	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 T-parameters to S-parameters

In matrix form, the formula is

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

While for each element, we obtain

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

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

Definitions

$\begin{bmatrix}A_1 \\B_1\end{bmatrix} = \mathbf{T}\begin{bmatrix}B_2 \\A_2\end{bmatrix}$

$\begin{bmatrix}B_1 \\B_2\end{bmatrix} = \mathbf{S}\begin{bmatrix}A_1 \\A_2\end{bmatrix}$

The incident and reflected waves are defined as

$\begin{align*}A_1 &= k_{1}\,\left(V_{1}+I_{1}\,Z_{1}\right)\qquad B_1 &= k_{1}\,\left(V_{1}-I_{1}\,Z_{1}\right)\\A_2 &= k_{2}\,\left(V_{2}+I_{2}\,Z_{2}\right)\qquad B_2 &= k_{2}\,\left(V_{2}-I_{2}\,Z_{2}\right)\\\end{align*}$

with $Z_{0,i}$ the reference impedance for port $i$ and $k_i$ defined as

$k_i=\frac{1}{2\sqrt{\Re\left( Z_{0,i}\right) }}\qquad k_i=\alpha\frac{\sqrt{\Re\left( Z_{0,i} \right) }}{2\left|Z_{0,i}\right|}$

depending on whether you are using power- or pseudowaves.