Adam Cooman

YZSHGABT
Y Y→Z Y→S Y→H Y→G Y→A Y→B Y→T
Z Z→Y Z→S Z→H Z→G Z→A Z→B Z→T
S S→Y S→Z S→H S→G S→A S→B S→T
H H→Y H→Z H→S H→G H→A H→B H→T
G G→Y G→Z G→S G→H G→A G→B G→T
A A→Y A→Z A→S A→H A→G A→B A→T
B B→Y B→Z B→S B→H B→G B→A B→T
T T→Y T→Z T→S T→H T→G T→A T→B

From G-parameters to B-parameters

In matrix form, the formula is

B=([0100]G+[0001])([0010]G+[1000])1\mathbf{B} =\left(\begin{bmatrix} 0 & 1\\ 0 & 0 \end{bmatrix}\,\mathbf{G}+\begin{bmatrix} 0 & 0\\ 0 & -1 \end{bmatrix}\right)\,{\left(\begin{bmatrix} 0 & 0\\ 1 & 0 \end{bmatrix}\,\mathbf{G}+\begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix}\right)}^{-1}

While for each element, we obtain

B11=G11G22G12G21G12B12=G22G12B21=G11G12B22=1G12\begin{align*}B_{11} &=-\frac{G_{11}\,G_{22}-G_{12}\,G_{21}}{G_{12}}\\B_{12} &=\frac{G_{22}}{G_{12}}\\B_{21} &=\frac{G_{11}}{G_{12}}\\B_{22} &=-\frac{1}{G_{12}}\\\end{align*}

The formulas are obtained with the methods explained here. The MATLAB implementation can be found in circuitconversions on Gitlab.

Definitions

[I1V2]=G[V1I2]\begin{bmatrix}I_1 \\V_2\end{bmatrix} = \mathbf{G}\begin{bmatrix}V_1 \\I_2\end{bmatrix}

[V2I2]=B[V1I1]\begin{bmatrix}V_2 \\-I_2\end{bmatrix} = \mathbf{B}\begin{bmatrix}V_1 \\I_1\end{bmatrix}