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Yagi antenna design question
This will be the last word I have on this topic.
I have placed two files he www.k6mhe.com/n7ws/N7WS_Yagi_Resonant.EZ and he www.k6mhe.com/n7ws/N7WS_Yagi_Shortened.EZ The files are models of my 20-meter three-element Yagi that are as nearly representative of the physical antenna and its location as I can make them. The only difference between them is the half-length of the DE. The actual antenna uses the shortened version with a stub (Beta) matching/balun arrangement. Two photos of the details of this are he www.k6mhe.com/n7ws/YagiFeed-1a.jpg and he www.k6mhe.com/n7ws/YagiFeed-2a.jpg The photos were taken with the antenna mounted on the tower and the tower folded over in case you're wondering about the orientation. For the purposes of the discussion I have removed the stub matching system from the model. The following transformation and matching exercise can be performed using a Smith Chart, your favorite computer program or with pencil on the back of an envelope. I happen to prefer, and highly recommend, AC6LA's XLZIZL.xls Excel workbook for this stuff. First let's analyze the full-length, resonant DE version. After running the analysis we (should) have a feedpoint Z of 26.76 +j0 and a gain at the selected elevation of 12.91 dBi. The SWR is 1.87:1. Instead of the integral stub, which Yuri believes is part of the antenna that is "folded back" along the boom, I will move the matching system away from this location using an ideal ½ wavelength (34.7 foot) transmission line with an ideal current balun at the antenna end. I don't believe anyone would argue that the feedpoint impedance is not replicated exactly at the input end of this line. At the input end of the lossless line, the Z is of course, 26.76 +j0. Because, as will be shown, the stub matching system is nothing more than an L-network; I will use the same at the input of the half- wavelength line. I begin by inserting a series capacitor, C = 448 pF and Q = 1000. At the input side of this capacitor the Z is now: 26.785 -j25.062. If using XLZIZL, the loss in this capacitor is shown as 0.004 dB, because Q is not infinite. Continuing, I place a shunt inductor, L = 0.6, Q = 200 across the input of the series capacitor. The resulting input Z = 50.00 +j0.2. The total network loss is 0.02 dB. This is the baseline. Returning to the shortened driven element version, after analysis, we find that the input Z = 24.55 -j25.2 and the gain is unchanged at 12.91 dBi. At the input end of our magical ½ wavelength line, the Z remains 24.55 -j25.2. Once again using the L-network system, I find that the series capacitor is unnecessary and I can proceed by adding a shunt inductance. Rather than using Yuri's "preferred" discrete inductor, let's use a "lossy" stub. Instead of using the large diameter, parallel tube stub of the actual antenna, I'll use a standard transmission line for the stub. XLZIZL has a number if transmission lines and their parameters "built in," including the Wireman ladder lines. The parameters for these are those I derived in my ladder line paper. http://www.k6mhe.com/n7ws/Ladder_Line.pdf Selecting Wireman 553, shorting one end and placing the other in parallel with the input to the lossless line and doing a little manipulation and I find that a 14.85" length makes the Z = 50.12 +j0.18. The network loss remains 0.02 dB. So much for this less than ideal stub vs. Yuri's preferred discrete inductor. There you have it. The stub matching method is equal to a discrete L- network in efficiency, it does not detract from the antenna efficiency one bit, it can incorporate the balun function without additional components, it grounds the feedpoint, with a little sealant on the cable, it is weatherproof and unlike Gammas and Tee-matches, it will handle full power without being prone to capacitor breakdown. It is not part of the radiator; it is part of the matching network. Period. |
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