Summing Amplifier
Three-channel summing node
Each channel's weight is −Rf/Ri; the output is the weighted, inverted sum. Enter 0 V to switch a channel off.
Mixed output
How to Use This Calculator
The summing amplifier adds several input signals at the op-amp's inverting node, where each is scaled by its own resistor before being combined. With three channels the output is Vout = −(Rf·V1/R1 + Rf·V2/R2 + Rf·V3/R3) — every channel contributes a weighted copy of itself, and the whole sum comes out inverted. The weight of each channel is set independently by its input resistor: smaller Ri means larger weight for that channel. Enter the feedback resistor Rf, then each channel's voltage Vi and resistor Ri (with unit selectors), and the calculator shows every channel's gain and the total mixed output live.
Input fields
| Field | Symbol | Unit | What to enter |
|---|---|---|---|
| Feedback resistor | Rf | Ω / kΩ / MΩ | The common feedback resistor. It sets the scale of every channel's weight. |
| Channel voltages | V1…V3 | V | Each input signal, positive or negative. Enter 0 to switch a channel off without removing its resistor. |
| Channel resistors | R1…R3 | Ω / kΩ / MΩ | One per channel; must be positive. Equal Ri values give equal weights (an averaging node when Rf = Ri·N/(N−k) — see FAQ). |
Step by step
- Set Rf first — with the defaults (Rf = 100 kΩ and all Ri = 100 kΩ) every channel has a gain of −1, so the output is simply the negative sum of the inputs.
- Enter your signal voltages. With V1 = 0.5 V and V2 = 0.25 V you get contributions of −0.5 V and −0.25 V; channel 3 at 0 V adds nothing, so the output reads −0.75 V.
- To weight a channel more heavily, reduce its Ri (e.g. R2 = 50 kΩ doubles channel 2's gain to −2). To attenuate it, increase Ri.
- Check that the sum stays inside your supply rails: with ±15 V supplies there is comfortable headroom here, but a mix of large same-sign inputs can clip (see the Slew Rate calculator for the dynamic side of that limit).
Two practical notes. Because each channel's source sees only its own Ri to a virtual ground, channels do not load one another — that isolation is the main reason to build a summing stage instead of tying sources together with plain resistors. And because this is an inverting topology, every contribution arrives at the output 180° out of phase; if you need a non-inverted mix, add a unity-gain inversion afterwards (a follower stage will not do it — use a gain-of-−1 inverting stage).
What It Means in a Real Circuit
The node where R1, R2, R3 and Rf meet is held at virtual ground, so the current from each source is simply Vi/Ri — independent of what the other channels are doing. The op-amp's feedback forces all those currents to leave through Rf, which is why the output voltage equals minus the sum of the individual drops. That current-mode mixing is what makes the circuit robust: audio mixers use exactly this node to combine several sources with per-channel trim resistors, and data-acquisition front ends use it to scale and add sensor signals before an ADC. The input impedance of each channel is just its Ri (the virtual ground swallows the rest), so a 100 kΩ channel resistor presents 100 kΩ to that source regardless of Rf or the other channels.
The trade-offs are set by the same node. First, noise gain: stability and offset multiplication depend on 1 + Rf/(R1∥R2∥R3), the parallel combination of all input resistors — which is always larger than any single channel's noise gain, so a summing stage with small Ri values demands more GBW and shows more offset error than its per-channel gains suggest. Second, bias current: the inverting terminal's bias current flows through Rf and appears at the output as an offset of roughly Ib·Rf; placing a resistor equal to R1∥R2∥R3 in series with the non-inverting input (to ground) balances the DC conditions and cancels most of it. Third, tolerance: each channel's weight error is the sum of Rf's and Ri's tolerances, so 1% resistors give roughly ±2% per-channel accuracy — fine for mixing, marginal for precision scaling.
A concrete example: a three-mic mixer with Rf = 47 kΩ. Setting R1 = R2 = 47 kΩ and R3 = 94 kΩ gives gains of −1, −1 and −0.5 — the third mic is trimmed down by half. The parallel input resistance is 47k∥47k∥94k ≈ 18.8 kΩ, so the noise gain is about 3.5; with a 1 MHz-GBW op-amp the bandwidth is roughly 280 kHz (far beyond audio), and a 1 mV input offset becomes at most 3.5 mV at the output — inaudible, but it would matter if you were summing millivolt sensor signals, where you would choose a low-offset part or AC-couple the stage. If the required weights are all equal and you want the output to equal the average of the inputs, set Rf = Ri/N (N channels), which is the classic averaging-amplifier configuration.
Frequently Asked Questions
The summing node sits on the op-amp's inverting input, so the feedback action that makes the sum work also flips the polarity. The circuit adds currents at a virtual ground and develops their total across Rf with the sign of an inverting amplifier. If you need a non-inverted sum, cascade a second gain-of-−1 inverting stage after it.
Each channel's gain is −Rf/Ri, so make that channel's Ri smaller to boost it or larger to attenuate it. With Rf = 100 kΩ: R = 100 kΩ gives ×1, R = 50 kΩ gives ×2, R = 200 kΩ gives ×0.5. The other channels are unaffected — that independence is the point of per-channel resistors.
No. Every source sees only its own resistor to a virtual ground, so changing one channel's signal or resistance does not alter the current drawn by another. This is why summing nodes are preferred over tying sources together with plain resistors, where each source would load the others.
Set its voltage to 0 V — the channel then contributes nothing while its resistor stays in place, which keeps the DC bias conditions (and the offset-compensation balance) unchanged. Physically, this is equivalent to grounding that channel's source.
The supply rails: if the algebraic sum exceeds what the op-amp can swing (typically a volt or two inside each rail), the output clips. Add up the worst-case same-sign contributions before choosing supplies, and remember the noise gain — 1 + Rf/(R1∥R2∥R3) — sets both bandwidth and offset multiplication.