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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

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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
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
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, LabVIEWand 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 5·10-6in the 1-1000V and 1-100 Hzranges.
correcting rms simulation part
CORRECTING RMS – SIMULATION PART

RMS’ =RMS + A·(1 – sinc (π·ta [T]))