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

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Schematic of the **subtractor** is presented in Fig. 1. **Two input voltages** V_{1} and V_{2} are applied through resistors to negative and positive inputs of **operational amplifier**. A **voltage divider** is created by R_{3} and R_{4} resistors, while R_{1} and R_{2} resistors serve as a **feedback loop**.

Figure 1: Subtractor.

Let’s make some calculations to see how V_{OUT} output voltage depends on V_{1} and V_{2} input voltages.

Firstly, let’s assume that:

and let’s notice that:

where I_{1}, I_{2}, I_{3} and I_{4} are currents flowing through R_{1}, R_{2}, R_{3} and R_{4} resistors, respectively.

Fig. 2 presents the subtractor schematic with marked voltages:

Figure 2: Subtractor with notes.

Now, we can make some calculations:

Knowing that:

V_{OUT} from Eq. 8 can be expressed as:

Eq. 11 presents a sophisticated dependence of V_{OUT} output voltage on V_{1} and V_{2} 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.

subtractor circuit using OP AMP3 years ago