Alinear circuit is anelectronic circuit which obeys thesuperposition principle. This means that the output of the circuitF(x) when a linear combination ofsignalsax₁(t) + bx₂(t) is applied to it is equal to the linear combination of the outputs due to the signalsx₁(t) andx₂(t) applied separately:

${\displaystyle F(a{x}_1+b{x}_2)=aF(x_1)+bF(x_2)}$

It is called a linear circuit because the output voltage and current of such a circuit arelinear functions of its input voltage and current.^[1][2][3] This kind of linearity is not the same as that ofstraight-line graphs.

In the common case of a circuit in which the components' values are constant and don't change with time, an alternate definition of linearity is that when asinusoidal inputvoltage orcurrent offrequencyf is applied, anysteady-state output of the circuit (thecurrent through anycomponent, or thevoltage between any two points) is also sinusoidal with frequencyf.^[1][4] A linear circuit with constant component values is calledlinear time-invariant (LTI).

Informally, a linear circuit is one in which theelectronic components' values (such asresistance,capacitance,inductance,gain, etc.) do not change with the level of voltage or current in the circuit. Linear circuits are important because they can amplify and process electronic signals withoutdistortion. An example of an electronic device that uses linear circuits is asound system.

The superposition principle, the defining equation of linearity, is equivalent to two properties,additivity andhomogeneity, which are sometimes used as an alternate definition

• ${\displaystyle F(x_1+x_2)=F(x_1)+F(x_2)}$  Additivity
• ${\displaystyle F(hx)=hF(x)}$  Homogeneity

That is, a linear circuit is a circuit in which (1) the output when a sum of two signals is applied is equal to the sum of the outputs when the two signals are applied separately, and (2) scaling the input signal${\displaystyle x(t)}$  by a factor${\displaystyle h}$  scales the output signal${\displaystyle F(x(t))}$  by the same factor.

A linear circuit is one that has nononlinear electronic components in it.^[1][2][3] Examples of linear circuits areamplifiers,differentiators, andintegrators, linearelectronic filters, or any circuit composed exclusively ofidealresistors,capacitors,inductors,op-amps (in the "non-saturated" region), and other "linear"circuit elements.

Some examples of nonlinear electronic components are:diodes,transistors, andiron coreinductors andtransformers when the core is saturated. Some examples of circuits that operate in a nonlinear way aremixers,modulators,rectifiers, radio receiverdetectors anddigital logic circuits.

Linear time-invariant circuits are important because they can processanalog signals without introducingintermodulation distortion. This means that separate frequencies in the signal stay separate and do not mix, creating new frequencies (heterodynes).

They are also easier to understand and analyze. Because they obey thesuperposition principle, linear circuits are governed bylinear differential equations, and can be analyzed with powerful mathematicalfrequency domain techniques, includingFourier analysis and theLaplace transform. These also give an intuitive understanding of the qualitative behavior of the circuit, characterizing it using terms such asgain,phase shift,resonant frequency,bandwidth,Q factor,poles, andzeros. The analysis of a linear circuit can often be done by hand using ascientific calculator.

In contrast,nonlinear circuits usually do not have closed form solutions. They must be analyzed using approximatenumerical methods byelectronic circuit simulation computer programs such asSPICE, if accurate results are desired. The behavior of suchlinear circuit elements as resistors, capacitors, and inductors can be specified by a single number (resistance, capacitance, inductance, respectively). In contrast, anonlinear element's behavior is specified by its detailedtransfer function, which may be given by a curved line on a graph. So specifying the characteristics of a nonlinear circuit requires more information than is needed for a linear circuit.

"Linear" circuits and systems form a separate category within electronic manufacturing. Manufacturers of transistors andintegrated circuits often divide their product lines into 'linear' and 'digital' lines. "Linear" here means "analog"; the linear line includes integrated circuits designed to process signals linearly, such asop-amps,audio amplifiers, andactive filters, as well as a variety ofsignal processing circuits that implement nonlinear analog functions such as logarithmic amplifiers,analog multipliers, and peak detectors.

Nonlinear elements such as transistors tend to behave linearly when small AC signals are applied to them. So in analyzing many circuits where the signal levels are small, for example those in TV and radio receivers, nonlinear elements can be replaced with a linearsmall-signal model, allowinglinearanalysis techniques to be used.

Conversely, all circuit elements, even "linear" elements, show nonlinearity as the signal level is increased. If nothing else, thepower supply voltage to the circuit usually puts a limit on the magnitude of voltage output from a circuit. Above that limit, the output ceases to scale in magnitude with the input, failing the definition of linearity.

• Network analysis (electrical circuits)