Any general RC circuit is never underdamped?

[pawnfork]

My first post!

Question: Is a general RC circuit, with any topology of interconnected R and C elements, never underdamped?

This is a bonus question in one of my homeworks. The answers to the earlier questions in the problem indeed show that two example RC circuits are not underdamped.

I understand how one identifies over-damped, critically damped and under-damped for a small circuit, using the Laplace transform on the differential equation. But for any general RC network, I do not know how to write the equations.

I attempted a proof by induction, but dint get far.

Thanks for the help!

 

[ehild]

What do you mean on "underdamped"?

ehild

 

[pawnfork]

I have been thinking about it for a while and came up with the following reasoning:

If all the poles of the transfer function (in s-domain) are in the L.H.P. (left half plane, real part < 0), then the system is not underdamped. So what remains is to show it for a general RC circuit. Any ideas?

Thanks!

 

[pawnfork]

What do you mean on "underdamped"?

ehild

Ehild,

I checked, but we are not given a definition as such of underdamped. But intuitively, afaik, it means a system where the impulse response oscillates rather than moving monotonically. Actually now I am not sure.

 

[ehild]

Well, I also think that you have to prove that an RC circuit can not oscillate by "itself". I think it can be connected with energy storage. If there are both capacitors and inductors in a circuit, the energy stored in a capacitor is stored in the electric field, that in an inductor is stored in the magnetic field, and it oscillates between the two. Resistors only dissipate (consume) energy.
I do not know how to get an exact mathematical proof...

 

[pawnfork]

Hi Ehild,

Thanks for the reasoning. It really helps a lot. Let me think and see if I can write it out mathematically.