Question E4B07:
What do the subscripts of S parameters represent?  

Choices:  
A: The port or ports at which measurements are made  
B: The relative time between measurements  
C: Relative quality of the data  
D: Frequency order of the measurements    

Correct Answer is  A: The port or ports at which measurements are made  

Correct answer: A — The port or ports at which measurements are made

1) Why A is correct
- In S-parameters, the subscripts indicate ports. $S_{ij}$ means “the ratio of the outgoing wave at port $i$ to the incident wave at port $j$, with all other ports terminated in $Z_0$ (matched).”
- Think “from $j$ to $i$.” Example for a 2-port:
  - $S_{11}$: reflection at port 1 (input return)
  - $S_{21}$: forward transmission from port 1 to port 2 (gain or insertion loss)
  - $S_{12}$: reverse transmission from port 2 to port 1 (isolation)
  - $S_{22}$: reflection at port 2 (output return)

2) Why the other choices are incorrect
- B: Not time. S-parameters are frequency-domain quantities; subscripts do not encode time.
- C: Not data quality. Subscripts don’t rate accuracy or quality.
- D: Not frequency order. Frequency is indicated separately as $S_{ij}(f)$; the subscripts only label ports.

3) Useful formulas and rules of thumb
- Definition with waves $a_k$ (incident) and $b_k$ (outgoing):
  - $b_1 = S_{11} a_1 + S_{12} a_2$
  - $b_2 = S_{21} a_1 + S_{22} a_2$
  - All unused ports are terminated in $Z_0$.
- Return loss from reflection coefficient:
  - $RL_{in} = -20\log_{10}\lvert S_{11}\rvert$ dB
  - $RL_{out} = -20\log_{10}\lvert S_{22}\rvert$ dB
- Insertion loss (passive device):
  - $IL \approx -20\log_{10}\lvert S_{21}\rvert$ dB
- VSWR from reflection:
  - $\Gamma = \lvert S_{11}\rvert$, then $\text{VSWR} = \dfrac{1+\Gamma}{1-\Gamma}$
- Frequency dependence:
  - $S_{ij} = S_{ij}(f)$; subscripts do not carry frequency info.