An investigation into the effects of sliding scale averaging on nuclear pulse height analysis

The purpose of this investigation was to study the effects of sliding scale averaging on nuclear pulse-height analysis. The operation of a sliding scale successive approximation analog-to-digital converter was studied in detail.

Sliding scale averaging was shown to be capable of improving the differential linearity performance of a successive approximation ADC. However, a consequence of the averaging is an alteration of the channel profile characteristics of the converter. A uniformly distributed slider creates channel profiles containing front and • back "porches." Expressions were derived which describe the heights and widths of these porches in terms of the differential nonlinearity of the converter and the width of the compensating slider.

The precise shape of a digitized output distribution was shown to be a function of the moments of the channel profiles of the ADC. Since the shapes of the effective channel profiles of a sliding scale converter are distorted by the slider, distortions are introduced into the digitized distribution by the ADC.

A worst-case analysis was performed for a converter containing a differential nonlinearity error in a single channel located at mid-scale. This model was shown to be a good approximation of an actual sliding scale converter in a high resolution PHA application. Expressions were derived for the centroid shift and the second and third central moments of a sliding scale digitized gaussian distribution. These expressions describe the worst-case behavior of the converter when the input distribution lies entirely within channels affected by the slider. The magnitudes of these moments are related to the derivative of the linear function which describes the centroid shifts of the effective channel profiles. This function is proportional to the differential linearity error in the converter and is inversely proportional to the width of the slider.

Data from a computer simulation of a sliding scale converter are presented which graphically illustrate the variations in the first three moments of a sliding scale digitized gaussian distribution. These results corroborate the expressions for the output moments and provide additional data in areas within the range of the converter which were not analytically characterized.