Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How Do You Measure Time Constant of RLC Circuit?

  1. Feb 24, 2013 #1
    The image attached is of an underdamped RLC step response. I know that I can find the damped frequency of the response by first finding the period of the wave, and manipulating the period such that I can do 2*pi*f.

    If I'm looking at this waveform and the only info I know about it is this period and damping frequency, how could I figure the time constant?

    Attached Files:

  2. jcsd
  3. Feb 24, 2013 #2
  4. Feb 25, 2013 #3


    User Avatar

    Staff: Mentor

    RLC circuits are 2nd order. We don't usually speak of a time constant, for oscillatory responses we speak of their damping factor (or, instead, the Q-factor).
  5. Feb 25, 2013 #4
    The time constant of a first or second order LTI system characterizes its rate of exponential decay. The impulse response of an underdamped second order system is a sinusoid of exponentially decaying amplitude, so the term is still well defined.

    Four time constants would put the signal within 2 percent of its steady state value so you could just eyeball it. Alternatively, the time constant, tau, of an underdamped second order system is given analytically as:

    tau = 1/(zeta*omega_n)

    where zeta is the system damping factor and omega_n is its natural frequency of oscillation.

    Edit: Correction, 2 percent - not 5.
    Last edited: Feb 25, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook