# How to find new ABCD parameters when reversing 2-port network

I have an ABCD matrix represenataion which is defined as: For such a problem, what approach should I follow in order to organize the new ( reversed) network ports voltages and currents properly. I have tried to keep the currents of ports same and making voltages switching places but this did not make any sense in the substituted-general form calculations.

• Is there a restriction on the type of network? Like it's a network composed only of passive components? – The Photon Dec 5 '18 at 23:17
• Not sure if this helps, but at least you can see the basics from this:\begin{align*}\left[\begin{matrix}V_2\\ I_2\end{matrix}\right]&=\left[\begin{matrix}A&B\\ C&D\end{matrix}\right]\left[\begin{matrix}V_1\\ I_1\end{matrix}\right]\\\\ \left[\begin{matrix}A&B\\ C&D\end{matrix}\right]^{-1}\left[\begin{matrix}V_2\\ I_2\end{matrix}\right]&=\left[\begin{matrix}A&B\\ C&D\end{matrix}\right]^{-1}\left[\begin{matrix}A&B\\ C&D\end{matrix}\right]\left[\begin{matrix}V_1\\ I_1\end{matrix}\right] \end{align*} – jonk Dec 6 '18 at 1:23
• and:\begin{align*} \left[\begin{matrix}A&B\\ C&D\end{matrix}\right]^{-1}\left[\begin{matrix}V_2\\ I_2\end{matrix}\right]&=\left[\begin{matrix}V_1\\ I_1\end{matrix}\right]\\\\ \frac{1}{A\cdot D-B\cdot C}\left[\begin{matrix}D&-B\\ -C&A\end{matrix}\right]\left[\begin{matrix}V_2\\ I_2\end{matrix}\right]&=\left[\begin{matrix}V_1\\ I_1\end{matrix}\right] \end{align*} – jonk Dec 6 '18 at 1:23
• This is very straightforward. I do not think that few manipulations in linear algebra will solve the problem. I am worried more about the reconstruction of the network ports, currents, ...etc. No specific restriction on the type of the network. But due to RF purposes, it can be assumed to contain only passive elements if that can simplify the issue. – utdlegend Dec 6 '18 at 6:46
• Different lengths of the forward and back parts of the network may point to asymmetric network ! – utdlegend Dec 6 '18 at 6:49

No full solutions to homeworks, only guidance!

The new matrix is in math called the inverse matrix of the original. You can find it by solving V1, I1 from the equations which the matrix present. In numerical cases one can use software. For ex. Excel can find the inverses of numerical matrices. Complex numbers are accepted. But your case is not numerical because A,B,C,D are variables.

The inverse does not always exist. That's the case when several inputs can cause the same output.

The inverse of a 2x2 matrix is so simple and often used that many people remember the inversion result as a general formula. It's shown also here: