Question E9E07:
What parameter describes the interaction of a load and transmission line?  

Choices:  
A: Characteristic impedance  
B: Reflection coefficient  
C: Velocity factor  
D: Dielectric constant    

Correct Answer is  B: Reflection coefficient  

Correct answer: B — Reflection coefficient

1) Why it’s correct
- The reflection coefficient, usually written as $\,\Gamma\,$, quantifies how a load interacts with a transmission line by indicating how much of the incident wave is reflected due to mismatch.
- It is defined at the load as:
  $$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$$
  where $Z_L$ is the load impedance and $Z_0$ is the line’s characteristic impedance.
- $|\Gamma|$ ranges from 0 (perfect match, no reflection) to 1 (total reflection, open/short).

2) Why the others are incorrect
- Characteristic impedance (A): $Z_0$ is a property of the line itself, not the interaction. It’s used in the formula for $\Gamma$ but doesn’t, by itself, describe the mismatch.
- Velocity factor (C): Describes wave speed in the line relative to $c$; unrelated to how the load reflects power.
- Dielectric constant (D): A material property that influences $Z_0$ and velocity factor, but does not directly describe load–line interaction.

3) Useful formulas and rules of thumb
- Reflection coefficient:
  $$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$$
- Voltage Standing Wave Ratio (SWR):
  $$\text{SWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}$$
- Return loss (dB):
  $$\text{RL} = -20\log_{10}|\Gamma|$$
- Reflected power fraction:
  $$P_{\text{refl}}/P_{\text{fwd}} = |\Gamma|^2$$
- Mismatch loss (dB):
  $$\text{ML} = -10\log_{10}\big(1 - |\Gamma|^2\big)$$

Quick benchmarks:
- Perfect match: $|\Gamma|=0$, SWR = 1:1.
- 2:1 SWR: $|\Gamma| \approx 0.333$, RL ≈ 9.5 dB, reflected power ≈ 11%.
- 1.5:1 SWR: $|\Gamma| = 0.2$, RL ≈ 14 dB, reflected power = 4%.