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Small-signal modeling is a common analysis technique inelectronics engineering used to approximate the behavior ofelectronic circuits containingnonlinear devices, such asdiodes,transistors,vacuum tubes, andintegrated circuits, withlinear equations. It is applicable to electronic circuits in which the ACsignals (i.e., the time-varying currents and voltages in the circuit) are small relative to the DCbias currents and voltages.^[1] A small-signal model is an ACequivalent circuit in which the nonlinear circuit elements are replaced by linear elements whose values are given by the first-order (linear) approximation of their characteristic curve near the bias point.

Many of theelectrical components used in simple electric circuits, such asresistors,inductors, andcapacitors arelinear.^{[citation needed]} Circuits made with these components, calledlinear circuits, are governed bylinear differential equations, and can be solved easily with powerful mathematicalfrequency domain methods such as theLaplace transform.^{[citation needed]}

In contrast, many of the components that make upelectronic circuits, such asdiodes,transistors,integrated circuits, andvacuum tubes arenonlinear; that is the current through^{[clarification needed]} them is not proportional to thevoltage, and the output oftwo-port devices like transistors is not proportional to their input. The relationship between current and voltage in them is given by a curved line on a graph, theircharacteristic curve (I-V curve). In general these circuits don't have simple mathematical solutions. To calculate the current and voltage in them generally requires eithergraphical methods or simulation on computers usingelectronic circuit simulation programs likeSPICE.

However in some electronic circuits such asradio receivers, telecommunications, sensors, instrumentation andsignal processing circuits, the AC signals are "small" compared to the DC voltages and currents in the circuit. In these,perturbation theory can be used to derive an approximateAC equivalent circuit which is linear, allowing the AC behavior of the circuit to be calculated easily. In these circuits a steadyDC current or voltage from the power supply, called abias, is applied to each nonlinear component such as a transistor and vacuum tube to set its operating point, and the time-varyingAC current or voltage which represents thesignal to be processed is added to it. The point on the graph of the characteristic curve representing the bias current and voltage is called thequiescent point (Q point). In the above circuits the AC signal is small compared to the bias, representing a small perturbation of the DC voltage or current in the circuit about the Q point. If the characteristic curve of the device is sufficiently flat over the region occupied by the signal, using aTaylor series expansion the nonlinear function can be approximated near the bias point by its first orderpartial derivative (this is equivalent to approximating the characteristic curve by a straight linetangent to it at the bias point). These partial derivatives represent the incrementalcapacitance,resistance,inductance andgain seen by the signal, and can be used to create a linearequivalent circuit giving the response of the real circuit to a small AC signal. This is called the "small-signal model".

The small signal model is dependent on the DC bias currents and voltages in the circuit (theQ point). Changing the bias moves the operating point up or down on the curves, thus changing the equivalent small-signal AC resistance, gain, etc. seen by the signal.

Any nonlinear component whose characteristics are given by acontinuous,single-valued, smooth (differentiable) curve can be approximated by a linear small-signal model. Small-signal models exist forelectron tubes,diodes,field-effect transistors (FET) andbipolar transistors, notably thehybrid-pi model and varioustwo-port networks. Manufacturers often list the small-signal characteristics of such components at "typical" bias values on their data sheets.

• DC quantities (also known asbias), constant values with respect to time, are denoted by uppercase letters with uppercase subscripts. For example, the DC input bias voltage of a transistor would be denoted${\displaystyle V_{\mathrm{I}\mathrm{N}}}$. For example, one might say that${\displaystyle V_{\mathrm{I}\mathrm{N}}=5}$.
• Small-signal quantities, which have zero average value, are denoted using lowercase letters with lowercase subscripts. Small signals typically used for modeling are sinusoidal, or "AC", signals. For example, the input signal of a transistor would be denoted as${\displaystyle v_{\mathrm{i}\mathrm{n}}}$. For example, one might say that${\displaystyle v_{\mathrm{i}\mathrm{n}}(t)=0.2\cos (2\pi t)}$.
• Total quantities, combining both small-signal and large-signal quantities, are denoted using lower case letters and uppercase subscripts. For example, the total input voltage to the aforementioned transistor would be denoted as${\displaystyle v_{\mathrm{I}\mathrm{N}}(t)}$. The small-signal model of the total signal is then the sum of the DC component and the small-signal component of the total signal, or in algebraic notation,${\displaystyle v_{\mathrm{I}\mathrm{N}}(t)=V_{\mathrm{I}\mathrm{N}}+v_{\mathrm{i}\mathrm{n}}(t)}$. For example,${\displaystyle v_{\mathrm{I}\mathrm{N}}(t)=5+0.2\cos (2\pi t)}$

The (large-signal) Shockley equation for a diode can be linearized about the bias point or quiescent point (sometimes calledQ-point) to find the small-signalconductance, capacitance and resistance of the diode. This procedure is described in more detail underdiode modelling#Small-signal_modelling, which provides an example of the linearization procedure followed in small-signal models of semiconductor devices.

A large signal is any signal having enough magnitude to reveal a circuit's nonlinear behavior. The signal may be a DC signal or an AC signal or indeed, any signal. How large a signal needs to be (in magnitude) before it is considered alarge signal depends on the circuit and context in which the signal is being used. In some highly nonlinear circuits practically all signals need to be considered as large signals.

A small signal is part of a model of a large signal. To avoid confusion, note that there is such a thing as asmall signal (a part of a model) and asmall-signal model (a model of a large signal).

A small signal model consists of a small signal (having zero average value, for example a sinusoid, but any AC signal could be used) superimposed on a bias signal (or superimposed on a DC constant signal) such that the sum of the small signal plus the bias signal gives the total signal which is exactly equal to the original (large) signal to be modeled. This resolution of a signal into two components allows the technique of superposition to be used to simplify further analysis. (If superposition applies in the context.)

In analysis of the small signal's contribution to the circuit, the nonlinear components, which would be the DC components, are analyzed separately taking into account nonlinearity.

• Diode modelling
• Hybrid-pi model
• Early effect
• SPICE – Simulation Program with Integrated Circuit Emphasis, a general purpose analog electronic circuit simulator capable of solving small signal models.

• Electronic device modeling

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