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Parallel Compensation

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promach

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How do I derive expressions 4-4 and 4-5 for the two additional poles and zeroes due to parallel compensation (Rc and Cc) ?

I have derived the equivalent impedance , but I still could not obtain expressions (4-4 and 4-5)

parallel_compensation.png

parallel_compensation_impedance_derivation.png
 

promach said:
How do I derive expressions 4-4 and 4-5 for the two additional poles and zeroes due to parallel compensation (Rc and Cc) ?
Click to expand...

I would expect to see terms of both the numerator and denominator of the last equation rearranged on its canonical format (s3+a2s2+a1s+a0) in order to obtain their roots, which with some luck could be simplified through cutting numerator and denominator if the same, which is not easy to see in the current format. Anyway, why don`t you try to calculate the roots for the penultimate equation?
 

I meant to take the roots of the last but one equation above, the one in the format s2+a1s+a2=0
 

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