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}