## What is a differential amplifier?

A device that amplifies the difference between two input voltages is called a differential amplifier. It also suppresses those voltages which are common to two inputs. It is a type of amplifier that has two inputs one is positive that is ${{V}_{in}}^{+}$ and the other is negative that is ${{V}_{in}}^{-}$ and one output ${V}_{out}$ . The output here is proportional to the difference between two voltages and is given by the equation-

where A = Gain of the amplifier

## Theory

For an ideal differential amplifier, the output is given by-

where, ${A}_{d}$= Differential gain and ${{V}_{in}}^{+}$and ${{V}_{in}}^{-}$ are the input voltages (µV). In practical situations, the gain is not equal to the two inputs. So, if ${{V}_{in}}^{+}$and ${{V}_{in}}^{-}$are equal then output is never equal to zero like an ideal situation. The output of a differential amplifier is given by one more equation which is realistic in nature-

where, ${A}_{c}$= common-mode gain of the amplifier.

A low common-mode gain is generally desired because differential amplifiers are used to null out the bias voltages or noise signals that appear in both the positive and negative inputs. The ratio between two types of gain, that is differential-mode gain and common-mode gain, is called as common-mode rejection ratio or CMRR. The voltages that are common to both the inputs are canceled by the differential amplifier and the ability is decided by this ratio and is given by the following equation-

In an ideal differential amplifier, ${A}_{c}$ = zero and the

## Configurations

There are two amplifying stages with common degeneration in a differential amplifier.

### Differential output

A differential amplifier has two types of inputs and two types of outputs. The transistor pair differential amplifies the two inputs. The differential amplifier may be fed with two input pulses or signals or else one input can be grounded so that a phase spitter circuit forms. A floating load or another amplifier stage with different inputs can be driven with an amplifier that has differential output.

### Single-ended output

The other output can be disregarded if the differential output is not desired and only one output can be used and this configuration is called as single-ended output. In comparison to differential output the gain is half here. A differential to single-ended converter can be used to avoid sacrificing the gain. This is done with the help of current mirror.

### Single-ended input

If one of the inputs p-p of the difference amplifier is fixed to a reference voltage or is grounded then the differential amplifier can be used as an amplifier with a single-ended input. This arrangement is the type of cascaded common-base stages or also as a buffered common-base stage.

## Operation of a differential amplifier

Four types of isolated modes are described below to explain the circuit operation. Some of them act simultaneously and also their effects are superimposed in practical situations.

### Biasing

A differential amplifier is biased from the side of the emitter by injecting the total amount of quiescent current in contrast with those classic amplifying stages that are biased from the side of the base and so they are highly dependent on current gain $\beta$. The transistor acts as a voltage stabilizer due to the series of negative feedback. To pass the quiescent current through, their collector-emitter junctions forces them to adjust to their ${V}_{\mathrm{BE}}$ voltages. The quiescent current depends slightly on the transistor's current gain $\beta$ due to the negative feedback. The quiescent current is usually evoked by the biasing base currents. This biasing base current comes from the ground, passes through the input sources, and enters the bases. To not create a significant voltage drop across them, the sources have to be low resistive enough and have to be DC to ensure paths for the biasing current. Otherwise between the bases and the ground another additional DC element needs to be connected.

### Common mode

The two voltage emitter or followers cooperate with each other while working together on the common high-resistive emitter load. The voltage of the common emitter point altogether increases or decreases the voltage. Keeping up the constant total resistance between the two supply rails, the dynamic load helps them in the same direction as the input voltages by changing their instant ohmic resistance. There is 100% negative feedback. The collector currents and the total current do not change but the two input base voltages and the emitter voltage change suddenly. Therefore the output collector voltage does not change as a result.

### Differential mode

#### Normal

The two voltage followers oppose each other in differential mode. One tries to increase the voltage of the point of the common-emitter whereas the other tries to decrease it and vice versa. The common voltage points behave as a virtual ground with a magnitude determined by the common-mode input voltage and do not change its voltage. The high resistance emitter is shunted by the other low resistance emitter follower and it does not play any role. When the input base voltage changes, the emitter voltage does not change at all so there is no negative feedback. The two emitters are mutually grounded by the transistor. So even if they are common-collector stages, they act as common-emitter stages respectively with the maximum amount of gain.

#### Overdriven

The transistor driven by the lower input terminal voltage is turned off and the positive supply rail is reached by its collector voltage if the input terminal differential voltage changes significantly. All the current is driven by the other transistor. The transistor will saturate if the resistor at the collector is relatively large. The emitter can follow the input signal without any saturation with a relatively small collector resistor and moderate overdrive. This mode is generally used in emitter-coupled logic (ECL) gates and differential switches.

#### Breakdown

The base to emitter junction of the transistor is driven by the lower input voltage breaking down if the input voltage continues to increase and exceeds the base to emitter breakdown voltage. A huge and unlimited amount of current will flow through the diode bridge between the two input sources and will damage them if the input sources are low resistive in nature.

## Operational amplifier (Op-Amp) as a differential amplifier

An op-amp type of differential amplifier circuit has very high input impedance, very high-gain, and low output impedance. By applying negative feedback, an op-amp type of differential amplifier can be built with predictable and stable gain. Several simpler differential amplifiers are included in some kinds of the difference amplifier. The op-amp's two inputs are called inverting and non-inverting terminals. One terminal input is connected to the ground and the other terminal is used to amplify the other input. The resistors in op-amp type differential amplifiers are input and output resistors and feedback resistors.

## Context and Applications

• Bachelors in Electrical Engineering
• Bachelors in Electronics and Telecommunication Engineering
• Masters in Electrical Engineering
• Masters in Electronics and Telecommunication Engineering

## Practice Problems

1. What type of common-mode gain is generally desired in differential amplifiers?

1. low common-mode gain
2. high common-mode gain
3. Both a and b
4. None of these

Explanation: A low common-mode gain is generally desired because differential amplifiers are used to null out the bias voltages or noise signals that appear in both the positive and negative inputs.

2. What is the common-mode gain for an ideal differential amplifier?

1. Zero
2. Infinite
3. One
4. None of these

Explanation: The common-mode gain for a differential amplifier is always zero.

3. With the help of what technique the differential to single-ended converter can be used to avoid sacrificing the gain?

1. Wheatstone-bridge
2. Current mirror
3. DC-coupled amplifier
4. Open-loop amplifier

Explanation: With the help of the current mirror technique the differential to single-ended converter can be used to avoid sacrificing the gain.

4. What type of input impedance does an op-amp have?

1. High input impedance
2. Low input impedance
3. Closed-loop impedance
4. None of these

Explanation: An op-amp type of differential amplifier has very high input impedance, very high gain, and low output impedance.

5. What is true in the case of single-ended input?

1. One input is used and the other is grounded
2. Both the inputs are used
3. Both the inputs are grounded
4. None of these

Explanation: If one of the inputs of the difference amplifier is fixed to a reference voltage or is grounded then the differential amplifier can be used as an amplifier with a single-ended input.

• Gilbert cell
• Instrumentation amplifier
• Emitter-coupled logic
• Op-amp differential configuration

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