Determination of T1 matrix parameters

Circuit diagram

T1 matrix

The T1 matrix of the device under test is found as:

\begin{equation} T=\left[\begin{matrix}\frac{- R_{a} g - 1}{R_{b} g - 1} & \frac{- R_{a} - R_{b}}{R_{b} g - 1}\\- \frac{g}{R_{b} g - 1} & - \frac{1}{R_{b} g - 1}\end{matrix}\right] \end{equation}

The matrix equation for the two-port (DUT) is found as:

Matrix equation:

\begin{equation} \left[\begin{matrix}V_{i}\\I_{i}\end{matrix}\right]=\left[\begin{matrix}\frac{- R_{a} g - 1}{R_{b} g - 1} & \frac{- R_{a} - R_{b}}{R_{b} g - 1}\\- \frac{g}{R_{b} g - 1} & - \frac{1}{R_{b} g - 1}\end{matrix}\right]\cdot\left[\begin{matrix}V_{o}\\I_{o}\end{matrix}\right] \end{equation}

Input and output impedances

\begin{equation} Z_{i}=\frac{R_{a} + R_{b} + R_{\ell} \left(R_{a} g + 1\right)}{R_{\ell} g + 1} \end{equation} \begin{equation} Z_{o}=\frac{R_{a} + R_{b} + R_{s}}{R_{a} g + R_{s} g + 1} \end{equation}

Transfers

\begin{equation} A_{v}=- \frac{R_{\ell} \left(R_{b} g - 1\right)}{R_{a} + R_{b} + R_{\ell} \left(R_{a} g + R_{s} g + 1\right) + R_{s}} \end{equation} \begin{equation} A_{y}=\frac{- R_{b} g + 1}{R_{a} + R_{b} + R_{\ell} R_{s} g + R_{\ell} \left(R_{a} g + 1\right) + R_{s}} \end{equation}

For $A_z$ and $A_i$, the voltage source V1 in series with R4 is replaced with a current source in parallel with R4.

\begin{equation} A_{z}=\frac{R_{\ell} R_{s} \left(- R_{b} g + 1\right)}{R_{a} R_{\ell} g + R_{a} + R_{b} + R_{\ell} R_{s} g + R_{\ell} + R_{s}} \end{equation} \begin{equation} A_{i}=\frac{R_{s} \left(- R_{b} g + 1\right)}{R_{a} R_{\ell} g + R_{a} + R_{b} + R_{\ell} R_{s} g + R_{\ell} + R_{s}} \end{equation}

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Last project update: 2024-10-22 11:36:22