A differential amplifier frequent use is the amplification of the voltage difference between its inputs, while rejecting the common-mode level. However, the output common-mode level cannot be zero. The operational amplifier technological limitations, as well as the outside resistor tolerances let the common-mode voltage to make it to the amplifier output as an output error. As a consequence, the amplifier output voltage is the input signal difference times gain, plus the output common-mode voltage.
To reduce the output common-mode voltage one would have to match the resistors as much as possible, or at least their ratios: R2/R1 = R4/R3. One way to do this is to choose resistors with the lowest tolerance possible. Based on the resistor tolerances, this calculator will show the output common-mode voltage, Vocm, and the total voltage, Vout, at the differential amplifier output. Vocm will alter the ideal output voltage, which can be calculated when the resistors are perfectly matched. More about this subject can be found in these articles: The Differential Amplifier Common-Mode Error – Part 1 and Part 2. Also, in these articles there are the equations I used for this calculator.
Enter the resistors
|R1 =||kOhm||R2 =||kOhm|
|R3 =||kOhm||R4 =||kOhm|
Choose the resistors’ tolerance
Choose V1 and V2
|V1 =||V||V2 =||V|
Calculate the output voltage, Vout, and the output common mode voltage, Vocm. This assumes a worst-case resistor mismatch due to tolerances.
|Vout =||V||Vocm =||V|
You can play with different values. If the tolerance is zero, Vocm is zero, and the differential amplifier output is the ideal output voltage, which is gain times the input difference. As you increase the tolerance, the output voltage is altered two fold: one, the gain is altered by the fact that R2/R1 is not exactly equal with R4/R3, and second, Vocm appears as an error in Vout. That is why, this calculator shows both values at the output, as a handy aid in design.
Some times we need a certain level for the output common-mode voltage. In this case the common-mode voltage is not an error, but a needed output voltage that helps us design a function. For example, the differential amplifier can be used to design a unipolar to bipolar converter. After you design this circuit, you can use this calculator to verify your design. More on this subject can be found in this article: Design a Unipolar to Bipolar Converter for a Unipolar Voltage Output DAC.