RC step response example (3 of 3)
About this video
This worked example applies the step response of an RC circuit to real values. A step input moves from 0.2 V to 1.2 V (the narrator corrects an earlier misread), with R = 1 kOhm and C = 4 microfarads, so the time constant RC is 4 ms. The capacitor voltage starts at the initial value, follows a smooth exponential curve, and approaches the final forced value.
You'll be able to
- compute the time constant RC from resistance and capacitance values.
- describe how the capacitor voltage moves from its initial value toward the final value.
- predict the fraction of the transient remaining after one time constant.
Key words
- Step response
- The output of a circuit when its input suddenly changes from one constant level to another.
- Time constant (RC)
- The product of resistance and capacitance, which sets how quickly the RC circuit responds.
- Initial value (V0)
- The capacitor voltage at the moment the step is applied.
- Forced response
- The final steady voltage the circuit settles toward after the transient ends.
Transcript
- [Voiceover] In the last video, we worked out the step response of an RC circuit, and now we're gonna look at a real example. So, this is our answer, this is the step response, the total response to our circuit, to a step input. And what does this look like? Well, I'm gonna move down a little bit.
We'll make up a circuit and we'll do a real example here. Let's say we do a step, and the step goes from .2 volts up to, say 1.1 volts. And let's let R equal one K, ohm. K, ohm. And let the capacitor equal four microfarads. So now let's plug these values over here into our solution and see what we get.
Now, first I'm gonna work out RC. RC is equal to one K, ohm times four microfarads. And what does that equal? K is plus three. And micro is minus six. So one times four is four. And plus three minus six is times 10 to the minus three. And that is in seconds, so that's equal to four milliseconds.
Now, let's plug the rest of our values in here. V of T. The total response, or the step response equals v naught, .2, minus V, S, that's the step voltage, 1.1, times e to the minus t over four milliseconds plus V, S. V, S is 1.1. So I went ahead and I plotted this using a computer, and we'll see how close this comes to what we sketched earlier.
So here's V, T. Or, the step response, the total response of our RC network to a step voltage. The step voltage is here in rose color. And it goes from .2 volts up to, ooh, I got it wrong. 1.2 volts, let's change that to the right number. 1.2, 1.2. And this is what it looks like.
And if you go back and compare this to what we saw, what we sketched at the beginning, it'll look pretty similar. So, the output voltage, the voltage on the capacitor here, starts at V naught, which is .2, it ends up at V, S, which is 1.2 in this case, and that's the forced response up here.
And in between, it did that smooth exponential curve. That's what the step response of an RC circuit looks like.
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