# How Do You Measure Time Constant of RLC Circuit?

1. Feb 24, 2013

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?

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• ###### TEK00001- Circuit A - i.PNG
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2. Feb 24, 2013

### jsgruszynski

3. Feb 25, 2013

### 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).

4. Feb 25, 2013

### milesyoung

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