The amplifier is supposed to be an electronic circuit. Electronic circuits are nonlinear circuits, which may be modeled in the time domain by means of nonlinear differential equations and nonlinear algebraic equations. The kernel of the solution of the nonlinear equations is the solution of a linear equation system i.e. the nonlinear components and couplings are approximated with linear relations valid for small signals. Iterations are performed until the laws of Kirchhoff are fulfilled. The instant set of linear equations is the small signal model for the amplifier. If the amplifier is excited with a dc power source it assumes an active state called the bias point or quiescent point. If the relation between the input and the output signals of the amplifier is measured to be (almost) linear in the bias point then we assume a small signal amplifier with time independent bias point else we assume a large signal amplifier.
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to amplify a small signal to sufficient level,so that it can travel to a large distance from first stage till the last stage
All negative feedback systems, whether they be electronic, biological, or anything else, work by applying a negative feedback to the source signal, which is proportional in some way to the source signal. If the factor by which the amplifier corrects is high enough, oscillation will result (perhaps even runaway oscillation) How you make it happen depends upon the amplifier you use however -- though most work similarly enough. You could use a delay between output and feedback, or you could rely on a large amplifier gain.
in general the CE amplifiers are called low-signal amplifiers as they use only small values of voltage as a source of input which cant be used in practical purposes, whereas power amplifiers deal with practical values of input and output voltages
Each step in a cascade produces a large number of activated products, causing signal amplification as the cascade progresses.
It's voltage that's being amplified by a voltage amplifier. Small changes in voltage at the input of the stage cause large changes of voltage at the output of the stage. That larger signal is then coupled out. The stage is said to have amplified the signal, amplified its voltage. And the stage's gain is a measure of how much. This is the simple answer. A further investigation into amplifiers and the underlying ideas in electronics will be needed to take this answer further.