"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\\0\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{array}{cccccccccccccccccccc}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 & 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 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & - 0.5 R_{\ell} & 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 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 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\\0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{1}{R_{c}} + \frac{1}{R_{b}} & - \frac{1}{R_{b}} & - \frac{1}{R_{c}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{1}{R_{b}} & \frac{1}{R_{c}} + \frac{1}{R_{b}} & 0 & - \frac{1}{R_{c}} & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & - \frac{1}{R_{c}} & 0 & \frac{1}{R_{c}} + \frac{1}{R_{a}} & 0 & - \frac{1}{R_{a}} & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{1}{R_{c}} & 0 & \frac{1}{R_{c}} + \frac{1}{R_{a}} & 0 & - \frac{1}{R_{a}} & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & - \frac{1}{R_{a}} & 0 & \frac{2}{R_{s}} + \frac{1}{R_{a}} & 0 & 0 & 0 & - \frac{2}{R_{s}} & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{1}{R_{a}} & 0 & \frac{2}{R_{s}} + \frac{1}{R_{a}} & 0 & 0 & 0 & - \frac{2}{R_{s}}\\0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.5 C_{ocm} s & 0 & 0 & 0\\0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.5 C_{ocm} s & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{2}{R_{s}} & 0 & 0 & 0 & \frac{2}{R_{s}} & 0\\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{2}{R_{s}} & 0 & 0 & 0 & \frac{2}{R_{s}}\end{array}\right]\cdot\left[\begin{matrix}I_{VsP}\\I_{VsN}\\I_{RlP}\\I_{RlN}\\Io_{N1 XP}\\I_{V1 XP}\\Io_{N1 XN}\\I_{V1 XN}\\V_{3 XN}\\V_{3 XP}\\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: all

Matrix equation:

\begin{equation} \left[\begin{matrix}V_{in}\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{array}{cccccccccccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & - R_{\ell} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 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 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & \frac{0.5}{R_{c}} + \frac{1}{R_{b}} & - \frac{0.5}{R_{c}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & -1 & 0 & 0 & - \frac{0.5}{R_{c}} & \frac{0.5}{R_{c}} + \frac{0.5}{R_{a}} & - \frac{0.5}{R_{a}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & - \frac{0.5}{R_{a}} & \frac{1}{R_{s}} + \frac{0.5}{R_{a}} & 0 & - \frac{1}{R_{s}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0.25 C_{ocm} s & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\1 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{1}{R_{s}} & 0 & \frac{1}{R_{s}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 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 & 0 & 0 & - 0.25 R_{\ell} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 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 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{2}{R_{c}} & - \frac{2}{R_{c}} & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & - \frac{2}{R_{c}} & \frac{2}{R_{c}} + \frac{2}{R_{a}} & - \frac{2}{R_{a}} & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & - \frac{2}{R_{a}} & \frac{4}{R_{s}} + \frac{2}{R_{a}} & 0 & - \frac{4}{R_{s}}\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & C_{ocm} s & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{4}{R_{s}} & 0 & \frac{4}{R_{s}}\end{array}\right]\cdot\left[\begin{matrix}I_{Vs D}\\I_{Rl D}\\Io_{N1 X D}\\I_{V1 X D}\\V_{3 X D}\\V_{Nul D}\\V_{fb D}\\V_{in D}\\V_{out D}\\V_{source D}\\I_{Vs C}\\I_{Rl C}\\Io_{N1 X C}\\I_{V1 X C}\\V_{3 X 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\\0\\0\\0\end{matrix}\right]=\left[\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & - R_{\ell} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & \frac{0.5}{R_{c}} + \frac{1}{R_{b}} & - \frac{0.5}{R_{c}} & 0 & 0 & 0\\0 & 0 & -1 & 0 & 0 & - \frac{0.5}{R_{c}} & \frac{0.5}{R_{c}} + \frac{0.5}{R_{a}} & - \frac{0.5}{R_{a}} & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & - \frac{0.5}{R_{a}} & \frac{1}{R_{s}} + \frac{0.5}{R_{a}} & 0 & - \frac{1}{R_{s}}\\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0.25 C_{ocm} s & 0\\1 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{1}{R_{s}} & 0 & \frac{1}{R_{s}}\end{matrix}\right]\cdot\left[\begin{matrix}I_{Vs D}\\I_{Rl D}\\Io_{N1 X D}\\I_{V1 X D}\\V_{3 X 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\\0\\0\\0\end{matrix}\right]=\left[\begin{matrix}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & - 0.25 R_{\ell} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 0\\0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & \frac{2}{R_{c}} & - \frac{2}{R_{c}} & 0 & 0 & 0\\0 & 0 & -1 & 0 & 0 & - \frac{2}{R_{c}} & \frac{2}{R_{c}} + \frac{2}{R_{a}} & - \frac{2}{R_{a}} & 0 & 0\\0 & 0 & 0 & 1 & 0 & 0 & - \frac{2}{R_{a}} & \frac{4}{R_{s}} + \frac{2}{R_{a}} & 0 & - \frac{4}{R_{s}}\\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & C_{ocm} s & 0\\1 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{4}{R_{s}} & 0 & \frac{4}{R_{s}}\end{matrix}\right]\cdot\left[\begin{matrix}I_{Vs C}\\I_{Rl C}\\Io_{N1 X C}\\I_{V1 X C}\\V_{3 X C}\\V_{Nul C}\\V_{fb C}\\V_{in C}\\V_{out C}\\V_{source C}\end{matrix}\right] \end{equation}

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Last project update: 2023-11-25 20:52:48