Theveninequivalent

Thevenin equivalent is a method in circuit analysis that replaces a linear network of sources and impedances by a single voltage source in series with a resistor, as seen from two output terminals. This simplified model allows easy analysis of how the rest of the circuit responds to different loads.

To find the Thevenin equivalent, determine two key quantities. The open-circuit voltage, Vth, is the voltage across the output terminals with the load removed. The Thevenin resistance, Rth, is the resistance seen from the output terminals with all independent sources deactivated (voltage sources shorted and current sources opened). If the network contains dependent sources, they must remain active when calculating Rth. In such cases, Rth is typically found by applying a test source at the output and computing the resulting voltage or current, or by other methods that preserve the behavior of dependent sources.

The Thevenin equivalent is related to the Norton equivalent, which represents the same network as a current source in parallel with a resistor. The two representations are interchangeable: Vth equals In times Rth, where In is the short-circuit current, and the resistances are equal (Rth = Rn).

Applications and limitations: Thevenin equivalents are used to analyze how a network drives various loads, simplify circuit topology, and facilitate source transformations. They are valid for linear, bilateral networks and are applicable in both DC and linear AC (where impedances may be complex) analysis. They are not appropriate for nonlinear or time-variant networks without linearization.