Error Budget Calculations

No matter how perfect your circuit or SPICE simulation, an analog circuit always produces less-than-perfect signals. That lack of perfection stems from slight mismatches between components, noise, offset voltages, nonlinear responses, component tolerances, temperature and other characteristics that affect a signal as it goes from input to output.

To create a design's error budget that lists error sources and amounts so as to determine beforehand how a circuit will affect a signal, you first need a goal. Say you have a 12-bit analog-to-digital converter that resolves one part in 4096 or 244 parts per million (ppm). Thus, any errors should not affect the input signal by more than 1/2 LSB, or 122 ppm, which becomes your target error-budget figure. (Some might argue this figure should be higher or lower.)

A typical instrumentation amplifier (in-amp), for example, will contribute offset and gain errors and add noise to a signal (see figure). And the resistor used to adjust the in-amp's gain will contribute a small error due to normal tolerances, which is why you use a high-precision external resistor or internal gain choices. In general you compare all errors to the original input signal and express errors in parts per million. By comparing errors to the original input signal, you have a common reference point. An Analog Devices' application note (see references) provides a good example of how to create an error budget for two in-amps and also how the budget for a monolith in-amp compares to that for a "home brew" in-amp circuit.

Small errors caused by differential nonlinearity, offset, gain and drift also contribute to errors during the conversion process.

As a first step, determine the errors for your signal based on component characteristics and represent them in ppm. For a worst-case analysis, simply add the errors. But in most cases the circuit will not experience the maximum error values simultaneously. So, the root-of-the-sum-of-squares (RSS) method can offer a more realistic error-budget value. You square each error, add the sums and take its square root. Keep in mind that you can often adjust for offset and similar static errors and adjust measurements to account for errors due to temperature changes. So, your first error budget might look bad, but all hope is not lost.