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


          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.


subtractor - schematic

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:

eq. 1

          and let’s notice that:

eq. 2

          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:

subtractor - notes

Figure 2: Subtractor with notes.


          Now, we can make some calculations:

eq. 3-8


          Knowing that:

eq. 9


          VOUT from Eq. 8 can be expressed as:

eq. 10-11


          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:

eq. 12-14


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

eq. 15


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

eq. 16-17



subtractor - summary

Figure 3: Subtractor examples of circuits.