**Introduction**

A differential Amplifiers are most extensively used building blocks in the analog integrated circuit design. A differential amplifier is basically an electronic circuit which consists of two inputs, inverting and non-inverting input operated in a negative feedback configuration. The differential amplifier basically amplifies the difference between the applied input voltages in these two input terminals and rejects any common signal to these two input terminals

Basically, all operational amplifiers are Differential Amplifiers because all of them have the same input configuration. If an input voltage signal is applied on one of the input pin and one more voltage signal is applied to the other pin rather than being grounded, the resultant output voltage proportionate to the variance between the two input voltages connected in the two respective input terminals.

**Construction and working**

Consider the circuit, which is shown in fig (a), with inputs V_{i1} and V_{i2}. To analyze the circuit, we will use the concept of superposition and virtual short. Fig (b) demonstrate the circuitry with V_{i2} = 0. No current will flow in R_{3} and R_{4}; therefore, V_{2a} = 0. The resulting circuit will behave as an inverting amplifier so,

The difference amplifier in the above circuit consists of both inverting and non-inverting amplifier configuration.

Whereas, if the inverting pin is grounded, the circuit acts as a non-inverting amplifier, as shown in the respective circuit diagrams. When the inverting input terminals are grounded, R_{2}, and R_{1} functions as the feedback components connecting the output terminal and the inverting terminal and a suitable feedback condition is achieved for the non-inverting amplifier.

Fig (c) shows the circuit with V_{i1 }= 0. Now, the current of the op-amp is 0. So, R_{3} and R_{4} form a voltage divider. Therefore,

From the concept of virtual short we get, V_{1b} = V_{2b} and the circuit becomes a non-inverting amplifier, for which

Substituting in the above equations, we obtain

Or

Since the net output voltage is the sum of individual terms, we have

V_{0 }= V_{01 }+ V_{02}

Or

A property of an ideal differential amplifier is that the output voltage is zero when V_{i1 }= V_{i2}. On analysis of the last equation, this condition is met if

The output voltage is then,

We can appropriately add supplementary resistors in parallel connection with the input resistors as per our necessity, and the differential amplifier circuit can be configured to either add or subtract it as per our need.

**Some important terms related to differential amplifier**

**Differential input resistance**:

In the figure, we have set the condition that and have set R_{1 }= R_{3} and R_{2 }= R_{4}. The input resistance is then defined as,

Taking into account the concept of virtual short, we can write the following loop equation,

V_{i }= iR_{1 }+ iR_{1} = i(2R_{1})

Therefore, the input resistance is R_{i }= 2R_{1}

**Common-mode input signal**:

: In the ideal difference amplifier, a common mode input Vcm would make the inputs (V_{i1} + V_{cm}) and (V_{i2} + V_{cm}), i.e., gets added to each of the input applied voltages and hence, it will get cancelled out when the difference of the two input voltages are being taken and amplified.

The output V_{0 }is zero when V_{i1 }= V_{i2}. However, if these resistor ratios are not precisely equal i.e.

, then, as a result, the common-mode voltage V_{cm} will not cancel out completely.

As practically it is impossible to have resistor ratios of perfectly exact values, it is likely that some common-mode output voltage will be present.

When V_{i1 }= V_{i2}, the input is called a common-mode input signal. The common-mode input voltage can be expressed as

the common mode gain can then be expressed as,

**Common Mode Rejection Ratio (CMRR): **

The CMRR can be explained as the modulus value of the ratio of differential gain to common-mode gain. Basically, it is the capability of a differential amplifier to reject input signals which are in common mode.

** **CMRR =

Generally, the CMRR is expressed in dB,

CMRR(dB) =

In an ideal world, the common-mode rejection ratio is infinite. In the actual differential amplifier case, we desire CMRR to be as large as possible.

**Applications of Differential Amplifier**

**Wheatstone Bridge Differential Amplifier**

In this case, the resistors are arranged in a Wheatstone (resistive) bridge such a manner, can works as a differential voltage comparator by comparing the input voltages.

When a fixed reference input voltage is applied on one end of the Wheatstone bridge network and a thermistor or a light-dependent resistor (LDR) on the other end of the network, then the circuit can be used to detect different levels of temperature or light intensity. The output voltage of this differential operational amplifier circuit is a linear function of the differences in the active end of the circuit in which is the thermistor or LDR.

A Wheatstone bridge differential circuitry utilized to calculate the value of the unknown resistance by pro tem as a comparator between the input voltages across the individual resistances.

**LIGHT-SENSITIVE DIFFERENTIAL AMPLIFIER**

The light-dependent differential circuit works as a light-dependent switch, which will either gives the output as “on” or “off” with the help of a relay. The applied voltage at V1 sets the amplifier’s trip point (provides the threshold value), and a variable resistance acting as a potential meter VR_{2} is used for hysteresis switching.

On the inverting terminal of the differential amplifier, a standard light dependant resistor is connected, which changes its value of resistance value depending on the amount of light on its incident on it. The photodiode resistance present in the LDR is proportional to the light level and decreases with increasing intensity of light, and hence, the voltage level at point V2 will also vary and depending on whether it is above or below the threshold point, the variable resistor VR_{1} will indicate its value.

Now, as the light incidents on the light-dependent resistor (LDR), on the basis of its intensity, whether it exceeds or remains below the set threshold value at the non-inverting input terminal V1, the output shows ON or OFF.

The light level trip or threshold value position can be adjusted with the help of the potentiometer VR_{1} and the switching hysteresis potentiometer VR_{2}. Therefore in this way, a light-sensitive switch can be made using a differential amplifier.

The circuit can be configured to detect changes in temperature, by replacing the VR_{1} and the LDR, with a thermistor and a suitable variable resistor to detect heat or cold. The disadvantage of a differential amplifier is that the input impedance’s are much lower as compared to that of the other operational amplifier circuit configurations. A differential amplifier circuit works well for low impedance sources but not for high impedance sources. By using a Unity Gain Buffer Amplifier, this problem can be overcome.

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