# Handout 4: Superposition and Source Transform

## An algorithm for using Thevenin’s Theorem

- Given any linear circuit, rearrange it in the form of two networks, A and B, connected by two wires. We will simplify A and leave B alone.

- Disconnect network B. Define a voltage \(V_\mathrm{oc}\) (open circuit) as the voltage now appearing across the terminals of network A. Calculate \(V_\mathrm{oc}\).

- Turn off or “zero out” every independent source in network A to form an inactive network. Leave dependent sources unchanged. Solve for \(R_\mathrm{th}\) if you have no dependent sources.

- Connect an independent voltage source with value \(V_\mathrm{oc}\) in series with the inactive network. Do not complete the circuit; leave the two terminals disconnected.

- Connect network B to the terminals of the new network A. All currents and voltages in B will remain unchanged.

- All dependent sources in A must have their control variables in network A. Same for B.
- Networks A and B may have unlimited numbers of linear circuit elements. We are simply assuming B is a load resistor.
- The dead network A can be represented by a single resistor \(R_\mathrm{th}\), wich is called the Thevenin equivalent resistance. This is true even if there’s a dependent source in network A.
- A Thevenin equivalent consists of two components: a voltage source in series with a resistance. Either may be zero, but this is uncommon.

## An algorithm for using Norton’s Theorem

- Given any linear circuit, rearrange it in the form of two networks, A and B, connected by two wires.

- Disconnect network B, and short the terminals of A. Define a current \(I_\mathrm{sc}\) as the current now flowing through the shorted terminals of network A. Calculate \(I_\mathrm{sc}\).

- Turn off or “zero out” every independent source in network A to form an inactive network. Leave dependent sources unchanged. Solve for \(R_\mathrm{th}\) if you have no dependent sources.

- Connect an independent current source with value \(I_\mathrm{sc}\) in parallel with the inactive network. Do not complete the circuit; leave the two terminals disconnected.

- Connect network B to the terminals of the new network A. All currents and voltages in B will remain unchanged.

Last updated:

January 6, 2018