In electrical engineering, an equivalent circuit refers to a theoretical circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that simplifies calculation, and more broadly, that is a simplest form of a more complex circuit in order to aid analysis. In its most common form, an equivalent circuit is made up of linear, passive elements. However, more complex equivalent circuits are used that approximate the nonlinear behavior of the original circuit as well. These more complex circuits often are called macromodels of the original circuit. An example of a macromodel is the Boyle circuit for the 741 operational amplifier. Examples Thévenin and Norton equivalents One of linear circuit theory's most surprising properties relates to the ability to treat any two-terminal circuit no matter how complex as behaving as only a source and an impedance, which have either of two simple equivalent circuit forms: Thévenin equivalent - Any linear two-terminal circuit can be replaced by a single voltage source and a series impedance. Norton equivalent - Any linear two-terminal circuit can be replaced by a current source and a parallel impedance. However, the single impedance can be of arbitrary complexity (as a function of frequency) and may be irreducible to a simpler form. DC and AC equivalent circuits In linear circuits, due to the superposition principle, the output of a circuit is equal to the sum of the output due to its DC sources alone, and the output from its AC sources alone. Therefore, the DC and AC response of a circuit is often analyzed independently, using separate DC and AC equivalent circuits which have the same response as the original circuit to DC and AC currents respectively. The composite response is calculated by adding the DC and AC responses: A DC equivalent of a circuit can be constructed by replacing all capacitances with open circuits, inductances with short circuits, and reducing AC sources to zero (replacing AC voltage sources by short circuits and AC current sources by open circuits.) An AC equivalent circuit can be constructed by reducing all DC sources to zero (replacing DC voltage sources with short circuits and DC current sources with open circuits) This technique is often extended to small-signal nonlinear circuits like tube and transistor circuits, by linearizing the circuit about the DC bias point Q-point, using an AC equivalent circuit made by calculating the equivalent