Duplexer for half-power airport surveillance radar

Reading of the problem

The radar must feed the antenna with half of the transmitter power, and the same antenna must be used for receiving (duplexing). Both needs are met by a magic tee used as a duplexer:

• Transmitter at the H-arm (port 3).
• Antenna at collinear port 1; matched dummy load at collinear port 2.
• Receiver at the E-arm (port 4).

               RX (4, E-arm)
                  | |
 ANT (1) ========+   +======== (2) matched load
                  / /
                 / /
           TX (3, H-arm)

S-matrix of the duplexer (ideal magic tee)

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

Transmit mode

TX sends a3 = a (power Pt = |a|²/2); antenna and load are matched, a1 = a2 = a4 = 0:

 b1 = a3/√2   -> power to antenna = Pt/2
 b2 = a3/√2   -> power to dummy load = Pt/2
 b4 = 0       -> no power to receiver (S43 = 0)
 b3 = 0       -> no reflection to TX

So the antenna gets exactly half the transmitter power (−3 dB), and the receiver is isolated from the high-power transmitter.

Receive mode

The echo enters at port 1 (a1 = e):

 b3 = e/√2  -> half to transmitter arm
 b4 = e/√2  -> half to receiver (E-arm)
 b2 = 0     -> nothing to the load

The receiver gets half the received echo power.

Remarks

• Total loss in the duplexer is 3 dB on transmit and 3 dB on receive, but the arrangement is passive, reciprocal and needs no switching, and the receiver is protected by the E–H isolation.
• If no power loss were acceptable, a ferrite circulator duplexer [[0,0,1],[1,0,0],[0,1,0]] would be used instead; the magic tee version fits this requirement because the antenna needs only half the power.
• Practical systems add a TR (transmit-receive) limiter before the receiver for extra protection against leakage from imperfect isolation.