A Thévenin equivalent circuit is used to replace a complex section of a circuit with a voltage source and a resistor. This makes larger circuits easier to create and analyze as the Thévenin equivalent circuit reduces a large number of components to only two. A Thévenin equivalent circuit can also be used to replace a current source.

This method will focus on combining resistors until the only remaining parts are a resistor and voltage source.

The above image is an example of a Thévenin equivalent circuit. The V1 is the voltage source, the R1 is the resistor, and the two circles are where the Thévenin equivalent circuit connects to the larger circuit.

Supplies needed:

- Pencil
- Paper
- Calculator

It is recommended that you have a basic understanding of how circuits work but is not needed to calculate the Thévenin equivalent circuit. The following link will help you if you wish to learn more about circuits.

## Step 1: Background Information

In order to create a Thévenin equivalent circuit you will need the equations shown above.

The first equation covers series resistors. Series resistors are arranged in a chain with nothing in between them. Series resistors can be combined into a single, equivalent resistor, reducing the complexity of the circuit. The equation for finding the equivalent resistor for series resistors is Req = R1+R2.

The second equation covers parallel resistors. Parallel resistors have their heads and tails connected to the same line. Much like series resistors, parallel resistors can be combined into a single, equivalent resistor.The equation for finding the equivalent resistor for parallel resistors is Req = (R1*R2)/(R1+R2).

The final equation is over Ohm's law. Ohm's law will be used later to do source transformations.

The image in the bottom right shows the components used in a circuit and their names.

## Step 2: Isolate the Part of the Circuit Being Changed

The first step in creating a Thévenin equivalent circuit is to isolate the part of the circuit being changed. The rest of the circuit is irrelevant so removing it is fine.

The image above shows the example circuit being isolated from the rest of the circuit.

## Step 3: Replace Any Resistors in Series or Parallel

In order to make the circuit easier to work with it is a good idea to check for resistors in series or parallel and combine them. In the example shown above, the two 2Ω resistors are in series. They can be made into a single resistor using the equation in step 1.

## Step 4: Transform a Voltage Source Into a Current Source

Since there are no more series or parallel resistors to combine, you need to move resistors around. To do this you will use a source transformation. A source transformation changes a voltage source in series with a resistor into a current source in parallel with a resistor. If you look in the example above, you can see source and 15Ω resistor change from being in a chain, to being connected to the same two lines.

To calculate the current the current source has you will need to rearrange ohm's law from step 1. The equation will be rearranged to be I = V/R. In the example, I is found to be 60V/15Ω or 4A. The 4A will be the value of the current source. The resistor only changes its location in this step, not its value.

## Step 5: Replace Parallel Resistors

Doing a source transformation reveals a set of parallel resistors. Using the equation in step 1, you can find the equivalent resistor and remove one more resistor from the circuit.

In the example above, the equivalent resistor is found to be (15Ω*10Ω)/(10Ω+15Ω) = 6Ω.

## Step 6: Transform a Current Source Into a Voltage Source

Since there are no more series or parallel resistors , the resistors need to move around again. A source transformation is used again to change the current source back into a voltage source. If you look in the example above, you can see source and 6Ω resistor change from being connected to the same two lines, to being connected in a chain.

For this source transformation, you will use ohm's law from step 1. The equation is not rearranged so it stays as V=IR. In the example, V is found to be 4A*6Ω or 24V. The 24V will be the value of the voltage source. The resistor only changes its location in this step, not its value.

## Step 7: Replace Series Resistors

Doing a source transformation reveals a set of series resistors. Using the equation in step 1, you can combine the resistors and have only one resistor remaining.

As the circuit only has a voltage source and resistor remaining, it is a Thévenin equivalent circuit to the original circuit.

## Step 8: Repeat Steps As Needed

While the example shown ended nicely after showing all the steps, not all circuits are that way. Some may start with a current source or have many more resistors. In cases like those, you may need to repeat steps 4-7 or do them in a different order.

## Step 9: Conclusions

Having gone through these steps, you should have your Thévenin equivalent circuit that looks roughly like the one above. You should be able to insert it back into your original circuit and have it act exactly like the replaced part.

Here are some links to some additional practice problems.