Adam Cooman

YZSHGABT
YY→ZY→SY→HY→GY→AY→BY→T
ZZ→YZ→SZ→HZ→GZ→AZ→BZ→T
SS→YS→ZS→HS→GS→AS→BS→T
HH→YH→ZH→SH→GH→AH→BH→T
GG→YG→ZG→SG→HG→AG→BG→T
AA→YA→ZA→SA→HA→GA→BA→T
BB→YB→ZB→SB→HB→GB→AB→T
TT→YT→ZT→ST→HT→GT→AT→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}