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Only because while working with small signals, these basically non-linear and useless devices become useful and perfom the tasks that are usually desired from these (Like providing gain etc.) .
And any person will definitely try to analyze a thing as much as possible in a mode of operation which is most useful to him/her.
Because there are applications like reception of signals though metallic or aereal media and the signal at reception is very small, so we need first amplify that small signal in order the following circuits can process them.
Another example are the cassettes recording, or the vinyl discs. The first electrical signal is really very small that we need to amplify to process them.
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We basically use small signal analysis in order to find a linear model for non-linear devices ( e.g. BJT, MOSFETs, Diodes ) . Non-linear means that these devices depend on the current passing through them, unlike resistors for example which are linear, their resistivity is constant regardless of the current passing through.
If we consider BJTs, we usually find the bias currents at DC, these values for DC currents ( emitter, collector and base currents ) can be used to determine the internal resistances of the transistor ( eg. r(pi), g(m) ) for those certain values of currents.
When we determine these resistance values, we can then replace the BJT with a linear model (e.g Hybrid or T model) by using this model we can treat the transistor as any other linear device in our analysis.
We can use small signal anaysis for many reasons such as finding the gain of amplifiers.
most of the analog circuits (such as amplifiers) are biased to a fixed operating point and in the case of a small perturbation of the input signal we can approximately determine the response of the device with a simpler relation (may be a linear one) than large signal relations.
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