	Y	Z	S	H	G	A	B	T
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 A-parameters to Z-parameters

In matrix form, the formula is

$\mathbf{Z} =\left(\begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix}\,\mathbf{A}+\begin{bmatrix} 0 & 0\\ 1 & 0 \end{bmatrix}\right)\,{\left(\begin{bmatrix} 0 & 1\\ 0 & 0 \end{bmatrix}\,\mathbf{A}+\begin{bmatrix} 0 & 0\\ 0 & -1 \end{bmatrix}\right)}^{-1}$

While for each element, we obtain

$\begin{align*}Z_{11} &=\frac{A_{11}}{A_{21}}\\Z_{12} &=\frac{A_{11}\,A_{22}-A_{12}\,A_{21}}{A_{21}}\\Z_{21} &=\frac{1}{A_{21}}\\Z_{22} &=\frac{A_{22}}{A_{21}}\\\end{align*}$

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

Definitions

$\begin{bmatrix}V_1 \\I_1\end{bmatrix} = \mathbf{A}\begin{bmatrix}V_2 \\-I_2\end{bmatrix}$

$\begin{bmatrix}V_1 \\V_2\end{bmatrix} = \mathbf{Z}\begin{bmatrix}I_1 \\I_2\end{bmatrix}$