Q3Microwave Theory And Techniques

What is 'Magic' about a Magic Tee: a Magic Tee (hybrid Tee) is formed by combining an E-plane Tee and an H-plane Tee at the same junction on a common main waveguide, creating a 4-port device (two collinear arms plus the E-arm and H-arm side branches). Its 'magic' property is that the E-arm and H-arm ports are completely isolated from each other (S_EH = S_HE = 0) despite both connecting to the same junction — a signal fed into the E-arm splits equally between the two collinear arms (180° out of phase) but couples zero power directly into the H-arm, and vice versa; this isolation, not obviously guaranteed by the geometry alone, is what early microwave engineers found 'magical' about the device.

Applications: (1) duplexer — connecting a common transmitter, receiver and antenna, exploiting the E/H-arm isolation to keep transmitter power from directly overloading the receiver; (2) balanced mixer — combining a local oscillator and RF signal at the two collinear arms while feeding separate, phase-related outputs to two diode mixers connected at the E- and H-arms, cancelling LO noise; (3) impedance measurement bridge — comparing an unknown impedance connected to one collinear arm against a standard reference at the other, with the E-arm and H-arm serving as balanced input/output/null-detection ports, analogous to a Wheatstone bridge at microwave frequencies; (4) power divider/combiner — splitting or combining signals with a fixed 180° phase relationship between the two collinear-arm outputs.

Properties: it is a 4-port, reciprocal, lossless (ideally) junction; its scattering matrix is symmetric with S_EH=S_HE=0 (E/H isolation) and, with a suitable reference-plane choice, purely imaginary or purely real off-diagonal terms depending on convention, and — like the H-plane and E-plane Tees individually — it cannot be matched at all four ports simultaneously without additional matching elements (irises or posts) at the junction, since a lossless reciprocal 4-port network has fundamental constraints on how many ports can be simultaneously matched and isolated.