1. 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

2. 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

3. 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 1 - 1000 V and 1 - 100 Hz ranges.

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

5. CORRECTING RMS – SIMULATION PART RMS’ = RMS + A·(1 – sinc (π·t a [T])) NRDGS0,020,040,060,080,1 510,979400,998411,000090,998750,99557 1001,012501,013041,009031,003710,99538 1501,014041,013851,012491,005400,99905 2001,002201,006341,006731,003920,99810 f = 100 Hzt a [T]

6. CORRECTING RMS – REAL DATA

7. Difference (RMS’’- RMS’) [ppm] t a [T]0,050,10,15 1. sequence13,320112,6495-610,262 2. sequence34,892035,2091-208,972 3. sequence38,647244,1362-361,246 4. sequence27,710757,5519-445,994 7 V range, 50 Hz