How it works
The inverting amplifier applies the input signal Vin through R1 to the inverting (−) terminal; the non-inverting terminal is grounded; feedback resistor Rf connects output to the inverting input. Since the op-amp is ideal and has negative feedback, V− = V+ = 0 — the inverting terminal is a virtual ground. Current through R1: I1 = Vin/R1. Since no current enters the op-amp input, all of I1 flows through Rf: If = −Vout/Rf. Setting I1 = If gives Vout/Vin = −Rf/R1. Closed-loop gain ACL = −Rf/R1. Input impedance of the circuit is simply R1, not the op-amp's own Zin, because the virtual ground at the inverting terminal absorbs the input current. Output impedance is essentially zero due to the feedback. Bandwidth = GBW/|ACL|; for 741 GBW = 1 MHz, so gain of 10 gives bandwidth of 100 kHz.
Key points to remember
Closed-loop gain ACL = −Rf/R1; the negative sign indicates 180° phase inversion. Input impedance = R1 — not infinite, unlike the non-inverting configuration. Setting a compensating resistor R2 = R1 ∥ Rf at the non-inverting input minimises output offset due to bias currents; for R1 = 1 kΩ and Rf = 47 kΩ, R2 = 979 Ω ≈ 1 kΩ. Gain-bandwidth product is constant: for μA741, GBW = 1 MHz, so a gain of 100 gives bandwidth of only 10 kHz. To achieve gain of 1000 with flat response, a faster op-amp like the LM318 (GBW = 15 MHz) is needed. Gain error due to finite Aol: actual gain = −(Rf/R1)/(1 + (1+Rf/R1)/Aol), which approaches −Rf/R1 only when Aol >> 1 + Rf/R1.
Exam tip
Every VTU and Anna University paper asks you to derive the gain of an inverting amplifier using the virtual ground concept — state V− = 0, write KCL: Vin/R1 = −Vout/Rf, and conclude ACL = −Rf/R1 for guaranteed marks.