"Symbolic Pole-zero analysis"

Symbolic Pole-zero analysis

Circuit diagram

PZ analysis results

Gain type: gain

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

polevalue
$p_{0}$$- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \left(\frac{C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}}{3 C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{2}}{9 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\sqrt[3]{- \frac{3 R_{a} + 3 R_{b} + 3 R_{s}}{6 C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}\right)}{6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{\sqrt{3} \sqrt{4 C_{a}^{3} L_{g}^{3} R_{a}^{4} - C_{a}^{2} L_{g}^{4} R_{a}^{2} - R_{b}^{4} \left(- 4 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 8 C_{a}^{2} C_{b}^{2} + 20 C_{a} C_{b}^{3} + C_{b}^{4}\right) + L_{g} R_{a}^{4} \left(- 4 C_{a}^{4} C_{b} - 12 C_{a}^{3} C_{b}^{2} - 12 C_{a}^{2} C_{b}^{3} - 4 C_{a} C_{b}^{4}\right)\right) - R_{b}^{3} \left(L_{g}^{3} R_{a} \left(8 C_{a} C_{b}^{2} - 2 C_{b}^{3}\right) + L_{g}^{2} R_{a}^{3} \left(8 C_{a}^{3} C_{b} - 38 C_{a}^{2} C_{b}^{2} + 8 C_{a} C_{b}^{3}\right)\right) - R_{b}^{2} \left(C_{b}^{2} L_{g}^{4} + L_{g}^{3} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b} - 2 C_{a} C_{b}^{2}\right) + L_{g}^{2} R_{a}^{4} \left(C_{a}^{4} + 20 C_{a}^{3} C_{b} - 8 C_{a}^{2} C_{b}^{2}\right)\right) - R_{b} \left(- 2 C_{a} C_{b} L_{g}^{4} R_{a} + L_{g}^{3} R_{a}^{3} \left(- 2 C_{a}^{3} + 8 C_{a}^{2} C_{b}\right)\right) + R_{s}^{4} \left(- C_{a}^{4} C_{b}^{2} R_{a}^{4} R_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} R_{a}^{3} R_{b}^{3} - C_{a}^{2} C_{b}^{4} R_{a}^{2} R_{b}^{4}\right) - R_{s}^{3} \left(- 2 C_{a}^{4} C_{b} L_{g} R_{a}^{4} R_{b} + 2 C_{a}^{3} C_{b}^{2} L_{g} R_{a}^{3} R_{b}^{2} + R_{b}^{4} \left(- 2 C_{a} C_{b}^{4} L_{g} R_{a} + R_{a}^{3} \left(- 2 C_{a}^{3} C_{b}^{3} + 2 C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a}^{2} C_{b}^{3} L_{g} R_{a}^{2} + R_{a}^{4} \left(2 C_{a}^{4} C_{b}^{2} - 2 C_{a}^{3} C_{b}^{3}\right)\right)\right) - R_{s}^{2} \left(C_{a}^{4} L_{g}^{2} R_{a}^{4} + 2 C_{a}^{3} C_{b} L_{g}^{2} R_{a}^{3} R_{b} + R_{b}^{4} \left(C_{b}^{4} L_{g}^{2} + L_{g} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b}^{3} - 8 C_{a} C_{b}^{4}\right) + R_{a}^{4} \left(C_{a}^{4} C_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} + C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a} C_{b}^{3} L_{g}^{2} R_{a} + L_{g} R_{a}^{3} \left(10 C_{a}^{3} C_{b}^{2} + 10 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(- 6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} + L_{g} R_{a}^{4} \left(- 8 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2}\right)\right)\right) - R_{s} \left(- 2 C_{a}^{3} L_{g}^{3} R_{a}^{3} + R_{b}^{4} \left(L_{g}^{2} R_{a} \left(8 C_{a} C_{b}^{3} + 2 C_{b}^{4}\right) + L_{g} R_{a}^{3} \left(8 C_{a}^{3} C_{b}^{2} - 2 C_{a}^{2} C_{b}^{3} - 10 C_{a} C_{b}^{4}\right)\right) + R_{b}^{3} \left(- 2 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 20 C_{a}^{2} C_{b}^{2} + 10 C_{a} C_{b}^{3}\right) + L_{g} R_{a}^{4} \left(- 10 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2} + 8 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(2 C_{a} C_{b}^{2} L_{g}^{3} R_{a} + L_{g}^{2} R_{a}^{3} \left(10 C_{a}^{3} C_{b} - 20 C_{a}^{2} C_{b}^{2}\right)\right) + R_{b} \left(2 C_{a}^{2} C_{b} L_{g}^{3} R_{a}^{2} + L_{g}^{2} R_{a}^{4} \left(2 C_{a}^{4} + 8 C_{a}^{3} C_{b}\right)\right)\right)}}{18 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}}} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{3 R_{a} + 3 R_{b} + 3 R_{s}}{6 C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}\right)}{6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{\sqrt{3} \sqrt{4 C_{a}^{3} L_{g}^{3} R_{a}^{4} - C_{a}^{2} L_{g}^{4} R_{a}^{2} - R_{b}^{4} \left(- 4 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 8 C_{a}^{2} C_{b}^{2} + 20 C_{a} C_{b}^{3} + C_{b}^{4}\right) + L_{g} R_{a}^{4} \left(- 4 C_{a}^{4} C_{b} - 12 C_{a}^{3} C_{b}^{2} - 12 C_{a}^{2} C_{b}^{3} - 4 C_{a} C_{b}^{4}\right)\right) - R_{b}^{3} \left(L_{g}^{3} R_{a} \left(8 C_{a} C_{b}^{2} - 2 C_{b}^{3}\right) + L_{g}^{2} R_{a}^{3} \left(8 C_{a}^{3} C_{b} - 38 C_{a}^{2} C_{b}^{2} + 8 C_{a} C_{b}^{3}\right)\right) - R_{b}^{2} \left(C_{b}^{2} L_{g}^{4} + L_{g}^{3} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b} - 2 C_{a} C_{b}^{2}\right) + L_{g}^{2} R_{a}^{4} \left(C_{a}^{4} + 20 C_{a}^{3} C_{b} - 8 C_{a}^{2} C_{b}^{2}\right)\right) - R_{b} \left(- 2 C_{a} C_{b} L_{g}^{4} R_{a} + L_{g}^{3} R_{a}^{3} \left(- 2 C_{a}^{3} + 8 C_{a}^{2} C_{b}\right)\right) + R_{s}^{4} \left(- C_{a}^{4} C_{b}^{2} R_{a}^{4} R_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} R_{a}^{3} R_{b}^{3} - C_{a}^{2} C_{b}^{4} R_{a}^{2} R_{b}^{4}\right) - R_{s}^{3} \left(- 2 C_{a}^{4} C_{b} L_{g} R_{a}^{4} R_{b} + 2 C_{a}^{3} C_{b}^{2} L_{g} R_{a}^{3} R_{b}^{2} + R_{b}^{4} \left(- 2 C_{a} C_{b}^{4} L_{g} R_{a} + R_{a}^{3} \left(- 2 C_{a}^{3} C_{b}^{3} + 2 C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a}^{2} C_{b}^{3} L_{g} R_{a}^{2} + R_{a}^{4} \left(2 C_{a}^{4} C_{b}^{2} - 2 C_{a}^{3} C_{b}^{3}\right)\right)\right) - R_{s}^{2} \left(C_{a}^{4} L_{g}^{2} R_{a}^{4} + 2 C_{a}^{3} C_{b} L_{g}^{2} R_{a}^{3} R_{b} + R_{b}^{4} \left(C_{b}^{4} L_{g}^{2} + L_{g} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b}^{3} - 8 C_{a} C_{b}^{4}\right) + R_{a}^{4} \left(C_{a}^{4} C_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} + C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a} C_{b}^{3} L_{g}^{2} R_{a} + L_{g} R_{a}^{3} \left(10 C_{a}^{3} C_{b}^{2} + 10 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(- 6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} + L_{g} R_{a}^{4} \left(- 8 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2}\right)\right)\right) - R_{s} \left(- 2 C_{a}^{3} L_{g}^{3} R_{a}^{3} + R_{b}^{4} \left(L_{g}^{2} R_{a} \left(8 C_{a} C_{b}^{3} + 2 C_{b}^{4}\right) + L_{g} R_{a}^{3} \left(8 C_{a}^{3} C_{b}^{2} - 2 C_{a}^{2} C_{b}^{3} - 10 C_{a} C_{b}^{4}\right)\right) + R_{b}^{3} \left(- 2 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 20 C_{a}^{2} C_{b}^{2} + 10 C_{a} C_{b}^{3}\right) + L_{g} R_{a}^{4} \left(- 10 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2} + 8 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(2 C_{a} C_{b}^{2} L_{g}^{3} R_{a} + L_{g}^{2} R_{a}^{3} \left(10 C_{a}^{3} C_{b} - 20 C_{a}^{2} C_{b}^{2}\right)\right) + R_{b} \left(2 C_{a}^{2} C_{b} L_{g}^{3} R_{a}^{2} + L_{g}^{2} R_{a}^{4} \left(2 C_{a}^{4} + 8 C_{a}^{3} C_{b}\right)\right)\right)}}{18 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}} + \frac{- C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) - C_{b} L_{g} R_{b}}{3 C_{a} C_{b} L_{g} R_{a} R_{b}}$
$p_{1}$$- \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \left(\frac{C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}}{3 C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{2}}{9 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}\right)}{\sqrt[3]{- \frac{3 R_{a} + 3 R_{b} + 3 R_{s}}{6 C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}\right)}{6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{\sqrt{3} \sqrt{4 C_{a}^{3} L_{g}^{3} R_{a}^{4} - C_{a}^{2} L_{g}^{4} R_{a}^{2} - R_{b}^{4} \left(- 4 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 8 C_{a}^{2} C_{b}^{2} + 20 C_{a} C_{b}^{3} + C_{b}^{4}\right) + L_{g} R_{a}^{4} \left(- 4 C_{a}^{4} C_{b} - 12 C_{a}^{3} C_{b}^{2} - 12 C_{a}^{2} C_{b}^{3} - 4 C_{a} C_{b}^{4}\right)\right) - R_{b}^{3} \left(L_{g}^{3} R_{a} \left(8 C_{a} C_{b}^{2} - 2 C_{b}^{3}\right) + L_{g}^{2} R_{a}^{3} \left(8 C_{a}^{3} C_{b} - 38 C_{a}^{2} C_{b}^{2} + 8 C_{a} C_{b}^{3}\right)\right) - R_{b}^{2} \left(C_{b}^{2} L_{g}^{4} + L_{g}^{3} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b} - 2 C_{a} C_{b}^{2}\right) + L_{g}^{2} R_{a}^{4} \left(C_{a}^{4} + 20 C_{a}^{3} C_{b} - 8 C_{a}^{2} C_{b}^{2}\right)\right) - R_{b} \left(- 2 C_{a} C_{b} L_{g}^{4} R_{a} + L_{g}^{3} R_{a}^{3} \left(- 2 C_{a}^{3} + 8 C_{a}^{2} C_{b}\right)\right) + R_{s}^{4} \left(- C_{a}^{4} C_{b}^{2} R_{a}^{4} R_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} R_{a}^{3} R_{b}^{3} - C_{a}^{2} C_{b}^{4} R_{a}^{2} R_{b}^{4}\right) - R_{s}^{3} \left(- 2 C_{a}^{4} C_{b} L_{g} R_{a}^{4} R_{b} + 2 C_{a}^{3} C_{b}^{2} L_{g} R_{a}^{3} R_{b}^{2} + R_{b}^{4} \left(- 2 C_{a} C_{b}^{4} L_{g} R_{a} + R_{a}^{3} \left(- 2 C_{a}^{3} C_{b}^{3} + 2 C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a}^{2} C_{b}^{3} L_{g} R_{a}^{2} + R_{a}^{4} \left(2 C_{a}^{4} C_{b}^{2} - 2 C_{a}^{3} C_{b}^{3}\right)\right)\right) - R_{s}^{2} \left(C_{a}^{4} L_{g}^{2} R_{a}^{4} + 2 C_{a}^{3} C_{b} L_{g}^{2} R_{a}^{3} R_{b} + R_{b}^{4} \left(C_{b}^{4} L_{g}^{2} + L_{g} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b}^{3} - 8 C_{a} C_{b}^{4}\right) + R_{a}^{4} \left(C_{a}^{4} C_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} + C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a} C_{b}^{3} L_{g}^{2} R_{a} + L_{g} R_{a}^{3} \left(10 C_{a}^{3} C_{b}^{2} + 10 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(- 6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} + L_{g} R_{a}^{4} \left(- 8 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2}\right)\right)\right) - R_{s} \left(- 2 C_{a}^{3} L_{g}^{3} R_{a}^{3} + R_{b}^{4} \left(L_{g}^{2} R_{a} \left(8 C_{a} C_{b}^{3} + 2 C_{b}^{4}\right) + L_{g} R_{a}^{3} \left(8 C_{a}^{3} C_{b}^{2} - 2 C_{a}^{2} C_{b}^{3} - 10 C_{a} C_{b}^{4}\right)\right) + R_{b}^{3} \left(- 2 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 20 C_{a}^{2} C_{b}^{2} + 10 C_{a} C_{b}^{3}\right) + L_{g} R_{a}^{4} \left(- 10 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2} + 8 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(2 C_{a} C_{b}^{2} L_{g}^{3} R_{a} + L_{g}^{2} R_{a}^{3} \left(10 C_{a}^{3} C_{b} - 20 C_{a}^{2} C_{b}^{2}\right)\right) + R_{b} \left(2 C_{a}^{2} C_{b} L_{g}^{3} R_{a}^{2} + L_{g}^{2} R_{a}^{4} \left(2 C_{a}^{4} + 8 C_{a}^{3} C_{b}\right)\right)\right)}}{18 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{3 R_{a} + 3 R_{b} + 3 R_{s}}{6 C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}\right)}{6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{\sqrt{3} \sqrt{4 C_{a}^{3} L_{g}^{3} R_{a}^{4} - C_{a}^{2} L_{g}^{4} R_{a}^{2} - R_{b}^{4} \left(- 4 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 8 C_{a}^{2} C_{b}^{2} + 20 C_{a} C_{b}^{3} + C_{b}^{4}\right) + L_{g} R_{a}^{4} \left(- 4 C_{a}^{4} C_{b} - 12 C_{a}^{3} C_{b}^{2} - 12 C_{a}^{2} C_{b}^{3} - 4 C_{a} C_{b}^{4}\right)\right) - R_{b}^{3} \left(L_{g}^{3} R_{a} \left(8 C_{a} C_{b}^{2} - 2 C_{b}^{3}\right) + L_{g}^{2} R_{a}^{3} \left(8 C_{a}^{3} C_{b} - 38 C_{a}^{2} C_{b}^{2} + 8 C_{a} C_{b}^{3}\right)\right) - R_{b}^{2} \left(C_{b}^{2} L_{g}^{4} + L_{g}^{3} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b} - 2 C_{a} C_{b}^{2}\right) + L_{g}^{2} R_{a}^{4} \left(C_{a}^{4} + 20 C_{a}^{3} C_{b} - 8 C_{a}^{2} C_{b}^{2}\right)\right) - R_{b} \left(- 2 C_{a} C_{b} L_{g}^{4} R_{a} + L_{g}^{3} R_{a}^{3} \left(- 2 C_{a}^{3} + 8 C_{a}^{2} C_{b}\right)\right) + R_{s}^{4} \left(- C_{a}^{4} C_{b}^{2} R_{a}^{4} R_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} R_{a}^{3} R_{b}^{3} - C_{a}^{2} C_{b}^{4} R_{a}^{2} R_{b}^{4}\right) - R_{s}^{3} \left(- 2 C_{a}^{4} C_{b} L_{g} R_{a}^{4} R_{b} + 2 C_{a}^{3} C_{b}^{2} L_{g} R_{a}^{3} R_{b}^{2} + R_{b}^{4} \left(- 2 C_{a} C_{b}^{4} L_{g} R_{a} + R_{a}^{3} \left(- 2 C_{a}^{3} C_{b}^{3} + 2 C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a}^{2} C_{b}^{3} L_{g} R_{a}^{2} + R_{a}^{4} \left(2 C_{a}^{4} C_{b}^{2} - 2 C_{a}^{3} C_{b}^{3}\right)\right)\right) - R_{s}^{2} \left(C_{a}^{4} L_{g}^{2} R_{a}^{4} + 2 C_{a}^{3} C_{b} L_{g}^{2} R_{a}^{3} R_{b} + R_{b}^{4} \left(C_{b}^{4} L_{g}^{2} + L_{g} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b}^{3} - 8 C_{a} C_{b}^{4}\right) + R_{a}^{4} \left(C_{a}^{4} C_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} + C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a} C_{b}^{3} L_{g}^{2} R_{a} + L_{g} R_{a}^{3} \left(10 C_{a}^{3} C_{b}^{2} + 10 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(- 6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} + L_{g} R_{a}^{4} \left(- 8 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2}\right)\right)\right) - R_{s} \left(- 2 C_{a}^{3} L_{g}^{3} R_{a}^{3} + R_{b}^{4} \left(L_{g}^{2} R_{a} \left(8 C_{a} C_{b}^{3} + 2 C_{b}^{4}\right) + L_{g} R_{a}^{3} \left(8 C_{a}^{3} C_{b}^{2} - 2 C_{a}^{2} C_{b}^{3} - 10 C_{a} C_{b}^{4}\right)\right) + R_{b}^{3} \left(- 2 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 20 C_{a}^{2} C_{b}^{2} + 10 C_{a} C_{b}^{3}\right) + L_{g} R_{a}^{4} \left(- 10 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2} + 8 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(2 C_{a} C_{b}^{2} L_{g}^{3} R_{a} + L_{g}^{2} R_{a}^{3} \left(10 C_{a}^{3} C_{b} - 20 C_{a}^{2} C_{b}^{2}\right)\right) + R_{b} \left(2 C_{a}^{2} C_{b} L_{g}^{3} R_{a}^{2} + L_{g}^{2} R_{a}^{4} \left(2 C_{a}^{4} + 8 C_{a}^{3} C_{b}\right)\right)\right)}}{18 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}} + \frac{- C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) - C_{b} L_{g} R_{b}}{3 C_{a} C_{b} L_{g} R_{a} R_{b}}$
$p_{2}$$- \frac{\frac{C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}}{3 C_{a} C_{b} L_{g} R_{a} R_{b}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{2}}{9 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}}}{\sqrt[3]{- \frac{3 R_{a} + 3 R_{b} + 3 R_{s}}{6 C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}\right)}{6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{\sqrt{3} \sqrt{4 C_{a}^{3} L_{g}^{3} R_{a}^{4} - C_{a}^{2} L_{g}^{4} R_{a}^{2} - R_{b}^{4} \left(- 4 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 8 C_{a}^{2} C_{b}^{2} + 20 C_{a} C_{b}^{3} + C_{b}^{4}\right) + L_{g} R_{a}^{4} \left(- 4 C_{a}^{4} C_{b} - 12 C_{a}^{3} C_{b}^{2} - 12 C_{a}^{2} C_{b}^{3} - 4 C_{a} C_{b}^{4}\right)\right) - R_{b}^{3} \left(L_{g}^{3} R_{a} \left(8 C_{a} C_{b}^{2} - 2 C_{b}^{3}\right) + L_{g}^{2} R_{a}^{3} \left(8 C_{a}^{3} C_{b} - 38 C_{a}^{2} C_{b}^{2} + 8 C_{a} C_{b}^{3}\right)\right) - R_{b}^{2} \left(C_{b}^{2} L_{g}^{4} + L_{g}^{3} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b} - 2 C_{a} C_{b}^{2}\right) + L_{g}^{2} R_{a}^{4} \left(C_{a}^{4} + 20 C_{a}^{3} C_{b} - 8 C_{a}^{2} C_{b}^{2}\right)\right) - R_{b} \left(- 2 C_{a} C_{b} L_{g}^{4} R_{a} + L_{g}^{3} R_{a}^{3} \left(- 2 C_{a}^{3} + 8 C_{a}^{2} C_{b}\right)\right) + R_{s}^{4} \left(- C_{a}^{4} C_{b}^{2} R_{a}^{4} R_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} R_{a}^{3} R_{b}^{3} - C_{a}^{2} C_{b}^{4} R_{a}^{2} R_{b}^{4}\right) - R_{s}^{3} \left(- 2 C_{a}^{4} C_{b} L_{g} R_{a}^{4} R_{b} + 2 C_{a}^{3} C_{b}^{2} L_{g} R_{a}^{3} R_{b}^{2} + R_{b}^{4} \left(- 2 C_{a} C_{b}^{4} L_{g} R_{a} + R_{a}^{3} \left(- 2 C_{a}^{3} C_{b}^{3} + 2 C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a}^{2} C_{b}^{3} L_{g} R_{a}^{2} + R_{a}^{4} \left(2 C_{a}^{4} C_{b}^{2} - 2 C_{a}^{3} C_{b}^{3}\right)\right)\right) - R_{s}^{2} \left(C_{a}^{4} L_{g}^{2} R_{a}^{4} + 2 C_{a}^{3} C_{b} L_{g}^{2} R_{a}^{3} R_{b} + R_{b}^{4} \left(C_{b}^{4} L_{g}^{2} + L_{g} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b}^{3} - 8 C_{a} C_{b}^{4}\right) + R_{a}^{4} \left(C_{a}^{4} C_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} + C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a} C_{b}^{3} L_{g}^{2} R_{a} + L_{g} R_{a}^{3} \left(10 C_{a}^{3} C_{b}^{2} + 10 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(- 6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} + L_{g} R_{a}^{4} \left(- 8 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2}\right)\right)\right) - R_{s} \left(- 2 C_{a}^{3} L_{g}^{3} R_{a}^{3} + R_{b}^{4} \left(L_{g}^{2} R_{a} \left(8 C_{a} C_{b}^{3} + 2 C_{b}^{4}\right) + L_{g} R_{a}^{3} \left(8 C_{a}^{3} C_{b}^{2} - 2 C_{a}^{2} C_{b}^{3} - 10 C_{a} C_{b}^{4}\right)\right) + R_{b}^{3} \left(- 2 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 20 C_{a}^{2} C_{b}^{2} + 10 C_{a} C_{b}^{3}\right) + L_{g} R_{a}^{4} \left(- 10 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2} + 8 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(2 C_{a} C_{b}^{2} L_{g}^{3} R_{a} + L_{g}^{2} R_{a}^{3} \left(10 C_{a}^{3} C_{b} - 20 C_{a}^{2} C_{b}^{2}\right)\right) + R_{b} \left(2 C_{a}^{2} C_{b} L_{g}^{3} R_{a}^{2} + L_{g}^{2} R_{a}^{4} \left(2 C_{a}^{4} + 8 C_{a}^{3} C_{b}\right)\right)\right)}}{18 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}}} + \sqrt[3]{- \frac{3 R_{a} + 3 R_{b} + 3 R_{s}}{6 C_{a} C_{b} L_{g} R_{a} R_{b}} + \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right) \left(C_{a} R_{a} \left(R_{b} + R_{s}\right) + C_{b} \left(R_{a} R_{b} + R_{b} R_{s}\right) + L_{g}\right)}{6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} + \frac{\sqrt{3} \sqrt{4 C_{a}^{3} L_{g}^{3} R_{a}^{4} - C_{a}^{2} L_{g}^{4} R_{a}^{2} - R_{b}^{4} \left(- 4 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 8 C_{a}^{2} C_{b}^{2} + 20 C_{a} C_{b}^{3} + C_{b}^{4}\right) + L_{g} R_{a}^{4} \left(- 4 C_{a}^{4} C_{b} - 12 C_{a}^{3} C_{b}^{2} - 12 C_{a}^{2} C_{b}^{3} - 4 C_{a} C_{b}^{4}\right)\right) - R_{b}^{3} \left(L_{g}^{3} R_{a} \left(8 C_{a} C_{b}^{2} - 2 C_{b}^{3}\right) + L_{g}^{2} R_{a}^{3} \left(8 C_{a}^{3} C_{b} - 38 C_{a}^{2} C_{b}^{2} + 8 C_{a} C_{b}^{3}\right)\right) - R_{b}^{2} \left(C_{b}^{2} L_{g}^{4} + L_{g}^{3} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b} - 2 C_{a} C_{b}^{2}\right) + L_{g}^{2} R_{a}^{4} \left(C_{a}^{4} + 20 C_{a}^{3} C_{b} - 8 C_{a}^{2} C_{b}^{2}\right)\right) - R_{b} \left(- 2 C_{a} C_{b} L_{g}^{4} R_{a} + L_{g}^{3} R_{a}^{3} \left(- 2 C_{a}^{3} + 8 C_{a}^{2} C_{b}\right)\right) + R_{s}^{4} \left(- C_{a}^{4} C_{b}^{2} R_{a}^{4} R_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} R_{a}^{3} R_{b}^{3} - C_{a}^{2} C_{b}^{4} R_{a}^{2} R_{b}^{4}\right) - R_{s}^{3} \left(- 2 C_{a}^{4} C_{b} L_{g} R_{a}^{4} R_{b} + 2 C_{a}^{3} C_{b}^{2} L_{g} R_{a}^{3} R_{b}^{2} + R_{b}^{4} \left(- 2 C_{a} C_{b}^{4} L_{g} R_{a} + R_{a}^{3} \left(- 2 C_{a}^{3} C_{b}^{3} + 2 C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a}^{2} C_{b}^{3} L_{g} R_{a}^{2} + R_{a}^{4} \left(2 C_{a}^{4} C_{b}^{2} - 2 C_{a}^{3} C_{b}^{3}\right)\right)\right) - R_{s}^{2} \left(C_{a}^{4} L_{g}^{2} R_{a}^{4} + 2 C_{a}^{3} C_{b} L_{g}^{2} R_{a}^{3} R_{b} + R_{b}^{4} \left(C_{b}^{4} L_{g}^{2} + L_{g} R_{a}^{2} \left(- 2 C_{a}^{2} C_{b}^{3} - 8 C_{a} C_{b}^{4}\right) + R_{a}^{4} \left(C_{a}^{4} C_{b}^{2} + 2 C_{a}^{3} C_{b}^{3} + C_{a}^{2} C_{b}^{4}\right)\right) + R_{b}^{3} \left(2 C_{a} C_{b}^{3} L_{g}^{2} R_{a} + L_{g} R_{a}^{3} \left(10 C_{a}^{3} C_{b}^{2} + 10 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(- 6 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} + L_{g} R_{a}^{4} \left(- 8 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2}\right)\right)\right) - R_{s} \left(- 2 C_{a}^{3} L_{g}^{3} R_{a}^{3} + R_{b}^{4} \left(L_{g}^{2} R_{a} \left(8 C_{a} C_{b}^{3} + 2 C_{b}^{4}\right) + L_{g} R_{a}^{3} \left(8 C_{a}^{3} C_{b}^{2} - 2 C_{a}^{2} C_{b}^{3} - 10 C_{a} C_{b}^{4}\right)\right) + R_{b}^{3} \left(- 2 C_{b}^{3} L_{g}^{3} + L_{g}^{2} R_{a}^{2} \left(- 20 C_{a}^{2} C_{b}^{2} + 10 C_{a} C_{b}^{3}\right) + L_{g} R_{a}^{4} \left(- 10 C_{a}^{4} C_{b} - 2 C_{a}^{3} C_{b}^{2} + 8 C_{a}^{2} C_{b}^{3}\right)\right) + R_{b}^{2} \left(2 C_{a} C_{b}^{2} L_{g}^{3} R_{a} + L_{g}^{2} R_{a}^{3} \left(10 C_{a}^{3} C_{b} - 20 C_{a}^{2} C_{b}^{2}\right)\right) + R_{b} \left(2 C_{a}^{2} C_{b} L_{g}^{3} R_{a}^{2} + L_{g}^{2} R_{a}^{4} \left(2 C_{a}^{4} + 8 C_{a}^{3} C_{b}\right)\right)\right)}}{18 C_{a}^{2} C_{b}^{2} L_{g}^{2} R_{a}^{2} R_{b}^{2}} - \frac{\left(C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) + C_{b} L_{g} R_{b}\right)^{3}}{27 C_{a}^{3} C_{b}^{3} L_{g}^{3} R_{a}^{3} R_{b}^{3}}} + \frac{- C_{a} \left(C_{b} R_{a} R_{b} R_{s} + L_{g} R_{a}\right) - C_{b} L_{g} R_{b}}{3 C_{a} C_{b} L_{g} R_{a} R_{b}}$
zerovalue
$z_{0}$$- \frac{1}{C_{a} R_{a}}$

Symbolic Pole-zero analysis after compensation

PZ analysis results

Gain type: gain

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

polevalue
$p_{0}$$\frac{- C_{a} R_{a} R_{s} - L_{g} - \sqrt{C_{a}^{2} R_{a}^{2} R_{s}^{2} - 4 C_{a} L_{g} R_{a}^{2} - 4 C_{a} L_{g} R_{a} R_{b} - 2 C_{a} L_{g} R_{a} R_{s} + L_{g}^{2}}}{2 C_{a} L_{g} R_{a}}$
$p_{1}$$\frac{- C_{a} R_{a} R_{s} - L_{g} + \sqrt{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}}}{2 C_{a} L_{g} R_{a}}$
zerovalue

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Last project update: 2022-02-16 10:55:49