Fullscreen HTML5Med Res (??MB)HTML4

Antenna Analysis and Optimisation Last month, we introduced a range of concepts related to antennas, such as resonance, reactance, complex impedance, Smith charts and dipoles. We will now look at using software to tune antennas. It can save a lot of time compared to manual calculations and experimentation. Part 2 by Roderick Wall, VK3YC A fter reading the article last month, you should understand how the complex impedance of an antenna can be plotted on a Smith chart. You should also realise why it is important to use an antenna at its resonant point and with a VSWR as close to 1:1. The question then becomes, if you have a real-world antenna and can measure its complex impedance, how do you know how to make it resonant? And how do you improve the VSWR if it’s significantly worse than 1:1? Luckily, free computer software makes doing all that relatively straightforward. The “Smith V4.1” software I use can be downloaded from www.fritz. dellsperger.net There is a free version and a paid version that has extra features; the free version is suitable for our purposes. Fritz also has examples and a very good introduction to the Smith chart that can be downloaded. Before using this software, it needs to be set up correctly. After starting Smith, left-click on the “Tools” menu and select “Settings”. Under the “Smith chart” heading, make sure “Z-plane (on/off)” is selected and “Y-plane (on/off)” is not selected. This displays the results on a Z-Smith chart. Also make sure that under the “General” heading, the Default Zo = 50W, then click “OK”. Refer to Fig.8, an antenna impedance vs wavelength plot reproduced from last month. If the driven element length is increased from 0.25 of the wavelength at point (b) to 0.2654 of the wavelength at point (c), the real resistance increases from 36W to 50W, which is required to obtain a VSWR Screen 1: using the Smith V4.1 software, click the Keyboard button shown to be brought to Screen 2. Fig.8: reproduced from last month, this plot of the complex impedance of a Marconi antenna versus wavelength provides some useful examples for designing matching networks. 48 Silicon Chip Australia's electronics magazine Screen 2: for the first example, fill in this menu with the values as shown. siliconchip.com.au Screen 3: this toolbar lets you insert different elements into the circuit you want to test. It is located at the upper right of the main window as shown in Screen 4. of 1:1 for a 50W system. However, the antenna is no longer resonant; its reactance is +j65.65W (inductive). A series capacitor can be added to make the antenna resonate. Let’s use the Smith software to plot a Smith chart for the antenna at point (c) in Fig.8, with a length of 0.2654λ and a complex impedance of (50.1 + 65.65j)W. Example #1 To enter the antenna’s complex impedance, click the “Keyboard” button in the toolbar (see Screen 1). Select Cartesian and enter real resistance (Re) and imaginary/reactance (Im) values as shown in Screen 2. Also change the frequency to 28.3972MHz and click “OK”. On the Smith chart, you will see that DP 1 is sitting on the unity constant impedance (real resistance 50W) circle, between the +j50W and +j100W lines, indicating an inductive reactance of +j65.65W. In the “Schematic” window, the antenna is shown as Zl. To show what the VSWR would be if this antenna were connected to the transmitter without a matching circuit, leftclick “Tools” and select “Circles”, then select the VSWR Tab. Under the “Defined” heading, select both “3” and “5” then click OK. The Smith chart shows that the antenna VSWR will be between 3:1 and 5:1, then go back to the VSWR tab. Now click “Clear all” and type “3.5” under the “Select other” heading, then click “Insert” and click OK. This shows the VSWR to be 3.5:1. We want a VSWR of 1:1. To see where we want to move to, add a constant VSWR circle at 1.05 and click OK. For the best VSWR, we need to end up in the middle of the constant VSWR 1.05 circle. Click the insert Series Inductor “L” button, second from left in Screen 3. The cursor moves in the wrong direction as it moves further away from where the best VSWR is. The inductor is making it more inductive than it already is. To move the VSWR in the correct direction, a capacitive reactance of 65.65W is required to cancel the inductive reactance, making the antenna resonant at (50 + j0)W. Right click to remove the inductor and click the Insert Series Capacitor “C” button (on the left in Screen 3). Move the cursor and click in the middle of the VSWR 1.05 circle. Using maths, we see that a capacitance of 85.4pF gives a capacitive reactance of 65.65W at 28.4MHz. Xc = 1 ÷ (2πfC) and C = 1 ÷ (2πfƒXc). The Smith chart should now look as shown in Screen 4. The “Datapoints” window shows complex impedances for DP 1 and TP 2, while the Schematic window shows the equivalent circuit. We have just designed our first matching circuit by adding a series capacitor between the driven element and the antenna terminals. The capacitor cancels the inductive reactance, making the impedance (50 + j0)W. Screen 4: our initial example circuit (incorporating just a series capacitor) produces this Smith chart. siliconchip.com.au Australia's electronics magazine March 2025  49 The antenna can now be connected to any length of 50W coaxial cable to the transmitter, and the VSWR will be close to 1:1. The maximum possible power will be transferred to the antenna. There will be some losses in the transmission line and matching components; they should be kept as low as possible. Another method to determine capacitor value without using a Smith chart is to adjust the driven element length until the real resistance is 50W. Then add a series-connected variable capacitor and adjust it until a VSWR of 1:1 is obtained. You can then use a capacitance meter to measure the capacitance, allowing you to replace the variable capacitor with a fixed one of a similar value. You can also calculate the required capacitance, use the formula C = 1 ÷ (2πfƒXc). We know the necessary capacitive reactance (Xc) is 65.65W because the antenna inductive reactance is 65.65W, and the frequency (ƒ) in this case is 28.3972MHz. You can also use an online capacitor calculator. Example #2 (5/8-wavelength antenna) The next example is a 5/8-wavelength antenna, shown at point (e) in Fig.8. A 5/8 antenna is often used instead of a 1/4-wave Marconi antenna because it has a lower radiation angle. Select File → New, then enter the complex impedance (49.95 – j232)W and 28.3972MHz into the Smith chart software. The real resistance of 50W is already sitting on the unity resistance circle we call the Z-matching circle, the road to where VSWR is 1:1. This time, insert a series inductor, move the cursor and click on the middle of the Smith chart where the VSWR is 1:1, ie, (50 + j0)W. Screen 5 shows the results. Using maths, we see that a 1.3μH inductor gives an inductive reactance of 232W at 28.4MHz (XL = 2πƒL and L = XL ÷ 2πƒ). This time, an inductor is needed to cancel out the capacitive reactance to make the antenna resonant. There is a method to adjust a 5/8 antenna without using a Smith chart. Adjust the element length to obtain a real resistance of 50W, then use a series variable inductor to obtain a VSWR of 1:1. Mathematics can be used to calculate the required inductor value, L = XL ÷ 2πƒ. We know the required inductive reactance, XL, is 232W because the antenna’s capacitance reactance is 232W. In the above two examples, the real resistance part of the complex impedance was 50W, so it already sat on the unity constant resistance circle. The usual procedure to obtain a VSWR of 1:1 is to first get the point onto the unity resistance circle and then move it around to (50 + j0)W. For the above two examples, the matching capacitor or inductor was connected in series with the driven element at the antenna. Example #3 (parallel components) Another method of making an antenna resonant is with hairpin inductors. The hairpin matching component is connected in parallel with the antenna terminals. When parallel matching components are used, the admittance Y-plane must be used. To set this up, click File→ New and then Screen 5: the Smith chart for our second example using the complex impedance of (49.95 − j232)W. Screens 4-6 are measured with a fixed frequency of 28.3972MHz. 50 Silicon Chip Australia's electronics magazine siliconchip.com.au “Tools” menu and select “Settings”, then enable the Y-plane. Make sure the Z-plane is not selected. This will display results on a Y-Smith chart. Enter a complex impedance of (32.15 – j24.55)W and a frequency of 28.3972MHz into the Smith software. As the real resistive part is 32.15W and not 50W this time, it sits on the blue unity conductance circle at 20mS (millisiemens). This is what we also call the Y matching circle, another road to where the VSWR is 1:1. Click the “Insert Parallel Inductor” button and move the cursor to click in the middle of the Smith chart at the (50 + j0)W point. The parallel inductor value will be close to 374nH – see Screen 6. The curved lines on this chart are called constant susceptance circles. This example shows that a Marconi antenna shorter than a 1/4-wavelength can be made resonant with a parallel inductor. This may be suitable for a short (160m) vertical Marconi antenna if its capacitive reactance is high enough to get onto the Y-matching circle. If its capacitive reactance is not Fig.12: hairpin inductors formed from simple metal rods are often used to create a basic matching network for Yagi antennas, which are typically on the capacitive end of resonance. high enough, a capacitor can be added to get it there. Other possible solutions will be discussed overleaf. This example can also be used to show hairpin matching for a 1/2-­wavelength centre feed dipole. The 374.6nH inductor is half of the hairpin matching inductor. Hairpin inductors are often used on Yagi antennas where the driven element is a centre-­ feed dipole. When using two Marconi antennas to make a Hertz dipole antenna, as described last month, the antenna impedance is doubled: 50W × 2 = 100W. The other side element of the dipole also needs a parallel 374.6nH inductor, as shown in Fig.12. A 2:1 balun transforms the 100W impedance to match the transmitter’s 50W. The driven dipole element length is shorter than half the wavelength (1/4-wavelength per side), giving the complex impedance capacitive reactance and making it sit on the Ymatching circle. Each side of the dipole is similar to an LC matching circuit. The hairpin is the inductor, while the antenna complex impedance supplies the capacitive reactance without using a discrete capacitor. Screen 6: the Smith chart for example #3 with a complex impedance of (32.15 − j24.55)W. This one requires an inductor to be added in parallel with the antenna to achieve a VSWR of 1:1. siliconchip.com.au Australia's electronics magazine March 2025  51 Screens 7 & 8: two example solutions and Smith charts for example #4 with complex impedance (36.32 + j0)W. 52 Silicon Chip Australia's electronics magazine siliconchip.com.au Our example is a dipole antenna in free space with no directors or reflector elements. Suppose directors or reflector elements are added and placed above ground. In that case, the coupled complex impedance for the driven dipole element before matching will be different than for a self-impedance naked (uncoupled) element. The balun impedance ratio may also be different to this example. A 4:1 balun is used when the centre-feed dipole antenna impedance is 200W with the parallel inductors. Example #4 Let’s consider a 1/4-wavelength 36W resonant antenna. The VSWR is 1.4:1, below what might be acceptable. Two matching components can be used to fix this. The complex impedance is (36.32 + j0)W and is not sitting on the blue Y-matching circle or the red Zmatching circle. In this example, we can use a 251pF series capacitor to get it onto a matching circle. Then a parallel inductor brings us to the centre, (50 + j0)W – see Screen 7. Screen 8 shows another possible solution, with a series inductor and parallel capacitor forming a low-pass filter as in Screen 8 rather than a highpass filter. It also achieves a VSWR of 1:1. Fig.13: we want to get the antenna’s complex impedance onto one of these red circles, as we then only need to add one more component to achieve a VSWR close to 1:1. This diagram provides guidance on what component to add and how to add it to get the antenna onto one of those circles. General rules for achieving resonance The following rules can be used when designing matching circuits. Fig.13 provides guidance on whether to use a series or parallel capacitor or inductor, depending on where your antenna falls on the Smith chart. Similarly, Fig.14 shows the ‘forbidden areas’ and suggests the first component to add to get onto a matching circle. There may be two or more possible solutions to a matching requirement. Fig.15 shows another way of determining what components to use. To move from Capacitive (-j) to Inductive (+j), add an inductor in series or parallel, as shown. To move from Inductive (+j) to Capacitive (-j), add a capacitor, either in series or parallel, as shown. When selecting components for matching circuits, ensure their voltage and current ratings are sufficient for the power being transferred to the Fig.14: most antennas can be brought to a VSWR of 1:1 using one of these eight types of two-component matching networks. siliconchip.com.au Australia's electronics magazine March 2025  53 Silicon Chip Binders REAL VALUE AT $21.50* PLUS P&P Are your copies of Silicon Chip getting damaged or dog-eared just lying around in a cupboard or on a shelf? Can you quickly find a particular issue that you need to refer to? Keep your copies safe, secure and always available with these handy binders These binders will protect your copies of S ilicon C hip . They feature heavy-board covers, hold 12 issues & will look great on your bookshelf. H 80mm internal width H Silicon Chip logo printed in goldcoloured lettering on spine & cover Silicon Chip Publications PO Box 194 Matraville NSW 2036 Order online from www. siliconchip.com.au/Shop/4 or call (02) 9939 3295 and quote your credit card number. *see website for delivery prices. 54 Silicon Chip Fig.15: here’s another way to visualise what type of component needs to be added in which manner to achieve resonance in your antenna. antenna. They must also be suitable for radio-frequency use, at the frequency they will be used at. For inductors, that means either aircored inductors (which can operate at virtually any frequency) or those with core materials specifically designed for use up to the radio frequency range you will be using. For capacitors, you will generally need to use low-inductance, low-loss ceramic or plastic film types, depending on how high a frequency they will operate at. Many large parts suppliers have specific RF inductor and capacitor categories or search tags. Check the data sheets of the devices you plan to use to verify that they can operate at the required frequencies. When designing matching circuits for a band of frequencies: 1. Measure the complex impedance of the antenna at the lowest frequency. 2. Measure the complex impedance of the antenna at the highest frequency. 3. Measure the complex impedance of the antenna at the centre frequency. 4. Design the matching circuit for the centre frequency. Australia's electronics magazine 5. Enter one of the antenna band edge complex impedances and frequencies (lowest or highest) into Smith. 6. Insert the matching circuit components with the values determined for the centre frequency. 7. Add constant VSWR circles to determine the VSWR at the band edge. 8. Repeat for the other band edge (lowest or highest). Component values can be edited by clicking on a component in the schematic window, altering their values in the window that appears, then clicking “OK.” We still need to address the bandwidth of the matching components; that is the topic of the third and final instalment of this series, which will be published next month. In the meantime, you can perform an exercise to check that you have understood the information in this article. There are four ways to achieve resonance for an antenna with a complex impedance of (25 + j43)W in a 50W system. See if you can figure out all four possible matching networks. SC siliconchip.com.au