GATE Electrical – Analog Electronics
Page 13: Small Signal Model of BJT
In amplifier analysis, signals are usually small compared to the DC bias values. To analyze such circuits easily, the transistor is replaced with a simplified equivalent circuit called the Small Signal Model.
This model helps determine voltage gain, input resistance and output resistance of transistor amplifiers.
Why Small Signal Model is Needed
- Simplifies transistor analysis
- Helps calculate amplifier gain
- Used in AC analysis of amplifier circuits
Hybrid-π Model
The most widely used small signal model is the Hybrid-π Model.
It consists of the following elements:
- rπ → Base-emitter resistance
- gm vπ → Controlled current source
- ro → Output resistance
Important Small Signal Parameters
1. Transconductance (gm)
Transconductance represents the relationship between collector current and base-emitter voltage.
gm = IC / VT
Where:
- IC = Collector current
- VT ≈ 25 mV at room temperature
2. Input Resistance (rπ)
Input resistance between base and emitter is:
rπ = β / gm
3. Output Resistance (ro)
Output resistance is caused by Early effect.
ro = VA / IC
Where:
- VA = Early voltage
Voltage Gain of CE Amplifier
Using the small signal model, the voltage gain becomes:
Av = -gm RC
Negative sign indicates phase inversion.
Important GATE Points
- Small signal model is used for AC analysis.
- Hybrid-π model is most commonly used.
- gm increases with collector current.
- Voltage gain of CE amplifier is negative.
Next Page → CE Amplifier Analysis
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