In an inverting amplifier, the closed-loop gain is given by the ratio of the feedback resistor to the input resistor with a negative sign. This is

In an inverting amplifier, the closed-loop gain is given by the ratio of the feedback resistor to the input resistor with a negative sign. This is

• A. Rin/Rf
• B. -Rf/Rin
• C. 1 + (Rf/Rin)
• D. 1

Answer: (B)

In an inverting amplifier, the feedback network and the virtual ground at the inverting input set the gain. The non-inverting input is grounded, so the op-amp drives its output to keep the inverting node nearly at 0 V. The input signal Vin through Rin pushes a current into the summing node equal to Vin/Rin. That same current must flow through the feedback resistor Rf to the output, so the current through Rf is Vout/Rf in the opposite direction. Applying Kirchhoff’s current law at the summing node: Vin/Rin + Vout/Rf = 0, which gives Vout = - (Rf/Rin) Vin. Therefore, the closed-loop gain is negative and has magnitude Rf/Rin. That negative sign reflects the inversion, and the magnitude comes from the ratio of the feedback to input resistors.

In an inverting amplifier, the feedback network and the virtual ground at the inverting input set the gain. The non-inverting input is grounded, so the op-amp drives its output to keep the inverting node nearly at 0 V. The input signal Vin through Rin pushes a current into the summing node equal to Vin/Rin. That same current must flow through the feedback resistor Rf to the output, so the current through Rf is Vout/Rf in the opposite direction. Applying Kirchhoff’s current law at the summing node: Vin/Rin + Vout/Rf = 0, which gives Vout = - (Rf/Rin) Vin. Therefore, the closed-loop gain is negative and has magnitude Rf/Rin. That negative sign reflects the inversion, and the magnitude comes from the ratio of the feedback to input resistors.