theory of small signal and lage signal models

[krishik]

i want to know some basic questions regarding small signal and large signal analysis
what is the difference between the large signal and small signal analysis.
how we know that whether i can apply the small signal or large signal analysis for my circuit .
what is the need for linearity of the circuit .
how to define the q point in small signal and large signal models.

 

[ZekeR]

The entire premise of "large signal" and "small signal" analyses is that, when dealing with nonlinear circuit elements (diodes, transistors, etc), understanding and analyzing the circuit becomes impossible unless you can somehow "linearize" it. A large part of this is the need to be able to use analytical methods (like nodal analysis or loop analysis), which ONLY work on circuits with linear elements.

So, the idea is to do large signal analysis first. This will tell you the "bias point," also known as the "quiescent" point. The quiescent operating conditions dictate how much current flows in each loop or branch, and how much voltage is at each node, in steady-state (DC, or large-signal). The quiescent point also tells you more details about the nonlinear elements: their dynamic resistance (for diodes), and their transconductance (for transistors). Essentially, the dynamic resistance and transconductance are the "small signal" slope of the i/v curve for these elements. (The "small signal" slope is also called the "derivative" in mathematics).

Now that the large signal analysis has been done and all the small signal i/v relationships have been found, the circuit can be analyzed with no worries, as if the circuit didn't have any nonlinear elements at all. The nonlinear elements have been "linearized" by their small-signal equivalent models, simply by finding the slope of their i/v curves.

 

[LvW]

Hi ZekeR,
May a add one remark to your very good explanation: All voltages, currents, gain values ....which are derived using the small-signal model and its corresponding formulas may be applied only as long as the amplitudes within the circuit (with non-linearities) are sufficient small in order to justify this linear approach.
That means for example: In makes no sense to calculate a gain value for a circuit having a "heavy" non-sinusoidal output when the input is sinusoidal (non-linear distortions)

 

[ZekeR]

Yes, you may add that remark. =) Small-signal analysis can be applied when the signals are "sufficiently small" compared to the DC bias conditions. How small is "sufficiently small?" Well, it depends on your specific purposes, so I can't say.

Small-signal analysis is applied because it gives us all the nice analytical tools for linear systems that we lost when we placed nonlinear elements in the circuit. When we linearize to perform small-signal analysis, we're losing information though, and we begin to operate on only an approximation.

So, small-signal modeling is useful as a design tool (it simplifies analysis so we can design the circuit quickly), but it should NEVER be considered the end-all be-all. Nonlinear, time-domain analysis should be applied as the actual test of proper functionality.