Any general RC circuit is never underdamped?

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SUMMARY

A general RC circuit, regardless of its topology, is never underdamped due to the nature of its components. The discussion confirms that in an RC circuit, all poles of the transfer function reside in the left half-plane (L.H.P.), indicating stability and the absence of oscillations. The participants emphasize that underdamped systems exhibit oscillatory behavior, which is not possible in pure RC circuits as they lack inductors to facilitate energy oscillation. Therefore, the conclusion is that RC circuits cannot oscillate by themselves.

PREREQUISITES
  • Understanding of Laplace transforms and their application in circuit analysis
  • Knowledge of transfer functions and pole-zero analysis
  • Familiarity with circuit components: resistors (R), capacitors (C), and inductors (L)
  • Basic concepts of damping: underdamped, critically damped, and overdamped systems
NEXT STEPS
  • Study the derivation of transfer functions for RC circuits
  • Learn about the implications of pole locations in the s-domain
  • Explore the role of inductors in creating oscillatory behavior in RLC circuits
  • Investigate energy storage mechanisms in capacitors and inductors
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in understanding the stability and behavior of RC circuits in various configurations.

pawnfork
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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!
 
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What do you mean on "underdamped"?

ehild
 
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!
 
ehild said:
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.
 
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...
 
Hi Ehild,

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

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