"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
pole | Re [Hz] | Im [Hz] | Mag [Hz] | Q |
p1 | -4.494e+4 | | 4.494e+4 | |
p2 | -9.378e+5 | | 9.378e+5 | |
p3 | 8.131e+5 | -4.781e+6 | 4.849e+6 | 2.982 |
p4 | 8.131e+5 | 4.781e+6 | 4.849e+6 | 2.982 |
p5 | -9.462e+6 | | 9.462e+6 | |
p6 | -7.949e+7 | | 7.949e+7 | |
p7 | -7.958e+7 | | 7.958e+7 | |
p8 | -2.474e+8 | | 2.474e+8 | |
p9 | -4.814e+8 | | 4.814e+8 | |
p10 | -3.422e+9 | | 3.422e+9 | |
poles and zeros of the CM transfer
PZ analysis results
Gain type: gain
DC value = 1.000
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 | -9.462e+6 | | 9.462e+6 | |
p4 | -7.949e+7 | | 7.949e+7 | |
p5 | -4.814e+8 | | 4.814e+8 | |
zero | Re [Hz] | Im [Hz] | Mag [Hz] | Q |
z1 | -1.490e+7 | | 1.490e+7 | |
z2 | 1.669e+8 | -5.510e+7 | 1.758e+8 | 0.5265 |
z3 | 1.669e+8 | 5.510e+7 | 1.758e+8 | 0.5265 |
poles and zeros of the DM transfer
PZ analysis results
Gain type: gain
DC value = 366.2
pole | Re [Hz] | Im [Hz] | Mag [Hz] | Q |
p1 | -4.494e+4 | | 4.494e+4 | |
p2 | -9.378e+5 | | 9.378e+5 | |
p3 | -7.958e+7 | | 7.958e+7 | |
p4 | -2.474e+8 | | 2.474e+8 | |
p5 | -3.422e+9 | | 3.422e+9 | |
zero | Re [Hz] | Im [Hz] | Mag [Hz] | Q |
z1 | 8.005e+7 | | 8.005e+7 | |
z2 | -1.337e+9 | | 1.337e+9 | |
z3 | 1.576e+9 | | 1.576e+9 | |