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 ta = aperture time t0 = initial phase ta[T] = aperture time in percentage of a period F = frequency Fs = 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(t0[T] + F·360.0· i/Fs), • • • • for i = 0, 1, 2, …, n – 1. Sampling info: #s = ta[T]·NRDGS, Fs = 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. ta[T]=0,125 and t0[T]=0,1 CORRECTING RMS – SIMULATION PART RMS’ = RMS + A·(1 – sinc (π·ta [T])) 0,0 NRDGS=115 1,0 NRDGS=116 NRDGS=197 0,1 NRDGS=198 NRDGS=199 0,2 NRDGS=117 2,0 0,0 NRDGS=200 0,3 NRDGS=118 3,0 0,4 4,0 0,5 5,0 0,6 6,0 0,7 7,0 0,8 8,0 0,9 9,0 1,0 0,0 0,1 10,0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 ta [T] NRDGS 0,7 0,8 0,2 0,3 0,4 0,5 0,6 ta [T] 0,7 0,8 0,9 1,0 0,9 1,0 0,02 0,04 0,06 0,08 0,1 51 0,97940 0,99841 1,00009 0,99875 0,99557 100 1,01250 1,01304 1,00903 1,00371 0,99538 150 1,01404 1,01385 1,01249 1,00540 0,99905 200 1,00220 1,00634 1,00673 1,00392 0,99810 f = 100 Hz ta [T] CORRECTING RMS – REAL DATA CORRECTING RMS – REAL DATA Difference (RMS’’- RMS’) [ppm] ta [T] 0,05 0,1 1. sequence 13,3201 12,6495 2. sequence 34,8920 35,2091 3. sequence 38,6472 44,1362 4. sequence 27,7107 57,5519 7 V range, 50 Hz 0,15 -610,262 -208,972 -361,246 -445,994