# Thevenin & Norton Equivalents

## Quick Review

### Thevenin Equivalent

#### Why do it?

An equivalent circuit is a simpler form. You usually find an equivalent for a complex part of the circuit that you want to simplify. Don't try to simplify the branch of a circuit which you are interested in, since you will hide the variables of interest then. Simplify the REST of the circuit around the part you are interested in.

#### How do you do it?

Any linear circuit connected to two terminals can be simplified down to just a Thevenin voltage and a Thevenin impedance. This simplified version will have the same effect on any external circuit as the original (more complex) circuit you started with. That's why it is called an "equivalent".

1. Find the Thevenin Voltage, Vth, also known as the open circuit voltage. Open the circuit at the terminals of interest, removing any circuitry that is not part of the network to be simplified. Compute the voltage across the open terminals using your favorite technique (node-voltage, superposition, or whatever).
2. Find the Thevenin Resistance (or Impedance) by deactivating all independent sources. Voltage sources are shorted, current sources are opened. Then look into the terminals and find the total resistance (using series and parallel combinations.

#### What are some difficulties I might run into?

You might find a resistor ends up "hanging in the wind" after deactivating a current source, i.e., one end is not connected to anything. Since no current can flow through the resistor, it has no effect on Rth, so just ignore it. You might also find a resistor is shorted out after you deactivate a voltage source, i.e., a wire connects the two ends of the resistor together. Since the voltage across it is zero, it has no effect on Rth, so just ignore it.

You might find the resistance network is irreducible, or you might have dependent sources (these are drawn as diamonds and their value depends on some other voltage or current in the circuit). Either way, the method to solve for Thevenin Resistance is to add a test current source to the terminals of value 1 Amp. Compute the voltage, Vtest, across the test current source and then Rth = Vtest/Itest = Vtest/1.

### Norton Equivalent

The Norton is very similar to the Thevenin. In fact, you can find the Thevenin first, then just compute the Norton Current (Isc) by using Ohm's law:

Isc = Vth/Rth

You can also find it directly:

1. Find the Norton Current, also known as the short circuit current, by shorting the terminals (place a wire across them) and compute the current through the short using your favorite analysis method (node-voltage, superposition, or whatever).
2. Find the Norton Resistance the same way as the Thevenin Resistance.