Summing Amplifier
Vout = −Rf × (V1/R1 + V2/R2 + V3/R3)
Quick answer
This calculator solves Vout = −Rf × (V1/R1 + V2/R2 + V3/R3) for Output Voltage. With Input V1 26.4 V, Input V2 56.4 V, Input V3 5.64 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, Feedback Resistor 4.7 kΩ, the result is -25.02 V.
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Formula
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 — Input voltage 1 (V)
- V2 — Input voltage 2 (V)
- V3 — Input voltage 3 (V)
- R1 — Input resistor for V1 (Ω)
- R2 — Input resistor for V2 (Ω)
- R3 — Input resistor for V3 (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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vout | Output Voltage | V | pV, nV, µV, mV, V, kV |
| V1 | Input V1 | V | pV, nV, µV, mV, V, kV |
| V2 | Input V2 | V | pV, nV, µV, mV, V, kV |
| V3 | Input V3 | V | pV, nV, µV, mV, V, kV |
| R1 | R1 | kΩ | mΩ, Ω, kΩ, MΩ |
| R2 | R2 | kΩ | mΩ, Ω, kΩ, MΩ |
| R3 | R3 | kΩ | mΩ, Ω, kΩ, MΩ |
| Rf | Feedback Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Input V1 26.4 V, Input V2 56.4 V, Input V3 5.64 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, Feedback Resistor 4.7 kΩ
- 2. The relation: Vout = −Rf × (V1/R1 + V2/R2 + V3/R3)
- 3. Substitute: V1 = 26.4 V, V2 = 56.4 V, V3 = 5.64 V, R1 = 10 kΩ, R2 = 22 kΩ, R3 = 47 kΩ, Rf = 4.7 kΩ
- 4. Result: Output Voltage = -25.02 V
Related quantities from the same inputs
- P = V² / R = 69.7 mW
- I = V / R = 2.64 mA
Worked examples
Minimum range
Given: Input V1 0.726 V, Input V2 1.55 V, Input V3 155 mV, R1 100 Ω, R2 0.22 kΩ, R3 0.47 kΩ, Feedback Resistor 47 Ω
Result: Output Voltage = -0.6879 V
Low range
Given: Input V1 7.26 V, Input V2 15.5 V, Input V3 1.55 V, R1 1 kΩ, R2 2.2 kΩ, R3 4.7 kΩ, Feedback Resistor 0.47 kΩ
Result: Output Voltage = -6.879 V
Typical
Given: Input V1 26.4 V, Input V2 56.4 V, Input V3 5.64 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, Feedback Resistor 4.7 kΩ
Result: Output Voltage = -25.02 V
High range
Given: Input V1 0.506 kV, Input V2 1.08 kV, Input V3 108 V, R1 100 kΩ, R2 0.22 MΩ, R3 0.47 MΩ, Feedback Resistor 47 kΩ
Result: Output Voltage = -0.4793 kV
Maximum range
Given: Input V1 5.06 kV, Input V2 10.8 kV, Input V3 1.08 kV, R1 1 MΩ, R2 2.2 MΩ, R3 4.7 MΩ, Feedback Resistor 0.47 MΩ
Result: Output Voltage = -4.793 kV
How Output Voltage changes with Input V1
| Input V1 (input) | Output Voltage (result) |
|---|---|
| 2.64 V | -13.85 V |
| 6.6 V | -15.72 V |
| 13.2 V | -18.82 V |
| 19.8 V | -21.92 V |
| 26.4 V | -25.02 V |
| 39.6 V | -31.23 V |
| 52.8 V | -37.43 V |
| 105.6 V | -62.25 V |
| 0.1848 kV | -99.47 V |
| 0.264 kV | -136.7 V |
The same result in other units
| Unit | Value |
|---|---|
| mV | -25020 |
| V | -25.02 |
| kV | -0.02502 |
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<p><a href="https://vbatpower.com/formulas/opamp-summing/">Summing Amplifier</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Summing Amplifier?
Use Vout = −Rf × (V1/R1 + V2/R2 + V3/R3). With Input V1 26.4 V, Input V2 56.4 V, Input V3 5.64 V, R1 10 kΩ, R2 22 kΩ, R3 47 kΩ, Feedback Resistor 4.7 kΩ, Output Voltage works out to -25.02 V.
What is the formula for Summing Amplifier?
The formula is Vout = −Rf × (V1/R1 + V2/R2 + V3/R3). The summing amplifier is an extension of the inverting configuration that adds multiple input signals with individually controlled gains.
What units does Summing Amplifier use?
Output Voltage is shown in mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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