# Microwave Engineering - H-Plane T-shirt

Microwave engineering tutorial 2020-11-20 01:25:53# Microwave Engineering - H-Plane Tee

An H-Plane Tee junction is formed by attaching a simple waveguide to a guide waveform that already has two ports. The arms of the rectangular waveguides form two ports called ** collinear ports ** i.e. Port1 and Port2, while the new one, Port3 is called side arm or ** end arm. H **. This H-plane tee is also called a ** shunt tee **.

Since the side arm axis is parallel to the magnetic field, this junction is called the H-Plane Tee junction. This is also called ** Current Junction **, because the magnetic field

The following figure shows the connection made by the handgun to the bidirectional waveguide to form the serial port.

## Properties of H-Plane Tee

The properties of the H-Plane Tee can be defined by its matrix $ left [S right] _ {3 times 3} $.

This is a 3 × 3 matrix because there are 3 possible inputs and 3 outputs.

$ [S] = begin {bmatrix} S_ {11} & S_ {12} & S_ {13} S_ {21} & S_ {22} & S_ {23} S_ {31} & S_ {32} & S_ { 33} end {bmatrix} $ ** ........ Equation 1 **

Diffusion the coefficients $ S_ {13} $ and $ S_ {23} $ are equal here because the junction is symmetric in plane.

From the symmetric property,

$ S_ {ij} = S_ {ji} $

$ S_ {12} = S_ { 21}:: S_ {23} = S_ {32} = S_ {13}:: S_ {13} = S_ {31} $

The port is perfectly suited

$ S_ {33} = 0 $

Now the matrix $ [S] $ can be written as follows:

$ [S] = begin {bmatrix} S_ {11} & S_ {12} & S_ {13} S_ {12} & S_ {22} & S_ {13} S_ {13} & S_ {13} & 0 end {bmatrix} $ ** ........ Equation 2 **

We can say that we have four unknowns, given the symmetry property.

From the Unitary property

$$ [S] [S] ast = [I ] $$

$$ begin {bmatrix} S_ {11} & S_ {12} & S_ {13} S_ {12} & S_ {22} & S_ {13} S_ {13} & S_ {13} & 0 end {bmatrix}: begin {bmatrix} S_ {11} ^ {*} & S_ {12} ^ {*} & S_ {13} ^ {*} S_ {12} ^ {*} & S_ {22} ^ {*} & S_ {13} ^ {*} S_ {13} ^ {*} & S_ {13} ^ {*} & 0 end {bmatrix} = begin {bmatrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 end {bmatrix} $$

By multiplying we get,

(Noting R as row and C as column)

$ R_1C_1: S_ {11} S_ {11} ^ {*} + S_ {12} S_ {12} ^ {*} + S_ {13} S_ {13} ^ {*} = $ 1

$ left | S_ {11} right| ^ 2 + left | S_ {12} right | ^ 2 + left | S_ {13} right | ^ 2 = 1 $ ** ........ Eq uation 3 **

$ R_2C_2: left | S_ {12} right | ^ 2 + left | S_ {22} right | ^ 2 + left | S_ {13} right | ^ 2 = 1 $ ** ......... Equation 4 **

$ R_3C_3: left | S_ {13} right | ^ 2 + left | S_ {13} right | ^ 2 = 1 $ ** ......... Equation 5 **

$ R_3C_1: S_ {13} S_ {11} ^ {*} - S_ {13} S_ {12} ^ {*} = 0 $ ** ......... Equation 6 **

$ 2 left | S_ {13} right | ^ 2 = 1 quad or quad S_ {13} = frac {1} {sqrt {2}} $ ** ......... Equation 7 **

$ left | S_ {11} right | ^ 2 = left | S_{22} right | ^ 2 $

$ S_ {11} = S_ {22} $ ** ......... Equation 8 **

From equation 6, $ S_ {13} left (S_ {11} ^ {*} + S_ {12} ^ {*} right) = 0 $

Since, $ S_ {13} neq 0, S_ {11} ^ {*} + S_ {12} ^ {*} = 0,: or: S_ {11} ^ {*} = -S_ {12} ^ {*} $

Or $ S_ {11} = -S_ {12}:: or:: S_ {12} = -S_ {11} $ ** ......... Equation 9 **

Using these in equation 3,

Since, $ S_ { 13} neq 0, S_ {11} ^ {*} + S_ {12} ^ {*} = 0,: or: S_ {11} ^ {*} = -S_ {12} ^ {*} $

$ left | S_ {11} right | ^ 2 + left | S_ {11} right | ^ 2 + frac {1} {2} = 1 quad or quad 2 left | S_ {11} right | ^ 2 = frac {1} {2} quad or quadS_ {11} = frac {1} {2} $ ** ..... Equation 10 **

From equations 8 and 9,

$ S_ {12} = - frac {1} {2} $ ** ......... Equation 11 **

$ S_ {22} = frac {1} {2} $ ** ......... Equation 12 **

Replacement of $ S_ {13} $, $ S_ {11} $, $ S_ {12} $ and $ S_ {22} $ of equations 7 and 10, 11 and 12 of the 'equation 2,

We get,

$$ left [S right] = begin {bmatrix} frac {1} {2} & - frac {1} {2} & frac {1} {sqrt {2}} - frac {1} {2} & frac {1} {2} & frac {1} {sqrt {2}} frac {1} {sqrt {2}} & frac { 1} {sqrt {2}} & 0 end {bmatrix} $$

We know that $ [b] $ = $ [s] [a] $

$$ begin {bmatrix} b_1 b_2 b_3 end {bmatrix} = begin {bmatrix} frac {1} {2} & - frac {1} {2} & frac {1} {sqrt {2}} - frac {1} {2} & frac {1} {2} &frac {1} {sqrt {2}} frac {1} {sqrt {2}} & frac {1} {sqrt {2}} & 0 end {bmatrix} begin {bmatrix} a_1 a_2 a_3 end {bmatrix} $$

Here is the diffusion matrix for H-Plane Tee, which explains its diffusion properties.