Summing Amplifier

Vout = −Rf × (V1/R1 + V2/R2 + V3/R3)

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Result
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Formula

Vout = −Rf × (V1/R1 + V2/R2 + V3/R3)

Description

The summing amplifier is an extension of the inverting configuration that adds multiple input signals with individually controlled gains. Each input is connected through its own resistor to the inverting node (virtual ground), so the inputs do not interact with each other. The output is the inverted weighted sum of all inputs. When all input resistors are equal to Rf, the output is the inverted sum of all inputs. This circuit is fundamental in audio mixing, DAC output stages, and analog computation.

Variables

  • Vout — Output voltage (V)
  • V1, V2, V3 — Input voltages (V)
  • R1, R2, R3 — Input resistors (Ω)
  • Rf — Feedback resistor (Ω)

Practical Notes

The virtual ground ensures that each input is isolated from the others, allowing independent gain control per channel. For equal-weight summing, set all resistors equal. For weighted summing (as in a DAC), use binary-weighted resistors. The number of inputs is not limited to three; additional inputs simply add more input resistor branches.

Related Formulas

Non-Inverting Amplifier Inverting Amplifier Difference Amplifier Gain-Bandwidth Product Common-Mode Rejection Ratio Op-Amp Integrator Gain

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