40 m Inverted V Resonance, Feedline Loss, and Tuner Use
You use a center-fed 40 m inverted V with a 1:1 current balun at the feedpoint, an apex height of 12 m, and ends about 3 m above ground. The feedline is 100 ft of RG-8X. An antenna analyzer at the shack end shows a minimum SWR of 1.2 at 7.260 MHz. At 7.150 MHz it reads SWR 2.8 with R = 26 ohms and X = -42 ohms. Your transmitter folds back above SWR 2.0, so at 7.150 MHz it delivers less than 100 W. You want to operate 7.150 MHz SSB at 100 W. You have an antenna tuner at the shack, a spare 1:1 balun, and enough wire to lengthen the antenna. The coax loss at 7 MHz is about 1.0 dB per 100 ft.
1. Calculate the mismatch loss at 7.150 MHz and estimate the power actually delivered to the antenna before foldback.
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The reflection coefficient is |Γ| = |(Z - 50)/(Z + 50)|. With Z = 26 - j42, the numerator is -24 - j42, magnitude √(576 + 1764) = √2340 = 48.4. The denominator is 76 - j42, magnitude √(5776 + 1764) = √7540 = 86.8. Thus |Γ| = 0.557 and SWR = (1 + 0.557)/(1 - 0.557) = 3.5. The mismatch loss is -10 log10(1 - |Γ|²) = -10 log10(1 - 0.310) = 1.6 dB. Adding the 1.0 dB coax loss gives about 2.6 dB total. At 100 W input, the antenna would receive about 100 × 10^(-2.6/10) = 55 W. Because the transmitter folds back above SWR 2.0, the actual drive is lower still, so the station is losing both mismatch power and transmitter output.
2. Would the shack antenna tuner solve the problem? Explain what it does and does not fix.
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A shack tuner can transform the impedance seen by the transmitter to 50 ohms, so the transmitter will no longer fold back and will deliver full power. It does not remove the mismatch on the feedline: the line still carries a high SWR, so the additional coax loss and voltage stress remain. The tuner also does not change the antenna’s radiation pattern or its low feedpoint resistance. In this case, the mismatch loss is only about 1.6 dB, but the coax loss under high SWR may be somewhat higher than the 1.0 dB quoted. A tuner is an acceptable operating convenience, but it is not the best fix when the antenna is simply resonant at the wrong frequency. The better solution is to lengthen the antenna so resonance moves down to 7.150 MHz, then recheck the SWR and the feedpoint resistance.
3. How much should you lengthen the antenna, and what should you do if the feedpoint resistance remains low after retuning?
Read the worked answer
The antenna is resonant at 7.260 MHz and too short for 7.150 MHz. The required increase is roughly (7.260 - 7.150)/7.150 = 1.5 percent of the total wire length. For a 40 m dipole with about 20.5 m of wire, that is about 0.3 m total, or roughly 15 cm on each leg. Lengthen both legs equally, then re-measure at 7.150 MHz. If resonance moves to 7.150 MHz but R remains near 26 ohms, the low resistance is caused by the inverted-V geometry and ground proximity, not by the balun. Do not add a 4:1 balun; it would transform 26 ohms down to about 6.5 ohms and make the match worse. Use the 1:1 current balun, accept a modest mismatch, and use the tuner if necessary, or raise the apex and move the ends farther from ground to increase the feedpoint resistance.