How to Measure the Time Constant with an Oscilloscope

And more fun with RC circuits and RL circuits

Click to subscribe! ► http://bit.ly/Scopes_Sub ◄

Parasitic inductance: https://www.youtube.com/watch?v=heufatGyL1s

Questions? Ask me on Twitter: https://twitter.com/DanielBogdanoff

Check out the Keysight Podcasts YouTube channel: http://bit.ly/KeysPodcastSub

Facebook: https://www.facebook.com/keysightbench/

Measuring the time constant with an oscilloscope is easy. Simply make a quick calculation and a cursor measurement.

To measure the time constant of an RC circuit or an RL circuit with an oscilloscope, pick two reference points on an edge of your signal and see how long it takes to grow/decay 63.2%.

The time constant is useful because it gives information about how first-order circuits react to stimulus. First order circuits have only one energy storage component – an inductor or a capacitor – and can be described using a first-order differential equation.

TL;DR When a first order circuit experiences a voltage step up or step down, the circuit will settle to a constant voltage. The time constant, τ [tau], tells how long that settling will take.

Also, if you know the settling characteristics, then you can also determine the charge of a capacitor or inductor at a specific point in time.

Charge = (∆ Source) (1 – (1/e^(t/tau))) ∆ Source is the change in voltage or current applied to the RC or RL circuit. t is the time at which we want to know the charge on your inductor or capacitor (how long after the step up/step down) and τ is the time constant.

If we set t = τ, our formula becomes Charge = (∆ Source) * .632

What this means is that a capacitor will charge up to 63.2% of the source delta after one time constant.

From a settling perspective, if we wait a period of one time constant, we move 63.2% closer to our final value. After a second time constant, we move another 63.2%. Essentially it drops to 36.8% of its starting value.

Now think about this. For the period of the second time constant, we’re basically dealing with a new ∆ source value. Instead of moving from 10V to 0V, you’re now moving from 3.68V to 0V. So after the second time constant you’ll end up at 3.68 V * 36.8%, roughly 1.35V

After five time constants, you’ll be 99% of the way to your final voltage – After 5 time constants, people generally agree that, for all practical purposes, the signal has settled and the inductor or capacitor is fully charged or discharged. So, if you were to plot this out, you’re signal will look like an exponential curve. That’s where the oscilloscope comes in.

In this video, we’re probing the voltage across our capacitor, so it should be easy to measure the time constant.

For a more robust time constant measurement, do this a few times with a few differe ... https://www.youtube.com/watch?v=o-wegFuA3RA