# Small-signal model

﻿
Small-signal model

Small-signal modeling is a common analysis method used in electrical engineering to describe nonlinear devices in terms of linear equations. This linearization is done by first calculating (possibly by an iterative process if the circuit is complex) the DC bias point (that is, the voltage/current levels present when no signal is applied), and then forming linear approximations about this point.

Motivation

Electronic circuits generally involve small time-varying signals carried over a constant bias. This suggests using a method akin to approximation by differentials to analyze relatively small perturbations about the bias point.

Any nonlinear device which can be described quantitatively using a formula can then be 'linearized' about a bias point by taking partial derivatives of the formula with respect to all governing variables. These partial derivatives can be associated with physical quantities (such as capacitance, resistance and inductance), and a circuit diagram relating them can be formulated.Small-signal models exist for diodes, field-effect transistors (FET) and bipolar transistors, notably the hybrid-pi model and various two-port networks.

Notation

* Large-signal DC quantities are denoted by uppercase letters with uppercase subscripts. For example, the DC input bias voltage of a transistor would be denoted $V_\left\{IN\right\}$.

* Small-signal quantities are denoted using lowercase letters with lowercase subscripts. For example, the input signal of a transistor would be denoted as $v_\left\{in\right\}$.

* 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 $v_\left\{IN\right\}\left(t\right)=V_\left\{IN\right\}\left(t\right)+v_\left\{in\right\}\left(t\right)$.

Example: PN junction diodes

The (large-signal) Shockley equation for a diode can be linearized about the bias point or quiescent point (sometimes called Q-point) to find the small-signal conductance, capacitance and resistance of the diode. This procedure is described in more detail under diode modeling, which provides an example of the linearization procedure followed in all small-signal models of semiconductor devices.

ee also

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

References

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Large-signal model — Large signal modeling is a common analysis method used in electrical engineering to describe nonlinear devices in terms of the underlying nonlinear equations.In circuits containing nonlinear elements such as transistors, diodes, and vacuum tubes …   Wikipedia

• Signal integrity — or SI is a measure of the quality of an electrical signal. In digital electronics, a stream of binary values is represented by a voltage (or current) waveform. Over short distances and at low bit rates, a simple conductor can transmit this with… …   Wikipedia

• Model 45A — Image Type Battle rifle Light machine gun Place of origin …   Wikipedia

• Small-angle neutron scattering — (SANS) is a laboratory technique, similar to the often complementary techniques of small angle X ray scattering (SAXS) and light scattering. These are particularly useful because of the dramatic increase in forward scattering that occurs at phase …   Wikipedia

• Signal transduction — In biology, signal transduction refers to any process by which a cell converts one kind of signal or stimulus into another. Most processes of signal transduction involve ordered sequences of biochemical reactions inside the cell, which are… …   Wikipedia

• Model aircraft — A die cast Boeing 747 400 model. Model aircraft are flying or non flying models of existing or imaginary aircraft using a variety of materials including plastic, diecast metal, polystyrene, balsa wood, foam and fibreglass. Flying designs range… …   Wikipedia

• Model rocket — A typical model rocket during launch A model rocket is a small rocket that is commonly advertised as being able to be launched by anybody, to, in general, low altitudes (usually to around 100–500 m (300–1500 ft) for a 30 g (1 oz.) model) and …   Wikipedia

• Model lipid bilayer — A model lipid bilayer is any bilayer assembled in vitro, as opposed to the bilayer of natural cell membranes or covering various sub cellular structures like the nucleus. A model bilayer can be made with either synthetic or natural lipids. The… …   Wikipedia

• Signal Hill, California — Infobox Settlement official name = City of Signal Hill, California settlement type = City nickname = motto = imagesize = image caption = image imagesize = image caption = image mapsize = 250x200px map caption = Location of Signal Hill in Los… …   Wikipedia

• Model car — For the term referring to delineation of (non model) car ranges, see car model. This Norev model car is a good miniature representation of a real Renault 4CV and would have been sold as a children s toy. A model car or toy car is a miniature… …   Wikipedia