September 4, 2026
Inverting Op-Amp Circuits: Formula, Gain, and Design Examples
Share
Quick Answer: An inverting op amp amplifies a signal while reversing its polarity. The input connects to the inverting terminal through resistor Rin, and feedback resistor Rf connects the output back to that same node. For an ideal inverting op-amp, the voltage gain equals Av = −Rf / Rin.
Electronics students often memorize the formula for an inverting op amp without understanding why it works. An inverting op amp is an operational amplifier circuit that takes an input signal, amplifies it, and flips its polarity at the output. A ratio of two resistors sets the gain, and the circuit depends on a feedback mechanism that holds the inverting input node near a fixed reference voltage. This guide covers how the circuit functions, derives the gain formula, and explains resistor selection, real op-amp limitations, and PCB layout practices.
An op-amp is a high-gain differential amplifier with two inputs and one output: an inverting input (marked −) and a non-inverting input (marked +). In the inverting configuration, the input signal connects to the inverting input through resistor Rin, while feedback resistor Rf connects the output back to the same node. The non-inverting input ties to ground or another fixed reference.
Negative feedback through Rf keeps both input terminals at nearly the same voltage. The inverting input settles near the reference voltage, and the output swings in the opposite direction, so the output polarity ends up reversed from the input.
A schematic showing Vin, Rin, Rf, Vout, both inputs, and the supply rails makes this current path easier to trace than the equations alone.
Tracing what happens at each node is a direct route to understanding why the output flips sign.
The Vin node. This is just the source signal, unaffected by anything downstream. For example, if it's a positive-going voltage, the current pushes from this node through Rin toward the inverting input.
The inverting (−) node. Feedback through Rf holds this node pinned close to the reference voltage (commonly ground) no matter what Vin does. That's the key constraint: this node can't move. So when current arrives here from Rin, it doesn’t accumulate; it goes onward through Rf. For that current to keep flowing through Rf, the far end of Rf (the output) has to sit at a lower potential than this node. If the inverting node is fixed near 0 V, "lower than 0 V" means the output has to go negative. That's the inversion: a positive Vin forces current into a node that can't rise, and the only way to keep that current flowing is for Vout to fall.
The Vout node. The op-amp's output stage swings negative here, pulling the current through Rf and keeping the inverting node pinned at reference. The size of that swing is set by how much voltage drop Rf needs to carry the same current that Rin is delivering. This is where the Rf/Rin ratio in the gain formula comes from.
Flip the sign of Vin and the same logic runs in reverse: current flows out of the inverting node through Rin, so Rf has to supply it from a higher potential, so the output swings positive instead.
When the non-inverting input ties to ground, feedback holds the inverting input close to zero volts, even though no wire connects that node directly to ground. Engineers call this node a virtual ground. It cannot source or sink current the way an actual ground connection can, and the approximation only holds while the op-amp stays within its linear range.
Virtual ground resolves a common beginner mix-up: treating a feedback-created approximation as an actual low-impedance ground connection.
Gain follows directly from the virtual-ground behavior above. For an ideal op-amp within its linear range, the closed-loop voltage gain is:
Av is the voltage gain, Rf is the feedback resistance, and Rin is the input resistance. The negative sign confirms the output inversion.
| Parameter | Value |
|---|---|
| Rin | 10 kΩ |
| Rf | 50 kΩ |
| Gain (Av) | −5 |
| Vin | 0.2 V |
| Vout | −1.0 V |
A 5:1 ratio between Rf and Rin turns a 0.2 V input into a −1.0 V output. Two things limit the ideal result: the output can't exceed the supply rails no matter what the formula predicts, and frequency response reduces achievable gain as signal frequency rises.
A resistor ratio that produces the target gain is only the first step. The absolute values of Rin and Rf affect current draw, noise, and frequency performance in ways the gain formula doesn't capture.
| Rin/Rf values | Effect |
|---|---|
| Too low | Higher current draw, more source/output loading, more power dissipation |
| Too high | More thermal noise, greater bias-current error, parasitic capacitance limits high-frequency performance |
Selecting the op-amp itself matters as much as the resistor values:
The op-amp's own limits set the boundaries the resistors have to work within.
An ideal op-amp has infinite bandwidth, infinite input impedance, and zero output impedance. Real components fall short on each count, and the gaps become design constraints.
| Limitation | What it means |
|---|---|
| Gain-bandwidth product | Available gain drops as frequency increases |
| Slew rate | Caps how fast the output can change |
| Common-mode range | Limits the voltage the inputs can tolerate |
| Output swing/current | Limits how close output gets to the rails and how much current it can supply |
| Offset voltage | Small internal mismatch that moves output away from the ideal value |
| Saturation/clipping | Output flattens once it hits a supply rail |
Single-supply operation adds another constraint: a ground-referenced amplifier may call for a negative output, but a single-supply system can't produce voltage below ground. Such a circuit needs a mid-supply reference plus AC coupling or reference buffering to keep the signal centered, or the design ends up mathematically correct but physically impossible to build.
Choosing between the two configurations depends on the input impedance the source needs and whether polarity inversion matters.
| Attribute | Inverting | Non-Inverting |
|---|---|---|
| Output polarity | Reversed from input | Same as input |
| Input impedance | Approximately equal to Rin | Very high |
| Minimum gain | Can be above or below one | One or greater |
| Multiple inputs | Supports summing | Not directly |
Inverting configurations show up in amplification, attenuation with inversion, audio mixing, sensor conditioning, and active filters. A summing amplifier extends the basic circuit by adding more input resistors to the same inverting node, so the output reflects the weighted, inverted sum of every input.
A correctly calculated inverting op-amp circuit can still fail if the schematic or the PCB layout introduces errors the formula doesn't account for.
PCB layout matters as much as component selection:
Checking the schematic against the mistakes and layout guidance above catches most failures before the board reaches fabrication.
Moving from a calculated gain to a working board takes more than a schematic. Schematic capture tools can pull resistor and op-amp footprints from verified libraries, which reduces footprint mismatches before fabrication. Direct datasheet access also makes it easier to confirm gain-bandwidth product, slew rate, and supply range.
Flux connects schematic capture to PCB layout, so short feedback traces and nearby decoupling stay part of one design file. Collaborative review lets a second engineer check the analog section before fabrication, and revision history tracks what changed as the circuit moves toward production.
Reliable inverting op amp circuit performance depends on the schematic, component selection, and PCB layout working together. Flux brings schematic capture, verified component libraries, and connected PCB layout into one workflow, so an inverting op-amp design moves from calculation to a fabricated board. Start designing with Flux.
An inverting op amp is an operational amplifier circuit where the input connects to the inverting terminal through a resistor, and the output is amplified and reversed in polarity relative to the input.
The inverting amplifier gain formula is Av = −Rf / Rin, where Rf is the feedback resistor and Rin is the input resistor.
Negative feedback holds the inverting input near the reference voltage. A rise at the input pulls the output down to compensate, and a drop pushes the output up.
A virtual ground is a circuit node held near a fixed reference voltage by feedback action (the op-amp's own response to negative feedback), without a direct physical connection to that reference.
Rin and Rf selection starts with the target gain ratio, then accounts for noise, current draw, and parasitic effects at the chosen values, typically low kilohm to low hundreds-of-kilohm.
Yes. Gain depends only on the Rf-to-Rin ratio, so choosing Rf smaller than Rin attenuates the signal while the output stays inverted.
An inverting op amp can work from a single supply, but the circuit needs a mid-supply reference in place of true ground, since a single-supply system can't produce output below ground.
An inverting amplifier reverses the input signal's polarity with input impedance close to Rin. A non-inverting amplifier preserves polarity with very high input impedance.
A complete 555 timer guide covering pinout, internal operation, monostable and astable modes, timing calculations, and practical circuit examples. It also explains component selection and PCB layout tips for reliable designs.
A visual guide to capacitor schematic symbols, polarity markings, and specialized capacitor types. It explains how to choose the correct symbol and footprint to prevent assembly and design errors.
A practical guide to potentiometer wiring, including pin identification, voltage-divider and rheostat configurations, Arduino examples, and PCB footprint considerations. It helps designers avoid common wiring and layout mistakes.
A troubleshooting guide for DXF and SVG board-outline import failures, including open paths, unit mismatches, unsupported curves, and layer mapping issues. It shows how to clean CAD-to-EDA handoffs before PCB fabrication.
A troubleshooting guide for common JLCPCB Gerber upload errors, including unreadable files, missing board outlines, drill-file issues, and Gerber X2 compatibility problems. It explains how to export and verify clean Gerbers before ordering.
A practical guide to designing PCB enclosures around board geometry, clearances, mounting, assembly, and 3D-printed prototyping. It also explains how Flux can generate prototype enclosures directly from a PCB project.
Strategies for sourcing electronic components, managing BOMs, navigating lead times, and planning for component lifecycles to build a resilient hardware supply chain.
A practical guide to Design for Manufacturing (DFM) that helps hardware teams transition from validated prototypes to scalable, production-ready products.
