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

*Correct Answer is  B: Frequency synthesis and FM demodulation*  

### AI Response: (may contain errors)  

A phase-locked loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. It is widely used in radio, telecommunications, and other electronic applications. Let's explore why the correct answer is correct and why the other choices are incorrect.

### Correct Answer: Frequency synthesis and FM demodulation

1. **Frequency Synthesis**:  
   - A PLL can generate a range of frequencies from a single reference frequency. This is done by locking the phase of a voltage-controlled oscillator (VCO) to a reference signal, allowing the PLL to produce a stable and precise output frequency. This process is known as frequency synthesis.

2. **FM Demodulation**:  
   - A PLL can also be used to demodulate frequency-modulated (FM) signals. By locking onto the frequency of the incoming FM signal, the PLL can track the frequency variations and convert them into amplitude variations, effectively demodulating the signal.

### Why the Other Choices are Incorrect

- **Choice A: Wide-band AF and RF power amplification**  
  - PLLs are not used for power amplification. Amplification involves increasing the power level of a signal, which is not a function of a PLL. PLLs are used for frequency control and signal processing, not amplification.

- **Choice C: Photovoltaic conversion and optical coupling**  
  - Photovoltaic conversion involves converting light into electrical energy, and optical coupling involves transferring signals using light. These processes are unrelated to the functions of a PLL, which deals with electronic signal processing.

- **Choice D: Comparison of two digital input signals and digital pulse counting**  
  - While PLLs can compare phases of signals, they are not used for direct digital signal comparison or pulse counting. These tasks are typically handled by digital logic circuits or microcontrollers, not PLLs.

### Summary

A phase-locked loop is primarily used for frequency synthesis and FM demodulation, making option B the correct choice. The other options describe functions that are not related to the capabilities of a PLL. Understanding the role of a PLL in signal processing is crucial for recognizing its applications in frequency control and demodulation.