DM-CM decomposition

MNA matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}V_{s}\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{array}{cccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & - 2.75 \cdot 10^{10} s^{2} - 8.8 \cdot 10^{11} s \left(\pi + 1.562 \cdot 10^{7}\right) - 4.4 \cdot 10^{20} \pi & 0 & 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 0 & - 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 0 & 5.0 \cdot 10^{8} s^{2} + 1.6 \cdot 10^{10} s \left(\pi + 1.562 \cdot 10^{7}\right) + 8.0 \cdot 10^{18} \pi & 0 & 0 & 0\\0 & 0 & 0 & - 2.75 \cdot 10^{10} s^{2} - 8.8 \cdot 10^{11} s \left(\pi + 1.562 \cdot 10^{7}\right) - 4.4 \cdot 10^{20} \pi & 0 & 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 0 & - 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 0 & 5.0 \cdot 10^{8} s^{2} + 1.6 \cdot 10^{10} s \left(\pi + 1.562 \cdot 10^{7}\right) + 8.0 \cdot 10^{18} \pi & 0 & 0\\0 & 0 & 0 & 0 & 1.2 \cdot 10^{-11} s + \frac{1}{R_{b}} + \frac{1}{R_{a}} & - \frac{1}{R_{a}} & - 8.0 \cdot 10^{-12} s & 0 & - \frac{1}{R_{b}} & 0 & 0 & 0\\0 & 0 & 0 & 0 & - \frac{1}{R_{a}} & 1.2 \cdot 10^{-11} s + \frac{1}{R_{b}} + \frac{1}{R_{a}} & 0 & - 8.0 \cdot 10^{-12} s & 0 & - \frac{1}{R_{b}} & 0 & 0\\0 & 0 & 0 & 0 & - 8.0 \cdot 10^{-12} s & 0 & 1.2 \cdot 10^{-11} s + \frac{1}{R_{s}} & 0 & 0 & 0 & - \frac{1}{R_{s}} & 0\\0 & 0 & 0 & 0 & 0 & - 8.0 \cdot 10^{-12} s & 0 & 1.2 \cdot 10^{-11} s + \frac{1}{R_{s}} & 0 & 0 & 0 & - \frac{1}{R_{s}}\\0 & 0 & 1 & 0 & - \frac{1}{R_{b}} & 0 & 0 & 0 & 0.5 C_{c} s + C_{d} s + \frac{1}{R_{b}} & - C_{d} s & 0 & 0\\0 & 0 & 0 & 1 & 0 & - \frac{1}{R_{b}} & 0 & 0 & - C_{d} s & 0.5 C_{c} s + C_{d} s + \frac{1}{R_{b}} & 0 & 0\\0 & 1 & 0 & 0 & 0 & 0 & - \frac{1}{R_{s}} & 0 & 0 & 0 & \frac{1}{R_{s}} & 0\\1 & 0 & 0 & 0 & 0 & 0 & 0 & - \frac{1}{R_{s}} & 0 & 0 & 0 & \frac{1}{R_{s}}\end{array}\right]\cdot\left[\begin{matrix}I_{V1P}\\I_{V1N}\\Io_{E O1N}\\Io_{E O1P}\\V_{fbN}\\V_{fbP}\\V_{inN}\\V_{inP}\\V_{outN}\\V_{outP}\\V_{scN}\\V_{scP}\end{matrix}\right] \end{equation}

DM-CM matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}V_{s}\\0\\0\\0\\0\\0\\0.5 V_{s}\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{array}{cccccccccccc}0 & 0 & 0 & 0 & 0 & 1.0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & - 5.5 \cdot 10^{10} s^{2} - 1.76 \cdot 10^{12} s \left(\pi + 1.562 \cdot 10^{7}\right) - 8.8 \cdot 10^{20} \pi & 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & - 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 5.0 \cdot 10^{8} s^{2} + 1.6 \cdot 10^{10} s \left(\pi + 1.562 \cdot 10^{7}\right) + 8.0 \cdot 10^{18} \pi & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 6.0 \cdot 10^{-12} s + \frac{0.5}{R_{b}} + \frac{1.0}{R_{a}} & - 4.0 \cdot 10^{-12} s & - \frac{0.5}{R_{b}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & - 4.0 \cdot 10^{-12} s & 6.0 \cdot 10^{-12} s + \frac{0.5}{R_{s}} & 0 & - \frac{0.5}{R_{s}} & 0 & 0 & 0 & 0 & 0 & 0\\0 & 1.0 & - \frac{0.5}{R_{b}} & 0 & 0.25 C_{c} s + 1.0 C_{d} s + \frac{0.5}{R_{b}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\1.0 & 0 & 0 & - \frac{0.5}{R_{s}} & 0 & \frac{0.5}{R_{s}} & 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 & - 1.375 \cdot 10^{10} s^{2} - 4.4 \cdot 10^{11} s \left(\pi + 1.562 \cdot 10^{7}\right) - 2.2 \cdot 10^{20} \pi & 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & - 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 5.0 \cdot 10^{8} s^{2} + 1.6 \cdot 10^{10} s \left(\pi + 1.562 \cdot 10^{7}\right) + 8.0 \cdot 10^{18} \pi & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2.4 \cdot 10^{-11} s + \frac{2}{R_{b}} & - 1.6 \cdot 10^{-11} s & - \frac{2}{R_{b}} & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - 1.6 \cdot 10^{-11} s & 2.4 \cdot 10^{-11} s + \frac{2}{R_{s}} & 0 & - \frac{2}{R_{s}}\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1.0 & - \frac{2}{R_{b}} & 0 & C_{c} s + \frac{2}{R_{b}} & 0\\0 & 0 & 0 & 0 & 0 & 0 & 1.0 & 0 & 0 & - \frac{2}{R_{s}} & 0 & \frac{2}{R_{s}}\end{array}\right]\cdot\left[\begin{matrix}I_{V1 D}\\Io_{E O1 D}\\V_{fb D}\\V_{in D}\\V_{out D}\\V_{sc D}\\I_{V1 C}\\Io_{E O1 C}\\V_{fb C}\\V_{in C}\\V_{out C}\\V_{sc C}\end{matrix}\right] \end{equation}

DM matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}V_{s}\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{matrix}0 & 0 & 0 & 0 & 0 & 1.0\\0 & - 5.5 \cdot 10^{10} s^{2} - 1.76 \cdot 10^{12} s \left(\pi + 1.562 \cdot 10^{7}\right) - 8.8 \cdot 10^{20} \pi & 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & - 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 5.0 \cdot 10^{8} s^{2} + 1.6 \cdot 10^{10} s \left(\pi + 1.562 \cdot 10^{7}\right) + 8.0 \cdot 10^{18} \pi & 0\\0 & 0 & 6.0 \cdot 10^{-12} s + \frac{0.5}{R_{b}} + \frac{1.0}{R_{a}} & - 4.0 \cdot 10^{-12} s & - \frac{0.5}{R_{b}} & 0\\0 & 0 & - 4.0 \cdot 10^{-12} s & 6.0 \cdot 10^{-12} s + \frac{0.5}{R_{s}} & 0 & - \frac{0.5}{R_{s}}\\0 & 1.0 & - \frac{0.5}{R_{b}} & 0 & 0.25 C_{c} s + 1.0 C_{d} s + \frac{0.5}{R_{b}} & 0\\1.0 & 0 & 0 & - \frac{0.5}{R_{s}} & 0 & \frac{0.5}{R_{s}}\end{matrix}\right]\cdot\left[\begin{matrix}I_{V1 D}\\Io_{E O1 D}\\V_{fb D}\\V_{in D}\\V_{out D}\\V_{sc D}\end{matrix}\right] \end{equation}

CM matrix equation

Matrix equation:

\begin{equation} \left[\begin{matrix}0.5 V_{s}\\0\\0\\0\\0\\0\end{matrix}\right]=\left[\begin{matrix}0 & 0 & 0 & 0 & 0 & 1.0\\0 & - 1.375 \cdot 10^{10} s^{2} - 4.4 \cdot 10^{11} s \left(\pi + 1.562 \cdot 10^{7}\right) - 2.2 \cdot 10^{20} \pi & 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & - 1.6 \cdot 10^{10} \pi A_{0} \left(5.0 \cdot 10^{8} - s\right) & 5.0 \cdot 10^{8} s^{2} + 1.6 \cdot 10^{10} s \left(\pi + 1.562 \cdot 10^{7}\right) + 8.0 \cdot 10^{18} \pi & 0\\0 & 0 & 2.4 \cdot 10^{-11} s + \frac{2}{R_{b}} & - 1.6 \cdot 10^{-11} s & - \frac{2}{R_{b}} & 0\\0 & 0 & - 1.6 \cdot 10^{-11} s & 2.4 \cdot 10^{-11} s + \frac{2}{R_{s}} & 0 & - \frac{2}{R_{s}}\\0 & 1.0 & - \frac{2}{R_{b}} & 0 & C_{c} s + \frac{2}{R_{b}} & 0\\1.0 & 0 & 0 & - \frac{2}{R_{s}} & 0 & \frac{2}{R_{s}}\end{matrix}\right]\cdot\left[\begin{matrix}I_{V1 C}\\Io_{E O1 C}\\V_{fb C}\\V_{in C}\\V_{out C}\\V_{sc C}\end{matrix}\right] \end{equation}

poles of the transformed circuit

poles and zeros of the CM transfer

Poles analysis results

Gain type: gain

poleRe [Hz]Im [Hz]Mag [Hz]Q
p18.131e+54.781e+64.849e+62.982
p28.131e+5-4.781e+64.849e+62.982
p3-4.494e+404.494e+4
p4-9.378e+509.378e+5
p5-9.462e+609.462e+6
p6-7.949e+707.949e+7
p7-7.958e+707.958e+7
p8-2.474e+802.474e+8
p9-4.814e+804.814e+8
p10-3.422e+903.422e+9

poles and zeros of the DM transfer

Poles analysis results

Gain type: gain

poleRe [Hz]Im [Hz]Mag [Hz]Q
p1-4.494e+404.494e+4
p2-9.378e+509.378e+5
p3-7.958e+707.958e+7
p4-2.474e+802.474e+8
p5-3.422e+903.422e+9

Loop Gain of the DM transfer

\begin{equation} L_{G}=\left[ \right] \end{equation}

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