Thevenin's Theorem

Purpose

Thevenin’s and Norton’s theorems collapse any linear two-terminal circuit into a single source and a single resistor. That equivalent circuit makes whatever you attach at the terminals much easier to analyze.

Thevenin’s theorem

Any two-terminal circuit with only linear elements (resistors) and sources can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor. The voltage source is written $V_{th}$ and the resistor $R_{th}$.

To find the equivalent between terminals A and B:

1. Find $V_{th}$, the open-circuit voltage from A to B, using KCL and KVL.
2. Find $R_{th}$, the equivalent resistance between A and B, by replacing voltage sources with short circuits and current sources with open circuits.

Norton’s theorem

Any two-terminal circuit with only linear elements (resistors) and sources can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor. The current source is written $I_{no}$ and the resistor $R_{no}$.

1. Find $I_{no}$, the short-circuit current from A to B, using KCL and KVL.
2. Find $R_{no}$, the equivalent shunt (parallel with the source) resistance between A and B, by the same replacement of sources as above.

The two equivalents describe the same circuit

Both procedures compute the resistance the same way, so $R_{no}=R_{th}$. Matching the open-circuit voltage of the two equivalents gives $V_{th}=I_{no}{R}_{no}$. Converting between the two forms is called a source transformation.

Related

• Resistance
• Capacitors
• Electric Circuit Analysis