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<p>71.51.243.104: Undid revision 585862886 by 71.51.243.104 (talk)</p> <hr /> <div>{{Cleanup|date=March 2009}}<br /> '''Small-signal modeling''' is a common analysis technique in [[electrical engineering]] which is used to approximate the behavior of [[nonlinear device]]s with [[linear equations]]. This linearization is formed about the [[Direct current|DC]] [[biasing|bias]] point of the device (that is, the [[voltage]]/[[Electric current|current]] levels present when no signal is applied), and can be accurate for small excursions about this point.<br /> <br /> ==Motivation ==<br /> <br /> Many electronic circuits, such as [[radio receiver]]s, communications, and [[signal processing]] circuits, generally carry small time-varying ([[alternating current|AC]]) signals on top of a constant ([[direct current|DC]]) [[bias (electrical engineering)|bias]]. This suggests using a method akin to approximation by [[finite differences|finite difference method]] to analyze relatively small perturbations about the [[bias point]]. <br /> <br /> 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]], [[electrical resistance|resistance]] and [[inductance]]), and a circuit diagram relating them can be formulated.<br /> Small-signal models exist for [[electron tube]]s, [[diode]]s, [[field-effect transistor]]s (FET) and [[Bipolar junction transistor|bipolar transistors]], notably the [[hybrid-pi model]] and various [[two-port network]].<br /> <br /> ==Variable notation==<br /> <br /> * 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 &lt;math&gt;V_\mathrm{IN}&lt;/math&gt;.<br /> <br /> * Small-signal quantities are denoted using lowercase letters with lowercase subscripts. For example, the input signal of a transistor would be denoted as &lt;math&gt;v_\mathrm{in}&lt;/math&gt;.<br /> <br /> * 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 &lt;math&gt;v_\mathrm{IN}(t)=V_\mathrm{IN}+v_\mathrm{in}(t)&lt;/math&gt;.<br /> <br /> ==Example: PN junction diodes==<br /> {{main|Diode modelling#Small-signal modelling}}<br /> <br /> 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 [[Electrical conductance|conductance]], capacitance and resistance of the diode. This procedure is described in more detail under [[diode modelling#Small-signal modeling|diode modeling]], which provides an example of the linearization procedure followed in all small-signal models of semiconductor devices.<br /> <br /> ==Differences between small signal and large signal==<br /> <br /> A large signal is a DC signal (or an AC signal at a point in time) (one or more orders of magnitude larger than the small signal) used to analyse a circuit containing non-linear components and calculate an operating point (bias) of these components.<br /> <br /> A small signal is an AC signal superimposed on a circuit containing a large signal.<br /> <br /> In analysis of the small signal's contribution to the circuit, the non-linear components are modeled as linear components.<br /> <br /> ==See also==<br /> *[[Diode modelling]]<br /> *[[Hybrid-pi model]]<br /> *[[Early effect]]<br /> *[[SPICE]] - Simulation Program with Integrated Circuit Emphasis, a general purpose analog electronic circuit simulator capable of solving small signal models.<br /> <br /> ==References==<br /> {{reflist}}<br /> <br /> [[Category:Electronic device modeling]]</div>

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