Limiter-discriminator FM demodulation; need for pre-emphasis

FM demodulation by limiter–discriminator

A limiter–discriminator converts frequency variations of the FM wave into amplitude variations and then detects the envelope.

FM in +---------+ +-----+ +---------+ +--------+ m(t)
----->| Limiter |>| BPF |>|Differen-|>|Envelope|---->
      |(hard    | |     | |tiator   | |detector|
      | clipper)| +-----+ |(slope)  | +--------+
      +---------+         +---------+

1. Limiter and BPF: the received FM wave has unwanted amplitude variations due to noise and fading. The hard limiter clips it to a square-like wave of constant amplitude; the BPF centred at $f_c$ keeps only the fundamental. Output: $s(t) = A_c\cos[2\pi f_c t + \phi(t)]$, $\phi(t) = 2\pi k_f\int_0^t m(\tau)d\tau$.

2. Discriminator (differentiator): its output is proportional to frequency:

$$\frac{ds(t)}{dt} = -A_c\left[2\pi f_c + 2\pi k_f\, m(t)\right]\sin\left[2\pi f_c t + \phi(t)\right]$$

This is a wave that is both FM and AM; its envelope is $2\pi A_c [f_c + k_f m(t)]$, which follows the message.

3. Envelope detector: recovers $2\pi A_c[f_c + k_f m(t)]$. A DC-blocking capacitor removes the constant $2\pi A_c f_c$, leaving an output proportional to $m(t)$.

In practice the differentiator is a slope detector (a tuned circuit operated on the slope of its response), a balanced slope detector (two tuned circuits, one above and one below $f_c$, giving better linearity), or a Foster–Seeley discriminator. The limiter is essential: without it, amplitude noise would pass straight to the envelope detector.

Why pre-emphasis is needed

• In FM, the output noise power spectral density after detection increases with the square of frequency (a parabolic noise spectrum; the noise voltage itself rises linearly, which is why it is called triangular noise), so high audio frequencies suffer more noise.
• High-frequency components of speech and music have small amplitudes, so their SNR is poorest.
• Pre-emphasis (an RC high-pass network, time constant 75 μs, corner 2.1 kHz) boosts high audio frequencies before modulation. At the receiver a matching de-emphasis network attenuates them back, and also attenuates the high-frequency noise. The result is an SNR improvement of about 10–13 dB with no overall distortion of the message.