Understanding the Subtractor Op-Amp Derivation: A Detailed Guide
When it comes to operational amplifiers, the subtractor configuration is a fundamental circuit that plays a crucial role in various applications. In this article, we will delve into the derivation of the subtractor op-amp, exploring its working principles, advantages, and practical applications. By the end of this guide, you will have a comprehensive understanding of this essential circuit.
What is a Subtractor Op-Amp?
A subtractor op-amp is a type of operational amplifier circuit that subtracts the voltage of one input from the voltage of another input. It is widely used in signal processing, analog computing, and control systems. The subtractor circuit is formed by connecting two input terminals of the op-amp to the inverting and non-inverting inputs, respectively, and connecting the output terminal to the inverting input through a feedback resistor.
Derivation of the Subtractor Op-Amp
The derivation of the subtractor op-amp circuit can be achieved by analyzing the voltage at the inverting and non-inverting inputs of the op-amp. Let’s assume that the voltage at the inverting input is V鈭?/sub> and the voltage at the non-inverting input is V+. According to the virtual ground concept, the voltage at the inverting input is equal to the voltage at the non-inverting input, i.e., V鈭?/sub> = V+.
Now, let’s consider the voltage at the inverting input. The voltage across the feedback resistor (R2) is given by V鈭?/sub> – Vout, where Vout is the output voltage of the op-amp. Since the voltage at the inverting input is equal to the voltage at the non-inverting input, we can write the following equation:
| Term | Value |
|---|---|
| V鈭?/sub> | V+ |
| V鈭?/sub> | Vout – V鈭?/sub> |
Now, let’s consider the voltage at the non-inverting input. The voltage across the feedback resistor (R1) is given by V+ – Vout. Since the voltage at the inverting input is equal to the voltage at the non-inverting input, we can write the following equation:
| Term | Value |
|---|---|
| V+ | Vout – V+ |
By combining the two equations, we can derive the following expression for the output voltage (Vout):
Vout = (V+ – V鈭?/sub>) (R1 / R2)
This equation shows that the output voltage of the subtractor op-amp is proportional to the difference between the two input voltages and the ratio of the feedback resistors (R1 and R2).
Advantages of the Subtractor Op-Amp
The subtractor op-amp has several advantages that make it a popular choice in various applications:
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High input impedance: The input impedance of the subtractor op-amp is very high, which means that it draws minimal current from the input sources.
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Low output impedance: The output impedance of the subtractor op-amp is very low, which ensures that the output voltage is stable and accurate.
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High common-mode rejection ratio (CMRR): The subtractor op-amp has a high CMRR, which means that it can reject common-mode noise and interference effectively.
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High accuracy:
