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DETERMINING MEASUREMENT ACCURACY

by Hristo Stefanov

Start ý Defining the Terms ý A Little Theory ý Sources of Error ý Error Budget ý Error Budget Example ý Offset and Gain Errors ý Sources and PDF

ERROR BUDGET

Error budget is a systematic approach to analytical determination of overall accuracy at design time. As you saw previously, there is reason to consider the overall systematic error as the sum of error terms because every term corresponds to one source of error. Therefore, you can build a budget where every article corresponds to one error term, hence error budget. Every article includes the source of error, the expression that assesses the error, and the evaluation of the expression. You can summarize the building stages as follows:

ý collecting information about sources of error

ý calculating to assess the influence of componentsý characteristics on circuit performance

ý filling up the budget table

ý evaluating the totals

ý assigning the deviation of factors that affect sources of error (such factors are temperature, time, etc.).

ý evaluating the final overall error

ý analyzing the results

To simplify the calculations, assume that the error terms are small and not correlated. Because most of the error terms are bipolar (and not correlated), evaluate every error and total by modulus.

Letýs examine the linear converter (because of its common usage) and derive the most important equations needed to assess its accuracy.

The transfer function is given by:

Y = GX

where G = gain, X = input value, and Y = output value.

In the real transfer function, there is deviation in the gain and zero:

Y_R = (G + DG)X + Y₀

where D G = gain deviation and Y₀ = zero deviation (offset).

The absolute error () is given by:

Y_EER = Y_R ý Y

Y_EER = XDG + Y₀

where XD G = gain error and Y₀ = offset error.

You can see that the absolute error of the linear converter is the sum of two terms, gain error and offset error. Furthermore, the gain error is dependent on X and the offset error is independent of X. Maximum absolute error occurs when the value of X is maximum (X_MAX):

Letýs assume that the input span (input scale) is 0 ý X_MAX and the output span (output scale) is 0 ý Y_MAX. You can express the maximum absolute error as a fraction of the full output scale range Y_MAX:

Because:

the gain error can be expressed independently of the full-scale range, and the offset error:

is expressed as a fraction of the full-scale range.

Fractional errors can be converted to ppm (parts per million) by multiplying by 1 ý 10⁶ and to percent by multiplying by 100.

In the linear converters, absolute errors can be referred to the input (RTI) or output (RTO). You can convert RTI errors to RTO by multiplying by gain (G). Errors expressed as a fraction (of the full-scale range) are independent of the reference. Therefore, you can sum fractional errors obtained from RTI and RTO absolute errors.

In the following example, I will derive expressions for RTI and RTO absolute errors and evaluate them. And, I will express the obtained absolute errors as fractional ones and calculate the totals separating gain and offset errors.

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