"DM-CM decomposition"
DM-CM decomposition
MNA matrix equation
Matrix equation:
\begin{equation}
\left[\begin{matrix}0.5 V_{in}\\- 0.5 V_{in}\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{array}{cccccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & - 0.5 R_{\ell} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & - 0.5 R_{\ell} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0.5 c_{db XMiN} s + c_{dg XMiN} s + c_{dg XMiP} s + c_{dg XMoN} s + c_{gb XMoN} s + c_{gs XMoN} s + 0.5 g_{o XMiN} + s \left(0.5 c_{gb XMiP} + 0.5 c_{gs XMiP}\right) + \frac{1}{R_{c}} + \frac{1}{R_{b}} & - 0.5 g_{m XMiN} - \frac{1}{R_{b}} & - 0.5 c_{db XMiN} s - c_{gb XMoN} s - c_{gs XMoN} s - 0.5 g_{o XMiN} - \frac{1}{R_{c}} & - c_{dg XMiP} s & - c_{dg XMiN} s + 0.5 g_{m XMiN} & - s \left(0.5 c_{gb XMiP} + 0.5 c_{gs XMiP}\right) & - c_{dg XMoN} s & 0 & 0 & 0\\0 & 0 & 0 & 0 & - 0.5 g_{m XMiP} - \frac{1}{R_{b}} & 0.5 c_{db XMiP} s + c_{dg XMiN} s + c_{dg XMiP} s + c_{dg XMoP} s + c_{gb XMoP} s + c_{gs XMoP} s + 0.5 g_{o XMiP} + s \left(0.5 c_{gb XMiN} + 0.5 c_{gs XMiN}\right) + \frac{1}{R_{c}} + \frac{1}{R_{b}} & - c_{dg XMiN} s & - 0.5 c_{db XMiP} s - c_{gb XMoP} s - c_{gs XMoP} s - 0.5 g_{o XMiP} - \frac{1}{R_{c}} & - s \left(0.5 c_{gb XMiN} + 0.5 c_{gs XMiN}\right) & - c_{dg XMiP} s + 0.5 g_{m XMiP} & 0 & - c_{dg XMoP} s & 0 & 0\\0 & 0 & 0 & 0 & - 0.5 c_{db XMiN} s - c_{gb XMoN} s - c_{gs XMoN} s - g_{m XMoN} - 0.5 g_{o XMiN} - \frac{1}{R_{c}} & - c_{dg XMiN} s + 0.5 g_{m XMiN} & 0.5 c_{db XMiN} s + c_{db XMoN} s + c_{dg XMiN} s + c_{gb XMoN} s + c_{gs XMoN} s + g_{m XMoN} + 0.5 g_{o XMiN} + g_{o XMoN} + \frac{1}{R_{c}} + \frac{1}{R_{a}} & 0 & - 0.5 g_{m XMiN} - \frac{1}{R_{a}} & 0 & - c_{db XMoN} s - g_{o XMoN} & 0 & 0 & 0\\0 & 0 & 0 & 0 & - c_{dg XMiP} s + 0.5 g_{m XMiP} & - 0.5 c_{db XMiP} s - c_{gb XMoP} s - c_{gs XMoP} s - g_{m XMoP} - 0.5 g_{o XMiP} - \frac{1}{R_{c}} & 0 & 0.5 c_{db XMiP} s + c_{db XMoP} s + c_{dg XMiP} s + c_{gb XMoP} s + c_{gs XMoP} s + g_{m XMoP} + 0.5 g_{o XMiP} + g_{o XMoP} + \frac{1}{R_{c}} + \frac{1}{R_{a}} & 0 & - 0.5 g_{m XMiP} - \frac{1}{R_{a}} & 0 & - c_{db XMoP} s - g_{o XMoP} & 0 & 0\\0 & 0 & 0 & 0 & - c_{dg XMiN} s & - s \left(0.5 c_{gb XMiN} + 0.5 c_{gs XMiN}\right) & - \frac{1}{R_{a}} & 0 & c_{dg XMiN} s + s \left(0.5 c_{gb XMiN} + 0.5 c_{gs XMiN}\right) + \frac{2}{Z_{i}} + \frac{1}{R_{a}} & 0 & 0 & 0 & - \frac{2}{Z_{i}} & 0\\0 & 0 & 0 & 0 & - s \left(0.5 c_{gb XMiP} + 0.5 c_{gs XMiP}\right) & - c_{dg XMiP} s & 0 & - \frac{1}{R_{a}} & 0 & c_{dg XMiP} s + s \left(0.5 c_{gb XMiP} + 0.5 c_{gs XMiP}\right) + \frac{2}{Z_{i}} + \frac{1}{R_{a}} & 0 & 0 & 0 & - \frac{2}{Z_{i}}\\0 & 0 & 0 & 1 & - c_{dg XMoN} s + g_{m XMoN} & 0 & - c_{db XMoN} s - g_{m XMoN} - g_{o XMoN} & 0 & 0 & 0 & c_{db XMoN} s + c_{dg XMoN} s + g_{o XMoN} & 0 & 0 & 0\\0 & 0 & 1 & 0 & 0 & - c_{dg XMoP} s + g_{m XMoP} & 0 & - c_{db XMoP} s - g_{m XMoP} - g_{o XMoP} & 0 & 0 & 0 & c_{db XMoP} s + c_{dg XMoP} s + g_{o XMoP} & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{2}{Z_{i}} & 0 & 0 & 0 & \frac{2}{Z_{i}} & 0\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{2}{Z_{i}} & 0 & 0 & 0 & \frac{2}{Z_{i}}\end{array}\right]\cdot\left[\begin{matrix}I_{VsP}\\I_{VsN}\\I_{RlP}\\I_{RlN}\\V_{NulN}\\V_{NulP}\\V_{fbN}\\V_{fbP}\\V_{inN}\\V_{inP}\\V_{outN}\\V_{outP}\\V_{sourceN}\\V_{sourceP}\end{matrix}\right]
\end{equation}
DM-CM matrix equation
Matrix equation:
\begin{equation}
\left[\begin{matrix}V_{in}\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{array}{cccccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & - R_{\ell} & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0.25 c_{db XMi} s + c_{dg XMi} s + 0.5 c_{dg XMo} s + 0.5 c_{gb XMo} s + 0.5 c_{gs XMo} s + 0.25 g_{m XMi} + 0.25 g_{o XMi} + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{0.5}{R_{c}} + \frac{1}{R_{b}} & - 0.25 c_{db XMi} s + 0.5 c_{dg XMi} s - 0.5 c_{gb XMo} s - 0.5 c_{gs XMo} s - 0.25 g_{o XMi} - \frac{0.5}{R_{c}} & - 0.5 c_{dg XMi} s + 0.25 g_{m XMi} + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - 0.5 c_{dg XMo} s & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & - 0.25 c_{db XMi} s + 0.5 c_{dg XMi} s - 0.5 c_{gb XMo} s - 0.5 c_{gs XMo} s - 0.25 g_{m XMi} - 0.5 g_{m XMo} - 0.25 g_{o XMi} - \frac{0.5}{R_{c}} & 0.25 c_{db XMi} s + 0.5 c_{db XMo} s + 0.5 c_{dg XMi} s + 0.5 c_{gb XMo} s + 0.5 c_{gs XMo} s + 0.5 g_{m XMo} + 0.25 g_{o XMi} + 0.5 g_{o XMo} + \frac{0.5}{R_{c}} + \frac{0.5}{R_{a}} & - 0.25 g_{m XMi} - \frac{0.5}{R_{a}} & - 0.5 c_{db XMo} s - 0.5 g_{o XMo} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & - 0.5 c_{dg XMi} s + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - \frac{0.5}{R_{a}} & 0.5 c_{dg XMi} s + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{1}{Z_{i}} + \frac{0.5}{R_{a}} & 0 & - \frac{1}{Z_{i}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & - 0.5 c_{dg XMo} s + 0.5 g_{m XMo} & - 0.5 c_{db XMo} s - 0.5 g_{m XMo} - 0.5 g_{o XMo} & 0 & 0.5 c_{db XMo} s + 0.5 c_{dg XMo} s + 0.5 g_{o XMo} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\1 & 0 & 0 & 0 & - \frac{1}{Z_{i}} & 0 & \frac{1}{Z_{i}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - 0.25 R_{\ell} & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & c_{db XMi} s + 4 c_{dg XMi} s + 2 c_{dg XMo} s + 2 c_{gb XMo} s + 2 c_{gs XMo} s - g_{m XMi} + g_{o XMi} + 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{2}{R_{c}} & - c_{db XMi} s - 2 c_{dg XMi} s - 2 c_{gb XMo} s - 2 c_{gs XMo} s - g_{o XMi} - \frac{2}{R_{c}} & - 2 c_{dg XMi} s + g_{m XMi} - 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - 2 c_{dg XMo} s & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - c_{db XMi} s - 2 c_{dg XMi} s - 2 c_{gb XMo} s - 2 c_{gs XMo} s + g_{m XMi} - 2 g_{m XMo} - g_{o XMi} - \frac{2}{R_{c}} & c_{db XMi} s + 2 c_{db XMo} s + 2 c_{dg XMi} s + 2 c_{gb XMo} s + 2 c_{gs XMo} s + 2 g_{m XMo} + g_{o XMi} + 2 g_{o XMo} + \frac{2}{R_{c}} + \frac{2}{R_{a}} & - g_{m XMi} - \frac{2}{R_{a}} & - 2 c_{db XMo} s - 2 g_{o XMo} & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - 2 c_{dg XMi} s - 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - \frac{2}{R_{a}} & 2 c_{dg XMi} s + 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{4}{Z_{i}} + \frac{2}{R_{a}} & 0 & - \frac{4}{Z_{i}}\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & - 2 c_{dg XMo} s + 2 g_{m XMo} & - 2 c_{db XMo} s - 2 g_{m XMo} - 2 g_{o XMo} & 0 & 2 c_{db XMo} s + 2 c_{dg XMo} s + 2 g_{o XMo} & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & - \frac{4}{Z_{i}} & 0 & \frac{4}{Z_{i}}\end{array}\right]\cdot\left[\begin{matrix}I_{Vs D}\\I_{Rl D}\\V_{Nul D}\\V_{fb D}\\V_{in D}\\V_{out D}\\V_{source D}\\I_{Vs C}\\I_{Rl C}\\V_{Nul C}\\V_{fb C}\\V_{in C}\\V_{out C}\\V_{source C}\end{matrix}\right]
\end{equation}
DM matrix equation
Matrix equation:
\begin{equation}
\left[\begin{matrix}V_{in}\\0\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & - R_{\ell} & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0.25 c_{db XMi} s + c_{dg XMi} s + 0.5 c_{dg XMo} s + 0.5 c_{gb XMo} s + 0.5 c_{gs XMo} s + 0.25 g_{m XMi} + 0.25 g_{o XMi} + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{0.5}{R_{c}} + \frac{1}{R_{b}} & - 0.25 c_{db XMi} s + 0.5 c_{dg XMi} s - 0.5 c_{gb XMo} s - 0.5 c_{gs XMo} s - 0.25 g_{o XMi} - \frac{0.5}{R_{c}} & - 0.5 c_{dg XMi} s + 0.25 g_{m XMi} + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - 0.5 c_{dg XMo} s & 0\\0 & 0 & - 0.25 c_{db XMi} s + 0.5 c_{dg XMi} s - 0.5 c_{gb XMo} s - 0.5 c_{gs XMo} s - 0.25 g_{m XMi} - 0.5 g_{m XMo} - 0.25 g_{o XMi} - \frac{0.5}{R_{c}} & 0.25 c_{db XMi} s + 0.5 c_{db XMo} s + 0.5 c_{dg XMi} s + 0.5 c_{gb XMo} s + 0.5 c_{gs XMo} s + 0.5 g_{m XMo} + 0.25 g_{o XMi} + 0.5 g_{o XMo} + \frac{0.5}{R_{c}} + \frac{0.5}{R_{a}} & - 0.25 g_{m XMi} - \frac{0.5}{R_{a}} & - 0.5 c_{db XMo} s - 0.5 g_{o XMo} & 0\\0 & 0 & - 0.5 c_{dg XMi} s + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - \frac{0.5}{R_{a}} & 0.5 c_{dg XMi} s + 0.5 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{1}{Z_{i}} + \frac{0.5}{R_{a}} & 0 & - \frac{1}{Z_{i}}\\0 & 1 & - 0.5 c_{dg XMo} s + 0.5 g_{m XMo} & - 0.5 c_{db XMo} s - 0.5 g_{m XMo} - 0.5 g_{o XMo} & 0 & 0.5 c_{db XMo} s + 0.5 c_{dg XMo} s + 0.5 g_{o XMo} & 0\\1 & 0 & 0 & 0 & - \frac{1}{Z_{i}} & 0 & \frac{1}{Z_{i}}\end{matrix}\right]\cdot\left[\begin{matrix}I_{Vs D}\\I_{Rl D}\\V_{Nul D}\\V_{fb D}\\V_{in D}\\V_{out D}\\V_{source D}\end{matrix}\right]
\end{equation}
CM matrix equation
Matrix equation:
\begin{equation}
\left[\begin{matrix}0\\0\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & - 0.25 R_{\ell} & 0 & 0 & 0 & 1 & 0\\0 & 0 & c_{db XMi} s + 4 c_{dg XMi} s + 2 c_{dg XMo} s + 2 c_{gb XMo} s + 2 c_{gs XMo} s - g_{m XMi} + g_{o XMi} + 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{2}{R_{c}} & - c_{db XMi} s - 2 c_{dg XMi} s - 2 c_{gb XMo} s - 2 c_{gs XMo} s - g_{o XMi} - \frac{2}{R_{c}} & - 2 c_{dg XMi} s + g_{m XMi} - 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - 2 c_{dg XMo} s & 0\\0 & 0 & - c_{db XMi} s - 2 c_{dg XMi} s - 2 c_{gb XMo} s - 2 c_{gs XMo} s + g_{m XMi} - 2 g_{m XMo} - g_{o XMi} - \frac{2}{R_{c}} & c_{db XMi} s + 2 c_{db XMo} s + 2 c_{dg XMi} s + 2 c_{gb XMo} s + 2 c_{gs XMo} s + 2 g_{m XMo} + g_{o XMi} + 2 g_{o XMo} + \frac{2}{R_{c}} + \frac{2}{R_{a}} & - g_{m XMi} - \frac{2}{R_{a}} & - 2 c_{db XMo} s - 2 g_{o XMo} & 0\\0 & 0 & - 2 c_{dg XMi} s - 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) & - \frac{2}{R_{a}} & 2 c_{dg XMi} s + 2 s \left(0.5 c_{gb XMi} + 0.5 c_{gs XMi}\right) + \frac{4}{Z_{i}} + \frac{2}{R_{a}} & 0 & - \frac{4}{Z_{i}}\\0 & 1 & - 2 c_{dg XMo} s + 2 g_{m XMo} & - 2 c_{db XMo} s - 2 g_{m XMo} - 2 g_{o XMo} & 0 & 2 c_{db XMo} s + 2 c_{dg XMo} s + 2 g_{o XMo} & 0\\1 & 0 & 0 & 0 & - \frac{4}{Z_{i}} & 0 & \frac{4}{Z_{i}}\end{matrix}\right]\cdot\left[\begin{matrix}I_{Vs C}\\I_{Rl C}\\V_{Nul C}\\V_{fb C}\\V_{in C}\\V_{out C}\\V_{source C}\end{matrix}\right]
\end{equation}