# Explanation Of Small Signal VS Large Signal

Discussion in 'General Electronics Chat' started by Glenn Holland, Jan 19, 2015.

1. ### Glenn Holland Thread Starter Member

Dec 26, 2014
359
114
Books often use the term "Small Signal" and "Large Signal" to describe the input to a transistor amplifier.

I have done an online search of these terms and I still cannot find a clear explanation.

2. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
The large-signal model is a model that is acceptably accurate over a large range on input signals. For transistors and diodes, this model is polynomial or exponential, which makes it difficult to work with. But if you restrict the signals to small variations, then over the range of those variations the response can be approximated very well as being linear, which is very easy to work with.

Basically the idea is that you have a circuit in which the transistor is biased at a particular quiescent point and the signal is causing to move about that point. So you break the total response into two pieces -- the DC bias, or operating, point and the variation due to the signal. Usually the bias point is large compared to the signal, so the circuit model used to calculate the DC operating point and the circuit that is used to model the changes about that point due to the signal. The first is called the large signal model and the second is called the small signal model.

By assuming (or, more accurately, designing the circuit so ensure) that the variation about the bias point is small enough, the variation in the current due to a change in voltage (or vice-versa) is approximately linear so we can use all of the techniques developed for linear circuits to analyze/design this portion of the behavior. Because we are assuming that the DC operating point isn't changing, we turn this part of the problem into a one-time analysis of the non-linear circuit and more often than not the simple piecewise linear models are adequate. Very seldom to we have to resort to the full exponential models (such as the Ebers-Moll). We can then use superposition to find the total response because both are now linear (one is constant and the other is linearized about that constant).

If you would like, we can go through deriving the small signal model for a BJT starting from just the Ebers-Moll equations.

3. ### Glenn Holland Thread Starter Member

Dec 26, 2014
359
114
This explanation is similar to what I have read and to make along story short, a "small signal" excursion is approximately equal to the derivative taken at the Q point.

4. ### WBahn Moderator

Mar 31, 2012
18,087
4,917
Yep -- well, the small signal excursion (at the output) is approximately equal to the derivative taken at the Q point multiplied by the excursion of the input. The small-signal model is usually derived by taking the derivative of the small signal model and using the first order Taylor series approximation about the operating point. In essence:

$
f(x+\Delta x) \; \approx \; f(x) \; + \; \left( \left\ert \frac{df(x)}{dx}\right|_x \right)\cdot \Delta x
$

5. ### crutschow Expert

Mar 14, 2008
13,505
3,376
An explanation of how a simulator handles the two cases may help.

In Spice the Small Signal (AC) analysis uses a linear model for all components including transistors, with the linear parameters (gain, etc.) determined at the DC operating point of the circuit. This means the signal processing is unaffected by the magnitude of the signal, e.g. a 1V signal will be processed the same as a 1000V signal and the non-linear effects of a real device are ignored. This can give signal levels that would be impossible in a real circuit. (So obviously Small Signal in the simulator does not mean that the signal has to be small although the assumption is that the signal is small enough so that there are no non-linear effects).

In contrast, the Large Signal (Transient or DC operating point) analysis in Spice uses the complete non-linear model for the devices (such as the Gummel–Poon model for bipolar transistors) and includes the effects of the actual voltages in the circuit. It digitally computes the signal at small increments in time with an iterative process that closely approximates the continuous analog operation of the real device. Thus effects like non-linear distortion and clipping of he signal are displayed and the simulated results will normally be reasonably close to that experienced in the real circuit (largely depending upon the accuracy of the models).