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12.10 : Small-Signal Analysis of BJT Amplifiers

Small signal analysis is a fundamental approach used in electronics to understand how a Bipolar Junction Transistor (BJT) amplifier processes signals. In the active region, the BJT is designed for linear amplification. The transistor's behavior under these conditions is governed by its instantaneous base-emitter voltage VBE, a sum of the DC bias VBE, and a small AC signal VBE, resulting in the collector current iC. Here, the collector current has a DC component and an AC component.

Transistor equations, V_BE and i_C; formulas for AC analysis, amplification, circuit design.

Here, VT is the thermal voltage.

When the AC input signal VBE is significantly smaller than VT, a small signal approximation can be used to get the expression for the AC component of the collector current. The AC component of the collector current is the ratio of the product of the DC component of the collector with time-varying input voltage to the thermal voltage.

Transistor current equation, iC(AC)=iC(DC)(VBE(AC)/VT), electrical engineering formula.

The ratio of the AC component of the collector current to the input signal is known as transconductance. The voltage gain of the BJT is a function of the transconductance of the BJT and the load resistance.

Transistor amplifier equation, gain formula; symbols for gm, iC, VBE, AV, RC; electrical analysis

Here, the negative sign signifies a 180-degree phase shift between input and output signals.

At the base of the BJT, the small-signal base-emitter resistance rπ is crucial for input impedance considerations and is determined by:

Transistor biasing equation, \( r_{\pi} = \frac{V_T}{i_{B(DC)}} \), used in electronic circuits.

This resistance impacts the transistor's response to input signals and is inversely proportional to the DC bias current.

Through small signal analysis, the detailed performance of BJT amplifiers with small input variations can be precisely characterized and utilized in electronic circuit design.

Tags

Small signal AnalysisBJT AmplifierActive RegionLinear AmplificationBase emitter VoltageCollector CurrentThermal VoltageSmall Signal ApproximationTransconductanceVoltage GainBase emitter ResistanceInput Impedance

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