Digital instrumentation for the time integral-squared of a voltage and its error characteristics

Abstract

A 16-level instrument in which the input voltage is sampled and quantised to yield direct decimal readouts of 1/T∫v^2dt . and T is described. This is an improved version of an instrument previously constructed; The upper frequency limit has been extended from 5 Hz to about 2 kHz. The readout of the instrument can be in any code, the decimal code being implemented in the instrument described. The original error analysis has been extended. An extensive analysis of the overall error characteristics was carried out theoretically and the results were confirmed experimentally. The instrument is capable of measuring the mean square value of periodic waveform to within 2%. Normal distribution noise of standard deviation between 1V and 3V can be measured with similar accuracy. The accuracy and the upper frequency limit are determined by the ' aperture time'of the sampling process. The errors arising in the sampling instrument depend on the number of levels used.