Magic Tees (Hybrid Tees)

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A magic tees is a combination of the E-plane tee and H-plane tee

If two waves of equal magnitude and the same phase are fed into port 1 and port 2, the output will be zero at port 3 and additive at port 4.
If a wave is fed into port 4 (the H arm), it will be divided equally between port 1 and port 2 of the collinear arms and will not appear at port 3 (the E arm).
If a wave is fed into port 3 (the E arm), it will produce an output of equal magnitude and opposite phase at port 1 and port 2. The output at port 4 is zero. That is, $S_{43}=S_{34}=0$
If a wave is fed into one of the collinear arms at port 1 or port 2, it will not appear in the other collinear in the other collinear arm at port 2 or port 1 because the E arm causes a phase delay while the H arm causes a phase advance. That is, $S_{12}=S_{21}=0$

E - Arm & H - Arm are perfectly matched $S_{33}=S_{44}=0$
port 3 and port 4 are isolated to eachother $S_{34}=S_{43}=0$
If input at port 4 (E - Arm), then output at port-1 & port 2 is same and out of phase $S_{14}= - S_{24}$
If input is at port 3 (H - arm), then output at port 1 & port 2 is same and in-phase $S_{13}=S_{23}$

$S = \begin{bmatrix} 0 & 0 & S_{13} & S_{14} \\ 0 & 0 & S_{23} & S_{24} \\ S_{31} & S_{32} & 0 & 0 \\ S_{41} & S_{42} & 0 & 0 \end{bmatrix}$

The magic tee is commonly used for:

Suppose for example there are two identical radar transmitters in equipment stock.
A particular application requires twice more input power to an antenna than either transmitter can deliver.
A magic tee may be used to couple the two transmitters to the antenna in such a way that the transmitters do not load each other.
The two transmitters should be connected to ports 3 and 4.
Transmitter 1, connected to port 3, causes a wave to emanate from port 1 and another to emanate from port 2; these waves are equal in magnitude but opposite in phase.
Similarly, transmitter 2, connected to port 4, gives rise to a wave at port 1 and another at port 2, both equal in magnitude and in phase.
At port 1 two opposite phase cancel each other.
At port 2 the two in-phase waves add together; so double output power at port 2 is obtained for the antenna.