---
title: "Short note: S-parameters and their merits"
subject: "RF and Microwave Engineering"
chapter: 3
key: "semester_7/rf_and_microwave_engineering:s-parameters-note"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/s-parameters-note
site: BCT Engineering
---

# Short note: S-parameters and their merits

RF and Microwave Engineering · Chapter 3: RF and Microwave Network Theory and Analysis

- Asked in: 2079 Chaitra, 5 marks; 2071 Bhadra, 5 marks (asked 2 times)
- Video: [Scattering Parameters | Why S Parameters in Microwave measurement? | Calculation of S Parameters](https://www.youtube.com/watch?v=-PZQm_404Js) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/s-parameters-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-3

## Question

Write a short note on S-parameters (merits of S-parameters in microwaves).

## Short answer

S-parameters relate incident waves a_n and reflected waves b_n at ports terminated in Z0. Merits: measured with matched loads (no open/short), safe for active devices, valid for waveguides, directly give reflection coefficient, gain, and VSWR, and allow easy cascade via T-parameters.

## Answer

**Scattering (S) parameters** describe a linear microwave network in terms of the **incident waves (aₙ)** and **reflected waves (bₙ)** at its ports, measured when all other ports are terminated in a matched load Z0. For a two-port:

```text
 b1 = S11·a1 + S12·a2
 b2 = S21·a1 + S22·a2
```
- S11, S22: input and output reflection coefficients.
- S21: forward transmission (gain or insertion loss); S12: reverse transmission (isolation).
- aₙ = Vₙ⁺/√Z0, bₙ = Vₙ⁻/√Z0, so |aₙ|² and |bₙ|² are proportional to power.

**Merits of S-parameters at microwave frequencies:**
1. **Easy measurement:** they need matched terminations, not open or short circuits, which are hard to realise at microwave frequencies.
2. **Safe for active devices:** transistors stay stable when terminated in 50 Ω, whereas open/short terminations may cause oscillation.
3. **Defined for waveguides:** voltage and current are not unique in a waveguide, but incident and reflected waves are.
4. **Direct physical meaning:** |S11| gives return loss and VSWR; |S21|² gives power gain or insertion loss.
5. **Measured by VNA** with high accuracy, and the reference plane can be shifted mathematically (multiply by e^(−jβl)).
6. **Network properties are visible:** reciprocal → [S] symmetric; lossless → [S] unitary; matched → Sᵢᵢ = 0.
7. **Used in amplifier design:** stability factor, gain circles and noise circles are all computed from S-parameters.

**Example:** a matched 10 dB attenuator has S11 = S22 = 0 and |S21| = |S12| = 10^(−10/20) = 0.316.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why are S-parameters easier to measure than Z or Y parameters at microwave frequencies?
   A. They need matched terminations rather than open or short circuits
   B. They need a perfect short at each port
   C. They only need a multimeter
   D. They need no ports
   Answer: A. Matched loads are easy to build at microwave frequency, while good opens and shorts are not. (Key point: Easy measurement)

2. Why are S-parameters safe for transistors?
   A. Because transistors are measured open-circuited
   B. Because the 50 ohm termination keeps the device stable, while open or short may cause oscillation
   C. Because S-parameters apply no signal
   D. Because they avoid using power waves
   Answer: B. A matched termination avoids the oscillation or damage an open or short can cause. (Key point: Active device safety)

3. A matched 10 dB attenuator has |S21| equal to
   A. 10
   B. 0.1
   C. 0.316
   D. 3.16
   Answer: C. |S21| = 10^(-10/20) = 0.316, and S11 = S22 = 0 because it is matched. (Key point: Attenuator example)

## Related in RF and Microwave Engineering

- [Microwaves versus acoustic or seismic waves](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Amicrowaves-vs-acoustic-waves) — RF and Microwave Engineering, chapter 1, asked 2×

## Related in other subjects

- [Merits of functions; actual vs formal parameters](https://www.bctengineer.com/question.md?key=semester_1%2Fcomputer_programming%3Audf-merits-demerits-parameters) — Computer Programming, chapter 6