12.10:
Small-Signal Analysis of BJT Amplifiers
Consider a BJT transistor amplifier circuit operating in its active region to provide linear amplification.
The total instantaneous base-emitter voltage, which combines the DC voltage and the input signal, results in an instantaneous collector current.
The exponential term involving the base-emitter voltage is simplified using the small-signal approximation, where the input signal is significantly less than the thermal voltage.
So, the collector current comprises two components: the DC bias current and the signal component.
The ratio of the signal component to the varying base-emitter voltage is known as the BJT transconductance.
Here, the transconductance of the BJT is directly proportional to the DC bias current, which is determined by the slope of the tangent relative to the characteristic curve at the bias point.
So, the voltage gain equals the negative product of the transconductance and the load resistance. The negative sign indicates a 180 degrees phase shift between the amplified and input signals.
When examining the emitter, the small-signal base-emitter resistance is determined by dividing the thermal voltage by the respective DC bias current.
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.
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.
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.
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:
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.