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.

 

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

 

          Summarizing:

subtractor - summary

Figure 3: Subtractor examples of circuits.