Angle modulation (FM/PM)
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| instantaneous frequency | instantaneous frequency |
| frequency deviation | dịch tần số |
| Carson's rule | công thức Carson |
The message bends the frequency
- FM puts the message in the instantaneous frequency: $f_i = f_c + k_f x(t)$; the frequency deviation $\Delta f$ against $f_m$ gives $\beta = \Delta f/f_m$; Carson's rule $B \approx 2(\Delta f + f_m)$.
Broadcast: $\Delta f = 75$ kHz, $f_m = 15$ kHz → $\beta = 5$, $B = 180$ kHz — the 200 kHz spacing leaves a 20 kHz guard ✓.
{exercise:uni-ee1103-carson}
FM with 75 kHz deviation and 15 kHz message needs (Carson) about —
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B = 2(Δf + fm) = 2(75+15) = 180 kHz; the 200 kHz channel spacing leaves a 20 kHz guard band.
Halving the deviation (Δf = 37.5 kHz, fm still 15 kHz) changes β and B to —
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β = Δf/fm halves to 2.5; Carson gives 2(37.5+15) = 105 kHz — deviation enters Carson linearly, β as a ratio.
The SNR bargain
- Wideband FM buys post-detection SNR $\approx 3\beta^{2}/2$: 15.7 dB at $\beta = 5$, paid with 9× the AM bandwidth and lost below the ~10 dB threshold.
{exercise:uni-ee1103-bargain}
At beta = 5 the FM post-detection SNR gain is about —
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3β²/2 = 37.5 → 15.7 dB, bought with 180 kHz (9× the AM 20 kHz) and lost below the ~10 dB input threshold.