A Magic-Tee is a 4-port waveguide structure similar to a rat-race coupler fabricated with striplines or microstrip waveguides. The Magic-Tee, or EH plane Tee, is able to perform an apparently “magical” function, which is to allow for energy going into the E and H plane ports to be divided between the two colinear ports while isolating the E and H plane ports and the two colinear ports from each other. This microwave component was originally developed during WWII, and was first published by W. A. Tyrell in an IRE paper from 1947. It is thought that both L. Kyhi and Bob Dicke independently discovered and created Magic-Tees near the same time frame.
Different than other power dividers or couplers, the Magic-Tee performs different functions at the E plane and H plane ports. Where the H plane port, known as the sum port, will present the same phase at both colinear ports, the E plane port presents a 180 degree phase referenced to the different colinear ports. This function of a Magic-Tee is also symmetric, and will split the energy going into a colinear port to both the E and H plane ports. Hence, signals going into the colinear ports will be simultaneously divided, summed at the H plane port, and differenced at the E plan port.
The ideal S-Parameters of a Magic-Tee are as follows:
However, these functions are only possible under ideal or theoretical cases, and a real Magic-Tee has practical limitations based on its matching, balance, and isolation. The tuning and impedance matching mechanisms, necessary for a Magic-Tee to function, also impose a frequency range limit, insertion loss, limited E-H port isolation, and limited isolation between the collinear ports. Matching is needed for both the E plane and H plane ports, which also influences the match at the colinear ports. Assembly quality also affects a Magic-Tees performance, as the E plane and H plane ports need to be completely orthogonal to each other to maintain a high level of isolation.
A Magic-Tee can be used for several applications, such as an impedance measuring tool, duplexer, and even as a mixer. A Magic-Tee can be used to measure impedance by connecting a null detector to the E plane port, a microwave source to the H plane port, and by balancing the impedance bridge created with the colinear ports. To use a Magic-Tee as a duplexer, the transmitter and receiver can be connected to different colinear ports, while the antenna is connected to the E plane port and the H plane port is terminated in a matched load. If a Magic-Tee’s E plan port is connected to an antenna, and its H plane port is connected to a local oscillator, a mixer can be created with a terminated collinear port with a mixer circuit on the remaining colinear port.
For a deeper dive into the mathematics of a Magic-Tee, see this source