*Question E7C04:
How does an impedance-matching circuit transform a complex impedance to a resistive impedance?*  

*Correct Answer is  C: It cancels the reactive part of the impedance and changes the resistive part to the desired value*  

### AI Response: (may contain errors)  

To understand how an impedance-matching circuit transforms a complex impedance to a resistive impedance, let's break down the correct answer and the other choices.

### Correct Answer: C
**It cancels the reactive part of the impedance and changes the resistive part to the desired value.**

- **Explanation**: An impedance-matching circuit is designed to adjust the impedance seen by a load or source. It does this by:
  - **Cancelling the reactive part**: This is achieved using components like capacitors and inductors, which can offset the inductive or capacitive reactance present in the complex impedance.
  - **Adjusting the resistive part**: The circuit can also be designed to transform the resistive component to a specific value, ensuring maximum power transfer according to the maximum power transfer theorem.

### Why the Other Choices are Incorrect:

- **A: It introduces negative resistance to cancel the resistive part of impedance.**
  - **Explanation**: Negative resistance is a concept used in certain active circuits, but it does not apply to standard impedance matching. Impedance matching focuses on transforming impedances without introducing negative resistance.

- **B: It introduces transconductance to cancel the reactive part of impedance.**
  - **Explanation**: Transconductance refers to the relationship between the output current and input voltage in a transconductance amplifier. It is not a method used in impedance matching. Impedance matching primarily uses passive components (like capacitors and inductors) to cancel reactance.

- **D: Reactive currents are dissipated in matched resistances.**
  - **Explanation**: While matched resistances can help in power transfer, the goal of impedance matching is to cancel the reactive components rather than dissipate them. The reactive currents should ideally be minimized or eliminated, not dissipated.

### Useful Formulas and Rules of Thumb:
- **Maximum Power Transfer Theorem**: Maximum power is transferred when the load impedance ($Z_L$) matches the source impedance ($Z_S$).
- **Complex Impedance**: A complex impedance can be expressed as:
  $$Z = R + jX$$
  where:
  - $R$ = resistive part
  - $X$ = reactive part (inductive or capacitive)

- **Impedance Matching Techniques**: Common methods include:
  - **L-C Matching Networks**: Using inductors (L) and capacitors (C) to create a resonant circuit that cancels out reactance.
  - **Transformers**: Using turns ratio to match impedances.

By understanding these concepts, you can effectively grasp how impedance-matching circuits function and prepare for your exam.