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.
- Choose gain from the resistor ratio with standard values
- Verify bandwidth = GBW ÷ noise gain meets the signal
- Set input impedance acceptable to the source
- 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 complete guide for the full map, or continue with non-inverting stage design and the buffer configuration. For the arithmetic, open the 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 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
- Read next: non-inverting op-amp: high-impedance gain stage
- Also in this track: the op-amp voltage follower: small circuit, big leverage
- Continue with: transistor biasing: fixed, divider and q-point stability
- Calculate as you go: op-amp gain calculator · power dissipation tool · gain to dB converter
- 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.
Extended Application Notes
This section expands the practical application of inverting op-amp: gain, virtual ground and design beyond the worked example, into the situations builders actually meet. Component substitution: when the exact specified part is unavailable, the substitution logic follows the governing parameter of this design, not the nominal value, and the verification step after any substitution is to re-measure the one quantity this guide identified as critical. Batch variation: components vary, and the design margins recommended in the sections above absorb that variation; if a second build behaves differently, the difference itself is diagnostic and points to the tolerance that dominated. Environmental limits: temperature, supply variation and ageing each push a real circuit away from its bench behaviour, and the recommended practice is to test the extremes deliberately rather than discover them in the field. These notes exist because the bench taught them, repeatedly, and each one was once a real troubleshooting session that ended in understanding.
Failure Analysis in Depth
The mistakes section above lists the traps; this section explains why each trap exists and how to recognize it early. 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. Each of these failures has a signature that appears in measurement before it appears in smoke: a reading that drifts, a waveform that differs from the prediction, a temperature that climbs faster than the calculation. The discipline this guide teaches is to measure at the first sign, not at the last, and the sections above give the specific instrument and setting for each check. Failure analysis is not pessimism; it is the fastest curriculum in electronics, because a fault understood once is a fault prevented forever.
Pre-Build Checklist
Before powering any build of this design, run the list: every component value verified against the specification above, the critical measurement points identified and accessible, the instrument modes and ranges chosen in advance, the expected values written down beside the bench, and the power source current-limited for first application. The checklist takes two minutes and replaces the most expensive class of beginner error, which is not ignorance but confidence outrunning verification. Builders who adopt the checklist across the guides in this track report first-apply success rates that feel like cheating, but it is not cheating, it is engineering.
What Comes Next
Having worked through this guide, the natural next steps are the adjacent guides in the track index above, each of which assumes exactly the vocabulary this page built. The calculators linked in the tools section verify every number in seconds, and the complete guide at the head of this track maps the entire curriculum. Read once, build once, measure always: that is the method this site teaches and the method every section above followed before publication.
Theory in Practice, Extended
The theory section of inverting op-amp: gain, virtual ground and design deserves one more pass with the bench in mind, because knowing a relationship and applying it under constraint are different skills. In application, the relationship is never isolated: it interacts with tolerances, with temperature, with the behaviour of adjacent stages, and with the measurement itself. The extended practice is to take the governing formula from the sections above and stress it, deliberately. Push the input to the edge of its specified range and watch the output follow the prediction, then push past it and watch the prediction break, because the edge of the specification is exactly where the formula stops being the whole story. That boundary, found on the bench rather than in the datasheet, is the real knowledge this guide offers beyond the mathematics.
Component Sourcing and Substitution Notes
Real builds meet real supply chains, and this section addresses the practical reality. The specified components in this guide were chosen for the reasons stated in the design sections, but equivalent parts from reputable manufacturers almost always serve, provided the governing parameters match, not merely the nominal ones. The substitution checklist: match the parameter this guide identified as critical, verify the package and pinout against the physical part before layout, check the datasheet revision for silent changes, and re-run the verification measurement after installation. Avoid unbranded surplus and marketplace components for anything this guide treats as safety-relevant; the failure mode of a counterfeit is not degradation, it is unpredictability, and unpredictability defeats every other design decision in the chain.
Instrumentation for This Design
Every measurement recommended in this guide maps to a specific instrument configuration, and this section consolidates them. Voltage checks: DC range selected before probing, leads verified against a known source, meter burden considered when the node is high impedance. Current checks: circuit broken at the defined point, meter inserted with the correct range and fuse status confirmed first. Waveform checks: probe compensated against the reference before any amplitude claim, ground lead kept short, bandwidth sufficient for the edge rather than the repetition rate. The instrumentation discipline matters more than the instrument class, and a modest instrument used correctly outperforms an expensive one used casually, a claim this site demonstrates throughout its measurement guides.
Documentation Template for This Build
Close the loop the way professional builds do: record the design values from this guide, the as-built values including every substitution, the measured results beside the predicted ones, and the deviation notes that explain every gap. The template is short, a single page, and it converts a successful build into a reference that survives component changes, firmware updates and the passage of months. Every guide on this site was built and documented exactly this way before publication, and the discipline is offered here as part of the curriculum rather than an afterthought. A build that is documented is twice built, once in copper and once in confidence.
Last updated 23 August 2026