# Superposition

## Quick Review

Superposition allows you to break down a difficult circuit into multiple (but simpler) circuits. Here are the steps to analyze a circuit via superposition:

1. Write down the basic superposition equation. The unknown you are looking for is equal to the sum of the effects from each source. For an unknown current or voltage X in a circuit with n sources,

For example, if you are looking for the value Vx, and there are 4 sources in your circuit (1 V, 50 mA, 3 V, and 150 mA), then write:
2. Draw a circuit for each subproblem (you should have as many circuits as there are independent sources (current and voltage) in the original problem. In each circuit, keep one of the sources from the original circuit and deactivate the rest. If there are 4 sources, you should have 4 circuits, with one source in each. To deactivate a source, replace voltage sources with shorts (a wire) and current sources with opens.
3. Solve for the unknown in each circuit. The solution should be fairly easy since there is only one source. Watch for series and parallel combinations. Be careful! Sometimes the deactivated sources leave you with some strange circuits. For example, a resistor that is shorted out (connected at both ends with the same wire) has no voltage across it. A resistor that is not connected to anything else at one end (just hanging there) has no current through it.
4. Add the answers from each subcircuit together (as shown in the equation of step 1) to get the overall answer to the original circuit.