"Symbolic Pole-zero analysis"

PZ analysis results

Gain type: gain

DC gain = $\frac{R_{b}}{R_{a} + R_{b} + R_{s}}$

pole	value [Hz]
$p_{0}$	$\frac{- \frac{0.06999 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}} - \frac{2^{\frac{2}{3}} \left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}}{4} - \frac{0.1667 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}}}{\pi}$
$p_{1}$	$\frac{- \frac{0.06999 \left(-0.5 - 0.866 i\right) \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}} - \frac{2^{\frac{2}{3}} \left(-0.5 + 0.866 i\right) \left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}}{4} - \frac{0.1667 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}}}{\pi}$
$p_{2}$	$\frac{- \frac{0.06999 \left(-0.5 + 0.866 i\right) \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}} - \frac{2^{\frac{2}{3}} \left(-0.5 - 0.866 i\right) \left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}}{4} - \frac{0.1667 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}}}{\pi}$

pole

value [Hz]

$p_{0}$

$\frac{- \frac{0.06999 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}} - \frac{2^{\frac{2}{3}} \left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}}{4} - \frac{0.1667 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}}}{\pi}$

$p_{1}$

$\frac{- \frac{0.06999 \left(-0.5 - 0.866 i\right) \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}} - \frac{2^{\frac{2}{3}} \left(-0.5 + 0.866 i\right) \left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}}{4} - \frac{0.1667 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}}}{\pi}$

$p_{2}$

$\frac{- \frac{0.06999 \left(-0.5 + 0.866 i\right) \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}} - \frac{2^{\frac{2}{3}} \left(-0.5 - 0.866 i\right) \left(0.03704 \left(- 4 \left(- \frac{3 \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{2}}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)^{3} + \left(\frac{27 \left(R_{a} + R_{b} + R_{s}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{9 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{2}\right)^{0.5} + \frac{R_{a} + R_{b} + R_{s}}{C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{0.3333 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} R_{b} + C_{a} R_{a} R_{s} + C_{b} R_{a} R_{b} + C_{b} R_{b} R_{s} + L_{g}\right)}{C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{2 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}\right)^{0.3333}}{4} - \frac{0.1667 \left(C_{a} C_{b} R_{a} R_{b} R_{s} + C_{a} L_{g} R_{a} + C_{b} L_{g} R_{b}\right)}{C_{a} C_{b} L_{g} R_{a} R_{b}}}{\pi}$

zero	value [Hz]
$z_{0}$	$- \frac{0.5}{\pi C_{a} R_{a}}$

zero

value [Hz]

$z_{0}$

$- \frac{0.5}{\pi C_{a} R_{a}}$

PZ analysis results

Gain type: gain

DC gain = $\frac{R_{b}}{R_{a} + R_{b} + R_{s}}$

pole	value [Hz]
$p_{0}$	$- \frac{0.5}{\pi C_{a} R_{a}}$
$p_{1}$	$\frac{0.25 \left(- C_{a} R_{a} R_{s} - L_{g} - \left(C_{a}^{2} R_{a}^{2} R_{s}^{2} - 4 C_{a} L_{g} R_{a}^{2} - 4 C_{a} L_{g} R_{a} R_{b} - 2 C_{a} L_{g} R_{a} R_{s} + L_{g}^{2}\right)^{0.5}\right)}{\pi C_{a} L_{g} R_{a}}$
$p_{2}$	$\frac{0.25 \left(- C_{a} R_{a} R_{s} - L_{g} + \left(C_{a}^{2} R_{a}^{2} R_{s}^{2} - 4 C_{a} L_{g} R_{a}^{2} - 4 C_{a} L_{g} R_{a} R_{b} - 2 C_{a} L_{g} R_{a} R_{s} + L_{g}^{2}\right)^{0.5}\right)}{\pi C_{a} L_{g} R_{a}}$

pole

value [Hz]

$p_{0}$

$- \frac{0.5}{\pi C_{a} R_{a}}$

$p_{1}$

$\frac{0.25 \left(- C_{a} R_{a} R_{s} - L_{g} - \left(C_{a}^{2} R_{a}^{2} R_{s}^{2} - 4 C_{a} L_{g} R_{a}^{2} - 4 C_{a} L_{g} R_{a} R_{b} - 2 C_{a} L_{g} R_{a} R_{s} + L_{g}^{2}\right)^{0.5}\right)}{\pi C_{a} L_{g} R_{a}}$

$p_{2}$

$\frac{0.25 \left(- C_{a} R_{a} R_{s} - L_{g} + \left(C_{a}^{2} R_{a}^{2} R_{s}^{2} - 4 C_{a} L_{g} R_{a}^{2} - 4 C_{a} L_{g} R_{a} R_{b} - 2 C_{a} L_{g} R_{a} R_{s} + L_{g}^{2}\right)^{0.5}\right)}{\pi C_{a} L_{g} R_{a}}$

zero	value [Hz]
$z_{0}$	$- \frac{0.5}{\pi C_{a} R_{a}}$

zero

value [Hz]

$z_{0}$

$- \frac{0.5}{\pi C_{a} R_{a}}$

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Last project update: 2025-03-09 21:36:43

Symbolic Pole-zero analysis

Circuit diagram

PZ analysis results

Gain type: gain

Symbolic Pole-zero analysis after compensation

PZ analysis results

Gain type: gain