"DM-CM decomposition"

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 & - 55 \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 0 & - 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 0 & 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 0 & \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 0 & 0 & 0\\0 & 0 & 0 & - 55 \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 0 & - 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 0 & 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 0 & \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 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 & - 110 \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & - 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 6.0 \cdot 10^{-12} s + \frac{0.5}{R_{b}} + \frac{1}{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 & - \frac{0.5}{R_{b}} & 0 & 0.25 C_{c} s + C_{d} s + \frac{0.5}{R_{b}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\1 & 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 & - 27.5 \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & - 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 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 & - \frac{2}{R_{b}} & 0 & C_{c} s + \frac{2}{R_{b}} & 0\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 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 & - 110 \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & - 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 0\\0 & 0 & 6.0 \cdot 10^{-12} s + \frac{0.5}{R_{b}} + \frac{1}{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 & - \frac{0.5}{R_{b}} & 0 & 0.25 C_{c} s + C_{d} s + \frac{0.5}{R_{b}} & 0\\1 & 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 & - 27.5 \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & - 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & 32 \pi A_{0} \left(4.836 \cdot 10^{15} s - 2.418 \cdot 10^{24}\right) & \left(s + 32 \pi\right) \left(4.836 \cdot 10^{15} s + 2.418 \cdot 10^{24}\right) & 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 & - \frac{2}{R_{b}} & 0 & C_{c} s + \frac{2}{R_{b}} & 0\\1 & 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 analysis results

Gain type: gain

poleRe [Hz]Im [Hz]Mag [Hz]Q
p1-4.494e+44.494e+4
p2-9.378e+59.378e+5
p38.131e+5-4.781e+64.849e+62.982
p48.131e+54.781e+64.849e+62.982
p5-9.462e+69.462e+6
p6-7.949e+77.949e+7
p7-7.958e+77.958e+7
p8-2.474e+82.474e+8
p9-4.814e+84.814e+8
p10-3.422e+93.422e+9

poles and zeros of the CM transfer

PZ analysis results

Gain type: gain

DC value = 1.000

poleRe [Hz]Im [Hz]Mag [Hz]Q
p18.131e+5-4.781e+64.849e+62.982
p28.131e+54.781e+64.849e+62.982
p3-9.462e+69.462e+6
p4-7.949e+77.949e+7
p5-4.814e+84.814e+8
zeroRe [Hz]Im [Hz]Mag [Hz]Q
z1-1.490e+71.490e+7
z21.669e+8-5.510e+71.758e+80.5265
z31.669e+85.510e+71.758e+80.5265

poles and zeros of the DM transfer

PZ analysis results

Gain type: gain

DC value = 366.2

poleRe [Hz]Im [Hz]Mag [Hz]Q
p1-4.494e+44.494e+4
p2-9.378e+59.378e+5
p3-7.958e+77.958e+7
p4-2.474e+82.474e+8
p5-3.422e+93.422e+9
zeroRe [Hz]Im [Hz]Mag [Hz]Q
z18.005e+78.005e+7
z2-1.337e+91.337e+9
z31.576e+91.576e+9

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Last project update: 2023-06-12 11:36:41