Question E7H06:
Which of these functions can be performed by a phase-locked loop?  

Choices:  
A: Wide-band AF and RF power amplification  
B: Frequency synthesis and FM demodulation  
C: Photovoltaic conversion and optical coupling  
D: Comparison of two digital input signals and digital pulse counting    

Correct Answer is  B: Frequency synthesis and FM demodulation  

To understand why a PLL can do frequency synthesis and FM demodulation, remember what a phase-locked loop is: a control system that forces a voltage-controlled oscillator (VCO) to track the phase (and thus frequency) of a reference by comparing phases, filtering the error, and tuning the VCO.

Why B is correct (Frequency synthesis and FM demodulation):
- Frequency synthesis:
  - In an integer-N PLL, a divider in the feedback path lets the VCO run at an integer multiple of the reference.
  - The loop locks when the divided VCO matches the reference phase, giving:
    $$f_{out} = N \, f_{ref} \quad \text{(integer-N)}$$
  - Fractional-N synthesis generalizes this:
    $$f_{out} = (N + \text{fraction}) \, f_{ref}$$
  - This is the classic way radios generate stable, tunable LO frequencies.

- FM demodulation:
  - When locked to an FM signal, the VCO tracks instantaneous frequency changes of the input.
  - The loop’s control voltage (the VCO tuning voltage) is proportional to instantaneous frequency deviation, so taking the control-voltage output yields the demodulated audio:
    $$v_{ctrl}(t) \propto \Delta f(t)$$
  - With loop gains: if the VCO sensitivity is $K_v$ (rad/s/V), then for small deviations:
    $$v_{ctrl}(t) \approx \frac{\Delta \omega(t)}{K_v} = \frac{2\pi\,\Delta f(t)}{K_v}$$

Why the other choices are incorrect:
- A: Wide-band AF and RF power amplification
  - A PLL is a frequency/phase control system, not a power amplifier. While buffers may follow a VCO, “wide-band power amplification” is not a PLL function.

- C: Photovoltaic conversion and optical coupling
  - These are opto-electronic functions (solar cells, optocouplers), unrelated to PLL operation.

- D: Comparison of two digital input signals and digital pulse counting
  - Although a PLL contains a phase detector and may include digital dividers, its purpose is to lock a VCO to a reference, not to serve as a general digital comparator or counter. Pulse counting is done by counters; phase comparison here is specific to loop feedback.

Useful formulas and rules of thumb:
- Integer-N synthesis:
  $$f_{out} = N f_{ref}$$
- Fractional-N synthesis:
  $$f_{out} = (N + \alpha) f_{ref}, \quad 0 < \alpha < 1$$
- FM demod with a PLL (locked, small-signal):
  $$v_{ctrl}(t) \approx \frac{2\pi}{K_v}\,\Delta f(t)$$
- Practical tip: FM demodulation via PLL works only when the loop is locked and the deviation is within the loop’s tracking bandwidth.