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 A-parameters to B-parameters

In matrix form, the formula is

B=A−1\mathbf{B} ={\mathbf{A}}^{-1}

While for each element, we obtain

B11=A22A11 A22−A12 A21B12=−A12A11 A22−A12 A21B21=−A21A11 A22−A12 A21B22=A11A11 A22−A12 A21\begin{align*}B_{11} &=\frac{A_{22}}{A_{11}\,A_{22}-A_{12}\,A_{21}}\\B_{12} &=-\frac{A_{12}}{A_{11}\,A_{22}-A_{12}\,A_{21}}\\B_{21} &=-\frac{A_{21}}{A_{11}\,A_{22}-A_{12}\,A_{21}}\\B_{22} &=\frac{A_{11}}{A_{11}\,A_{22}-A_{12}\,A_{21}}\\\end{align*}

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

Definitions

[V1I1]=A[V2−I2]\begin{bmatrix}V_1 \\I_1\end{bmatrix} = \mathbf{A}\begin{bmatrix}V_2 \\-I_2\end{bmatrix}

[V2−I2]=B[V1I1]\begin{bmatrix}V_2 \\-I_2\end{bmatrix} = \mathbf{B}\begin{bmatrix}V_1 \\I_1\end{bmatrix}