---
title: "Short note: Directional coupler"
subject: "RF and Microwave Engineering"
chapter: 4
key: "semester_7/rf_and_microwave_engineering:directional-coupler-note"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/directional-coupler-note
site: BCT Engineering
---

# Short note: Directional coupler

RF and Microwave Engineering · Chapter 4: RF and Microwave Components and Devices

- Asked in: 2079 Chaitra, 5 marks; 2073 Bhadra, 6 marks (asked 2 times)
- Video: [Directional Coupler (Basics, Working, Structure, Scattering Parameters & Applications) Explained](https://www.youtube.com/watch?v=4poo1q3GvTg) — 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/directional-coupler-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-4

## Question

Write a short note on directional couplers.

## Short answer

A directional coupler samples a fraction of forward power to a coupled port while isolating reverse power. Key parameters: coupling factor, directivity, and isolation. A two-hole waveguide coupler uses holes spaced λg/4 apart for directivity. Typical uses: power monitoring, VSWR measurement, and signal injection.

## Answer

A **directional coupler** is a four-port passive device that samples a known small fraction of the power travelling in one direction in the main line, while ignoring power travelling in the opposite direction. Port 1 is the input, port 2 the through (direct) port, port 3 the coupled port and port 4 the isolated port. A two-hole waveguide coupler is a common example.

```text
 Input (1) ===================== Through (2)
                 o      o        main guide
             <-- λg/4 -->        (two holes)
 Isolated (4) ------------------ Coupled (3)
                                 auxiliary guide
```

**Two-hole principle:** waves coupled through the two holes, spaced λg/4 apart, travel the same distance to port 3 and add in phase, but differ by λg/2 (180°) on the way to port 4 and cancel. So power reaches port 3 only.

**Performance parameters** (P1 = input power, P2 through, P3 coupled, P4 isolated):
- **Coupling factor:** C = 10 log(P1/P3) dB (e.g. 3, 10, 20 dB)
- **Directivity:** D = 10 log(P3/P4) dB (ideally infinite, typically 30–40 dB)
- **Isolation:** I = 10 log(P1/P4) dB = C + D
- **Insertion loss:** IL = 10 log(P1/P2) dB

**S-matrix of an ideal symmetric coupler** (α² + β² = 1):
```text
       | 0   α   jβ  0  |
 [S] = | α   0   0   jβ |
       | jβ  0   0   α  |
       | 0   jβ  α   0  |
```
All ports matched, ports 1 and 4 (and 2 and 3) isolated.

**Types:** two-hole and multi-hole waveguide couplers, Bethe-hole coupler, branch-line (90° hybrid) coupler, coupled-line microstrip coupler, rat-race (180° hybrid).

**Applications:** power monitoring and sampling, reflectometers for VSWR and reflection coefficient measurement, signal injection, power splitting/combining and balanced amplifiers.

## Check yourself

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

1. In a two-hole coupler with holes lambda_g/4 apart, why is there no output at the isolated port?
   A. The waves reach it with a lambda_g/2 (180 degree) path difference and cancel
   B. The holes are blocked
   C. The waves are absorbed by the walls
   D. The waves add in phase there
   Answer: A. At port 3 the paths are equal so waves add. At port 4 they differ by lambda_g/2 and cancel. (Key point: Two-hole principle)

2. Isolation I is related to coupling C and directivity D by
   A. I = C - D
   B. I = C + D
   C. I = C x D
   D. I = D / C
   Answer: B. I = 10 log(P1/P4) = C + D in dB. (Key point: Isolation)

3. Directivity is defined as
   A. 10 log(P1/P3)
   B. 10 log(P3/P4)
   C. 10 log(P1/P2)
   D. 10 log(P2/P4)
   Answer: B. D = 10 log(P3/P4) compares coupled power with isolated-port power; ideally it is infinite. (Key point: Directivity)

## Related in RF and Microwave Engineering

- [Three-port directional coupler using S-parameters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Adirectional-coupler-three-port) — RF and Microwave Engineering, chapter 4
- [Air-filled 3 cm waveguide at 6 GHz; coupler parameters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Awaveguide-3cm-6ghz-directional-coupler) — RF and Microwave Engineering, chapter 4