*Question E9F11:
What impedance does a 1/8-wavelength transmission line present to an RF generator when the line is open at the far end?*  

*Correct Answer is  C: A capacitive reactance*  

### AI Response: (may contain errors)  

To determine the impedance presented by a 1/8-wavelength transmission line that is open at the far end, we can use the properties of transmission lines and their behavior at different lengths.

### Correct Answer: A: The same as the characteristic impedance of the line

1. **Why the correct answer is correct:**
   - A transmission line that is open at the far end presents a specific impedance to the generator based on its length. For a line that is 1/8 wavelength long, the impedance seen at the input (the generator end) is equal to the characteristic impedance ($Z_0$) of the line. This is due to the fact that the open circuit condition causes the line to behave in a way that reflects the characteristic impedance back to the generator.

### Why the other choices are incorrect:

2. **B: An inductive reactance**
   - An inductive reactance would imply that the line is presenting a higher impedance due to stored magnetic energy, which is not the case for an open line at this length. The 1/8 wavelength does not create a significant inductive effect.

3. **C: A capacitive reactance**
   - While an open line can present capacitive characteristics at certain lengths (like 1/4 wavelength), at 1/8 wavelength, the impedance is not purely capacitive. Instead, it reflects the characteristic impedance.

4. **D: Infinite**
   - An infinite impedance would suggest a complete open circuit with no reflection, which is not the case here. The line is open, but the 1/8 wavelength allows for the characteristic impedance to be seen.

### Useful Formulas and Rules of Thumb:
- The impedance transformation for a transmission line can be described by the formula:
  $$ Z_{in} = Z_0 \frac{Z_L + jZ_0 \tan(\beta l)}{Z_0 + jZ_L \tan(\beta l)} $$
  where:
  - $Z_{in}$ = input impedance
  - $Z_L$ = load impedance (in this case, infinite for an open circuit)
  - $Z_0$ = characteristic impedance of the line
  - $\beta$ = phase constant
  - $l$ = length of the line

- For a line that is $n/4$ wavelengths long, the input impedance is transformed to $Z_{in} = \frac{Z_0^2}{Z_L}$, and for $n/8$ wavelengths, it reflects the characteristic impedance directly.

This understanding of transmission line behavior is crucial for the Extra Class exam and practical applications in amateur radio.