*Question E4B05:
What three test loads are used to calibrate an RF vector network analyzer?*  

*Correct Answer is  B: Short circuit, open circuit, and 50 ohms*  

### AI Response: (may contain errors)  

To understand the calibration of an RF vector network analyzer (VNA), we need to look at the purpose of the test loads used. The correct answer is:

**Correct Answer: B: Short circuit, open circuit, and 50 ohms**

### Explanation of the Correct Answer:
- **Short Circuit**: This load provides a known impedance of 0 ohms. It helps the VNA measure how it responds to a complete reflection of the signal.
- **Open Circuit**: This load presents an infinite impedance, meaning no current flows. It allows the VNA to measure the response when there is no load.
- **50 Ohms**: This is the standard impedance for most RF systems. Calibrating with a 50-ohm load ensures that the VNA can accurately measure devices designed to operate at this impedance.

These three test loads allow the VNA to establish a reference for measuring the reflection coefficient and other parameters accurately.

### Why the Other Choices are Incorrect:
- **A: 50 ohms, 75 ohms, and 90 ohms**: While these are common impedances, they do not provide the necessary reference points (short and open circuits) for calibration. The VNA needs to know how to handle complete reflections and no reflections, which this choice does not provide.
  
- **C: Short circuit, open circuit, and resonant circuit**: A resonant circuit is not a fixed impedance and can vary with frequency. It does not provide the stable reference points needed for calibration like the short and open circuits do.

- **D: 50 ohms through 1/8 wavelength, 1/4 wavelength, and 1/2 wavelength of coaxial cable**: This choice describes lengths of transmission lines rather than fixed impedance loads. While these lengths can affect impedance due to standing waves, they do not serve as direct calibration standards for the VNA.

### Useful Formulas and Rules of Thumb:
- The reflection coefficient ($\Gamma$) is a key concept in understanding how these loads affect the signal:
  
$$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$$

where:
- $Z_L$ = load impedance (0 for short, $\infty$ for open, and 50 ohms for the standard load)
- $Z_0$ = characteristic impedance of the system (typically 50 ohms)

This formula helps in understanding how the VNA measures the reflection from different loads, reinforcing the importance of using short, open, and 50-ohm loads for calibration.