Equivalent circuit

An equivalent circuit refers to the simplest form of a 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....

 that retains all of the electrical characteristics of the original (and more complex) circuit. 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 equivalent circuit refers to the simplest form of a 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....

 that retains all of the electrical characteristics of the original (and more complex) circuit. 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 electrical circuit theory, Thévenin's theorem for non 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...
  
   - reduces a two-terminal circuit to a single voltage source
  Voltage source
  A voltage source is any device or system that produces an electromotive force between its terminals OR derives a secondary voltage from a primary source of the electromotive force. A primary voltage source can supply energy to a circuit while a secondary voltage source dissipates energy from a...
  
   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...
  
   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 is the biological membrane separating the interior of a cell from the outside environment....

. The latter is modelled as a capacitor

Capacitor

A capacitor or condenser is a passive electronic component consisting of a pair of conductors separated by a dielectric. When a voltage potential difference exists between the conductors, an electric field is present in the dielectric. This field stores energy and produces a mechanical force...

 (i.e. the lipid bilayer

Lipid bilayer

A 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 and...

) in parallel with resistance

Electrical resistance

The electrical resistance of an object is a measure of its opposition to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the...

-battery

Battery (electricity)

An electrical battery is a combination of one or more electrochemical cells, used to convert stored chemical energy into electrical energy. Since the invention of the first Voltaic pile in 1800 by Alessandro Volta, the battery has become a common power source for many household and industrial...

 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 all living 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 which 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

Artificial membrane also known as synthetic membrane is a syntheticly 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...

).