--- title: "Short note: Microwave magic tee" subject: "RF and Microwave Engineering" chapter: 4 key: "semester_7/rf_and_microwave_engineering:magic-tee-note" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/magic-tee-note site: BCT Engineering --- # Short note: Microwave magic tee RF and Microwave Engineering · Chapter 4: RF and Microwave Components and Devices - Asked in: 2080 Chaitra, 5 marks; 2079 Chaitra, 5 marks; 2079 Bhadra, 3 marks; 2071 Magh, 5 marks (asked 4 times) - Video: [Magic Tee (Basics, Working, Internal structure, S Matrix & Applications) Explained in Microwave](https://www.youtube.com/watch?v=if30sXaKWkY) — 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/magic-tee-note - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-4 ## Question Write a short note on microwave magic tee. ## Short answer A magic tee is a four-port hybrid junction combining E-plane and H-plane tees. H-arm input splits in phase between collinear arms, E-arm input splits 180° out of phase, and E/H arms are isolated. With matched E and H arms all ports match. Used in balanced mixers, duplexers, and sum/difference networks. ## Answer A **magic tee** (hybrid tee) is a four-port waveguide junction made by combining an **E-plane tee** and an **H-plane tee** at the same point of a main rectangular waveguide. Ports 1 and 2 are the collinear arms, port 3 is the **H-arm** (sum arm) and port 4 is the **E-arm** (difference arm). Matching posts or irises are placed inside so that the E and H arms are matched. ```text E-arm (4) | | | | ----------+ +---------- (1) ==========+ +========== (2) ----------+ +---------- / / / / H-arm (3) ``` **S-matrix of an ideal (matched) magic tee:** ```text | 0 0 1 1 | [S] = (1/√2) | 0 0 1 -1 | | 1 1 0 0 | | 1 -1 0 0 | ``` **Properties ("magic" behaviour):** 1. **H-arm input (port 3):** power divides equally between ports 1 and 2 **in phase**; nothing goes to port 4. 2. **E-arm input (port 4):** power divides equally between ports 1 and 2 **180° out of phase**; nothing goes to port 3. 3. **E and H arms are isolated** (S34 = S43 = 0), and ports 1 and 2 are isolated (S12 = 0). 4. **Input at port 1 (or 2):** splits equally to ports 3 and 4; nothing goes to port 2. 5. **Equal in-phase inputs at ports 1 and 2** add at port 3 (sum) and cancel at port 4 (difference). 6. When the E and H arms are matched, all four ports are automatically matched (S11 = S22 = S33 = S44 = 0). **Applications:** - Balanced mixers (LO and signal fed to E and H arms, diodes in arms 1 and 2). - Duplexers in radar (isolating transmitter and receiver). - Impedance bridges and measurement of unknown impedances. - Power combining/dividing and monopulse radar sum/difference networks. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A magic tee is made by A. Combining an E-plane tee and an H-plane tee at the same point of a waveguide B. Joining two circulators C. Placing two holes quarter wave apart D. Using a ferrite disc Answer: A. The E-arm (port 4) and H-arm (port 3) join the main guide at one point, with matching posts or irises. (Key point: Construction) 2. If power enters the E-arm (port 4), what happens? A. It divides equally between ports 1 and 2 in phase, with some at port 3 B. It divides equally between ports 1 and 2, 180 degrees out of phase, with none at port 3 C. All power goes to port 3 D. All power returns to port 4 Answer: B. The E-arm gives a difference output: equal split with opposite phase, and the H-arm is isolated. (Key point: Input at E-arm) 3. Equal in-phase signals fed to ports 1 and 2 give A. Sum at port 4 and difference at port 3 B. Sum at port 3 and cancellation at port 4 C. Everything reflected D. Equal output at 3 and 4 Answer: B. In-phase inputs add at the H-arm (sum port) and cancel at the E-arm (difference port). (Key point: Equal in-phase inputs) ## Related in RF and Microwave Engineering - [Three-port model and magic tee with shorted arms](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Athree-port-magic-tee-shorted-arms) — RF and Microwave Engineering, chapter 4 - [Magic tee diagram and S-parameter derivation](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Amagic-tee-s-parameter-derivation) — RF and Microwave Engineering, chapter 4 - [Waveguide junctions and magic tee operation](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Awaveguide-junctions-magic-tee) — RF and Microwave Engineering, chapter 4 - [Magic tee, degenerate modes, dominant mode for a = 3b](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Amagic-tee-modes-a-3b) — RF and Microwave Engineering, chapter 4 - [Short note: Two magic tees connected in H-plane](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Atwo-magic-tees-h-plane-note) — RF and Microwave Engineering, chapter 4 - [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