In the theory of

electrical network An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, c ...

s, a dependent source is a

voltage source A voltage source is a two-terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current. However, a real-world voltage source cannot supply unli ...

or a

current source A current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source. The term ''current sink'' is sometimes used for sources f ...

whose value depends on a voltage or current elsewhere in the network.I. D. Mayergoyz, Wes Lawson ''Basic electric circuit theory: a one-semester text'' Gulf Professional Publishing, 1996 , Chapter 8 "Dependent sources and operational amplifiers" Dependent sources are useful, for example, in modeling the behavior of amplifiers. A

bipolar junction transistor A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar ...

can be modeled as a dependent current source whose magnitude depends on the magnitude of the current fed into its controlling base terminal. An

operational amplifier An operational amplifier (often op amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential (relative to c ...

can be described as a voltage source dependent on the differential input voltage between its input terminals. Practical circuit elements have properties such as finite power capacity, voltage, current, or frequency limits that mean an ideal source is only an approximate model. Accurate modeling of practical devices requires using several idealized elements in combination.

Classification

Dependent sources can be classified as follows: * Voltage-controlled voltage source: The source delivers the

voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...

as per the voltage of the dependent element.

V=()

* Voltage-controlled current source: The source delivers the

current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...

as per the voltage of the dependent element.

I=()

* Current-controlled current source: The source delivers the current as per the current of the dependent element.

I=()

* Current-controlled voltage source: The source delivers the voltage as per the current of the dependent element.

V=()

Dependent sources are not necessarily linear. For example,

MOSFET The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...

switches can be modeled as a voltage-controlled current source when

V_>V_-V_T

and

V_>V_T

. However, the relationship between the current flowing through it and

V_

is approximately: :

I_ = \frac\frac(V_-V_)^2 \left(1+\lambda (V_-V_)\right).

In this case, the current is not linear to

V_

, but rather approximately proportional to the square of

V_-V_T

. As for the case of linear dependent sources, the proportionality constant between dependent and independent variables is dimensionless if they are both currents (or both voltages). A voltage controlled by a current has a proportionality factor expressed in units of resistance (

ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (b ...

s), and this constant is sometimes called "transresistance". A current controlled by a voltage has units of conductance (

siemens Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad. The principal divisions of the corporation are ''Industry'', '' ...

), and is called "transconductance". Transconductance is a commonly used specification for measuring the performance of

field effect transistor The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs (JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs control ...

s and

vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...

References

{{Reflist Power supplies Electrical power control

Classification

See also

References