---
title: "Waveguide junctions and magic tee operation"
subject: "RF and Microwave Engineering"
chapter: 4
key: "semester_7/rf_and_microwave_engineering:waveguide-junctions-magic-tee"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/waveguide-junctions-magic-tee
site: BCT Engineering
---

# Waveguide junctions and magic tee operation

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

- Asked in: 2072 Asoj, 3+3 marks
- Video: [Magic Tee Junction (Basics, Working, Structure & Scattering Parameters) Explained](https://www.youtube.com/watch?v=0Krr-FoWLeU) — 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/waveguide-junctions-magic-tee
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-4

## Question

What are waveguide junctions? Describe the operational principles of magic tee based on s-parameters.

## Short answer

Waveguide junctions are passive multiport connections for dividing, combining, or routing microwave power. The magic tee’s S-parameters show H-arm input gives equal in-phase outputs at ports 1 and 2; E-arm input gives equal anti-phase outputs; collinear arms are isolated. All ports are matched, lossless, and reciprocal.

## Answer

#### Waveguide junctions
**Waveguide junctions** are passive devices where three or more waveguide sections meet, used to divide, combine or route microwave power. The common types are:
- **E-plane tee:** side arm on the broad wall; splits power into two equal parts 180° out of phase.
- **H-plane tee:** side arm on the narrow wall; splits power equally in phase.
- **Magic tee (E-H tee):** combination of E- and H-plane tees; a four-port hybrid.
- **Hybrid ring (rat-race)** and directional couplers.

#### Operation of magic tee using S-parameters
Ports 1 and 2 are collinear, port 3 the H-arm, port 4 the E-arm:
```text
              | 0   0   1   1 |
 [S] = (1/√2) | 0   0   1  -1 |
              | 1   1   0   0 |
              | 1  -1   0   0 |
```
- **Input at H-arm:** b1 = b2 = a3/√2, b4 = 0 – equal in-phase split, nothing to E-arm.
- **Input at E-arm:** b1 = a4/√2, b2 = −a4/√2, b3 = 0 – equal anti-phase split.
- **Input at port 1:** b3 = b4 = a1/√2, b2 = 0 – collinear arms isolated.
- **Equal in-phase inputs at 1 and 2:** all power at H-arm (sum); anti-phase: all at E-arm (difference).
- All ports matched, lossless and reciprocal; used in mixers, duplexers and bridges.

## Check yourself

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

1. What is a waveguide junction?
   A. A device that stops all microwave power
   B. A passive device where three or more waveguide sections meet to divide, combine or route power
   C. An active amplifier
   D. A single straight waveguide section
   Answer: B. Junctions such as tees and couplers divide, combine or route microwave power. (Key point: Waveguide junction)

2. When a signal is applied to the E-arm of a magic tee, what appears at ports 1, 2 and 3?
   A. Equal in-phase outputs at 1 and 2, nothing at 3
   B. All power at port 3
   C. Equal outputs at 1 and 2, 180° out of phase, and nothing at the H-arm
   D. Power only at port 1
   Answer: C. b1 = a4/√2, b2 = −a4/√2 and b3 = 0 from the S-matrix. (Key point: E-arm input)

3. With input at port 1 only, how is the power shared in a matched magic tee?
   A. All goes to port 2
   B. Half to the H-arm and half to the E-arm, none to port 2
   C. Half to port 2 and half to port 3
   D. All is reflected
   Answer: B. b3 = b4 = a1/√2 and b2 = 0, so the collinear arms are isolated. (Key point: Input at a collinear port)

4. Equal in-phase signals are applied to ports 1 and 2. Where does the output appear?
   A. E-arm (difference)
   B. Both ports 1 and 2
   C. Nowhere
   D. H-arm (sum)
   Answer: D. In-phase inputs add at the H-arm; anti-phase inputs add at the E-arm. (Key point: Sum and difference)

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