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Op-amp summing amplifier explained

A summing amplifier adds several signals into one output. Each input feeds the op-amp's − input through its own resistor, and a feedback resistor Rf carries the total: Vout = −Rf × (V1 ÷ R1 + V2 ÷ R2 + ...). Each input gets its own gain, and none of them interferes with the others. It's the heart of every audio mixer.

Adding currents at a virtual ground

Start from an inverting amplifier: + input grounded, so negative feedback holds the − input at 0 V, a virtual ground. Now connect several inputs to that point, each through its own resistor. Each pushes a current Vn ÷ Rn into the virtual ground. No current enters the op-amp's input, so by Kirchhoff's current law all of it flows on through Rf:

Vout = −Rf × (V1 over R1 + V2 over R2)

Because every input sees 0 V at the far end of its resistor, none can push into another. Turn one channel up and the others don't change.

Live experiment

The stage inside a mixer

Each channel of a summing amplifier is an inverting stage, drawn here as a see-saw pivoting on the virtual ground at 0 V. R_in is 10 kΩ; change the feedback arm, push the input end, and the output moves −R_f ÷ R_in as far, until it hits ±10.5 V.

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.

Each input, its own gain

Each channel's gain is −Rf ÷ Rn. With Rf and three inputs all 10 kΩ, Vout = −(V1 + V2 + V3), an equal mix.

Example: a two-channel mixer. A microphone gives 50 mV and needs ×10; a music player gives 0.5 V and needs ×1. Choose Rf = 100 kΩ first, then each input resistor is Rf divided by the gain that input needs:

  • Microphone: 100 kΩ ÷ 10 = 10 kΩ
  • Music: 100 kΩ ÷ 1 = 100 kΩ

Each now reaches the output at about 0.5 V, so they're balanced, and their peaks together stay well inside the limits on ±12 V rails.

Averaging and weighting

Make Rf = R ÷ n with n equal inputs and the output is the average, inverted. Weight the resistors instead and some inputs count more than others. A simple DAC, which turns a binary number into a voltage, does exactly that: resistors of R, 2R, 4R and 8R give the bits weights of 8, 4, 2 and 1.

Things to watch

  • The output is inverted. The ear can't hear that, but a second inverting stage flips it back if you need to.
  • The output can't pass its limits, about ±10.5 V on ±12 V for a classic op-amp. The sum of the peaks must fit, or the mix clips.
  • More channels mean more noise gain, 1 + Rf ÷ (all the input resistors in parallel), which lowers the bandwidth a little.

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 holds its − input level with the grounded + input, so it can't follow the input voltage.
    • Why not “the supply voltage”? Negative feedback keeps the − input at the + input's 0 V, nowhere near the supply.
  2. Question 2 of 3Feeding an op-amp's output back to its + input gives…
    Show the answer

    Answer: positive feedback. Back to + is positive feedback: it helps the output along, so it snaps to a limit, as in a Schmitt trigger. Back to − is negative feedback, which holds it steady.

    • Why not “no feedback”? Any path from the output back to an input is feedback. Going to + makes it the positive kind.
    • Why not “negative feedback”? Negative feedback goes to the − input, as in a summing amplifier. To + it helps the change along instead.
  3. Question 3 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”? The gain-bandwidth product is roughly fixed, so the corner moves when the gain does.
    • Why not “gets higher”? More gain means a lower corner, because gain times bandwidth stays about the same.
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 formula for a summing amplifier?

V_out = −R_f × (V1 ÷ R1 + V2 ÷ R2 + ...). Each input has its own gain, −R_f ÷ R_n. With R_f and every input resistor equal, the output is simply −(V1 + V2 + ...).

Why don't the inputs of a summing amplifier interfere with each other?

Every input resistor ends at the virtual ground, held at 0 V by the op-amp. Each input pushes its own current, V ÷ R, into that point regardless of the others, so no input can push into another.

How do I make an averaging amplifier?

Give n inputs equal resistors R and make R_f = R ÷ n. With three 30 kΩ inputs and a 10 kΩ feedback resistor, V_out = −(V1 + V2 + V3) ÷ 3, the average, inverted.

Does the inverted output matter for audio?

Not for a single path: the ear can't hear a waveform turned upside down. It matters when you combine it with an uninverted copy of the same signal, where the two would cancel. A second inverting stage flips it back if needed.

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