*Question G5A10:
Which of the following devices can be used for impedance matching at radio frequencies?*  

*Correct Answer is  D: All these choices are correct*  

### AI Response: (may contain errors)  

To understand why the correct answer is "All these choices are correct," let's break down each option regarding impedance matching at radio frequencies.

1. **A transformer**:  
   - A transformer can be used to match impedances by utilizing its turns ratio. The impedance transformation is given by the formula:
   $$ 
   Z_{out} = Z_{in} \left( \frac{N_{out}}{N_{in}} \right)^2 
   $$
   where:
   - $Z_{out}$ = output impedance
   - $Z_{in}$ = input impedance
   - $N_{out}$ = number of turns in the output winding
   - $N_{in}$ = number of turns in the input winding  
   This allows for efficient power transfer between components with different impedances.

2. **A Pi-network**:  
   - A Pi-network is a type of impedance matching network that consists of two capacitors and one inductor (or vice versa) arranged in a "Pi" configuration. It can be designed to match a specific load impedance to the source impedance at a desired frequency. The design involves calculating the values of the reactive components to achieve the desired impedance transformation.

3. **A length of transmission line**:  
   - A transmission line can also be used for impedance matching through its electrical length. The input impedance of a transmission line can be calculated using:
   $$ 
   Z_{in} = Z_0 \frac{Z_L + jZ_0 \tan(\beta l)}{Z_0 + jZ_L \tan(\beta l)} 
   $$
   where:
   - $Z_{in}$ = input impedance
   - $Z_0$ = characteristic impedance of the line
   - $Z_L$ = load impedance
   - $\beta$ = phase constant
   - $l$ = length of the line  
   By adjusting the length of the line, you can achieve a desired impedance at the input.

### Conclusion:
- All three devices (transformer, Pi-network, and transmission line) can effectively match impedances at radio frequencies, making the correct answer **D: All these choices are correct**. Each method has its own applications and advantages depending on the specific requirements of the circuit.