6.13 : Norton Equivalent Circuits

Norton's theorem is a fundamental concept in the field of electrical engineering that allows for the simplification of complex AC circuits. The theorem states that any two-terminal linear network can be replaced with an equivalent circuit that consists of an impedance, which is parallel with a constant current source. Figure 1 shows the AC circuit portioned into two parts: Circuit A and Circuit B, while Figure 2 depicts the circuit obtained by replacing Circuit A by its Norton equivalent circuit.

Figure 1: A circuit portioned into two parts

Figure 2: Norton equivalent circuit

To calculate the value of the parallel impedance, one must replace the source with its internal impedance, resulting in a circuit with an equivalent impedance known as the Norton impedance. The Norton impedance is the same as the Thévenin impedance and is used to determine the Norton current, which is the current flowing through the circuit.

Determining the Norton current requires placing the sources back into the circuit and analyzing the open-circuit voltage, also known as the Thévenin voltage. The value of the Thévenin voltage is determined by multiplying the source current by the Thevenin impedance and is used to drop the same voltage across the load impedance when it is placed in a parallel configuration.

By using the relationship between the Norton current, the Thévenin voltage, and the Norton current values, one can determine the Norton current of the circuit. This relationship makes Norton's theorem beneficial for analyzing and designing systems containing complex AC circuits since it simplifies their analysis by breaking the circuit down into smaller, more manageable sections.