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Op-amp inverting amplifier explained

An inverting amplifier feeds the signal through a resistor, Rin, into an op-amp's − input, with a feedback resistor, Rf, from the output back to that input and the + input grounded. The output is a bigger copy of the input, upside down, with gain G = −Rf ÷ Rin.

The virtual ground

With negative feedback, an op-amp drives its output until its two inputs are equal. The + input is grounded, so the − input sits at 0 V too. It isn't wired to ground; the op-amp holds it there. That's the virtual ground.

It's like a see-saw with an off-centre pivot: push the short arm up and the long arm goes down further. The two resistors are the arms, and the − input is the pivot.

Live experiment

Rock the see-saw

An inverting amplifier drawn as a see-saw, with the − input as the pivot held at 0 V. R_in is 10 kΩ; push its end up 1 V with a 47 kΩ feedback arm and the output end goes down 4.7 V. Ask for more than ±10.5 V and it stops at the limit.

Try it yourself: free lesson

“Inverting and summing amplifiers” is lesson 5 of 6 in Amplifier Peaks, Electronics World 6. Free with an account. Lessons unlock in order, so you’ll do the 39 before it first.

G = −Rf ÷ Rin

Use Kirchhoff's current law at the − input. The current in Rin is Vin ÷ Rin, because its far end is at 0 V. No current enters the op-amp's input, so all of it flows on through Rf, which sets the output: Vout = −I × Rf.

G = − Rf over Rin

Example: Rf = 22 kΩ and Rin = 10 kΩ.

G = − 22 kΩ over 10 kΩ = −2.2

So 1 V peak in gives 2.2 V peak out, flipped: a phase shift of 180°. Unlike a non-inverting amplifier, the gain can be less than 1: Rf = 4.7 kΩ with Rin = 10 kΩ gives −0.47, a flipped, smaller copy.

Limits and choices

The output can't pass its limits, about 1.5 V inside each rail for a classic op-amp: ±10.5 V on ±12 V. Ask for more and the wave is clipped flat. The output current is limited too, about 25 mA, so keep the resistors in kilohms.

The input resistance is just Rin, since its far end sits at 0 V. Make Rin small and the source has to work hard; make everything huge and noise and the inputs' tiny leakage currents start to matter. Values from 1 kΩ to 100 kΩ are typical.

Where it's used

Because the − input is a virtual ground, several inputs can feed it, each through its own resistor, and the output is their weighted sum: a summing amplifier, the heart of every audio mixer. Swap Rf for a capacitor and a steady input makes the output ramp: an integrator.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Inverting and summing amplifiers” is lesson 5 of 6 in Amplifier Peaks, Electronics World 6. Free with an account. Lessons unlock in order, so you’ll do the 39 before it first.

Or start from the very first lesson, no account needed

Work it out

Practice questions

Three quick questions from the lessons. Pick an answer to check it.

  1. Question 1 of 3In an inverting amplifier with + grounded, the − input sits at…
    Show the answer

    Answer: about 0 V. Negative feedback makes V− match V+, and + is grounded, so − sits at about 0 V. It isn't wired to ground: the op-amp holds it there. That's the virtual ground.

    • Why not “the input voltage”? The op-amp works to keep its two inputs equal. With + grounded, that's 0 V, not the input voltage.
    • Why not “the supply voltage”? Negative feedback holds the − input level with the + input, which is grounded, far below the supply.
  2. Question 2 of 3Ask one op-amp for more gain, and the frequency where its gain starts to fall…
    Show the answer

    Answer: gets lower. Gain and bandwidth trade off, like a bike's gears. Their product, the gain-bandwidth product, stays about the same, so more gain means a lower corner.

    • Why not “stays the same”? Gain times bandwidth stays about the same, so more gain must lower the corner.
    • Why not “gets higher”? Gain and bandwidth trade off. Asking for more gain brings the corner down, not up.
  3. Question 3 of 3In a non-inverting amplifier, a bigger feedback resistor (the top of the divider) gives…
    Show the answer

    Answer: more gain. A bigger top resistor sends a smaller share of the output back, so the op-amp has to lift its output higher before that share matches the input. More gain.

    • Why not “less gain”? A bigger feedback resistor feeds back a smaller share of the output, so the op-amp has to push the output higher. That's more gain.
    • Why not “the same gain”? The gain depends on the resistor ratio, so changing the feedback resistor changes it.
Keep practising: free lesson

“Inverting and summing amplifiers” is lesson 5 of 6 in Amplifier Peaks, Electronics World 6. Free with an account. Lessons unlock in order, so you’ll do the 39 before it first.

Questions people ask

What is the gain of an inverting amplifier?

G = −R_f ÷ R_in, where R_in runs from the signal to the − input and R_f from the output back to the − input. With R_f = 22 kΩ and R_in = 10 kΩ, the gain is −2.2: 1 V in gives 2.2 V out, flipped.

What is a virtual ground?

In an inverting amplifier the + input is grounded, and negative feedback holds the − input at the same voltage, 0 V. It isn't wired to ground; the op-amp keeps it there by pushing just the right current through R_f.

Why is the output of an inverting amplifier negative?

Current flows from the input through R_in into the virtual ground, and all of it must continue through R_f to the output. For current to flow away from 0 V towards the output, the output has to sit below 0 V. Positive in, negative out.

What is the input resistance of an inverting amplifier?

Just R_in, because the far end of R_in sits at the virtual ground, 0 V. That's much lower than a non-inverting amplifier's, so a weak source may need a buffer in front.

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