Explain the transfer characteristics of differential amplifier.

Transfer Characteristics of Differential Amplifier

The differential amplifier is a fundamental building block in analog circuits. It is widely used in various applications due to its ability to amplify the difference between two input signals while rejecting common-mode signals. The transfer characteristics of a differential amplifier describe the relationship between the output voltage and the differential input voltage.

Small-Signal Analysis

To analyze the transfer characteristics of a differential amplifier, we consider a simplified model consisting of two input transistors, Q1 and Q2, and a current source, I. The input signals are applied to the bases of Q1 and Q2, and the output voltage is taken across the collector resistors, RC.

In the small-signal analysis, we assume that the transistors operate in the active region and that the collector current is proportional to the base-emitter voltage. Under these assumptions, the differential input voltage, Vd, is given by:

Vd = Vb1 - Vb2

Where Vb1 and Vb2 are the base voltages of Q1 and Q2, respectively.

The output voltage, Vo, is related to the differential input voltage by the following equation:

Vo = Ad * Vd

Where Ad is the differential gain of the amplifier.

The differential gain is determined by the circuit parameters, including the transistor characteristics and the feedback resistors. It is typically expressed as:

Ad = gm * RC

Where gm is the transconductance of the input transistors.

Common-Mode Rejection Ratio (CMRR)

An important characteristic of a differential amplifier is its ability to reject common-mode signals. Common-mode signals are those that appear simultaneously at both inputs. They are often caused by noise, power supply variations, or ground loops.

The common-mode rejection ratio (CMRR) is defined as the ratio of the differential gain to the common-mode gain. It is expressed in decibels (dB) and is given by:

CMRR = 20 * log(Ad / Acm)

Where Acm is the common-mode gain.

A high CMRR is desirable in differential amplifiers to ensure that the output is insensitive to common-mode signals.

Transfer Curve

The transfer curve of a differential amplifier is a graphical representation of the relationship between the output voltage and the differential input voltage. It is typically a straight line with a slope equal to the differential gain.

The transfer curve can be shifted vertically by adjusting the bias current of the amplifier. This allows the amplifier to be used for various applications, such as signal amplification, level shifting, and voltage comparison.

Conclusion

The transfer characteristics of a differential amplifier are essential for understanding its behavior and performance. By analyzing the small-signal model, we can determine the differential gain, common-mode rejection ratio, and transfer curve of the amplifier. These characteristics are crucial for designing and optimizing analog circuits.