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Quick question for you guys. How do you find alpha (damping coefficient, Neper frequency) for a circuit that's not strictly parallel or in series? For instance, α for a series RLC circuit is R/2L whereas α for a parallel circuit is 1/2RC; but what if it's different?

1. The problem statement, all variables and given/known data

Here's an example of what I mean. Suppose you have an inductor and a capacitor in series that's in parallel with a resistor and a current source (see attached). Although R, L, and C, are in series with each other (in their own loop), R and LC are in parallel with the source. How would you know which α to use? Is there a way to get α in terms of impedance?

2. Relevant equations

As mentioned before:

[itex]\alpha_{series}=\frac{R}{2L}[/itex]

and:

[itex]\alpha_{parallel}=\frac{1}{2RC}[/itex]

For what it's worth:

[itex]\zeta=\frac{\alpha}{\omega_{0}}[/itex]

where ζ is the damping ratio and:

[itex]\omega_{0}=\frac{1}{\sqrt{LC}}[/itex]

where ω0 is the natural or resonant frequency of the circuit (the same in series and parallel).

3. The attempt at a solution

Since this is more of a conceptual type question, I've tried looking it up in different sources but they all seem to only look at independent series or parallel cases. More curious for myself than anything. Maybe one of you EEs can point me in the right direction/explain this for me. Much appreciated.

Peace.

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# Homework Help: RLC Damping Coefficient

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