Question E9E03:
What matching system uses a short length of transmission line connected in parallel with the feed line at or near the feed point?  

Choices:  
A: Gamma match  
B: Delta match  
C: T-match  
D: Stub match    

Correct Answer is  D: Stub match  

Correct answer: D — Stub match

1) Why it’s correct
- A stub match uses a short section of transmission line (open- or short-circuited) connected in parallel (shunt) with the feed line at or near the antenna feed point.  
- The stub provides a susceptance that cancels the reactive part of the antenna’s admittance, bringing the total seen by the line to $1/Z_0$.

Useful relationships for a lossless line (characteristic impedance $Z_0$, electrical length $\ell$, phase constant $\beta$):
- Short-circuited stub input impedance:  
  $$Z_{in} = j Z_0 \tan(\beta \ell)$$
- Open-circuited stub input impedance:  
  $$Z_{in} = -j Z_0 \cot(\beta \ell)$$
- For a shunt stub, use admittance:  
  $$Y_{stub} = \frac{1}{Z_{in}}$$
- Matching condition at the tap point:  
  $$Y_{load} + Y_{stub} = \frac{1}{Z_0}$$
Rules of thumb:
- Shorted stub shorter than $\lambda/4$ is inductive; open stub shorter than $\lambda/4$ is capacitive.  
- At $\ell = \lambda/4$, a shorted stub looks open; an open stub looks short.

2) Why the others are incorrect
- Gamma match (A): An unbalanced-to-balanced match using a series capacitor and an adjustable rod alongside the driven element. It’s not a transmission-line stub placed in parallel with the feed line.
- Delta match (B): A triangular (delta-shaped) connection to a driven element that transforms impedance; again, not a parallel transmission-line stub.
- T-match (C): A balanced version of the gamma using two parallel conductors (often with series capacitors) across the driven element; not a shunt transmission-line stub connected in parallel with the feed line.