Determination of DC voltage ratio of a self calibrating DC voltage divider (ling xiang liu, sze wey chua, member, IEEE, and chee kiang ang) liu2005

Determination of DC Voltage Ratio of aSelf-Calibrating DC Voltage Divider Ling Xiang Liu, Sze Wey Chua, Member, IEEE, and Chee Kiang Ang Abstract—This paper presents two techniques for d

Determination of DC Voltage Ratio of a

Self-Calibrating DC Voltage Divider

Ling Xiang Liu, Sze Wey Chua, Member, IEEE, and Chee Kiang Ang

Abstract—This paper presents two techniques for determining

the ratios of resistive dc voltage dividers up to 1 kV The

tech-niques are based on absolute calibration methods The setup

re-quires equipment commonly available in most standard

laborato-ries and is capable of providing high-accuracy calibration under

practical laboratory working conditions.

Index Terms—Calibration, dc voltage, dc voltage ratio,

self-cali-brating divider.

I INTRODUCTION

FOR a resistive divider that offers access to its equally

divided resistance chain, its voltage ratio, a

dimension-less quantity, can be determined using an absolute calibration

method and without the need of a reference voltage divider

Such a divider is often referred to as being capable of being

“self-calibrated,” as any two individual sections of the divider

can be compared by a suitable procedure With a complete

independent set of comparison results, all voltage ratios of the

self-calibrating divider can be determined

Absolute calibration methods to determine the ratio of a dc

voltage divider have been reported and are used in standard

labo-ratories [1]–[10] In this paper, we present the techniques, setup

and results of the calibration of dc voltage ratios based on two

absolute calibration methods initially reported in [2] The setup

requires equipment commonly available in most standard

labo-ratories and is capable of providing high-accuracy calibrations

under practical laboratory working conditions

II REFERENCEVOLTAGESOURCEBOOTSTRAPMETHOD

Fig 1 shows the schematic circuit diagram for determining

the dc voltage ratio of a self-calibrating resistive divider with

10 equal section taps The guarding and shielding

arrange-ments are not shown in the diagram

This method requires two dividers—a divider under test

and an interim divider , each having equal sections

and are lead compensators for equalizing the voltage drops

of the leads to and A stable Zener voltage standard is used

as reference voltage source and a high-impedance null detector

is used to measure the voltage difference between the taps of the

two dividers All parameters associated with the interim divider

are denoted by a superscript

Manuscript received July 2, 2004; revised November 5, 2004.

The authors are with the Electrical Metrology Department, National

Metrology Center, Standards, Productivity and Innovation Board (SPRING),

Singapore 118221, Republic of Singapore (e-mail: llx@spring.gov.sg).

Digital Object Identifier 10.1109/TIM.2004.843089

Fig 1 Schematic circuit of the reference voltage source bootstrap method The configuration shown is for comparing n sections of divider D with (n01) sections of D connected in series with the Zener voltage standard.

The sections’ ratio is the cumulative ratio (0 to tap)

of the th tap with a nominal value of We assume that

, where is the ratio of a particular section and is the sections’ ratio of the divider at the

th tap The ratio error of section is given by

(1) For a ratio device with sections, we have

(2)

where is the ratio error of the th section of the device The operation of the reference voltage source bootstrap method is

as follows: with the switch in position , the voltages at the same taps of the two dividers are directly compared using the null detector We obtain

(3)

0018-9456/$20.00 © 2005 IEEE

where is the null detector reading expressed as a fraction

of the nominal input voltage Hereafter, all reference to a

null detector reading will refer to the reading expressed in this

manner

The switch is then turned to position II to introduce a stable

reference voltage with nominal value of

Compar-isons are now made between sections of against

sections of in series with the reference voltage source We

obtain

(4) where is the reading from the null detector divided by the

input voltage

The cumulated ratio error of sections’ ratio from

its nominal value , is then

(5)

Equation (5) gives the cumulative ratio error of the voltage

di-vider from the observed null detector readings The ratio errors

of the individual sections of the divider can be calculated

test have been determined, the ratios of the interim divider

can be calculated using (3)

III REVERSESTAGGERMETHOD

The schematic circuit in Fig 2 illustrates the operation

prin-ciple of the reverse stagger method for calibrating a resistive

divider with equal section taps Here, provides the

re-versing operation and provides the staggering operation

is a standard resistor with the same nominal resistance value as

a single section of the interim divider

First, the ratio differences between the corresponding

indi-vidual sections of and from to for an even

number or for an odd number are measured We

obtain

(6) where is the null reading at the th sections tap divided

by the nominal input voltage , and the subscript denotes the

“forward” connection reading The null reading of an individual

section is therefore

(7) where is the null reading at the th taps Hence,

the ratios and for the th section of the dividers can be

related by

(8)

Fig 2 Schematic circuit of the reverse stagger method The configuration shown is for S in the forward position and S set so that R is connected

in series with the sections 0 to 9 of D

Similarly, by reversing , we can obtain

(9) From (8) and (9), we have

(10)

standard resistor is connected in series with the Sections 0

to of using switch The position of switch determines whether is connected at tap 0 or tap

By repeating the same procedure, we obtain equations similar

to (10)

(11)

the ratio error of each section becomes

(12)

Together with (2), the relative error of each section can be obtained from the unique solution of the set of equations from all these measurements as shown below

TABLE I

M EASURED R ELATIVE R ATIO E RRORS 1 , IN 10 , FOR TWO 4902S D C V OLTAGE D IVIDERS , U SING THE R EFERENCE V OLTAGE S OURCE B OOTSTRAP M ETHOD

When is odd

(13)

When is even

(14)

TABLE II

M EASURED R ATIO E RRORS 1 , IN 10 , FOR ONE 4902S DC V OLTAGE D IVIDER U SING THE R EVERSE S TAGGER M ETHOD AND THE

R EFERENCE V OLTAGE B OOTSTRAP M ETHOD

TABLE III

U NCERTAINTY B UDGET FOR C ALIBRATION OF THE D IVIDER U SING THE

R EFERENCE V OLTAGE B OOTSTRAP M ETHOD

Due to measurement noise, short-term drift, etc., the system

of equation in (13) and (14) will not be consistent Hence, a

statistical estimation method should be used to evaluate the best

estimates of the ratio errors

IV MEASUREMENTRESULTS

Measurements were carried out on three Datron 4902S dc

voltage dividers The experimental results using the reference

voltage source bootstrap method with the reference voltage from

one 10-V Zener voltage standard for the 100 V/10 V range

ra-tios, and ten 10-V Zener voltage standards connected in series

for the 1 kV/100 V range ratios showed good repeatability The

agreement between the ratio errors of the individual sections

of the same unit using different interim dividers, was better

than 1 10 and 3 10 on the 100 V/10 V range and the

1 kV/100 V range, respectively, as shown in Table I

The experimental results using the reverse stagger method

are shown in Table II A comparison between the

experi-mental results obtained using the reference voltage source

bootstrap method and those obtained using the reverse stagger

method, for measuring the ratios of the individual sections

of the same divider under test, shows that the differences

between corresponding measured voltage ratios using the two

different methods are less than 1.5 10 and 3.5 10 on

the 100 V/10 V range and the 1 kV/100 V range, respectively

The estimated expanded uncertainties are less than

2 10 and 5 10 for the 100 V/10 V range ratios and the

TABLE IV

U NCERTAINTY B UDGET FOR C ALIBRATION OF THE D IVIDER U SING THE

R EVERSE S TAGGER M ETHOD

1 kV/100 V range ratios, respectively Typical measurement un-certainties expressed as a fraction of the nominal input voltage are summarized in Tables III and IV

V CONCLUSION

In this paper, two methods for absolutely determining the dc voltage ratios of a self-calibrating divider, the reference voltage source bootstrap method, and the reverse stagger method are discussed Experimental results have shown that for a divider under test, the differences between the voltage ratio errors determined by the two methods are less than 1.5 10 and 3.5 10 for the 100 V/10 V and 1 kV/100 V ratio taps, respectively These two methods are now used in the SPRING Singapore’s Electrical Metrology Laboratory for calibration of

dc voltage dividers as well as providing a means for the labora-tory to crosscheck the calibration results for any discrepancy in the dc voltage ratio measurements

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