Passive device to split power into half

Choice: magic tee (hybrid tee) fed at the H-arm

To split power into two equal halves, a magic tee is a good choice: power fed into its H-arm (port 3) divides equally and in phase between the collinear arms 1 and 2, while all ports remain matched and the outputs are isolated. (A simple H-plane tee also splits power equally, but its output arms are not matched or isolated; in microstrip circuits the equivalent device is the Wilkinson divider.)

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

S-matrix

              | 0   0   1   1 |
 [S] = (1/√2) | 0   0   1  -1 |
              | 1   1   0   0 |
              | 1  -1   0   0 |

Power split

With input a3 = a (power P = |a|²/2) and matched outputs:

 b1 = a/√2  -> P1 = |a|²/4 = P/2   (−3 dB)
 b2 = a/√2  -> P2 = P/2            (−3 dB, same phase)
 b4 = 0     -> no power to E-arm
 b3 = 0     -> input matched, no reflection

Result: each output gets exactly half the input power, in phase. If anti-phase halves are needed, the input is applied at the E-arm instead (b1 = a/√2, b2 = −a/√2).

Properties of the magic tee

1. Equal split: |S13| = |S23| = |S14| = |S24| = 1/√2 (3 dB).
2. Phase: H-arm gives in-phase outputs; E-arm gives 180° out-of-phase outputs.
3. Isolation: E and H arms are isolated (S34 = 0); collinear arms are isolated (S12 = 0), so a mismatch on one output does not disturb the other output.
4. Matching: all ports matched (Sᵢᵢ = 0) when E and H arms are matched with posts or irises.
5. Lossless and reciprocal: [S] is unitary and symmetric. If the two loads are unequal, the difference between their reflections goes to the E-arm, which can be terminated in a matched load.
6. Reverse use: equal in-phase inputs at 1 and 2 combine at the H-arm, so the same device works as a power combiner.

Comparison with an H-plane tee