*Question G9A01:
Which of the following factors determine the characteristic impedance of a parallel conductor feed line?*  

*Correct Answer is  A: The distance between the centers of the conductors and the radius of the conductors*  

### AI Response: (may contain errors)  

The characteristic impedance of a parallel conductor feed line is determined by the physical dimensions of the line, specifically:

1. **Correct Answer: A**  
   - **Distance between the centers of the conductors**: This affects how the electric field is distributed between the conductors.
   - **Radius of the conductors**: This influences the capacitance and inductance per unit length of the line.

   The characteristic impedance \( Z_0 \) of a parallel conductor line can be approximated by the formula:  
   $$ Z_0 = \frac{276}{\sqrt{\epsilon_r}} \log_{10} \left( \frac{D}{r} \right) $$  
   where:
   - \( D \) = distance between the centers of the conductors
   - \( r \) = radius of the conductors
   - \( \epsilon_r \) = relative permittivity of the material between the conductors (usually air, so \( \epsilon_r \approx 1 \))

2. **Why the other choices are incorrect**:
   - **B: The distance between the centers of the conductors and the length of the line**  
     The length of the line does not affect the characteristic impedance. It affects the total impedance but not the characteristic impedance, which is a property of the line's cross-sectional geometry.
   
   - **C: The radius of the conductors and the frequency of the signal**  
     The frequency of the signal does not directly affect the characteristic impedance. While frequency can affect losses and other parameters, the characteristic impedance is determined by the line's geometry.
   
   - **D: The frequency of the signal and the length of the line**  
     Neither the frequency nor the length of the line determines the characteristic impedance. These factors influence other aspects like attenuation and phase velocity but not the characteristic impedance itself.

Understanding these principles helps in designing and analyzing transmission lines for efficient signal transfer.