• BME 210
• # Handout 4: Superposition and Source Transform

## An algorithm for using Thevenin’s Theorem

1. 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.
2. Disconnect network B. Define a voltage $$V_\mathrm{oc}$$ (open circuit) as the voltage now appearing across the terminals of network A. Calculate $$V_\mathrm{oc}$$.
3. 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.
4. 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.
5. 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

1. Given any linear circuit, rearrange it in the form of two networks, A and B, connected by two wires.
2. 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 $$I_\mathrm{sc}$$.
3. 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.
4. 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.
5. 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
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