Norton's Theorem is a fundamental concept in circuit theory that simplifies the analysis of linear electrical networks. It is a counterpart to Thevenin's Theorem and helps in finding equivalent circuits for complex networks. Norton's Theorem states that any linear two-terminal network containing independent sources and resistances can be replaced by an equivalent current source and a parallel resistance at the terminals.
When dealing with sinusoidal excitation (AC circuits), the principles of Norton's Theorem still hold true, but you'll be working with phasor quantities to represent voltages and currents. Here's how Norton's Theorem works with sinusoidal excitation:
Original Network: Consider the original linear two-terminal network with sources and resistances.
Short Circuit Current (Isc): Find the short-circuit current (Isc) across the terminals where you want to apply Norton's Theorem. This is the current that would flow if you short-circuit the terminals (replace the load with a short circuit). You can use AC circuit analysis techniques like mesh analysis or nodal analysis to find Isc in terms of phasor current.
Norton Current Source (In): The Norton equivalent current source (In) is the same as the short-circuit current (Isc) you calculated in step 2. It has the same amplitude (peak value) and phase as Isc.
Norton Equivalent Resistance (Rn): To find the Norton equivalent resistance (Rn), you need to calculate the impedance looking into the terminals with all independent sources turned off. This can be achieved by setting all voltage sources to zero and current sources to an open circuit. The resulting impedance will be the Norton equivalent resistance.
Equivalent Norton Circuit: Replace the original network with the Norton equivalent circuit, which consists of the Norton current source (In) connected in parallel with the Norton equivalent resistance (Rn).
It's important to note that while the principles of Norton's Theorem remain the same, the calculations involve phasor quantities, impedance, and phase angles due to the sinusoidal nature of the excitation.
In summary, Norton's Theorem is a valuable tool for simplifying AC circuit analysis by replacing a complex network with a single current source and a parallel resistance. When working with sinusoidal excitation, you'll use phasor analysis to determine the Norton current source and the Norton equivalent resistance.