CORRECTING RMS VALUE OF A SINE WAVEFORM SAMPLED DUE LIMITED NUMBER OF PERIODS AND DETERMINATE APERTURE TIME ON DMM Keywords: Digital Multimeter (DMM), Root Mean Square (RMS) Error, Sampling, Aperture Time, Number of Samples

NOMENCLATURE DC = direct current AC = alternating current A/D = analog-to-digital RMS = root-mean-square t a = aperture time t 0 = initial phase t a [T] = aperture time in percentage of a period F = frequency F s = sampling frequency n = number of samples ppm = part per million

ROOT MEAN SQUARE Sine waveform segments can be generated according to the following equation: y[i] = A· sin(t 0 [T] + F·360.0· i/F s ), for i = 0, 1, 2, …, n – 1. Sampling info: #s = t a [T]·NRDGS, F s = F·NRDGS. Initial phase can vary. From collected mean values, LabVIEW and Swerlein algorithm (implemented in DMM 3458A instruments) calculates RMS value of a signal waveform. The standard uncertainty associated with the RMS estimate depends on the waveform stability, harmonic content, and noise variance, was evaluated to be less than 5·10 -6 in the V and Hz ranges.

t a [T]=0,125 and t 0 [T]=0,1

CORRECTING RMS – SIMULATION PART RMS’ = RMS + A·(1 – sinc (π·t a [T])) NRDGS0,020,040,060,080,1 510,979400,998411,000090,998750, ,012501,013041,009031,003710, ,014041,013851,012491,005400, ,002201,006341,006731,003920,99810 f = 100 Hzt a [T]

CORRECTING RMS – REAL DATA

Difference (RMS’’- RMS’) [ppm] t a [T]0,050,10,15 1. sequence13,320112, , sequence34,892035, , sequence38,647244, , sequence27,710757, ,994 7 V range, 50 Hz