Consider the following statements in case of a magic Tee:

1. The collinear arms are isolated from each other

2. One of the collinear arms is isolated from E-arm

3. One of the collinear arms is isolated from H-arm

4. E and H arms are isolated from each other

Which of these statements are correct?

Magic Tee:

A magic tee (or magic T or hybrid tee) is a hybrid or 3 dB coupler used in microwave systems.

It is an alternative to the rat-race coupler.

In contrast to the rat-race, the three-dimensional structure of the magic tee makes it less readily constructed in planar technologies such as microstrip or stripline.

• The magic tee 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 and is also called the Σ port, sum port, or the P-port (for "parallel").
• Port 4 is the E-plane port and is also called the Δ port, difference port, or S-port (for "series"). There is no single established convention regarding the numbering of the ports.

Example:

Magic-tree scattering matrix:

\(s = \left[ {\begin{array}{*{20}{c}} {{s_{11}}}&{{s_{12}}}&{{s_{13}}}&{{s_{14}}}\\ {{s_{21}}}&{{s_{22}}}&{{s_{23}}}&{{s_{24}}}\\ {{s_{31}}}&{{s_{32}}}&{{s_{33}}}&{{s_{34}}}\\ {{s_{41}}}&{{s_{42}}}&{{s_{44}}}&{{s_{44}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0&0&{\frac{1}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 2 }}}\\ 0&0&{\frac{1}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 2 }}}\\ {\frac{1}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 2 }}}&0&0\\ {\frac{1}{{\sqrt 2 }}}&{\frac{1}{{\sqrt 2 }}}&0&0 \end{array}} \right]\)

∴ All four powers are Perfectly matured.

s₁₁ = s₂₂ = s₃₃ = s₄₄ = 0

∵ \({s_{13}} = {s_{31}} = \frac{1}{{\sqrt 2 }}\;\;\;\;\;\;{s_{14}} = {s_{41}} = \frac{1}{{\sqrt 2 }}\)

\({s_{23}} = {s_{32}} = \frac{1}{{\sqrt 2 }}\;\;\;\;\;\;\;\;\;\;{s_{24}} = {s_{42}} = \frac{1}{{\sqrt 2 }}\)

∵ H part (3) and E-arm port (4) are isolated port

s₃₄ = s₄₃ = 0

∵ s₁₂ = s₂₁ = 0

Collinear ports [(1) and (2)] are isolated ports.