PLL components and AM demodulation using PLL

A phase-locked loop (PLL) is a negative-feedback system that makes the phase and frequency of a local oscillator follow those of an input signal.

Essential components of a PLL

 vin ->[Phase    ]-> ve ->[Loop  ]-> vc --+
       [detector ]        [filter]        |
           ^                              |
           |                              v
           +-------------[  VCO  ]<-------+
                  vo (output)

1. Phase detector (multiplier): compares the input $v_{in}$ with the VCO output $v_o$ and produces an error voltage $v_e$ proportional to their phase difference, e.g. $v_e\propto\sin(\theta_i-\theta_o)$.
2. Loop filter (low-pass): removes the high-frequency (sum) terms of the phase detector output and sets the loop dynamics: lock range, capture range and noise bandwidth.
3. Voltage-controlled oscillator (VCO): its frequency changes in proportion to the control voltage: $f_o=f_{free}+K_vv_c$. It is pulled until its frequency equals the input frequency.
4. (Often) a loop amplifier to increase loop gain.

When locked, the VCO has the same frequency as the input, with a small fixed phase difference (90° for a multiplier phase detector at zero error).

PLL used to demodulate AM

Coherent (synchronous) AM detection needs a local carrier exactly matching the received carrier. The PLL extracts it.

 AM in --+-->[ PLL ]-->[ 90 deg ]--+  c(t)=cos(wc t)
         |   (locks to carrier)    |
         |                         v
         +----------------------->(X)-->[ LPF ]--> m(t)
                              product detector

Operation:

1. The received AM signal is $s(t)=A_c[1+k_am(t)]\cos\omega_ct$. It has a strong carrier component at $f_c$.
2. The PLL locks to this carrier. Because the multiplier phase detector settles at $90°$ phase difference, the VCO output is $\sin\omega_ct$ (quadrature).
3. A $90°$ phase shifter converts the VCO output to $\cos\omega_ct$, a clean carrier in phase with the received carrier.
4. A product detector multiplies the AM signal by this carrier:

$$\begin{aligned} v(t)&=A_c[1+k_am(t)]\cos\omega_ct\cdot\cos\omega_ct\\ &=\frac{A_c}{2}[1+k_am(t)]+\frac{A_c}{2}[1+k_am(t)]\cos2\omega_ct \end{aligned}$$

5. The low-pass filter removes the $2\omega_c$ term; a DC-blocking capacitor removes $A_c/2$, leaving $\frac{A_ck_a}{2}m(t)$, the message.

Advantages over envelope detection: works for modulation index above 100% and for weak, noisy signals, gives less distortion, and the PLL's narrow loop bandwidth rejects noise. The PLL automatically tracks carrier drift. For DSB-SC (no carrier), a Costas loop or squaring loop is used instead.