Norton's Theorem

Norton's theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a single current source in parallel with a resistor. This simplification allows engineers to analyze complex circuits more efficiently by substituting the entire network with just two components: Norton's current (the short-circuit current) and Norton's resistance (the input resistance with sources deactivated).

Norton's resistance is determined by setting all independent sources to zero and calculating the equivalent input resistance between the two terminals. This deactivation of sources removes their effects, leaving only the passive resistive elements. The resulting resistance value represents Norton's resistance, which forms one half of the Norton equivalent circuit.

To find Norton's current, restore all independent sources to their original positions and calculate the short-circuit current flowing between the marked terminals. This short-circuit current represents the maximum current that would flow if the terminals were directly connected with zero resistance, providing the current source value in the Norton equivalent circuit.

Norton's and Thévenin's theorems are closely related and can be converted between each other using source transformation. Both theorems require knowledge of open-circuit voltage, short-circuit current, and input resistance to establish their equivalent circuits. The relationship between these theorems, combined with Ohm's law, provides powerful tools for resolving complex electrical circuits.

First, remove the load resistor from the two terminals. Next, find Norton's resistance by deactivating all sources and calculating input resistance. Then, restore sources and calculate Norton's current as the short-circuit current between terminals. Finally, replace the network with the Norton equivalent circuit and reconnect the load resistor to complete the transformation.

Three parameters are essential: the open-circuit voltage across the terminals, the short-circuit current between the terminals, and the input or equivalent resistance when all independent sources are deactivated. These three values provide complete information to construct the Norton equivalent circuit consisting of a current source in parallel with a resistor.

Norton's theorem is valuable because once the equivalent circuit is determined, the same Norton equivalent can be used to analyze the network's behavior with different load resistors without recalculating the entire circuit. This efficiency makes it particularly useful for design scenarios where load conditions vary, allowing engineers to quickly determine circuit response across multiple configurations.