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My syllabus shows that I have to study about transistor amplifiers - including small signal analysis.

What exactly does small signal analysis mean? I googled it but I couldn't find an exact answer.

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Strictly speaking, transistors are very non-linear devices. Bipolar transistors don't amplify at all until the base/emitter voltage rises high enough for the base/emitter junction to be forward biased, and you don't get significant current through a MOSFET until the gate/source voltage approaches the threshold voltage.

However, we can use clever circuits to bias the transistors, which means that fairly large d.c. voltages and currents are applied. The bias conditions hold the transistor at an operating bias point such that the behavior of the transistor is fairly linear over a small range of voltages or currents surrounding the bias point. Large-signal analysis pertains to setting up the bias conditions and deals with the non-linear behavior of the transistor. Small-signal analysis assumes that the transistor is correctly biased and concentrates on the linear behavior for small signals, ignoring the messy non-linear stuff.

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Small-signal analysis consists of:

(1) Finding the quiescent or operating point of a circuit. This is found by zeroing all signal sources leaving just the DC sources and then solving for the DC voltages and currents in the circuit.

(2) Linearizing the non-linear circuit elements at the operating point. For example, a diode is replaced with a resistor that models the dynamic resistance at the particular operating point. The dynamic, or small-signal resistance is the ratio of the change in voltage to a small (actually infinitesimal) change in current from the operating point.

(3) Finding the small-signal solution. The DC sources are zeroed, the signal sources are activated, and linear circuit analysis is used to solve for the small-signal voltages and currents.

Having solved for the small-signal voltages and currents, the total solution is simply the sum of the DC solution and the small-signal solution. This total solution is an approximation that is valid only when the signals are in some sense small, i.e., that the variations of the voltages and currents in the circuit are small relative to the DC voltages and currents.

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small signal analysis is carried out on non-linear elements,where non-linear elements are replaced by linear elements(R,L,C) around the operating point of the non-linear device,where the linear equations can be used.

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