Microwave Engineering, Supplementary Notes

[Network Parameters]

1. Impedance matrix

T-network

Series connection of a two-port network

Conversion into the scattering matrix

2. Admittance matrix

Pi-network

Shunt connection of a two-port network

Conversion into the scattering matrix

3. ABCD parameters

Definition

Reverse ABCD matrix

ABCD matrix of the basic circuits

Network
Series resistor	{\displaystyle {\begin{bmatrix}1&R\\0&1\end{bmatrix}}}	{\displaystyle {\begin{bmatrix}1&-R\\0&1\end{bmatrix}}}
Shunt resistor	{\displaystyle {\begin{bmatrix}1&0\\{\frac {1}{R}}&1\end{bmatrix}}}	{\displaystyle {\begin{bmatrix}1&0\\-{\frac {1}{R}}&1\end{bmatrix}}}
Transmission line		{\displaystyle {\begin{bmatrix}\cosh \left(\gamma l\right)&-Z_{0}\sinh \left(\gamma l\right)\\-{\frac {1}{Z_{0}}}\sinh \left(\gamma l\right)&\cosh \left(\gamma l\right)\end{bmatrix}}}