### CORRECTING RMS VALUE OF A SINE WAVEFORM SAMPLED DUE LIMITED NUMBER

```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
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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),
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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
```