RC and RL Circuits
Introduction
This topic is pretty dense, so bear with as we explain all the different terms and equations. The best way to learn is to follow through bit by bit and ensure you grasp the smaller parts while you look at the big picture.
Circuits
Now that we have an understanding of the basics of capacitors and inductors, we can start to look at them in action!
Response of a Circuit
A circuit's response is essentially a description of how the circuit behaves normally (the components and how they interact with each other) and then how this changes when some sort of power supply or signal (like hooking up a battery, flicking the switch at the wall, yelling into a microphone, anything) is added.
We’ll see a lot of confusing terminology come up in this section. There’s five main terms which get thrown around, however four of them are just the way that you split up the ‘step response’ equation. So let’s break down that term, ‘step response’.
Step Response
Our input is a step - it jumps from one voltage to another at some time instant. When we look at what the capacitor voltage or inductor current does during this change, it is called the ‘step response’ (fair enough!).
Most of the time, this will look like a switch being flicked on and another flicking off at t = 0s.
We can also use the fancy u(t) - the unit step function. This is purely mathematical; include it to look fancy.
The Step Equation
Please refer to your lecture slides or here for the derivation of the following equation.
This is the step response equation, I recommend memorising it. As a sanity check, the voltage at t = 0 should be Vo and the voltage as t → ∞ should be VS (steady state).
This equation can be divided in two ways: