more formally known as the J antenna, serves as a vertical omnidirectional transmitting antenna designed for use in the shortwave frequency bands. This ingenious antenna system traces its roots back to 1909 when it was first conceived by Hans Beggerow for deployment in Zeppelin airships. In this initial configuration, the J antenna was suspended behind the airship and comprised a single wire radiator that was half a wavelength long, in series with a quarter-wave parallel transmission line tuning stub. This arrangement was crucial for matching the antenna’s impedance to the feedline.
As technology evolved, so did the J antenna’s applications. By 1936, it had found its way to land-based transmitters, with both the radiating element and the matching section mounted vertically. This new arrangement gave the antenna its characteristic “J” shape, and it was formally christened the “J antenna” by 1943. The J antenna’s versatility and omnidirectional characteristics have made it a staple in the world of radio communication and broadcasting.
Multiband J-Pole Antenna Design
In scenarios where a multiband antenna is required, the deployment of individual J-pole antennas for each band can lead to installation complexities. The design presented in the figure below offers an elegant solution – a vertical element consisting of 5 J-poles, enabling operation across 5 different bands using a single pole.
In this configuration, each “J” corresponds to a specific band, and the position of the feed point is adjusted according to the operating frequency. The corresponding resonance frequency is conveniently indicated in proximity to the feed point for each “J”: 27 MHz, 52.5 MHz, 139 MHz, 224 MHz, and 435 MHz. It’s worth noting that the resonance frequency can be fine-tuned by modifying the feed point’s position. As a result, this design enables self-resonance, eliminating the need for a matching network and yielding a compact, robust solution that spans a considerable range of VHF and UHF frequencies.
The overall height of the pole in this configuration is approximately 5 meters, making it a practical choice for diverse radio communication and broadcasting applications.
Analyzing Current Distribution and Radiation Patterns
The figure provides a comprehensive view of the antenna’s behavior across its operational frequencies. Here, the current distribution on the antenna is depicted, allowing us to identify the active section of the antenna responsible for radiation at each frequency.
At the lower section of the figure, the radiation patterns are presented. Notably, these patterns showcase the antenna’s ability to maintain an omnidirectional radiation pattern in the horizontal plane, ensuring coverage in all directions. However, as the operating frequency increases, the pattern gradually distorts, as clearly demonstrated.
For in-depth analysis and simulations of this antenna’s performance, we offer the AN-SOF model, which includes pre-calculated data. You can easily access this model by clicking the provided button below the figure. It’s important to note that this model intentionally excludes a ground plane, allowing us to isolate and examine the antenna’s behavior without external factors that may influence its performance.
This 5-in-1 J-Pole Antenna solution empowers engineers and radio enthusiasts with a versatile tool for achieving multiband excellence. If you have a keen interest in J antennas, we invite you to explore our article, where we model a J-fed collinear antenna designed for the 2 m band.
- More compatibility for those who use the NEC format: RP, LD, GM, GS, GH, GA, and EX5 commands can now be imported into AN-SOF.
- The Note panel now displays an error report when importing NEC files.
- New Zin button on the toolbar for quick access to input impedances and VSWR.
Here is a relatively compact array of 5 square loops for 145 MHz. It does not need a matching network since the input impedance is practically 50 Ohm. Gain 12 dBi. Beamwidth 50 deg. F/B 20 dB.
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.
- See how the radiation pattern changes with frequency in AN-3D Pattern. The near field heatmap and current distribution can also be viewed dynamically by changing the operating frequency.
- You can chat directly with technical support by going to the Help menu in AN-SOF (only available for the licensed version).
Enjoy this new version!
In amateur radio satellite communication, the use of directional antennas is a fundamental necessity. Operating on both the VHF and UHF bands with a single antenna can present a considerable challenge. In this article, we introduce a dual-band antenna design that covers both VHF and UHF bands, accomplished by combining two distinct antenna types: the Moxon antenna for VHF frequencies and the Yagi antenna for UHF frequencies. One of the notable advantages of this design is that it utilizes a single feeding point.
The Moxon antenna, also known as the Moxon rectangle, stands as a simple yet mechanically robust antenna configuration composed of two elements: a driven element and a parasitic element. It derives its name from the renowned radio amateur, Les Moxon, with the call sign G6XN. In essence, the Moxon antenna resembles a Yagi-Uda antenna with two folded dipole elements, one serving as the driven element and the other as the reflector element. A tunable gap exists between these two folded dipoles, allowing for adjustments to minimize the VSWR (Voltage Standing Wave Ratio) at VHF frequencies. Consequently, it is a mechanically tunable antenna that eliminates the need for an impedance matching network. In our dual-band design, as illustrated below, the Moxon segment of the antenna serves as the excitation point.
The accompanying figure also depicts the Yagi-Uda portion of the dual antenna. This section adheres to the conventional Yagi array configuration, comprising a reflector element, a driven element, and three directors. However, the driven element in this context does not receive direct excitation; instead, it is powered indirectly through electromagnetic induction from the driven element of the Moxon array. The gap separating the Moxon and Yagi sections of the combined antenna can be mechanically adjusted to minimize the VSWR at UHF frequencies.
In the analyzed frequency ranges, this VHF/UHF dual-band antenna exhibits self-resonance with an input impedance close to 50 Ohms, obviating the requirement for a matching network. To optimize performance in each band, fine-tune the gaps as indicated in the figure below.
Additionally, the figure provides VSWR curves as a function of frequency. In the upper section, it is evident that the antenna resonates at 147 MHz, while in the lower section, it resonates at 442 MHz. The figure also presents radiation patterns for both frequency bands, with gains of 6.3 dBi at VHF and 12 dBi at UHF.
Detailed AN-SOF models, along with antenna dimensions and calculations, are available for download through the buttons located below the figure.
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.
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.
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.
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.
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
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.
- 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.
The Scilab script shown in this video, Isocontours script, is ready to use together with AN-SOF. It allows us to plot level curves or isocontours of a field pattern. The example shows the electric field pattern at the soil level just below an Inverted-V antenna.
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.
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.
- 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
When creating an antenna model or a wire structure in the AN-SOF workspace, several crucial aspects must be considered to ensure the model’s validity. Particularly, when dealing with complex structures composed of numerous wires, the possibility of errors arises. However, AN-SOF provides three essential commands that can be executed in any order and whenever needed to aid in error detection within the model. These commands can be accessed by navigating to the AN-SOF main menu and selecting Tools, Fig. 1, where the following options are available:
Checking Individual Wires
The Check Individual Wires command performs a comprehensive assessment of three essential parameters associated with each wire individually. Wires with errors will be highlighted in red, while those with warnings will be highlighted in yellow. The parameters subjected to evaluation are illustrated in Fig. 2(a) and are as follows:
- Segment Length / Shortest Wavelength (ΔL/λmin): This parameter examines the ratio between each wire segment’s length, ΔL, and the shortest wavelength, λmin, within the frequency sweep. It is essential to ensure that the segment length is sufficiently small compared to the shortest wavelength, representing the worst-case scenario. The criteria defining whether a wire is considered “OK,” “Warning,” or “Error” are as follows:
- ΔL/λmin ≤ 0.1 → The wire is considered OK.
- 0.1 < ΔL/λmin ≤ 0.2 → The wire is marked as a warning.
- ΔL/λmin > 0.2 → The wire is identified as having an error.
- Cross-Section Size / Shortest Wavelength (d/λmin): This parameter focuses on the wire’s cross-section diameter, d, relative to the shortest wavelength, λmin, within the frequency sweep. If the wire’s cross-section is not circular, the equivalent radius is calculated to determine the diameter. The cross-section of each wire must be sufficiently small compared to the wavelength. The criteria for evaluating a wire’s status are as follows:
- d/λmin ≤ 0.05 → The wire is considered OK.
- 0.05 < d/λmin ≤ 0.1 → The wire is marked as a warning.
- d/λmin > 0.1 → The wire is identified as having an error.
- Thin-Wire Ratio (Segment Diameter / Length): This parameter is particularly relevant when increasing the segmentation in a given wire for purposes such as convergence analysis. As the segmentation increases, the segment lengths decrease, causing each segment to become “thicker” in the sense that its diameter, d, approaches its length, ΔL. AN-SOF provides two different Kernels for calculations: the default Exact Kernel, which allows precise calculations on very thick wires, and the Extended Kernel designed for wire segments with a diameter up to 3 times their length (d/ΔL = 3). If the Exact Kernel is not enabled in the Setup tab > Settings, the segment diameter-to-length ratio, d/ΔL, will be checked. This ratio is referred to as the “thin-wire ratio,” and the evaluation criteria are as follows:
- d/ΔL ≤ 2 → The wire is considered OK.
- 2 < d/ΔL ≤ 3 → The wire is marked as a warning.
- d/ΔL > 3 → The wire is identified as having an error.
Errors associated with a wire segment that is too long (ΔL/λmin > 0.2) can be easily rectified by increasing the number of segments for the affected wire. However, it is crucial to enable the “Exact Kernel” option when significantly increasing the number of segments, as each segment becomes thicker. Only disable the Exact Kernel when prioritizing computational speed over accuracy.
For cases involving very thick wires (d/λmin > 0.1), it is advisable to represent them using a cylinder composed of a grid of wires, instead of a single wire.
By conducting these individual wire checks, users can proactively identify and address any potential issues related to wire segment length, cross-section size, and thin-wire ratios within their antenna models, ensuring accurate and reliable simulation results.
Checking Wire Spacing
The Check Wire Spacing command plays a critical role in verifying that each wire within the model does not overlap with others, Fig. 2(b). The proximity between two wires is permitted as long as their radii allow it, without resulting in an actual overlap. Wires found to be in error due to overlapping will be highlighted in red, while those with warnings will be marked in yellow. In cases where multiple wires’ ends are connected at a common point, as Fig. 2(c) shows, overlaps may be detected and categorized as errors or warnings. However, it is important to note that such overlaps do not adversely affect the simulation calculations, as long as the limits specified in the previous evaluation items are adhered to.
At points where multiple wires are interconnected, AN-SOF ensures that Kirchhoff’s currents law is strictly enforced. This law states that the algebraic sum of currents meeting at a point must be zero. By fulfilling this requirement, AN-SOF effectively eliminates any errors that could potentially arise due to overlapping between wires.
In summary, the Check Wire Spacing command serves to identify and flag any instances of wire overlap, providing a visual indication of errors or warnings. Nevertheless, it is reassuring to know that such overlaps, particularly at points where multiple wires converge, do not compromise the accuracy of the calculations, as AN-SOF guarantees the fulfillment of Kirchhoff’s currents law at these interconnected points.
Deleting Duplicate Wires
The Delete Duplicate Wires command serves the crucial purpose of identifying and removing any duplicate wires present within the model. A duplicate wire is defined as one that completely overlaps another wire along its entire length. In the case of linear wires, mere coincidence of their endpoints is sufficient for them to be duplicates. Such duplicates are not permissible in a model because they lead to a singular matrix in the Method of Moments, analogous to repeating an equation in a system of linear equations. Running this command ensures the elimination of all duplicate wires from the model.
To ensure a robust and accurate simulation, it is considered a best practice to check specifically for duplicate wires before initiating any calculations.
In summary, we have explored crucial commands for detecting and correcting errors in AN-SOF antenna simulations. “Check Individual Wires” validates wire parameters, such as segment length, cross-section size, and thin-wire ratio, ensuring model integrity. “Check Wire Spacing” identifies overlaps between wires, essential for precise simulations. “Delete Duplicate Wires” eliminates redundancy, preventing singular matrices in calculations. By adopting these practices, users can achieve robust simulations, enhancing the accuracy and reliability of AN-SOF antenna models.
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.
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).
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.
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.
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.
When it comes to simulations, there is always a trade-off between speed and accuracy. However, in the initial stages of antenna design, prioritizing speed is often crucial. To help you speed up your calculations in AN-SOF, here are some valuable tips:
- Start with the minimum number of segments: Begin with 10 segments per wavelength. AN-SOF allows you to set the minimum recommended number of segments by entering “0” (zero) as the number of segments for any wire. In the case of a wire grid, use one segment per cell side if the electrical size of each cell is less than 10% of the wavelength.
- Adjust the Quadrature Tolerance: Navigate to the Setup tab > Settings panel and set the Quadrature Tolerance between 5% and 10%. This parameter primarily affects simulations involving parallel wires that are very close to each other, approximately two wire radii apart.
- Reduce the Interaction Distance: Go to the Setup tab > Settings and set the Interaction Distance to zero. This setting is relevant only for parallel wires that are in close proximity to one another.
- Optimize spatial resolution for gain, directivity, and efficiency calculations: For calculating gain, directivity, and efficiency, a spatial resolution of 5 or 10 degrees in the far-field is usually sufficient. Access the Setup tab > Far-Field panel and set Theta Step to 5 degrees and Phi Step to 10 degrees.
- Calculate only what you need: Instead of running unnecessary calculations, focus on what you really require. If you need currents and far-field data, click on Run Currents and Far-Field (F11). In the case of solely being interested in the input impedance, go to Run > Run Currents (Ctrl + R) in the main menu.
By implementing these strategies, you can significantly enhance simulation speed. In fact, the figure provided illustrates an example where the simulation runs more than three times faster, especially when setting the Interaction Distance to zero. You can find the “car.emm” project in the Examples folder, which is installed along with AN-SOF, or you can download the model by clicking on the button below.
Remember, finding the right balance between speed and accuracy is essential, and these tips will help you achieve faster simulations in AN-SOF Antenna Simulation Software.