Equivalent Impedance Help (C // RLC)

Thread Starter

Rafael B

Joined May 15, 2016
5
Ok, I have to wear my humility hat and ask for some assistance.
I am trying to calculate the impedance of a Capacitor (Co) in parallel with an RLC branch. Are the following assumptions and calculations correct?

Just to illustrate this is the circuit.
circuito_equivalente (Custom).png

I started simplifying each branch (Zo and Z1).
eq_1 (Custom).png

So, let's develop the equation for Zeq:
eq_2 (Custom).png

To further simplify, we substitute s for jw:
eq_3 (Custom).png

Some housekeeping, separating real and imaginary:
eq_4 (Custom).png

Let's the fun begin, rationalizing to get rid of the j in the denominator:
eq_5 (Custom).png
And that looks not good...
So before going any further, could someone point if this is the right direction?
 

WBahn

Joined Mar 31, 2012
29,979
Why do you think it looks not good?

Have you checked it at limiting and other special values, such as resonance, to see if it reduces to the expected results?
 
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