1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Any general RC circuit is never underdamped?

  1. Aug 15, 2010 #1
    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!!!
     
  2. jcsd
  3. Aug 15, 2010 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    What do you mean on "underdamped"?

    ehild
     
  4. Aug 15, 2010 #3
    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!
     
  5. Aug 15, 2010 #4
    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.
     
  6. Aug 15, 2010 #5

    ehild

    User Avatar
    Homework Helper
    Gold Member

    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...
     
  7. Aug 15, 2010 #6
    Hi Ehild,

    Thanks for the reasoning. It really helps a lot. Let me think and see if I can write it out mathematically.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Any general RC circuit is never underdamped?
  1. RC circuits voltage (Replies: 1)

  2. RC circuit and voltage (Replies: 8)

  3. RC circuit complete (Replies: 2)

Loading...