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Comparative Analysis in Capacity Measurements

Veselka Ivancheva1), Radoslav Deliyski1) Krasimir Galabov1),
Bozhidar Dzhudzhev
1), Silviya Kachulkova1)

1) Technical University-Sofia, Faculty of Automatics, Department of Electrical Measurements, Sofia 1000, 8 Kliment Ohridski blvd,

e-mails: ivancheva@, rdeliyski@yahoo.co.uk, k_galabov@tu-sofia.bg, bojidar.djudjev@abv.bg, kachulkova@abv.bg

Web address: www.tu-sofia.bg

Abstract: In this paper comparative analysis in capacity measurements is accomplished. Multiple capacity readings are sampled trough RLC meters, Vin’s bridge as well as NI ELVIS II. A multifunctional calibrator CX 1651 is used to reproduce a true capacity values within the range of 1nF to 50μF. The data was analyzed through determination of relative and mean square errors as well as Hellinger and Bray Curtis distances.

Key-Words: capacity, dissipation factor, AC bridges, conformance measures, Hellinger and Bray Curtis metrics.

1. Introduction

Measuring components of the complex impedance (real and imaginary part, modulus and phase) and the parameters of the circuits (active resistors, capacities, inductances, mutual inductance, dissipation factor, quality factor, etc.) is one of the traditional tasks of the electrical measurements…..

…..Consequently different compartment approaches can be applied. In this paper MSE, Hellinger and Bray-Curtis distance are used.

2. Methodology

Bridge circuits are among the most commonly used method for capacity measurement. …..

2.1. Methods for measuring parameters of a capacitor

The state of a linear circuit with a sine AC depends on the complex impedance . Having a capacitor, the impedance Z is completely determined if we know two of its scalars values - capacity C and dissipation factor [1]. …….

The determination of the two components of the complex impedance is carried out most accurate with Vin’s AC Bridge. This circuit is used to measure the capacity of capacitors with small losses.

2.2. Comparative metrics

When compare measurement readings, variety of metrics can be applied. Among the most common are absolute and relative errors. However the math theory gives us more metrics to find similarity between two vectors or scalars….

Relative error is not the only metric include in the analysis. Mean square error, Bray-Curtis distance [3] and Hellinger distance [4] are additional metrics used. Bray–Curtis metrics is usually used in ecology and biology to quantify the dissimilarity between two different sites. On the other hand Hellinger distance is used to quantify the similarity between two probability distributions. Though both of them are famous in the math society, no indication they are used in measurement techniques. Equations defining the metrics used in the analysis are as follow:

(1)

(2)

(3)

(4),

where: BC is BrayCurtis distance; H is Hellinger distance; MSE is Mean square error;  is relative error; X is true value; Xm is average measured value.

3. Experiments

Four different measurement tools were used to collect the data for processing. Every one of the tools measured ten times the applied true value. By multifunctional calibrator CX 1651 the following true values of capacity were reproduced: 950 pF, 2 nF, 5 nF, 9 nF, 20nF, 40 nF, 90 nF, 200nF, 500 nF, 750 nF, 1, 2, 3, 5, 7, 5, 10, 20, 50. The measurement tools used in experiments were: LCR meter Escort ELC-131D, Digital LCR meter E7-8, ELVIS II and Instrumentation module TK2941A by Feedback. The connection between the measuring instruments and the calibrator is shown in figure 1.

Fig, 1. Experimental set

3.1. Multifunction Calibrator CX 1651.

CX 1651 is used for calibration of measuring instruments for the next values: voltage, current, resistance, capacitance, ….

The capacity range is from 900 pF to 50 μF (Table 1). The basic accuracy of the capacity range is 0.5%. Frequency range in resistance is 300 Hz to 1 kHz.

Table 1

range

uncertainty of value [%]

max. frequency

900 pF - 2.5 nF

0.5 + 15 pF

1000 Hz

2.5 nF - 10 nF

0.5 + 5 pF

1000 Hz

10 nF - 50 nF

0.5

1000 Hz

50 nF – 250 nF

0.5

1000 Hz

250 nF - 1μF

0.5

500 Hz

1μF – 2.5μF

1

300 Hz

2.5μF - 5μF

1

300 Hz

5μF – 10μF

1.5

300 Hz

10μF - 50μF

2.0

300 Hz

When measuring the parameters of a circuit, specific air conditions must be monitored ……

3.2. Metrological characteristics of measuring instruments.

In table 2 the metrological characteristics of the instruments used for measuring the parameters of the capacitor are given.

Table 2

Measuring instrument

Range

Accuracy for Capacitance

Selectable Test Frequency:

1

Escort ELC-131D

1,000 pF to 10 mF

0.7% Basic

120Hz/1kHz

2

LCR E7-8

0.01 pF to 100µF

n/a

1000Hz

3

NI ELVIS II

50 pF to 500 pF

500 pF to 500 μF

1%

10 kHz

1 kHz

4

Instrumentation module TK2941A by Feedback.

n/a

n/a

300 to 1000Hz

4. Results

The statistic gives us lots of tools to process measured data and represent every sample with only one point. Among the most famous are: range, standard deviation, median, mode…….

All results were processed by the software product Octave [8]. Octave is distributed under General Public License GNU and is free open source solution used in numerical computations through high-level language very similar to those used in Matlab. Its graphical and visual capabilities as well as its portability turn it into a great substitution of Matlab.

Table 3. True measured values used

True value

950pF

2nF

5nF

90nF

200nF

500nF

750nF

1μF

2μF

3μF

5μF

7,5μF

10μF

20μF

50μF

Escort ELC-131D

Measured

average value

0.960

2.013

5.011

89,986

200,2

500

750,86

1,001

1,999

3,012

5,028

7,551

10,061

20,05

47,531

LCR E7-8

Measured average value

n/a-

1.800

4.80

89,7

199,9

499,3

749,8

1,004

2,018

3,042

5,04

7,558

10,7

20,88

49,92

NI ELVIS II

Measured average value

n/a

n/a

5.08

90,58

201,84

503,73

756,62

1,01

2,02

3,05

5,09

7,68

10,29

20,84

50,8

Vine bridge

Measured average value

n/a

n/a

n/a

90

200

500

750

1

1,99

2,99

4,99

7,403

9,9

n/a

n/a

Table 3 above presents true and measured average values for the fourth measurement tools when 950 pF, 2 nF and 5 nF were applied. The results clearly show that …..

A bit more readable results are provided by Hellinger distance (Fig. 3). Again Digital meter LCR E7-8 and NI ELVIS give the highest value in 10 µF. …..

All results presented above follow the pattern of increasing the error/distance when increasing the true value. However, much more reliable results could be obtained if relative errors/distances are used…….

Fig. 3.Hellinger distance

From the other side, Bray-Curtis distance (Figure 4) gives the lowest values in the range of about 0.50 µF. When ….

Fig. 4. Bray-Curtis distance

……………………

5. Conclusions

All methods proved that the most inaccurate measurement tool used in experiments is the Digital LCR Meter E7-8 followed by NI ELVIS II. On the other hand when …

To eliminate these disadvantage relative methods could be applied. However, there is no analogy between the relative Hellinger and Bray-Curtis distances and classical relative methods (Relative MSE). Consequently relative Hellinger and Bray-Curtis distances are not applicable to capacity comparatives.

6. References

[1] H. K. Radev. Metrologiya i izmervatelna tehnika, tom 1,2,3, Sofiya, Softreyd, 2010, ISBN 978-954-334-094-1

[2] B. I. Matrakov. Elektricheski izmervaniya, Sofiya, IPK pri TU, 1999

[3] /

mathematica/guide/DistanceAndSimilarity

Measures.html, accessed on June 24th, 2013

……………

[8] /software/octave/,

accessed on June 24th, 2013

Acknowledgments

This paper presents the results obtained from the work of the project …..

Authors:

Veselka Marinova Ivancheva, MSc in Electronics (1978), PhD in Electronics (2000), Assoc. prof. (2002) in the Department of Electrical Measurements, Faculty of Automatics, Technical University Sofia, Bulgaria. Scientific field and interests: Electrical Measurements, Measurement of Non-electrical Quantities.

Radoslav Tsvetkov Deliyski. MSc in Automatics, Informatics and Control Engineering (2002), PhD in Robotics and Manimulators (2009). Senior assistant professor (2009) in the Department of Electrical measurenments, Faculty of Automatics, Technical University of Sofia, Bulgaria. Scientific field and interests: Statistical Process Control, Visual Quality Control System, Intelligent Measurment Systems.

Krasimir Simeonov Galabov, MSc in Automatics, Informatics and Control Engineering (2007), Assistant professor (2010) in the Department of Electrical Measurements, Faculty of Automatics, Technical University Sofia, Bulgaria. Scientific field and interests: metrology, virtual instruments.

Сравнительный анализ измерений емкости

Веселка Иванчева1), Радослав Делийски1), Kрасимир Гълъбов1),
Божидар Джуджев1), Силвия Качулкова1)

1)Технический университет-София, Факультет Автоматики, Кафедра „Электроизмерительной техники“, София 1000, бул. Климент Охридски № 8

e-mails: ivancheva@yahoo.com , rdeliyski@yahoo.co.uk, k_galabov@tu-sofia.bg , bojidar.djudjev@abv.bg , kachulkova@abv.bg

Web address: www.tu-sofia.bg

Резюме: В докладе представляется сравнительный анализ измерений емкости. Многократно измерены данные значения емкости RLC прибором, мостом Вина, а так же и NI ELVIS II. Для задания эталонного значения емкости в диапазоне от 1nF до 50μF использован многофункциональный калибратор CX 1651. Полученные данные анализированы определением относительной и средно-квадратической погрешностью, а так же и через определеним расстоянием Хелингера и Брей-Картиса.

Ключевые слова: емкость, мосты переменного тока, определение соответствия, расстояния Хелингера и Брей-Картиса

Сравнителен анализ при измерване на капацитет

Веселка Иванчева1), Радослав Делийски1), Kрасимир Гълъбов1),
Божидар Джуджев1), Силвия Качулкова1)

1)Технически университет-София, Факултет Автоматека, Катедра „Електроизмервателна техника“, София 1000, бул. Климент Охридски № 8

e-mails: ivancheva@yahoo.com , rdeliyski@yahoo.co.uk, k_galabov@tu-sofia.bg , bojidar.djudjev@abv.bg , kachulkova@abv.bg

Web address: www.tu-sofia.bg

Резюме – В този доклад се извършва сравнителен анализ при измерване на капацитет. Многократно са измерени стойности на капацитет с RLC уреди, мост на Вин, както и с NI ELVIS II. За задаване на еталонна стойност в обхвата от 1nF до 50μF е използван многофункционален калибратор CX 1651. Получените данни са анализирани чрез определяне на относителната и средно-квадратична грешка, а също така и чрез определяна на разстоянието на Хелингер и на Брей-Къртис.

Ключови думи: капацитет, мостове за променлив ток, определяне на съответствие, разстояния на Хелингер и Брей-Къртис

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