Differential Amplifier Explained: Working, CMRR, and Applications

The differential amplifier is one of the most fundamental circuits in analog design. It amplifies the difference between two input signals while rejecting any signals common to both inputs. Differential amplifiers form the building block of operational amplifiers (op-amps), instrumentation amplifiers, and many mixed-signal systems.

1. What is a Differential Amplifier?

A differential amplifier has two inputs (V₁ and V₂) and one output. Its ideal function is:

V_out = A_d(V₁ – V₂)

Where A_d is the differential gain. If the same signal is applied to both inputs, the output should ideally be zero.

2. Mathematical Expression

The general expression for the output is:

V_out = A_d(V₁ – V₂) + A_cm(V₁ + V₂)/2

Where:
A_d = Differential gain
A_cm = Common-mode gain

3. Common-Mode Rejection Ratio (CMRR)

The effectiveness of a differential amplifier is measured using CMRR:

CMRR = A_d / A_cm

In dB: CMRR = 20 log (A_d / A_cm)

High CMRR ensures the amplifier rejects external noise (common to both inputs) and only amplifies the useful signal difference.

4. Transfer Characteristics

The transfer curve of a differential amplifier shows how output varies with the differential input (V₁ – V₂). Ideally, it is linear within a certain range.

5. Practical Implementation (BJT Pair)

The most common implementation is using a long-tailed pair of BJTs or MOSFETs. A constant current source in the tail improves CMRR.

6. Applications of Differential Amplifiers

• Operational Amplifiers: Input stage of every op-amp is a differential pair.
• Instrumentation Amplifiers: High precision measurement circuits rely on high CMRR.
• Noise Reduction: Rejects common noise in sensor applications.
• Analog-to-Digital Interfaces: Ensures clean signal conditioning before digitization.

7. Example Calculation

Suppose a differential amplifier has:

• A_d = 1000
• A_cm = 0.5

CMRR = 1000 / 0.5 = 2000

CMRR (dB) = 20 log(2000) ≈ 66 dB

This shows the amplifier rejects common noise by a factor of 2000.

8. Limitations

• Finite CMRR due to transistor mismatch.
• Requires accurate biasing for symmetry.
• Performance degrades at high frequencies.

9. Interview Questions

• Explain the working principle of a differential amplifier.
• Why is CMRR important?
• What is the role of a current source in the tail of a differential pair?
• Where are differential amplifiers used in practical IC design?

Conclusion

Differential amplifiers are the backbone of analog circuits. Their ability to reject noise and amplify only the difference between inputs makes them indispensable in amplifiers, ADCs, and measurement systems. Understanding their working and CMRR is a must for analog design engineers and interview preparation.