Tags: feedback, opamp, operational amplifier, subtractor, voltage divider

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Schematic of the subtractor is presented in Fig. 1. Two input voltages V1 and V2 are applied through resistors to negative and positive inputs of operational amplifier. A voltage divider is created by R3 and R4 resistors, while R1 and R2 resistors serve as a feedback loop.

Figure 1: Subtractor.

Let’s make some calculations to see how VOUT output voltage depends on V1 and V2 input voltages.

Firstly, let’s assume that:

and let’s notice that:

where I1, I2, I3 and I4 are currents flowing through R1, R2, R3 and R4 resistors, respectively.

Fig. 2 presents the subtractor schematic with marked voltages:

Figure 2: Subtractor with notes.

Now, we can make some calculations:

Knowing that:

VOUT from Eq. 8 can be expressed as:

Eq. 11 presents a sophisticated dependence of VOUT output voltage on V1 and V2 input voltages. However, let’s see two examples.

Firstly, when R1 = R3 and R2 = R4:

Additionally, when R2 = R1 (thus R1 = R2 = R3 = R4), Eq. 14 reduces to:

Secondly, it is interesting to notice that when R1 = R4 and R2 = R3, Eq. 11 is equal to:

Summarizing:

Figure 3: Subtractor examples of circuits.