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How to measure ADC's offset, gain error

22 May 2014  | Abhijan Chakravarty, Sambhav Jain

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A number of measurement applications require converting a slowly varying analogue signal into digital with high accuracy and linearity. These often occur in industrial control, environmental monitoring, battery testing, and power consumption. All ADCs introduce static errors to measurements. Static parameters include offset error, full-scale error, gain error, and total unadjusted error. Non-linear errors include integral non-linearity error and differential non-linearity error. In this article, we'll focus on offset and gain errors and compare two measurement methodologies.

Offset error is the difference between the actual first transition voltage and the ideal first transition voltage. Ideally, first transition takes place at a voltage equal to ½ LSB (least-significant bit).

Figure 1 shows the ideal and the actual transfer functions of an ADC. Here, offset error is measured at the first code transition.

Figure 1: Offset Error causes the first code transition to occur at a higher input voltage than expected.


Full-scale error is the difference between the actual last transition voltage and the ideal last transition voltage. Ideally, last transition takes place at ½ LSB before the rail voltage.

Figure 2 shows the full-scale error at the last code transition. Here, the ADC has reached its highest digital value before it sees the maximum input voltage.

Figure 2: Full-scale error occurs at the last code transition.


Gain error is the difference in slope of actual transfer function and the ideal transfer function as illustrated in figure 3.

Figure 3: Gain Error Measurement in this 3bit ADC causes the output code to reach maximum too early.


Gain error can be calculated as:

Gain Error = Full-Scale Error – Offset Error


Practical limitations
Analog signals are susceptible to noise. Often amplitude of noise is comparable to the resolution of the ADC. Hence the converted code corresponding to a voltage level can randomly vary. This statistical nature of ADC output codes make the code transition measurement complicated. To confidently find the digital code corresponding to an analogue level, you must perform several ADC conversions and then consider the average of the codes as the converted code. Unfortunately, the distribution of the ADC converted codes is not Gaussian distribution near voltage rails. The codes corresponding to the voltage rails will have more hits. So we can't accurately find the first and last transition voltages in practice.

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