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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



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