Op-Amp Inverting Amplifier

Analyzing ideal op-amp circuits using virtual short and KCL

Golden Rule: Use two ideal op-amp rules: (1) V⁺ = V⁻ (virtual short), (2) no current flows into the input terminals. Apply KCL at the inverting node.

• Step 1: Apply the virtual short principle — With negative feedback, the op-amp drives its output to force V⁺ = V⁻. For the inverting configuration: V⁺ = 0 V (grounded non-inverting input), so V⁻ = 0 V. This node is called a virtual ground.
• Step 2: Apply KCL at the inverting node — Current from Vin through R1: I1 = (Vin − 0)/R1 = Vin/R1. Current through Rf into the output: If = (0 − Vout)/Rf. By KCL at V⁻: I1 + If = 0 (no current into op-amp terminal).
• Step 3: Solve for the gain — From KCL: Vin/R1 = Vout/Rf → Vout = −(Rf/R1)·Vin. The gain is −Rf/R1. The negative sign indicates phase inversion.