\(S = \left[ {\begin{array}{*{20}{c}} 0&0&{{S_{13}}}&{{S_{14}}}\\ 0&0&{{S_{23}}}&{{S_{24}}}\\ {{S_{31}}}&{{S_{32}}}&0&0\\ {{S_{41}}}&{{S_{42}}}&0&0 \end{array}} \right]\)

The above is the scattering matrix of

The magic Tee junction is represented as:

The properties of the Magic Tee (E-H plane tee) is defined by a 4×4 matrix [S]_4×4 as:

\(\left[ S \right] = \left[ {\begin{array}{*{20}{c}} {{s_{11}}}&{{s_{12}}}&{{s_{13}}}&{{s_{14}}}\\ {{s_{21}}}&{{s_{22}}}&{{s_{23}}}&{{s_{24}}}\\ {{s_{31}}}&{{s_{32}}}&{{s_{33}}}&{{s_{34}}}\\ {{s_{41}}}&{{s_{42}}}&{{s_{43}}}&{{s_{44}}} \end{array}} \right]\)

For a magic Tee, the E-Arm port and H-Arm port are so isolated that the other won't deliver an output if the input is applied at one of them. 

∴ S₃₄ = S₄₃ = 0

Also, If ports 3 and 4 are perfectly matched to the junction:

S33 = S44 = 0

Also S11 = S22 = 0

The S matrix becomes:

\(S = \left[ {\begin{array}{*{20}{c}} 0&0&{{S_{13}}}&{{S_{14}}}\\ 0&0&{{S_{23}}}&{{S_{24}}}\\ {{S_{31}}}&{{S_{32}}}&0&0\\ {{S_{41}}}&{{S_{42}}}&0&0 \end{array}} \right]\)

• Magic tee is a combination of one H-plane Tee and one E-plane Tee, i.e. it is a combination of E and H plane tees.
• Arm 3 forms an H-plane tee with arms 1 and 2.
• Arm 4 forms an E-plane tee with arms 1 and 2. Arms 1 and 2 are sometimes called the side or collinear arms.
• Port 3 is called the H plane port.