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 H-parameters

In matrix form, the formula is

H=G−1\mathbf{H} ={\mathbf{G}}^{-1}

While for each element, we obtain

H11=G22G11 G22−G12 G21H12=−G12G11 G22−G12 G21H21=−G21G11 G22−G12 G21H22=G11G11 G22−G12 G21\begin{align*}H_{11} &=\frac{G_{22}}{G_{11}\,G_{22}-G_{12}\,G_{21}}\\H_{12} &=-\frac{G_{12}}{G_{11}\,G_{22}-G_{12}\,G_{21}}\\H_{21} &=-\frac{G_{21}}{G_{11}\,G_{22}-G_{12}\,G_{21}}\\H_{22} &=\frac{G_{11}}{G_{11}\,G_{22}-G_{12}\,G_{21}}\\\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}

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