---
title: "Short note: Two magic tees connected in H-plane"
subject: "RF and Microwave Engineering"
chapter: 4
key: "semester_7/rf_and_microwave_engineering:two-magic-tees-h-plane-note"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/two-magic-tees-h-plane-note
site: BCT Engineering
---

# Short note: Two magic tees connected in H-plane

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

- Asked in: 2078 Chaitra, 5 marks
- 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/two-magic-tees-h-plane-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-4

## Question

Write a short note on combinational effect of two magic tees connected in H-plane.

## Short answer

Two magic tees joined at their H-arms form a six-port network. Power at port 1 goes half to E-arm 4 and a quarter each to ports 5 and 6 in phase; the E-arms are isolated. It separates sum and difference signals.

## Answer

When two magic tees are connected by joining their **H-arms** with a short piece of waveguide, a six-port network is obtained. Let tee A have ports 1, 2 (collinear), 3 (H) and 4 (E); tee B have ports 5, 6 (collinear), 7 (H) and 8 (E). Port 3 is joined to port 7, so a7 = b3 and a3 = b7 (zero-length link assumed).

```text
        (4) E                   E (8)
         |                       |
 (1) ===[A]=== (2)       (5) ===[B]=== (6)
         |                       |
         +------ H-H link -------+
```

Using b3 = (a1 + a2)/√2 and b7 = (a5 + a6)/√2 for each tee:
```text
 b1 = a4/√2 + (a5 + a6)/2      b5 =  a8/√2 + (a1 + a2)/2
 b2 = -a4/√2 + (a5 + a6)/2     b6 = -a8/√2 + (a1 + a2)/2
 b4 = (a1 - a2)/√2             b8 = (a5 - a6)/√2
```

**Properties of the combination:**
- Power fed at port 1 goes **half to E-arm 4** and **a quarter each to ports 5 and 6, in phase**; nothing returns to port 1 or reaches port 2 directly.
- The **sum (in-phase) part** of the signals at tee A passes through the H-link to tee B, while the **difference part** comes out of A's own E-arm. So the pair separates common-mode and differential signals.
- The two E-arms (4 and 8) are completely isolated from each other.
- The network stays matched, lossless and reciprocal (the 6 × 6 S-matrix is symmetric and unitary).

**Uses:** sum/difference networks in monopulse radar, balanced duplexers and mixers, and power combining arrangements where in-phase signals must be transferred between two hybrid circuits.

## Check yourself

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

1. Joining two magic tees by their H-arms forms
   A. a six-port network
   B. a four-port network
   C. a circulator
   D. a two-port filter
   Answer: A. Each tee has 4 ports; the two joined H-arms leave 6 external ports. (Key point: Connection)

2. Power fed to port 1 of tee A goes
   A. all to port 2
   B. half to E-arm 4 and a quarter each to ports 5 and 6 in phase
   C. half to port 2 and half to port 4
   D. equally to ports 5 and 6 in anti-phase
   Answer: B. Sum component passes through the H-link while the difference goes to A's own E-arm. (Key point: Power from port 1)

3. What does the combination separate?
   A. Different frequencies
   B. TE and TM modes
   C. Common-mode (sum) and differential signals
   D. Forward and reflected waves only
   Answer: C. Sum passes via the H-link; difference exits the E-arm. (Key point: Separation)

## Related in RF and Microwave Engineering

- [Two magic tees connected at E-arms](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Atwo-magic-tees-e-arms) — RF and Microwave Engineering, chapter 4