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 A-parameters to G-parameters

In matrix form, the formula is

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

While for each element, we obtain

G11=A21A11G12=A11A22A12A21A11G21=1A11G22=A12A11\begin{align*}G_{11} &=\frac{A_{21}}{A_{11}}\\G_{12} &=-\frac{A_{11}\,A_{22}-A_{12}\,A_{21}}{A_{11}}\\G_{21} &=\frac{1}{A_{11}}\\G_{22} &=\frac{A_{12}}{A_{11}}\\\end{align*}

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

Definitions

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

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