GATE Electrical – Analog Electronics
Page 20 : Differential Amplifier Gain Derivation
The differential amplifier amplifies the difference between two input signals. To understand its operation, we derive the expression for differential gain.
Basic Differential Amplifier Circuit
The circuit consists of two identical transistors:
- Q1 and Q2
- Collector resistors RC
- Emitter resistor RE
- Two inputs V1 and V2
The output is taken from one of the collectors.
Differential Input Voltage
The differential input signal is:
Vd = V1 − V2
Each transistor receives half of the differential signal.
Input to each transistor = Vd / 2
Small Signal Model
For small signal analysis:
- Each transistor has emitter resistance re
- Collector resistor = RC
The emitter resistance is:
re = 25mV / IE
Output Voltage
The output voltage for one transistor becomes:
Vo = (RC / re) × (Vd / 2)
Differential Gain
Differential gain is defined as:
Ad = Vo / Vd
Substituting values:
Ad = RC / (2re)
Important Observations
- Differential gain depends on RC and emitter resistance.
- Higher RC increases gain.
- Lower emitter resistance increases gain.
Important GATE Points
- Differential amplifier gain = RC / (2re)
- Emitter resistance re = 25mV / IE
- Differential amplifier is the core of Op-Amp circuits
- High CMRR is desirable
Next Page → Current Mirror Circuit
.png)
No comments:
Post a Comment