DM-CM decomposition

MNA matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}0\\I_{B}\\I_{A}\end{matrix}\right]=\left[\begin{matrix}\frac{1}{R_{c}} + \frac{2}{R_{a}} & - \frac{1}{R_{a}} & - \frac{1}{R_{a}}\\- \frac{1}{R_{a}} & \frac{1}{R_{a}} & 0\\- \frac{1}{R_{a}} & 0 & \frac{1}{R_{a}}\end{matrix}\right]\cdot\left[\begin{matrix}V_{C}\\V_{inN}\\V_{inP}\end{matrix}\right] \end{equation}

DM-CM matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}0.5 I_{A} - 0.5 I_{B}\\I_{A} + I_{B}\\0\end{matrix}\right]=\left[\begin{matrix}\frac{0.5}{R_{a}} & 0 & 0\\0 & \frac{2}{R_{a}} & - \frac{2}{R_{a}}\\0 & - \frac{2}{R_{a}} & \frac{1}{R_{c}} + \frac{2}{R_{a}}\end{matrix}\right]\cdot\left[\begin{matrix}V_{in D}\\V_{in C}\\V_{C}\end{matrix}\right] \end{equation}

DM matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}0.5 I_{A} - 0.5 I_{B}\end{matrix}\right]=\left[\begin{matrix}\frac{0.5}{R_{a}}\end{matrix}\right]\cdot\left[\begin{matrix}V_{in D}\end{matrix}\right] \end{equation}

DM transfer

\begin{equation} Z_{dm}=2.0 R_{a} \end{equation}

CM matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}I_{A} + I_{B}\\0\end{matrix}\right]=\left[\begin{matrix}\frac{2}{R_{a}} & - \frac{2}{R_{a}}\\- \frac{2}{R_{a}} & \frac{1}{R_{c}} + \frac{2}{R_{a}}\end{matrix}\right]\cdot\left[\begin{matrix}V_{in C}\\V_{C}\end{matrix}\right] \end{equation}

CM transfer to V_C

\begin{equation} Z_{cm}=R_{c} \end{equation}

CM transfer to V_in_C

\begin{equation} Z_{cm}=0.5 R_{a} + R_{c} \end{equation}

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Last project update: 2024-10-05 15:15:53