RC step response 3 of 3 example

In the last video, we worked out the step response of an RC circuit, and now we're going to 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. What does this look like?

So, I'm going to 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. Let's let R equal 1 kΩ (K ohm) and let the capacitor equal 4 microfarads. So now let's plug these values over here into our solution and see what we get.

Now, first I'm going to work out RC. RC is equal to 1 kΩ times 4 microfarads. And what is that equal? K is +3, and micro is -6, so 1 * 4 is 4 and +3 - 6 is * 10 -3, and that is in seconds. So, that's equal to 4 milliseconds.

Now let's plug the rest of our values in here. V of T, the total response or the step response, equals V2 minus vs. That's the step voltage, 1.1 times e to the us T over 4 milliseconds plus vs plus VSS. VSS 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 VT, 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 0.2 volts up to—oh, I got it wrong—1.2 volts. Let's change that to the right number: 1.2.

And this is what it looks like. 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 VKN, which is 0.2. It ends up at VS, which is 1.2 in this case, and that's the forced response up here.

In between, it did that smooth exponential curve. That's what the step response of an RC circuit looks like.