Inverting Op-Amp: Gain, Virtual Ground and Design

The inverting amplifier is the op-amp circuit everyone meets first. Signal into the negative input through Rin, feedback through Rf. Output is inverted and scaled by −Rf ÷ Rin. Its “virtual ground” node makes the analysis beautifully mechanical.
> At a glance: 7 minute guide · part 1 of 10 in the amplifiers complete guide track · includes a worked example and a quick-reference table.

## How virtual ground does the work

Here is the working theory in one pass. Negative feedback drives the two inputs to the same voltage. With the positive input grounded, the inverting node sits at 0 V a virtual ground. All input current (Vin ÷ Rin) therefore flows through Rf, making Vout = −Vin × Rf ÷ Rin.

| Parameter | Formula | Design note |
| — | — | — |
| Gain | −Rf ÷ Rin | Set by resistor ratio |
| Input impedance | Rin | Also the load seen by source |
| Bandwidth | GBW ÷ gain | Check at your gain |
| Noise gain | 1 + Rf ÷ Rin | Drives stability |
| Summing | Add Rin per input | Mixer topology |

## Design constraints

Input impedance equals Rin a 10 kΩ Rin loads the source by 10 kΩ. Gain × bandwidth is constant. A 1 MHz GBW op-amp at gain 100 has only 10 kHz bandwidth. Keep feedback resistors in the 1–100 kΩ range to balance noise, bias error and loading.

## Stability and layout

Inverting stages with long feedback traces ring. Keep the feedback loop tight, add a small feedback capacitor when driving capacitive loads. Respect the output current limit. The inverting configuration also naturally sums multiple inputs the heart of mixers.

## How to apply this in your build

Work through the sequence below each step assumes the previous one passed. For numbers that need calculating, the linked tools at the end of this guide do the arithmetic instantly.
1. Choose gain from the resistor ratio with standard values
2. Verify bandwidth = GBW ÷ noise gain meets the signal
3. Set input impedance acceptable to the source
4. Lay out the feedback loop tight with a ground-referenced return

### Worked example

Audio preamp: Rin = 10 kΩ, Rf = 100 kΩ gives gain −10 (20 dB). A 5532-class op-amp (10 MHz GBW) leaves 900 kHz bandwidth flat far beyond audio. Run the numbers yourself with the opamp-gain and the result should agree to within rounding.

> Practical note from the bench. Our preamp boards standardise on 10 k/100 k first stages 20 dB, sane impedance, easy math, repeatable.

## Common mistakes to avoid

– Very large feedback resistors inviting noise and bias offset
– Expecting high input impedance from the inverting topology it is Rin by definition
– Ignoring the inverting sign in level plans and phase-sensitive chains

## Key takeaways

– How virtual ground does the work the foundation of this guide. Revisit it if any measurement here surprises you.
– Design constraints the foundation of this guide; revisit it if any measurement here surprises you.
– Stability and layout the foundation of this guide; revisit it if any measurement here surprises you.

## Who this guide is for

Beginners get a single focused topic instead of a whole textbook chapter. It works as an early stop in the amplifiers complete guide path. Intermediate readers use it as a reference the table, the worked example and the mistake list answer the questions that come up mid-build. If you teach, the structure (theory, application, example, failure modes) maps cleanly onto a lab session.

## What you need before starting

Nothing exotic: the parts or tools named in the guide, a multimeter. The opamp-gain open in a tab. Choose gain from the resistor ratio with standard values before you begin the guide assumes it and keep the quick-reference table above within sight while you work through the steps.

### Quick reference card

| Aspect | Where to find it in this guide |
| — | — |
| Core theory | How virtual ground does the work |
| Application steps | How to apply this in your build |
| Worked numbers | Worked example |
| Failure modes | Common mistakes to avoid |

## How this fits the amplifiers complete guide track

This guide is one stop in the structured learning path. Start from the [amplifiers complete guide](/tutorial/amplifiers-complete-guide) pillar page for the full map, or continue with [non-inverting stage design](/tutorial/non-inverting-op-amp-configuration) and [the buffer configuration](/tutorial/op-amp-voltage-follower). For the arithmetic, open the [opamp-gain](/tools/opamp-gain).

## Frequently asked questions

Why is the gain negative?
The configuration inverts phase 180°. In audio this rarely matters; in control loops it can be fatal.

Can I sum several signals?
Yes each source gets its own Rin into the virtual ground; the node is a natural summing junction.

Is there a calculator for this?
Yes the [opamp-gain](/tools/opamp-gain) tool runs the formulas from this guide instantly, client-side, with no signup.

## Continue the learning path

– The complete amplifiers & audio guide: [Amplifiers & Audio complete guide](/tutorial/amplifiers-complete-guide)
– Read next: [non-inverting op-amp: high-impedance gain stage](/tutorial/non-inverting-op-amp-configuration)
– Also in this track: [the op-amp voltage follower: small circuit, big leverage](/tutorial/op-amp-voltage-follower)
– Continue with: [transistor biasing: fixed, divider and q-point stability](/tutorial/transistor-biasing-methods)
– Calculate as you go: [op-amp gain calculator](/tools/op-amp-gain) · [power dissipation tool](/tools/electrical-power) · [gain to dB converter](/tools/opamp-gain)
– Bookmark this page against the day a measurement surprises you. Most readers return to the table and the mistake list first, and that is the correct order.

## Measurement discipline

When a result here disagrees with your expectation, write down both numbers before changing anything. The gap between predicted and measured is where the real engineering lives. It is usually a tolerance, a parasitic or an assumption that was never checked.

Keep a lab notebook entry for every build in this track. The measured values, the deviations from the guide and the reason for each. Six months from now, those notes are worth more than any tutorial. They describe your bench and your components rather than a general case.
## Formulas and checks from this guide

Verification checklist for this track: measure bias at idle before signal testing, check heatsink temperature under load. Confirm gain across frequency rather than at 1 kHz alone. Amplifiers forgive nothing at their edges.

Bookmark this page against your next build in the track. The checklist above is the same one used across 19 guides in this series.

## Hard-won notes

Across the emitter resistors at idle, no signal. Compare each output device.

Thermal drift in bias. Check the bias tracker is bolted to the heatsink and re-set per the service values.