# How do we write damping factor for a general RLC circuit

I am not sure how do I calculate the damping factor of a general RLC circuit. I have searched many books and they all talk about only when RLC in parallel or series.

What if I don't have a circuit in which all are not exactly in series/parallel, so in the case where there is only one independent voltage source and a network of R,L,C is there, if I make the voltage source 0 and combine the R,L,C in such a way that it becomes a perfect series/parallel is that method correct?

If not then how am I supposed to solve this?

• Show an example that confuses you. Commented Feb 27, 2021 at 9:40
• I think i understood how to solve this, what i did is i wrote the 2nd order differential equation and then i tried to solve it. then i put the voltage source as 0 and found the solution and that will be the damping factor Commented Mar 2, 2021 at 7:46

For a general RLC circuit -

1.Indentify the output asked(given) in question !

2.Find transfer function i.e $$T(s)=Vout(s)/Vin(s)$$ using KVL, KCL , Mesh , nodal etc. Methods

3.And once you get the Transfer function(which will be 2nd order most likely ) then convert that Transfer function into standard form i.e

$$\mathrm{ H(s)=K \frac{\omega_n^2}{s^2 + (2\zeta\omega_n)s + \omega_n^2} }$$

4.And after comparing with standard form you'll find $$\zeta$$ which is damping factor

4.without prior knowledge of output, transfer function of any system cannot be obtained and hence asking for damping factor without output doesn't make sense !

• How do i find damping factor from transfer function and what if the question has not given any output Commented Feb 27, 2021 at 4:51
• @superflash see edits! Commented Feb 27, 2021 at 5:18