Question E9E04:
What is the purpose of the series capacitor in a gamma match?  

Choices:  
A: To provide DC isolation between the feed line and the antenna  
B: To cancel unwanted inductive reactance  
C: To provide a rejection notch that prevents the radiation of harmonics  
D: To transform the antenna impedance to a higher value    

Correct Answer is  B: To cancel unwanted inductive reactance  

Correct answer: B — To cancel unwanted inductive reactance

Why B is correct:
- A gamma match effectively creates an L-network. The off-center feed and the “gamma rod/shorting bar” arrangement make the feedpoint look inductive. A series capacitor is inserted to add a capacitive reactance that cancels this inductive reactance so the input becomes purely resistive (resonant).
- At resonance, the net series reactance is zero:
  $$X_L + X_C = 0 \;\;\Rightarrow\;\; X_C = -X_L$$
  where:
  - $X_L = 2\pi f L$
  - $X_C = -\dfrac{1}{2\pi f C}$

Why the others are incorrect:
- A: To provide DC isolation between the feed line and the antenna  
  While a series capacitor does block DC, DC isolation is not the design purpose of the gamma-match capacitor. The goal is RF impedance matching by canceling inductive reactance. In many gamma implementations, the antenna element is still at DC ground via the boom/shorting bar.

- C: To provide a rejection notch that prevents the radiation of harmonics  
  A single series capacitor at the feed does not create a selective notch for harmonics. Harmonic suppression requires filters (e.g., low-pass) with multiple reactive elements, not a single matching capacitor.

- D: To transform the antenna impedance to a higher value  
  The impedance step-up in a gamma match primarily comes from the current division/transformer action due to geometry (rod-to-element spacing and diameters). The series capacitor does not perform the step-up; it tunes out the inductive reactance to make the transformed impedance resistive.

Useful formulas and tips:
- Cancel the inductive part with a series capacitor:
  $$X_C = -X_L \quad\Rightarrow\quad C = \frac{1}{2\pi f |X_L|}$$
- Increasing $C$ makes $|X_C|$ smaller; to cancel a larger inductive reactance, you need a smaller capacitance (larger-magnitude negative reactance).
- Practical tuning: adjust the series capacitor for minimum SWR at the operating frequency, which indicates the inductive reactance has been canceled and the input is near purely resistive.