# Gain formula calculation of inverting amplifier and non-inverting amplifier

Basic textbooks all describe op amp based inverting and non-inverting amplifiers. These amplifiers all have different gain formulas.

Basic textbooks all describe op amp based inverting and non-inverting amplifiers. These amplifiers all have different gain formulas.

The gain of an inverting op amp is the ratio of the feedback resistance to the input resistance, while the gain of a non-inverting op amp is one more term. In some designs, the inverting and non-inverting amplifiers have a simple proportional gain ratio (representing gains greater than 1 and gains less than 1) for simplicity. The non-inverting Amplifier shown in Figure 1 has a simple proportional gain formula: VOUT=VIN(R2/2R1). This gain is proportional to a Resistor ratio and can take any value. R3 has no effect ON gain. If you need a noninverting amplifier with the same gain ratio as the inverting amplifier, the circuit shown in Figure 2 will suffice. Its approximate gain formula is VOUT=VIN (R2/R1).

However, in the circuit, there are some restrictions on the choice of R4. The gain formula for this circuit depends on the value of R4 being much smaller than either R1 or R2. Nonetheless, comparing the gain formula for , with the approximation above, proves that the value of R4 is 1/10 of R1 or R2, or even smaller, and the gain error of the approximation is less than 5%. When calculated, the gain error is equal to R4/2×(1/R1-1/R2). When choosing R4, you should take into account that most op amp ICs have an output current of around 20mA.

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