Amplitude limiter; FM demodulation using PLL

Role of the amplitude limiter

In a limiter–discriminator FM detector, the amplitude limiter removes all amplitude variations of the received FM signal before it reaches the discriminator.

• Noise, interference and fading change the amplitude of the FM wave, but the information is only in its frequency.
• A discriminator's output depends on both frequency and amplitude, so amplitude changes would appear as noise and distortion.
• The limiter (a hard clipper followed by a band-pass filter at the IF) produces a constant-amplitude signal with the same zero crossings, i.e. the same instantaneous frequency.

 FM + AM noise  -> [Hard limiter] -> [BPF] -> constant-
 /\/\/\  /\/\        square-ish     at fc    amplitude FM

So the discriminator sees only frequency variations, which gives FM its noise immunity.

FM demodulation using PLL

A phase-locked loop is a feedback system in which a voltage-controlled oscillator (VCO) is forced to follow the phase, and hence the frequency, of the input. The control voltage needed to do this is the demodulated message.

 s(t) -->[ Phase    ]-->[ Loop  ]--+--> v(t) = output
         [ detector ]   [ filter]  |    (message)
              ^                    |
              |                    |
              +------[  VCO  ]<----+

Blocks

• Phase detector (multiplier): compares input and VCO phases and gives an error voltage.
• Loop filter: low-pass; removes the $2f_c$ term and sets loop dynamics.
• VCO: its frequency is $f_c + k_vv(t)$.

Analysis

Input FM wave and VCO output:

$$s(t) = A_c\sin[\omega_ct + \phi_1(t)], \quad \phi_1(t) = 2\pi k_f\int_0^t m(\tau)d\tau$$ $$r(t) = A_v\cos[\omega_ct + \phi_2(t)], \quad \phi_2(t) = 2\pi k_v\int_0^t v(\tau)d\tau$$

The multiplier output, after removing the $2\omega_c$ term, is

$$e(t) = K_m\sin[\phi_1(t) - \phi_2(t)] = K_m\sin\phi_e(t)$$

When the loop is locked, $\phi_e$ is small, so $\sin\phi_e \approx \phi_e$ (linear model). With high loop gain the loop drives $\phi_e \to 0$, so

$$\phi_2(t) \approx \phi_1(t) \;\Rightarrow\; 2\pi k_v\int v(t)dt \approx 2\pi k_f\int m(t)dt$$

Differentiating both sides:

$$v(t) \approx \frac{k_f}{k_v}m(t)$$

The loop filter output is therefore proportional to the message. The PLL demodulator has good threshold performance, needs no tuned circuits, and is available as a single IC (e.g. 565).