Limiter-discriminator FM demodulation

The limiter–discriminator is a direct method of FM demodulation. It first removes amplitude variations (limiter), then converts frequency variations into amplitude variations (discriminator), and finally detects the envelope.

FM in +-------+ +-----+ +-----------+ +--------+ m(t)
----->| Hard  |>| BPF |>|Discrimina-|>|Envelope|---->
      |limiter| | fc  | |tor (d/dt) | |detector|
      +-------+ +-----+ +-----------+ +--------+

1. Limiter and band-pass filter

The received FM signal is $A(t)\cos[2\pi f_c t + \phi(t)]$, where $A(t)$ varies due to noise and fading. The hard limiter clips it into a rectangular wave of fixed amplitude whose zero crossings carry the frequency information. The BPF centred at $f_c$ removes the harmonics. The output is a constant-amplitude FM wave:

$$s(t) = A_c\cos\left[2\pi f_c t + 2\pi k_f\int_0^t m(\tau)\,d\tau\right]$$

2. Discriminator

An ideal discriminator has a transfer function $H(f) = j2\pi a f$ over the FM band, i.e. it acts as a differentiator:

$$\frac{ds(t)}{dt} = -A_c\left[2\pi f_c + 2\pi k_f\, m(t)\right]\sin\left[2\pi f_c t + 2\pi k_f\int_0^t m(\tau)\,d\tau\right]$$

The output is a hybrid AM–FM wave whose envelope $2\pi A_c[f_c + k_f m(t)]$ varies linearly with $m(t)$ (provided $f_c > k_f |m(t)|_{max}$, so the envelope never becomes negative).

Practical discriminators:

• Slope detector: a tuned circuit detuned so that $f_c$ sits on the linear slope of its response; output amplitude rises with frequency. Simple but not very linear.
• Balanced slope detector: two tuned circuits at $f_c + \delta$ and $f_c - \delta$, each with a diode detector; outputs subtracted. Gives a wider linear range and cancels the DC term.
• Foster–Seeley discriminator / ratio detector: phase-shift discriminators with good linearity.

3. Envelope detector

A diode detector recovers $2\pi A_c[f_c + k_f m(t)]$. A DC-blocking capacitor removes the $2\pi A_c f_c$ term, giving an output proportional to $m(t)$.

Why the limiter is essential: the discriminator output amplitude depends on $A_c$. Without the limiter, any amplitude noise on the received signal would appear directly in the output. The limiter makes the detector respond only to frequency changes, which is the main reason for FM's noise immunity.