## What is differential amplifier ? – Differential amplifier theory

# What is differential amplifier ? – Differential amplifier theory

## What is differential amplifier

The differential amplifier is one of the important circuits in analog systems and circuit designs. It is an electronic amplifier that has two inputs and amplifies the voltage difference between those inputs. There are mainly two types of differential amplimers; ones made using Op-Amps and ones made using transistors (BJTs or FETs). Among these, the commonly used differential amplifier is the amplifier made using Op-Amps because they are suitably configured to result in a much practical differential amplifier.

**Operation of Differential amplifier**

In the differential amplifier made using BJTs, input signals (V1 and V2) are applied to the base terminal of the transistors and the outputs are collected from the collector terminal of the transistors.

Considering the differential amplifier built using BJTs, if the input voltage V1 at transistor Q1 is sinusoidal, then as V1 goes on increasing, the transistor Q1 starts conduction which results in a large collector current in Q1 increasing the voltage drop across Rc1, causing a decrease in output voltage V01. Due to the same effect, even IE1 increases which increases the common emitter current (IE1) resulting in an increase of voltage drop across emitter resistor (RE).

Therefore, this shows that the emitter terminals of two transistors Q1 and Q2 are moving to the positive that in turn indicates a more negative base terminal at the transistor Q2. The above process leads to less amount of collector current(IC2) in transistor Q2 which reduces the voltage drop through the collector terminal resistor (RC2) of transistor Q2 and increases in the voltage output . Therefore, this evidence supports the conclusion of the fluctuations in the input sinusoidal signal of the transistor Q2 is reflected as the same through the collector terminal of transistor and appear with a phase difference of 180 degrees through the collector of the transistor Q1. The differential amplification procedure can be implied by observing the outputs of the collectors of the two transistors Q1 and Q2. There are mainly four configurations for the differential amplifiers. They are as follows;

- Single input unbalanced output
- Single input balanced output
- Dual input unbalanced output
- Dual input balanced output

The differential amplifier using op-amp is a combination of both inverting and non-inverting amplifiers. When the non-inverting terminal is connected to the ground, the circuit operates as an inverting amplifier then the input voltage signal V1 is amplified by the gain of -(Rf/R1). When the input terminal is connected to the ground the circuits operate as a non-inverting amplifier.

Input voltage V2 is potentially divided across the resistors R2 and R3 to give VR3, and then VR3 is amplified by (Rf+R1)/R1.

With V2 = 0,

With V1 = 0,

If the input resistances R1 = R2 and Rf = R3, then V02 = [ Rf/R1 ] * V2

When both the input signals V1 and V2 are present, the output voltage is,

V0 = V02 + V01 = -V1 * (Rf + R1) / R1 + (Rf / R1) * V2

V0 = -(Rf / Rf) * [V1 – V2]

Differential gain (AD) is the gain obtained at the output signal with respect to the difference in the input signal (V1 – V2) is applied. Therefore, we can conclude that the gain (AD) of the differential amplifier circuit which is made using Op-Amp is given by -(Rf/R1).

## Differential amplifier gain

The output of an ideal differential amplifier is denoted as follows:

V0 = AD * [(VIN+) – (VIN-)]

Where AD is Differential amplifier gain and VIN+ and -VIN- are the input voltages.

But in practical conditions the differential gain is denoted as follows:

V0 = AD * [(VIN+) – (VIN-)] + AC * [(VIN+) + (VIN-)]/2

Where AC is the common mode gain of the amplifier.

## Input resistance

The problem arises when selecting the difference amplifier resistors as R1 = R2 and Rf = R3 is that the input resistances of the inverting amplifier and non-inverting amplifier are not equal.

This difference in the input resistances results in one of the input signals to be more amplified than the other. The output equation of the difference amplifier V0, can be obtained by making the ratio R3/R2 the same as Rf/R1, instead of making R1 = R2 and Rf = R3.

If the signal source resistances are smaller than the input resistances the input resistance difference will not cause a serious issue. Also, it is usually desirable to have R1 = R2 and Rf = R3, which will reduce the input offset voltages.

## Common mode Input

The differential amplifier amplifies the difference between the two input voltages. Therefore, in ideal conditions, common mode input VCM will get canceled out since the inputs voltages are (V1 + VCM) and (V2+ VCM).

When considering the practical conditions, the output depends upon the ration of the input resistances. When these resistor ratios are not equal, one input voltage is amplified by a considerable amount than the other input. Therefore, the common mode voltage VCM will not be completely canceled. Because it is practically difficult to match resistor ratios perfectly, so the presence of common mode output voltage is inevitable in practical scenarios.

## Common Mode Rejection Ratio (CMRR)

Common mode rejection ratio is the ability of a differential amplifier to reject common mode input signals. This can be mathematically expressed as the ratio of the differential voltage gain of the differential amplifier to its common mode gain.

Common Mode Rejection Ratio (CMRR) = | AD / AC |

When considering an ideal amplifier, the common mode voltage gain of a differential amplifier is zero and CMRR is infinite. But in real life implantations, it is not so and has a finite value.

## Characteristics of a Differential Amplifier

A differential input signals results in variations in the output currents and voltages, whereas a common mode input sign does not result in any output current/voltage variations. Above mentioned characteristics of a differential pair is as shown in the diagram below.

## Differential Amplifier Equation

According to the above diagram differential amplifier equation can be expressed as follows:

V0 = -(R3 / R1) * [V1 – V2]

If all the resistors have the same resistor values the circuit will become a unity gain differential amplifier. Then the voltage gain will be exactly one or unity. Therefore, the output voltage expression will be:

V0 = -[V1 – V2]

## Differential amplifier applications

Differential amplifiers are used in circuits which support series negative feedback, whereas one input is used for the feedback and other one for the input signal. Another general use of the differential amplifier is it can be used as a volume control circuit. We can observe these circuits mostly in motor or servo controllers and signal amplification applications.

### Fully differential amplifier

A fully differential amplifier also known as FDA is a DC-coupled high-gain electronic voltage amplifier having differential inputs and differential outputs. In its normal usage, the output of the fully differential amplifier is controlled by two feedback paths which, because of the amplifier’s gain is gain, almost completely determine the output voltage for any specified input.

Fully differential amplifiers have special use as part of a mixed-signal integrated circuit because it can reject common mode noise such as power supply disturbances.

A fully differential amplifier is used in many modern high-precision analog to digital converters, to convert an analog signal into a form more suitable for driving into an analog-to-digital converter.

Real fully differential amplifiers have limitations such as DC imperfections, AC imperfections, nonlinear imperfections and power considerations.

### BJT differential amplifier

As shown in diagram V1 and V2 are the two inputs and V01 and V02 are the outputs for the differential amplifier built using BJTs. The emitters of the two transistors are connected to a common emitter resistor RE, because of that the two outputs get affected by the common emitter VCC and the VEE supplies voltage to the circuit. This circuit also works without any errors with a single voltage supply. Working of this amplifier is briefly discussed at the beginning of the article.

### Single ended differential amplifier

Single ended differential amplifiers can be made when the output voltage is taken out from the connection point of C. This output is one times smaller than the output gives by the normal differential amplifier. When the increase of input voltages occurs, in both ends collector voltages reduces, therefore the common mode signal cannot be suppressed when the signal ended outputs. But increasing emitter resistance will increase negative feedback to the common mode signals and also the suppression of the output.

### Differential amplifier as a comparator

A differential amplifier circuit can be also used as a comparator circuit, since it can be configured to either addition or subtraction of the input voltages, by suitably adding more resistors in parallel with the input resistors. Wheatstone bridge differential amplifier and Light activated differential amplifier are some of the examples for this.

### Wheatstone bridge differential amplifier

In the figure below circuit design of a Wheatstone bridge differential amplifier can be observed. This circuit behaves as a differential voltage comparator as discussed previously.

The differential amplifier circuit can detect high or low levels of temperature (or intensity of light) as the output voltage becomes a linear function of the changes in the active leg of the resistive bridge network, by connecting one input to a fixed voltage and the other input to a thermistor or a light-dependent resistor.

Another use of the Wheatstone bridge differential amplifier is to find the resistance values of unknown resistors in the resistive ridge network. This can be done by comparing the input voltages across the resistors in the resistive ridge network.

### Light Activated Differential Amplifier

A circuit which acts as a light-dependent switch is shown in the diagram below. The circuit turns the output relay either switch ON or switch OFF as the intensity of the light falling upon the light-dependent resistor exceeds or falls below a given value at the non-inverting input terminal.

The voltage at the non-inverting terminal (V2) is determined by the variable resistor VR1. The resistors R1 and R2 act as a potential divider in the connected network. A fixed reference voltage is applied to the inverting input (V1), through the resistors R1 and R2.

Circuit of the light-dependent switch can be modified to sense variations in temperature, simply by replacing the light-dependent resistor by a thermistor. By interchanging the positions of light-dependent resistor/thermistor and resistor VR1, the circuit can be made to detect dark or light and heat or cold.

**Differential Amplifier – Tasks for students**

If you are a student or simply want to learn how to solve Differential Amplifier tasks, please visit **this section** of our website where you can find a wide variety of electronic tasks.