## What is a Differential Amplifier?

A **differential amplifier** (also known as a **difference amplifier** or **op-amp subtractor**) is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs. A differential amplifier is an analog circuit with two inputs (V_{1} and V_{2}) and one output (V_{0}) in which the output is ideally proportional to the difference between the two voltages.

The formula for a simple differential amplifier can be expressed:

Where

- V
_{0}is the output voltage - V
_{1}and V_{2}are the input voltages - A
_{d}is the gain of the amplifier (i.e. the differential amplifier gain)

From the formula above, you can see that when V_{1} = V_{2}, V_{0} is equal to zero, and hence the output voltage is suppressed. But any difference between inputs V_{1} and V_{2} is multiplied (i.e. amplified) by the differential amplifier gain A_{d}.

This is why the differential amplifier is also known as a difference amplifier – the difference between the input voltages is amplified.

## Differential Amplifier Circuit

There are two different types of differential amplifier circuits:

- BJT Differential Amplifier – This is a differential amplifier built using transistors, either Bipolar Junction Transistors (BJTs) or Field Effect Transistors (FETs)
- Opamp Differential amplifiers built using Operational Amplifiers

BJT and Opamp subtractor circuits are shown below.

## BJT Differential Amplifier

Figure 1 shows such a BJT differential amplifier circuit made of two BJTs (Q_{1} and Q_{2}) and two power supplies of opposite polarity, V_{CC} and –V_{EE} which uses three resistors among which two are the collector resistors, R_{C1} and R_{C2} (one for each transistor) while one is the emitter resistor R_{E} common to both transistors.

Here the input signals (V_{1} and V_{2}) are applied to the base of the transistors while the output is collected across their collector terminals (V_{o1} and V_{o2}). The circuit diagram for a BJT differential amplifier is shown below:

In this case, if the V_{1} at Q_{1} is sinusoidal, then as V_{1} goes on increasing, the transistor starts to conduct and this results in a heavy collector current I_{C1} increasing the voltage drop across R_{C1}, causing a decrease in V_{o1}.

Due to the same effect, even I_{E1} increases which increases the common emitter current, I_{E} resulting in an increase of voltage drop across R_{E}.

This means that the emitters of both transistors are driven towards positive which in turn implies that the base of Q_{2} would start to become more and more negative.

This results in a decrease of collector current, I_{C2} which in turn decreases the voltage drop across the collector resistor R_{C2}, resulting in an increase in the output voltage V_{o2}.

This indicates that the changes in the sinusoidal signal observed at the input of transistor Q_{1} are reflected as such across the collector terminal of Q_{2} and appear with a phase difference of 180^{o} across the collector terminal of Q_{1}.

The differential amplification can be driven by considering the output in-between the collector terminals of the transistors, Q_{1} and Q_{2}.

## Opamp Differential Amplifier

An Op-Amp operating in differential mode can readily act as a **subtractor amplifier** as it results in an output voltage given by:

Where V_{1} and V_{2} represent the voltages applied at its inverting and non-inverting input terminals (can be taken in any order) and A_{d} refers to its differential gain.

As per this equation, the output of the Op-amp must be zero when the voltages applied at its terminals are equal to each other.

However, practically it will not be so as the gain will not be the same for both of the inputs.

Thus, in a practical scenario, the mathematical expression for the output of the subtractor amplifier can be given as:

Where A_{C} is called the common-mode gain of the amplifier. Thus, functionally-good difference amplifiers are expected to exhibit a high common-mode rejection ratio (CMRR) and high impedance.

However, it is to be noted that an Op-Amp can be suitably configured to result in a much practical **differential amplifier**, as shown in Figure 2.

If closely observed, one can note that this circuit is just a combination of inverting and non-inverting amplifiers.

Hence its output voltage will be equal to the sum of the output voltages produced by the Op-Amp circuit operating as an inverting amplifier and the Op-Amp circuit operating as a non-inverting amplifier. Thus, one gets:

Now, if R_{1} = R_{2} and R_{3} = R_{f}, then:

This implies that the gain of the **differential amplifier** circuit shown in Figure 2 is given by .

In addition, it is to be noted that the basic circuit shown in Figure 2 can be modified in many ways resulting in various circuit designs including the Wheatstone bridge differential amplifier, light-activated **subtractor amplifier,** and instrumentation amplifier.

These devices are used as motor and/or servo controllers, signal amplifiers, analog multipliers, switches, volume controllers, automatic gain controllers, amplitude modulators, etc., and cover a wide range of applications including those in instrumentation systems, microphones, analog to digital converters and myriad applications.