Short note: Microwave magic tee

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.

             E-arm (4)
               | |
               | |
     ----------+ +----------
 (1) ==========+   +========== (2)
     ----------+ +----------
              /   /
             /   /  H-arm (3)

S-matrix of an ideal (matched) magic tee:

              | 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.