Differential Amplifier – Voltage Subtractor

An op-amp can provide a wide range of mathematical operations depending on its input configurations. A standard operational amplifier is used in two common configurations: inverting and non-inverting op-amp configurations. However, in both of these configurations, a single voltage input is applied while the other is taken as a reference. The differential op-amp makes use of both the input voltages. We will discuss in detail the operation, circuit diagram, mathematical implementations, and parameters of the differential amplifier.

Differential Amplifier – Voltage Subtractor

When two distinct voltage inputs are applied to the operational amplifier’s two terminals, it functions as a differential amplifier. The amplifier in such a configuration subtracts the voltages at inputs and then amplifies its voltage difference. In the differential amplifier case, two different voltages are applied as shown below:

The major reason for including the feedback path is to achieve a controllable voltage gain. Without the feedback path, the open loop gain may reach a very high indeterminate value and the operation of the op-amp would not be as per the design requirements. The addition of a feedback path with a feedback resistor R₃ along with voltage dividers R₂ & R₄ keeps the voltage gain within the controllable limits.

In the above figure, V₊ denotes non-inverting terminal voltage while V_– is inverting terminal voltage. On the non-inverting terminal, resistances R₂ and R₄ act as voltage divider circuits with V₂ input voltage and V₊ as the output voltage. The V_out =V₊ for the above voltage divider configuration at the non-inverting terminal is given by:

In the above figure, the current entering node and leaving node shall be the same; so:

Applying KCL:

The op-amp tends to maintain input voltages at the same value when applied to its two terminals:

Using the expression of V₊from the first equation above in KCL:

If resistor values are the same; R₂=R₁:

The differential op-amp gain now be calculated as the ratio of V_out to different input voltages V₁ – V₂:

Common Mode Voltage Gain

Considering the two input voltages are the same, then in this case it looks obvious that the voltage subtractor shall provide a zero output. However, in practical cases, there still exists a minor voltage output in ranges of microvolts when common input signals are applied.

The common mode op-amp gain is given by:

Common Mode Rejection Ratio

Common mode input voltages are not desired in differential amplifiers. Op-amps tend to reject common mode signals, and this ability to oppose such signals is defined in terms of CMRR.

The ratio of differential mode gain (A_d) to common mode gain (A_c) is defined as the common mode rejection ratio, as given below:

CMMR can also be expressed in decibels (dB):

Output Voltage in Common Mode Configuration

Similarly, in common code, the common voltage expression can also be derived as:

The output voltage of the differential op-amp shall be modified as:

Example

Calculate the output voltage of differential op-amp with input voltages V₁=400µV & V₂=300µV, A_d=7000, CMRR=500 as shown in the below configuration.

As we know:

In common mode, V_OUT is given by:

For V_DM and V_CM, we can calculate as:

Substituting in V_OUT:

Conclusion

The differential operational amplifier subtracts input voltages when two different voltages are applied at its two terminals. The output is an amplification of the difference in input voltages. In this tutorial, we discussed differential amplifiers in detail.