In a transimpedance amplifier, Vout is proportional to the input current with a negative sign: Vout = -Iin × Rf.

In a transimpedance amplifier, Vout is proportional to the input current with a negative sign: Vout = -Iin × Rf.

• A. Vout = -Iin × Rf.
• B. Vout = Iin × Rf.
• C. Iout = gm Vin.
• D. Vout = Vin × Aol.

Answer: (A)

A transimpedance amplifier converts an input current into a proportional output voltage with a 180-degree phase inversion. In this inverting configuration, the op-amp keeps the summing node at virtual ground (near zero volts). The input current Iin must flow through the feedback resistor Rf, creating a voltage drop. The current through Rf is (0 − Vout)/Rf = −Vout/Rf, which must equal the input current Iin. Solving gives Vout = − Iin × Rf. The negative sign comes from the inversion of the inverting input: as input current enters the summing node, the output swings negative to keep the node at virtual ground. This is the defining relation: a current-to-voltage converter where the gain is set by the feedback resistor. The other forms don’t describe this setup: one omits the necessary inversion, another describes a transconductance stage (Iout = gm Vin), and the last refers to open-loop gain, not the closed-loop current-to-voltage conversion.

A transimpedance amplifier converts an input current into a proportional output voltage with a 180-degree phase inversion. In this inverting configuration, the op-amp keeps the summing node at virtual ground (near zero volts). The input current Iin must flow through the feedback resistor Rf, creating a voltage drop. The current through Rf is (0 − Vout)/Rf = −Vout/Rf, which must equal the input current Iin. Solving gives Vout = − Iin × Rf. The negative sign comes from the inversion of the inverting input: as input current enters the summing node, the output swings negative to keep the node at virtual ground.

This is the defining relation: a current-to-voltage converter where the gain is set by the feedback resistor. The other forms don’t describe this setup: one omits the necessary inversion, another describes a transconductance stage (Iout = gm Vin), and the last refers to open-loop gain, not the closed-loop current-to-voltage conversion.