MEASUREMENT 2017, Proceedings of the 11th International Conference, Smolenice, Slovakia
Comparison of DMM characterization methods based on
RMS noise and standard deviation noise
H. Hegeduš1, J. Konjevod1, P. Mostarac1, R. Malarić1
1
Faculty of electrical engineering and computing, Zagreb, Croatia,
Email: {hrvoje.hegedus, jure.konjevod, petar.mostarac, roman.malaric}@fer.hr
Abstract. Analogue to digital converters (ADCs) are very important component of digital
multimeters for defining their accuracy. Along with ADC’s specifications that are described in
this paper, there are also “real” parameters that describe how DMMs and ADCs fare in real
world with the presence of noise. Those parameters include, but are not limited to signal-tonoise ratio, effective resolution, effective bits, noise free resolution, etc. The purpose of this
paper is to test and compare different DMMs in 6,5-7,5 digit range using the specific formula
for effective resolution.
Keywords: Effective resolution, RMS noise, Standard deviation noise, Voltage range
1. Introduction
Analogue to digital converters (ADCs) are the main components of digital multimeters
(DMMs) that define their final accuracy. DMMs and ADCs usually come with very different
specifications. While DMMs are usually defined by number of digits (6,5 digit being the most
common, and 8,5 the most accurate but also the most expensive), the analogue to digital
converters are defined primarily with number of bits (16 and 24 bits being the most common,
32 bits the most accurate). Number of digits (NOD) in DMM is analogous to number of bits
(NOB) and both are related to the total number of counts (NOC), and NOC is related to total
span (TS) divided by absolute unit of resolution (AUOR):
𝑇𝑆
𝑁𝑂𝐵 = log 2 𝑁𝑂𝐶 = log 2 𝐴𝑈𝑂𝑅,
𝑇𝑆
𝑁𝑂𝐷 = log10 𝑁𝑂𝐶 = log10 𝐴𝑈𝑂𝑅.
(1)
(2)
While NOB and NOD are specified by manufacturer, from the user perspective more interested
parameter is effective resolution: effective number of bits (ENOB) for ADCs and effective
number of digits (ENOD) for DMMs [1]. This effective resolution tells end user how really
good ADC or DMM is. It depends on effective absolute unit of resolution (EAUOR) which is
depended on real RMS noise of ADC or DMM [3] and:
𝐸𝐴𝑈𝑂𝑅 = 𝑅𝑀𝑆 𝑁𝑜𝑖𝑠𝑒 ∙ √12
𝐸𝑁𝑂𝐵 = log 2
𝑇𝑆
𝐸𝐴𝑈𝑂𝑅
𝑇𝑆
= log 2
𝑇𝑆
𝑅𝑀𝑆 𝑁𝑜𝑖𝑠𝑒∙√12
𝑇𝑆
𝐸𝑁𝑂𝐷 = log10 𝐸𝑁𝑂𝐶 = log10 𝑅𝑀𝑆 𝑁𝑜𝑖𝑠𝑒∙√12
(3)
(4)
(5)
These formulas, not only the one Holub and Vedral described [4] but all the other ones are
centered around the RMS noise, and sometimes peak to peak noise. Noise, as it turns out is not
so difficult to measure, as one only needs the jumper wire to short the input of the DMMs and
measure the zero value at different settings (NPLC and range).
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MEASUREMENT 2017, Proceedings of the 11th International Conference, Smolenice, Slovakia
2. Measurement Method
Testing method used in this paper is based on measuring noise on all DC voltage ranges across
all sample rates (NPLC) with shorted DMM input terminals. On every voltage range and sample
rate an acquisition of 1000 samples were made and analyzed by calculating average value (𝑥̅ ),
standard deviation (𝜎) and RMS (𝛹):
1
1
1
𝑁
𝑁
2
2
𝑥̅ = 𝑁 ∑𝑁
𝑖=1 𝑥𝑖 , 𝜎 = √𝑁−1 ∑𝑖=1(𝑥𝑖 − 𝑥̅ ) , 𝛹 = √𝑁 ∑𝑖=1 𝑥𝑖 .
(6, 7, 8)
On every combination of voltage range and sample rate each DMM is tested 10 times so the
̅ ) can be calculated using next equations:
average values of standard deviation (𝜎̅) and RMS (𝛹
1
̅ 1 10
𝜎̅ = 𝑁 ∑10
𝑗=1 𝜎𝑗 , 𝛹 = 𝑁 ∑𝑗=1 𝛹𝑗 .
(9, 10)
From this point, ENOB and ENOD can be easily calculated, but in this paper RMS Noise and
standard deviation of noise are presented in relative form in relation to measurement range (or
total span TS) expressed as PPM of range:
̅
̅
𝜎
̅𝑟 = 𝛹 ∙ 106
𝜎̅𝑟 = 𝑇𝑆 ∙ 106 , 𝛹
𝑇𝑆
(11, 12)
For the purpose of automated testing of these DMMs two applications were developed in
LabVIEW software. First application was developed for PC platform for testing DMMs that
were connected to PC with GPIB or USB connections. Second application was developed for
NI PXI real time platform and was used for testing DMMs in form of NI PXI cards.
3. Results
Results of testing six DMMs with shorted input terminals are presented on next six figures.
Fig. 1.
Agilent 34461A RMS noise and Standard deviation noise acros all ranges and NPLCs
Fig. 2.
GWinstek GDM-8261 RMS noise and Standard deviation noise acros all ranges and NPLCs
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MEASUREMENT 2017, Proceedings of the 11th International Conference, Smolenice, Slovakia
Fig. 3.
Keithley 2000 RMS noise and Standard deviation noise acros all ranges and NPLCs
Fig. 4.
NI PXI-4071 RMS noise and Standard deviation noise acros all ranges and NPLCs
Fig. 5.
NI PXI-4072 RMS noise and Standard deviation noise acros all ranges and NPLCs
Fig. 6.
NI PXI-4071 and PXI-4072 RMS noise with option autozero OFF
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MEASUREMENT 2017, Proceedings of the 11th International Conference, Smolenice, Slovakia
Fig. 7.
Rigol DM3061 RMS noise and Standard deviation noise acros all ranges and NPLCs
For all tested DMMs ENOD RMS is calculated based on RMS noise and ENOD Stdev is
calculated based on standard deviation of noise (all measured at 1 V and 1 NPLC, except Rigol
at 2 V and 2,2 NPLC). This ENODs are compared in Table 1. with factory specified NOD.
Table 1. Comparison of DMM’s factory specified NOD with measured ENOD RMS and ENOD Stdev (results in
brackets for NI-PXI DMMs are with Autozero ONCE option)
DMM model
Factory NOD
Range [V]
Sampling time
[NPLC]
ENOD RMS
(1V, 1 NPLC)
ENOD Stdev
(1V, 1 NPLC)
GDM-8261
Keithley
2000
NI-PXI
4071
NI-PXI
4072
Rigol DM
3061
6,5
0,1 - 1000
6,5
0,1 – 1000
6,5
0,1 – 1000
7,5
0,1 – 1000
6,5
0,1 – 300
6,5
0,2 – 1000
0,02 – 100
0,1 – 12
0,01 – 10
0,01 – 20
0,01 – 20
2,5 – 22
5,37
5,21
5,41
4,02 (5,86)
3,94 (5,66)
4,40
5,71
5,48
5,77
6,00
5,73
5,67
Agilent
34461A
GW Instek
4. Conclusions
This paper showed two similar approaches of calculating effective number of digits (ENOD).
Calculating ENOD based on RMS noise includes error of offset which can often be reduced
with autozero function on DMMs. Calculating ENOD based on standard deviation noise will
produce a better results on same DMM because offset error is not included in measured noise.
References
[1] IEEE Std 1241-2000, IEEE Standard for Terminology and Test Methods for Analog-toDigital Converters
[2] http://zone.ni.com/reference/en-XX/help/370384N-01/dmm/resolution_bits_digits/,
National Instruments
[3] Jerome J. Blair, Thomas E. Linnenbrink, Corrected rms error and effective number of bits
for sine wave ADC tests. Computer Standards & Interfaces 26, 2003, USA
[4] Vedral, J., Holub, J.. Measurements of Effective Resolution of ADC in Microconvertor
ADUC834. 7th IEEE International Workshop on DDECS, April 18 – 21, 2004, Slovakia.
Acknowledgments
This paper is fully supported by Croatian Science Foundation under the project Metrological
infrastructure for smart grid IP-2014-09-8826.
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