Difference Amplifier
Vout = (Rf/Ri) × (V2 − V1)
Quick answer
This calculator solves Vout = (Rf / Ri) × (V2 − V1) for Output Voltage. With Input V1 26.4 V, Input V2 56.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, the result is 13.64 V.
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Formula
Description
The difference amplifier amplifies the voltage difference between two inputs while rejecting any signal common to both (common-mode rejection). It uses matched resistor pairs on each input to achieve balanced operation. The gain is set by the Rf/Ri ratio. Ideal CMRR requires perfect resistor matching; even 0.1% mismatch significantly degrades common-mode rejection. For high CMRR applications, instrumentation amplifiers with laser-trimmed internal resistors are preferred over discrete difference amplifier circuits.
Variables
- Vout — Output voltage (V)
- V1 — Inverting input voltage (V)
- V2 — Non-inverting input voltage (V)
- Rf — Feedback resistor (Ω)
- Ri — Input resistor (Ω)
Practical Notes
CMRR of a discrete difference amplifier is limited by resistor matching: 0.1% resistors give about 60 dB CMRR, 0.01% about 80 dB. Dedicated difference amplifier ICs like the INA143 achieve 80-100 dB CMRR. Use this topology for current sensing across shunt resistors and measuring small differential signals in the presence of large common-mode voltages.
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 |
| Rf | Feedback Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
| Ri | Input Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Input V1 26.4 V, Input V2 56.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ
- 2. The relation: Vout = (Rf / Ri) × (V2 − V1)
- 3. Substitute: V1 = 26.4 V, V2 = 56.4 V, Rf = 10 kΩ, Ri = 22 kΩ
- 4. Result: Output Voltage = 13.64 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, Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ
Result: Output Voltage = 0.3745 V
Low range
Given: Input V1 7.26 V, Input V2 15.5 V, Feedback Resistor 1 kΩ, Input Resistor 2.2 kΩ
Result: Output Voltage = 3.745 V
Typical
Given: Input V1 26.4 V, Input V2 56.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ
Result: Output Voltage = 13.64 V
High range
Given: Input V1 0.506 kV, Input V2 1.08 kV, Feedback Resistor 100 kΩ, Input Resistor 0.22 MΩ
Result: Output Voltage = 0.2609 kV
Maximum range
Given: Input V1 5.06 kV, Input V2 10.8 kV, Feedback Resistor 1 MΩ, Input Resistor 2.2 MΩ
Result: Output Voltage = 2.609 kV
How Output Voltage changes with Input V1
| Input V1 (input) | Output Voltage (result) |
|---|---|
| 5.81 V | 53.72 V |
| 14.53 V | 49.76 V |
| 29.05 V | 43.16 V |
| 43.58 V | 36.56 V |
| 58.1 V | 29.95 V |
| 87.15 V | 16.75 V |
| 116.2 V | 3.545 V |
| 0.2324 kV | -49.27 V |
| 0.4067 kV | -128.5 V |
| 0.581 kV | -0.2077 kV |
The same result in other units
| Unit | Value |
|---|---|
| mV | 13640 |
| V | 13.64 |
| kV | 0.01364 |
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<p><a href="https://vbatpower.com/formulas/opamp-diff/">Difference Amplifier</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Difference Amplifier?
Use Vout = (Rf / Ri) × (V2 − V1). With Input V1 26.4 V, Input V2 56.4 V, Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, Output Voltage works out to 13.64 V.
What is the formula for Difference Amplifier?
The formula is Vout = (Rf / Ri) × (V2 − V1). The difference amplifier amplifies the voltage difference between two inputs while rejecting any signal common to both (common-mode rejection).
What units does Difference 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.
Related Concepts
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