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Antenna Analysis and Optimisation Over the last two articles, we have explained how antenna matching and VSWR work and given instruction on using the free “Smith” software to design antenna matching networks. This final part in the series explains how to determine the bandwidth of an antenna matching network. Part 3 by Roderick Wall, VK3YC A fter reading the article last month, you should know how to use the free “Smith” software to design an antenna matching network. This will allow you to bring most antennas to resonance and achieve a VSWR close to the ideal of 1:1 at a specific frequency. Of course, radio transmitters and receivers often need to operate over a range of frequencies. You need to be able to design the matching network with enough bandwidth to pass signals over the range of interest. We will now look at using another free software package to achieve that. Smith charts also have ‘constant-Q curves’ that can be used to control the bandwidth of a matching network. For this, we will use the Iowa Hills Smith Chart software; like the Smith program we used last month, it is also a free download. This software used to be available from https://iowahills.com but that website is unfortunately gone. Luckily, someone kept a copy of it, so you can download a zip of the whole website from siliconchip.au/link/ac0y Within that zip, navigate to the subdirectory “cb.wunderkis.de\wk-pub\ www.iowahills.com\Downloads” and you will find a file named “Iowa Hills Smith Chart.zip”. Extract that, then unzip it, and you will be able to run the executable. We tested it on Windows Screen 9: this C/L/C/L matching network comes close to the black Q = 1 curve. 48 Silicon Chip 10 and 11, and it worked fine on both versions. Screens 9-12 show two different matching networks that match a (118 – j99.5)W load to a 50W source. One using a Q = 1 curve (Screens 9 & 10) and the other using a Q = 6 curve (Screens 11 & 12). The matching networks were kept within the constant-Q curves as shown. The Return Loss graph (Screen 10) shows that the bandwidth for the Q = 1 network in Screen 9 is 4MHz wide for a VSWR of 1.22:1. On the other hand, Screen 12 shows that the bandwidth for the Q = 6 network (Screen 11) is 1MHz. To achieve the wider bandwidth for the Q = 1 network, four Screen 10: the frequency response plot of the matching network/antenna combination shown in Screen 9. Australia's electronics magazine siliconchip.com.au components were used, while the Q = 6 network used just three components. The antenna Q sets the lowest possible Q and the widest possible bandwidth. If the antenna Q is high, the bandwidth will be narrow regardless of the matching network. The Q = 6 matching network demonstrates that the bandwidth can be controlled to make it narrow if required. These plots were modelled using ideal capacitors and inductors, although the Iowa Hills Smith Chart software can also model non-ideal components. The return loss graph in Screen 12 indicates the bandwidth is around 1.25MHz for a VSWR of 1.22:1. Using the Iowa Hills software This software works similarly to Fritz’s Smith chart software but it has its own quirks and procedures. Let’s go through the steps required to reproduce Screens 9 through 12. Launch SmithChart.exe and make the window larger if you’d like to. Then, in the upper-left corner, change the frequency (F0) to 28.4 (MHz) and the Span to 5 (MHz). Go to the “Set Load” menu and choose the “Load, Source, and Parasitics” menu option. In the dialog box that pops up, change the Load Impedance to 118 real and -99.5 imaginary numbers giving (118 – j99.5)W, click Apply, then click Close. You will then see the red (antenna) and blue (source) points in the correct positions on the Smith chart. Next, we add the Q = 1 curve by selecting the “Q and VSWR Circles” option, also under the “Set Load” menu. In the right-hand column under Q, change the first 0 to 1 (for Q = 1), click Apply and then click Close. Now we can build our matching network. We insert components starting at the Load end, so open the “Shunt” menu and click “Inductor”. Click on the upper black Q = 1 curve, and you will see that the inductor inserted in the lower-left corner of the screen has a value of 620nH. Next, click “Series” and then “Capacitor”, then click on the horizontal blue line running across the middle of the chart to add a 56pF capacitor. Repeat those two steps to add a 560nH shunt inductor and a 110pF series capacitor to reach the blue dot in the middle of the chart. You should then have a display that matches Screen 9. Next, click on the Return Loss radio button at centre left of the screen and you will be greeted by a plot that matches Screen 10. The steps to reproduce Screen 11 & Screen 12 are similar to the above except that you add the Q = 6 curve Screen 11: this C/C/L matching network touches the black Q = 6 curve so it has a smaller bandwidth than Screen 9. siliconchip.com.au instead of Q = 1 and then you add a shunt inductor, followed by a series capacitor and finally, a shunt capacitor. Refer to Screen 11 to see where to click to get the same values of 200nH, 270pF & 240pF, respectively. After returning to the Smith chart, you can right-click on it four times to remove the components you added, change the Q curve via the “Q and VSWR Circles” menu option and then proceed to add the new matching components. Screen 13 shows the result of clicking the “Sweep SC” radio button on the left after setting the span to 1.25 (MHz) for the example in Screens 11 & 12. This Sweep value is the same as the bandwidth, and the black line on the chart confirms that the 1.25MHz sweep fits inside the constant VSWR 1.22 circle. In this example, hitting the Q = 6 curve while matching keeps the bandwidth narrow at 1.25MHz. You can use this approach to limit the bandwidth in your matching networks to just what is required for better selectivity. Transmission lines Smith charts can be used to determine what the impedance is at each end of a transmission line and to show how transmission lines transform impedance. Screen 12: the frequency response plot of the matching network/antenna combination shown in Screen 11. Australia's electronics magazine April 2025  49 ◀ Screen 13: by enabling the Sweep feature, we get the black line that shows how the VSWR varies over the frequency range of interest. Screen 1: click this Keyboard button in the Smith V4.1 software to type in the complex antenna impedance. The Velocity Factor (VF), also called wave propagation of velocity, is the ratio of the speed of an electromagnetic wave through a transmission line to that in a vacuum. Velocity Factor equals the reciprocal of the square root of the dielectric constant K (relative permittivity εr) of the transmission line. Use the following formulas to convert between VF and K: VF = 1 ÷ √K K = 1 ÷ VF2 For this analysis, we will return to Fritz’s Smith chart software that we introduced last month. Start a new chart and insert a point at (50 + j65.65)W at 28.4MHz using the Keyboard button shown in Screen 1 (reproduced from last month). Next, insert a transmission line by clicking the insert transmission line button shown in Screen 3. It’s the fourth from the left in that image. Leave the transmission line impedance as 50W and set the Dielectric Constant (εr) to 2.2956, which corresponds to a VF of 66%. This can be changed later if required for testing different transmission lines by clicking on the transmission line in the schematic window. The schematic window shows both the electrical length and the mechanical length for the transmission line, as you can see in Screen 14. When you click OK, you will need to set the length of the transmission line. Move the mouse to intersect with the 20m blue circle at lower left, visible in Screen 14, and click there. You will see that the transmission line length is set to 0.2495λ, effectively 1/4 of the wavelength. When both ends of a 50W transmission line are terminated with (50 + j0)W, the line will not transform the impedance and it can be virtually any length. However, in this example, the antenna is (50 + j65.65)W so the 50W transmission line will transform the antenna impedance to about (18.415 – j24.283)W. The impedance at the transmitter source end depends on the length of the transmission line. Note that the VSWR did not change from 3.4:1. VSWR is the same at both ends for any length of transmission line; the transmission line runs around the constant VSWR circle. Try different impedance transmission lines in Smith and see what happens. In this example, you can add a parallel inductor of around 214nH to bring the VSWR to 1:1. This demonstrates how a transmission line can be part of an impedance-matching circuit. Note how the matching component is at the transmitter end of the transmission line and not at the antenna end, so there will be power travelling in both directions along the transmission line as in Fig.10 (from part one). In this example, the 1/4-wavelength transmission line moves the antenna from one matching circle to another. This example demonstrates why, when you are analysing an antenna or antenna element, the coaxial cable between it and the antenna analyser should be short as possible for accurate measurements. If an antenna analyser were connected to the transmitter end of the transmission line in this case, it would give a reading of (18.356 – j24.101)W and not the antenna impedance of (50 + j65.65)W. Screen 3: this toolbar lets you insert different elements into the circuit you want to test. This image and Screen 1 have been reproduced from last month’s article. 50 Silicon Chip Australia's electronics magazine siliconchip.com.au Screen 14: using a 1/4-wavelength transmission line and a parallel inductor for antenna matching. Screen 15: using a short transmission line and a series capacitor for antenna matching. siliconchip.com.au Australia's electronics magazine April 2025  51 If a transmission line has the same impedance as the system and is 1/2-wavelength long or a multiple of 1/2-wavelength, the complex impedance will be the same at both ends of the transmission line. That’s another way of saying that a 1/2-wavelength transmission line goes in a complete circle on the Smith chart. If the transmission line is made exactly half a wavelength long, Smith will not show it because it is effectively just a point. Try different impedance transmission lines in Smith and see what happens. Screen 15 shows a transmission line being used to get onto a matching circle, with a series capacitor to complete the match. Transmission lines of different impedances and lengths are often used with antennas for matching impedances. Screen 16 shows a 50W open stub (OS) being used to complete a match. A parallel capacitor or shorted stub (SS) could have been used instead of the open stub. Fig.16 is a two-metre Zepp J-pole antenna. It uses a transmission line to match a half-wavelength radiator element. The radiator is just under half a wave parallel feedline for tuning. This concept evolved into the Zepp J-pole antenna. Exercises for the reader Fig.16: the Zepp antenna is a clever configuration (also known as a J-pole antenna) providing inherent transmission line matching. wavelength long, while the matching transmission matching line is around a quarter wavelength. The Zepp antenna was invented by Hans Beggerow for use on the German Zeppelin airships. Trailed behind the airship, it consisted of a half-wavelength long radiator with a quarter Antenna tuners sometimes use the high-pass T configuration, with series variable capacitors at each end and a parallel inductor (to ground) in the middle. By varying the capacitances, this allows them to get a decent match with a wide range of antennas. You can simulate this in Smith and experiment with component values to get various antennas to a VSWR of 1:1. Other antenna tuners use a low-pass pi configuration, which has a parallel variable capacitor at either end and a series inductor in the middle. You can experiment with that configuration too. Arguably, the low-pass configuration is better since it will filter out unwanted harmonics that may cause interference, whereas the high-pass T configuration will pass the harmonics through. As a final exercise for the reader, produce a Smith chart showing a 305W transmission line being used to match a Zepp antenna with a complex impedance of (1889 – j0.0212)W to a SC 50W system. Screen 16: a series transmission line along with an open stub transmission line can also be used for matching. 52 Silicon Chip Australia's electronics magazine siliconchip.com.au