The 2-Meter Feedline, SWR, and Quarter-Wave Question
You are setting up a 2-meter station at home. The transmitter delivers 50 W at 146.52 MHz into 50 ft of RG-58 coax. The coax is rated 4.5 dB loss per 100 ft at 146 MHz. An antenna analyzer connected at the antenna shows a 2.0:1 SWR at 146.52 MHz. The antenna is a vertical with 3 dBd gain. At the transmitter, your wattmeter shows 50 W forward. You also have a 19-inch piece of wire and a PL-259 connector, and you are considering building a quarter-wave ground-plane antenna instead of using the commercial vertical. A friend suggests replacing the RG-58 with RG-213, which has about 2.0 dB loss per 100 ft at 146 MHz. The run cannot be shortened.
1. What fraction of the power is reflected at a 2.0:1 SWR, and is this mismatch a serious problem?
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For a 2.0:1 SWR, the reflection coefficient is about 0.333, so the reflected power fraction is 0.333² ≈ 0.111, or 11.1%. The mismatch loss is only about 0.5 dB. That is not a serious problem for a modern solid-state 2-meter radio, which is designed to tolerate a 2:1 mismatch. The more important question is why the antenna shows 2:1: a poor connector, a damaged coax, a missing ground plane, or an antenna that is not resonant at 146.52 MHz. A 2:1 SWR is acceptable to operate, but it is worth correcting if the cause is a bad connection. Do not add an unnecessary antenna tuner at VHF; fix the antenna or feedline instead.
2. Calculate the power delivered to the antenna and the ERP. State your assumptions.
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The feedline loss is 4.5 dB per 100 ft × 0.50 = 2.25 dB. A 2.25 dB loss is a power ratio of 10^(2.25/10) ≈ 1.68. The forward power reaching the antenna is therefore 50 W / 1.68 ≈ 29.8 W. With a 2:1 SWR at the antenna, about 11.1% is reflected, so the antenna accepts roughly 29.8 W × 0.889 ≈ 26.5 W. The reflected power travels back down the line and is largely dissipated rather than radiated. The antenna gain is 3 dBd, a power factor of 2, so ERP ≈ 26.5 W × 2 = 53 W. This assumes the 50 W forward reading is accurate, the loss figure is correct for the actual cable, and the antenna is not detuned by nearby objects. EIRP would be about 53 W × 1.64 ≈ 87 W.
3. Would RG-213 be worth the change, and what is the quarter-wave radiator length for 146.52 MHz?
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RG-213 at 50 ft would have 2.0 dB per 100 ft × 0.50 = 1.0 dB loss, a power ratio of 10^(1.0/10) ≈ 1.26. The forward power at the antenna would be 50 W / 1.26 ≈ 39.7 W, and the accepted power would be 39.7 W × 0.889 ≈ 35.3 W. Compared with 26.5 W, that is an improvement of 10 log(35.3/26.5) ≈ 1.25 dB, or about 26% more radiated power. It is a real improvement but not dramatic; raising the antenna or reducing connector losses may matter more. A quarter-wave radiator for 146.52 MHz is approximately 234 / 146.52 = 1.60 ft, or 19.2 inches. The 19-inch wire you have is therefore close to a quarter wave; trim it for best SWR and provide an adequate ground plane or radials.