Inverting Amplifier Gain
Gain of an inverting op-amp.
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How it works
An inverting op-amp uses negative feedback to hold the inverting input at a "virtual ground" when the non-inverting input is grounded, so the input current through R_in must equal the feedback current through R_f. Because the op-amp input draws essentially no current, that current balance forces the output voltage to be a scaled, inverted version of the input. The minus sign means the output is 180° out of phase with the input, and the gain magnitude is set only by the resistor ratio.
When to use it
Use this relation when analyzing or designing inverting op-amp stages in signal conditioning, audio mixing, analog filtering, or sensor interfacing. It is especially useful whenever you need a precise, resistor-controlled voltage gain with inversion.
Worked example, step by step
Given: R_f = 47 kΩ, R_in = 5.6 kΩ, and input voltage V_in = 0.32 V Step 1: Write the gain formula: A_v = -R_f / R_in Step 2: Substitute the values: A_v = -(47,000 / 5,600) Step 3: Compute the ratio: A_v = -8.392857... Step 4: Find the output voltage: V_out = A_v × V_in = (-8.392857...)(0.32) Step 5: Calculate the result: V_out ≈ -2.69 V Final answer: the circuit provides a gain of about -8.39, so a 0.32 V input produces approximately -2.69 V at the output.
Common mistakes to avoid
- Using resistor values in different units incorrectly, such as mixing kΩ and Ω in the ratio
- Forgetting the negative sign and treating the amplifier as non-inverting
- Assuming the gain depends on the op-amp itself rather than the external resistor ratio
Did You Know?
The op-amp, born in analog computers, became the versatile workhorse behind countless amplifiers and filters.
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