In electrical engineering and science, an equivalent circuit refers to a theoretical circuit

Electrical network

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current...

 that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that is the 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.

There are two very renowned two-terminal equivalent circuits:

• Thévenin equivalent
  Thévenin's theorem
  In circuit theory, Thévenin's theorem for linear electrical networks states that any combination of voltage sources, current sources, and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the theorem...
  
   - reduces a two-terminal circuit to a single voltage source
  Voltage source
  In electric circuit theory, an ideal voltage source is a circuit element where the voltage across it is independent of the current through it. A voltage source is the dual of a current source. In analysis, a voltage source supplies a constant DC or AC potential between its terminals for any current...
  
   and a series Thévenin impedance
• Norton equivalent  - reduces a two terminal circuit to a current source
  Current source
  A current source is an electrical or electronic device that delivers or absorbs electric current. A current source is the dual of a voltage source. The term constant-current sink is sometimes used for sources fed from a negative voltage supply...
  
   and a parallel Norton impedance

For a restricted set of linear four-terminal circuits, equivalent two-port network

Two-port network

A two-port network is an electrical circuit or device with two pairs of terminals connected together internally by an electrical network...

s can be set up. The restriction upon a two-port representation is that of a port: the current entering each port must be the same as the current leaving that port. By linearizing a nonlinear circuit about its operating point, such a two-port representation can be made for transistors: see hybrid pi

Hybrid-pi model

The hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate...

 and h-parameter circuits.

Equivalent circuits also can describe and model the electrical properties of materials or biological systems like the cell membrane

Cell membrane

The cell membrane or plasma membrane is a biological membrane that separates the interior of all cells from the outside environment. The cell membrane is selectively permeable to ions and organic molecules and controls the movement of substances in and out of cells. It basically protects the cell...

. The latter is modelled as a capacitor

Capacitor

A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

 (i.e. the lipid bilayer

Lipid bilayer

The lipid bilayer is a thin membrane made of two layers of lipid molecules. These membranes are flat sheets that form a continuous barrier around cells. The cell membrane of almost all living organisms and many viruses are made of a lipid bilayer, as are the membranes surrounding the cell nucleus...

) in parallel with resistance

Electrical resistance

The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

-battery

Battery (electricity)

An electrical battery is one or more electrochemical cells that convert stored chemical energy into electrical energy. Since the invention of the first battery in 1800 by Alessandro Volta and especially since the technically improved Daniell cell in 1836, batteries have become a common power...

 combinations (i.e. ion channel

Ion channel

Ion channels are pore-forming proteins that help establish and control the small voltage gradient across the plasma membrane of cells by allowing the flow of ions down their electrochemical gradient. They are present in the membranes that surround all biological cells...

s powered by an ion gradient

Gradient

In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

 across the membrane

Artificial membrane

An artificial membrane, or synthetic membrane, is a synthetically created membrane which is usually intended for separation purposes in laboratory or in industry. Synthetic membranes have been successfully used for small and large-scale industrial processes since the middle of twentieth century. A...

).