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
pole | Re [Hz] | Im [Hz] | Mag [Hz] | Q |
p1 | 8.131e+5 | 4.781e+6 | 4.849e+6 | 2.982 |
p2 | 8.131e+5 | -4.781e+6 | 4.849e+6 | 2.982 |
p3 | -4.494e+4 | 0 | 4.494e+4 | |
p4 | -9.378e+5 | 0 | 9.378e+5 | |
p5 | -9.462e+6 | 0 | 9.462e+6 | |
p6 | -7.949e+7 | 0 | 7.949e+7 | |
p7 | -7.958e+7 | 0 | 7.958e+7 | |
p8 | -2.474e+8 | 0 | 2.474e+8 | |
p9 | -4.814e+8 | 0 | 4.814e+8 | |
p10 | -3.422e+9 | 0 | 3.422e+9 | |
poles and zeros of the DM transfer
Poles analysis results
Gain type: gain
pole | Re [Hz] | Im [Hz] | Mag [Hz] | Q |
p1 | -4.494e+4 | 0 | 4.494e+4 | |
p2 | -9.378e+5 | 0 | 9.378e+5 | |
p3 | -7.958e+7 | 0 | 7.958e+7 | |
p4 | -2.474e+8 | 0 | 2.474e+8 | |
p5 | -3.422e+9 | 0 | 3.422e+9 | |
Loop Gain of the DM transfer
\begin{equation}
L_{G}=\left[ \right]
\end{equation}