Short note: Two magic tees connected in H-plane

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).

        (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:

 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.