Summing Amplifier Calculator Formula

Understand the math behind the summing amplifier calculator. Each variable explained with a worked example.

Use the Summing Amplifier Calculator

Formulas Used

Output Voltage

v_output = -(rf_kohm / r_in_kohm) * (v1 + v2 + v3)

Gain per Input

gain_per_input = -(rf_kohm / r_in_kohm)

Variables

VariableDescriptionDefault
v1Input Voltage V1(V)1
v2Input Voltage V2(V)2
v3Input Voltage V3 (0 to skip)(V)3
r_in_kohmInput Resistors (equal)(kΩ)10
rf_kohmFeedback Resistor (Rf)(kΩ)10

How It Works

Inverting Summing Amplifier

Formula (equal input resistors)

V_out = -(Rf / Rin) x (V1 + V2 + V3)

When Rf = Rin the output is simply the inverted sum. Different input resistor values allow weighted summation.

Worked Example

Three inputs at 1 V, 2 V, 3 V with Rin = Rf = 10k.

v1 = 1v2 = 2v3 = 3r_in_kohm = 10rf_kohm = 10
  1. 01Sum = 1 + 2 + 3 = 6 V
  2. 02Gain = -10 / 10 = -1
  3. 03V_out = -1 x 6 = -6 V

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