FM Receiver Ghost Station and Harsh Audio
A student builds a single-conversion superheterodyne FM receiver for 88–108 MHz with an IF of 10.7 MHz and a 180 kHz ceramic IF filter. The local oscillator is designed to run on the high side of the incoming signal. On the bench the receiver works well at 98 MHz, but a signal from a nearby 119.4 MHz source produces the same audio, and every wanted frequency seems to be shadowed by a station 21.4 MHz above it. The RF stage is a single tuned circuit with a loaded Q of 40, and no image-reject filter is fitted. When tuned to a station with ±75 kHz deviation and 15 kHz audio, the recovered audio sounds harsh and the stereo pilot is weak compared with a commercial receiver. The student wants to raise the IF to 30 MHz "to fix the image" and to widen the ceramic filter to 280 kHz "to get more treble".
1. Verify the image frequency at 98 MHz and quantify the image rejection provided by the RF stage.
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Local oscillator. With high-side injection, fLO = fRF + fIF = 98 + 10.7 = 108.7 MHz.
Image. The image lies as far above the LO as the wanted signal lies below it: fimage = fLO + fIF = 108.7 + 10.7 = 119.4 MHz, which is 2 × IF = 21.4 MHz above the wanted signal. This exactly matches the ghost the student observed, so the diagnosis is confirmed: the receiver is responding to the image.
Rejection of the tuned RF circuit. The 3 dB bandwidth is f0/Q = 98/40 = 2.45 MHz. For a single tuned circuit the attenuation at an offset Δf is √(1 + (2QΔf/f0)²) = √(1 + (2 × 40 × 21.4/98)²) = √(1 + 17.47²) ≈ 17.5, i.e. 24.9 dB.
That is far too little. If a local 119.4 MHz signal is even 20 dB stronger than the wanted station, it arrives at the mixer at a comparable level and captures the IF. A single low-Q tuned circuit is a bandpass filter for the FM band, not an image filter; the rejection has to come from a higher-Q preselector, a dual-conversion scheme, or an image-reject mixer. Simply tuning the RF stage more sharply also narrows the wanted band and makes tracking harder.
2. Use Carson's rule to check the 180 kHz IF filter against the broadcast, and explain the harsh audio and weak stereo pilot.
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Carson's rule. BW = 2(Δf + fm) = 2(75 + 15) = 180 kHz.
The filter is exactly at the Carson bandwidth, which sounds correct only if the filter were ideal with vertical skirts. A real ceramic filter has rounded shoulders and wide tolerances, so components at the edges of the spectrum are attenuated. In stereo, the pilot at 19 kHz and the DSB subcarrier at 38 kHz carry sidebands out to 38 + 15 = 53 kHz, all within the deviation already accounted for; the energy near the band edges is what the filter is cutting. Losing the outer sidebands removes the high audio frequencies (harsh, muffled sound) and attenuates the subcarrier sidebands that the stereo decoder needs (weak or noisy stereo).
Verdict on the filter. 180 kHz is too narrow for full stereo with 75 kHz deviation. A 200–230 kHz filter is the usual compromise; 230 kHz leaves margin for filter tolerances while keeping adjacent-channel rejection acceptable.
On the 280 kHz proposal. It would restore the treble, but it also admits more of the adjacent channel and the next-door station's sidebands, and it does nothing for the image problem. The student is moving in the right direction but overshooting; 230 kHz is the defensible choice, and adjacent-channel selectivity should be recovered in the RF preselector.
3. Evaluate the proposal to move the IF to 30 MHz. What does it gain, what does it cost, and what would you do instead?
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Gain. Image separation becomes 2 × 30 = 60 MHz. For 98 MHz the LO moves to 128 MHz and the image to 158 MHz, well outside the FM band, where the same Q = 40 tuned circuit gives 2QΔf/f0 = 2 × 40 × 60/98 = 49, i.e. about 34 dB of rejection instead of 25 dB. The image also falls where there is no strong service, so the practical improvement is greater than 9 dB.
Costs. A 30 MHz IF filter with the required 200 kHz bandwidth and good shape factor is harder to obtain and more expensive than a 10.7 MHz ceramic unit. The LO must tune 118–138 MHz, where varactor tuning range, LO radiation and shielding become harder, and 30 MHz is a crowded band (amateur, land mobile) that can couple into the IF strip. The higher IF also makes the second-conversion or detector design less standard.
Better alternatives. Keep 10.7 MHz and add a two- or three-section front-end preselector with Q ≈ 100, which raises image rejection to roughly 40 dB; or use a dual-conversion design (high first IF for image rejection, low second IF for selectivity); or use an image-reject (Hartley/Weaver) mixer. These give the image performance without moving the whole receiver onto an awkward IF. The 30 MHz idea is technically valid but is not the most economical fix.