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Thévenin and Norton Equivalents#

Thévenin's Theorem

Every circuit comprised of only time-invariant linear resistors, time-invariant voltage sources and direct current sources is equivalent to one time-invariant ideal voltage source and one time-invariant linear resistor connected in series.

Thévenin Equivalent

Definition: Internal Resistance

We call \(R_{\text{th}}\) the internal resistance of the circuit.

Proof

TODO

Norton's Theorem

Every circuit comprised of only time-invariant linear resistors, time-invariant voltage sources and direct current sources is equivalent to one direct current source and one time-invariant linear resistor connected in parallel.

Norton Equivalent

Definition: Internal Conductance

We call \(G_{\text{no}}\) the internal conductance of the circuit.

Proof

TODO

Theorem: Thévenin-Norton Conversion

The quantities in the Thévenin equivalent and the Norton equivalent are related as follows:

\[ R_{\text{th}} = \frac{1}{G_{\text{no}}} \qquad V_{\text{th}} = R_{\text{th}} I_{\text{no}} \]
Proof

TODO