NIST Technical Note 1298

NIST Measurement Service for

DC Standard Resistors

Ronald F. Dziuba

Paul A. Boynton

Randolph E. Elmquist

Dean G. Jarrett

Theodore P. Moore

Jack D. Neal

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

November 1992

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u.s. Department of Commerce

Barbara Hackman Franklin, Secretary

Technology Administration

Robert M. White, Under Secretary for Technology

National Institute of Standards and Technology

John W. Lyons, Director
National Institute of Standards

and Technology

Technical Note 1298

Natl. Inst. Stand. Technol.

Tech. Note 1298

65 pages (Nov. 1992)

CODEN: NTNOEF

u.S. Government Printing Office

Washington: 1992

For sale by the Superintendent

of Documents

U.S. Government Printing Office

Washington. DC 20402
CONTENTS

1. INTRODUCTION 1

2. DESCRIPTION OF SERVICE 2

2.1 Special Standard Resistors (1 Q and 10 kQ) . . . . . . . . . . . . . . . . . . . . . . . .. 2

2.2 Standard Resistors (10.4Q to 106Q) 3

2.3 High-Value Standard Resistors (107 Q to 1012Q) 3

2.4 Resistance MAP Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3

2.5 Special Resistance Measurements 4

3. MEASUREMENT METHODS 4

4. DIRECT CURRENT COMPARATOR SySTEMS .. 5

4.1 Theory of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6

4.2 DCC Potentiometer System for 1 Q Measurements . . . . . . . . . . . . . .. 8

4.2.1 Description of System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8

4.3 DCC Potentiometer for 10 Q and 100 Q Measurements. . . . . . . . . . . . . . .. 12

4.3.1 Description of System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12

4.4 DCC Resistance Bridge 13

4.4.1 Description of System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 13

4.4.2 Measurement Parameters and Design 14

5. RESISTANCE-RATIO BRIDGES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15

5.1 Theory of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16

5.2 Modified Kelvin Bridge for 10 kQ Measurements. . . . . . . . . . . . . . . . . . .. 18

5.3 Guarded Wheatstone Bridge 20

6. RING METHOD ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22

6.1 Theory of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22

6.1.1 First Subset of Voltage Measurements. . . . . . . . . . . . . . . . . . . . .. 23

6.1.2 Second Subset of Voltage Measurements. . . . . . . . . . . . . . . . . . .. 25

6.1.3 Third Subset of Voltage Measurements. . . . . . . . . . . . . . . . . . . .. 25

6.2 .Data Analysis 25

6.3 Guard Network 27

7. TERAOHMMETER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27

7.1 Description of System . . .. 28

8. RESISTANCE SCALING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28

8.1 Quantized Hall Resistance Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29

8.2 Transfer Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30

8.3 DCC Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34

8.4 Teraohmmeter Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34

1lI
9. MEASUREMENT UNCERTAINTY 34

9.1 Model - Standard Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35

9.2 Model - Measurement Systems 35

9.3 Type A Standard Uncertainty 36

9.4 Type B Standard Uncertainty 41

9.4.1 Standard Resistors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41

9.4.2 Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42

9.5 Reported Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48

10. QUALITY CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48

11. ONGOING PROJECTS 49

12.ACKNO~EDGMENTS 49

13. REFERENCES 50

14. BIBLIOGRAPHY 52

15. APPENDIX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53

15.1 Typical Report of Calibration 54

15.2 Report for a 1 Q Standard Resistor 55

15.3 Report for a 10 kQ Standard Resistor. . . . . . . . . . . . . . . . . . . . . . . . . . .. 56

15.4 Report for a High Value Standard Resistor. . . . . . . . . . . . . . . . . . . . . . .. 57

15.5 Information Sheet on Standard Resistors. . . . . . . . . . . . . . . . . . . . . . . . .. 58

IV
--

NIST MEASUREMENT SERVICE FOR DC STANDARD RESISTORS

Ronald F. Dziuba, Paul A. Boynton, Randolph E. Elmquist,

Dean G. Jarrett, Theodore P. Moore, and Jack D. Neal

Abstract -At the National Institute of Standards and Technology (NIST), the US. representation

of the ohm is based on the quantum Hall effect, and it is maintained and disseminated at various

resistance levels by working reference groups of standards. This document describes the

measurement systems and procedures used to calibrate standard resistors of nominal decade

values in the resistance range from 10.4Q to 1012Q. Resistance scaling techniques used to

assign values to the working standards are discussed. Also included is an assessment of the

calibration uncertainties at each resistance level.

1. INTRODUCTION

Since January 1, 1990, the US. representation of the ohm has been based on the quantum Hall

effect in which a resistance is related to the ratio of fundamental constants hle2 [1,2]. The

quantized Hall resistance, RH,is defined as the quotient of the Hall voltage VHof the ithplateau

to the current I in the Hall device and is given by

RH(i) = VH(i)/I = RK/i,

where the von Klitzing constant RK is believed to be equal to hle2, and i is an integer of the

quantum Hall state. The value of the U S. representation of the ohm is consistent with the

conventional value of the von Klitzing constant, i. e.,

RK.90= 25,812.807 Q,

exactly, adopted internationally for use in representing the ohm beginning January 1, 1990. This

conventional value is believed to be consistent with the SI Q to within 0.005 Q which is the

value assigned to be the combined standard uncertainty, corresponding to a relative uncertainty

of 0.2 ppm. Because this uncertainty is the same for all national laboratories and is not relevant

for traceability to national standards, it is not included as a component of the uncertainties given

in NIST Reports of Calibration for standard resistors. However, its existence must be taken into

account when the utmost consistency between electrical and non-electrical measurements of the

same physical quantity is required.

For precision measurements using the quantum Hall effect, the integer i is usually chosen to be

either 2 or 4 resulting in quantized Hall resistances of 12,906.4035 Q or 6,453.20175 Q [3].

These odd resistance values, along with the complexity of the experiment, do not lend themselves

to the routine support of the calibration of standard resistors of nominal decade values.

Therefore, at NIST the ohm is maintained for calibration purposes at the 1 Q level via a group

of Thomas-type resistors whose predicted mean value is checkedperiodically against the quantum

Hall effect and adjusted, if necessary.

1
NIST provides a calibration service for standard resistors of nominal decade values (i.e., R = 10i

where i is an integer) in the range between 10-40 and 10120. To provide this wide-ranging

calibration service, NIST maintains a working reference group at each nominal decade value.

The working reference groups are calibrated against the 1 0 reference group using special ratio

techniques. A customer's resistor is calibrated against the NIST working reference group in a

manual or an automated comparison measurement system using either a resistive-ratio bridge, a

flux-balancing type of current comparator, or a capacitance-discharge system. The specific

measurement system used depends upon the value of the resistor being calibrated and on the

accuracy required or warranted. NIST procedures follow recognized dc measurement practices

such as current reversal, minimum power dissipation consistent with desired resolution and

accuracy, and the use of check standards and statistical data analysis techniques to monitor the

operation of the measurement systems.

2. DESCRIPTION OF SERVICE

NIST provides a calibration service for standard resistors with nominal decade values in the range

between 10-40 and 10120. In addition to this regular calibration service, NIST offers a

resistance Measurement Assurance Program (MAP) service at the 1 0 and 10 kO levels. Other

special resistance measurements are undertaken if they require the unique capabilities of NIST.

The latest issue of the NIST Special Publication 250 entitled "NIST Calibration Services Users

Guide" contains detailed descriptions of the currently available NIST calibration services [4]. It

also contains information on the scheduling of these services along with recommended procedures

for shipping a standard to NIST for calibration. A separate Fee Schedule, NIST Special

Publication 250 Appendix, lists the costs of services, and it is updated periodically to reflect

changes in prices and services.

2.1 Special Standard Resistors (1 0 and 10 kO)

NIST recognizes a special category of 1 0 and 10 kO standard resistors which exhibit small

corrections of < 10 ppm from nominal value, high stability, and a low temperature coefficient of

resistance (TCR); accordingly, these resistors merit the best possible measurement uncertainties.

In this category are the Thomas-type 1 0 resistors, or their equivalent, typically having drift rates

of < 10.11ppm/year and TCR's of (0 :i: 3) ppm/K, and the Evanohm*-type10 kO resistors

havingdrift rates of < I0.21 ppm/year and TCR's of (0 :i: 1) ppm/K. Measurement parameters

of temperature and current for these resistors are given in Table 2.1.

These resistors are acclimatized in their respective test environment for approximately one week

prior to calibration. The temperature of the resistor at the time of the measurement is given in

the Report of Calibration. Since some resistors have a significant pressure coefficient, the

*Evanohm is a commercial alloy having a resistivity of about 1.34 J.10-mwith a nominal

composition of 75% Ni, 20% Cr, 2.5% Cu, and 2.5% AI. By suitable annealing and heat

treatment, its TCR can be adjusted to nearly zero from 20 to 30°C.

2
---- ---

pressure at the time of the measurement is also reported for these 1 0 or 10 kO standards.

Table 2.1. Measurement parameters for special standard resistors

2.2 Standard Resistors (10-4n to 106 n)

Standard resistors with nominal decade values in the range between 10.4 n and 106 n are

calibrated by comparison with NIST working standards. In general, these resistors are

characterized by 1) resistance corrections within 500 ppm of nominal value, 2) TCR's of

(0 :i: 10) ppm/K at the temperature of use, and 3) drift rates of < 151 ppm/year. Usually, these

standard resistors are measured in an oil bath maintained at a temperature of (25.00 :i: 0.01) °C,

and at power dissipation levels of 10 mW to 100 mW. Resistors with fixed terminations and

designed for operation in an air environment are also accepted for calibration. At the levels of

uncertainties reported, four-terminal measurements are required for standard resistors of nominal

values ~ 100 n.

2.3 High-Value Standard Resistors (107 n to 1012 n)

High-value standard resistors in the range between 107n and 1012n are calibrated in an air bath

maintainedat a temperatureof (23 :i: 0.1) °C and at a relative humidity of (35 :i:5)%. Standard

resistors of nominal value up to and including the 1010n level are compared 1/1 with NIST

working standards of the same nominal value. Above 1010n, 10/1 and 100/1 ratio techniques

are used. The maximum test voltage is 500 V for resistors < 1010n, and 1000 V for resistors

~ 1010n. Only resistors that are mounted in a shielded enclosure, with permanently identifying

serial numbers and with suitable terminations, are accepted for calibration.

The resistance of a film-type, standard resistor is frequently highly voltage dependent. Hence,

the magnitude of the test voltage should be specified when this type of resistor is submitted for

calibration. The temperature, relative humidity, and test voltage of the resistor are given in the

NIST Report of Calibration.

2.4 Resistance MAP Service

Resistance MAP transfers [5] are offered at the 1 n and 10 kn resistance levels. Four wellcharacterized standard resistors are used as transport standards in each transfer. The suggested

3

Resistor Medium Tem12erature Current

10 oil (25.000:i: 0.003) °C 100 mA

10 kO oil (25.00 :i: 0.01) °C 1 mA

10 kn au (23.0 :i: 1.0) °C 1 mA
measurement schedule at the customer's laboratory consists of measurements on each transport

resistor three times a week for a period of 4 to 6 weeks depending upon the settling time of the

resistors due to effects caused by transportation.

Participation in this program is generally not advisable unless a laboratory is 1) required to

support resistance measurements at or near the state-of-the-art in accuracy, and 2) willing to adopt

a system for the continuous surveillance of standards during the intervals between MAP transfers.

A successful transfer requires a considerable amount of data collection and a willingness to

become involved in the data analysis process. Data supplied during routine NIST calibrations

suffice for normal measurement requirements of standards laboratories if proper methods are used

by the laboratory to quantify the additional uncertainties caused by transportation and their own

measurement process.

2.5 Special Resistance Measurements

Special resistance measurements such as: the determination of the temperature or pressure

coefficient of resistance of a standard resistor; testing or evaluation of prototype state-of-the-art

resistance standards; unique resistance measurements; and other calibration services not specified

above are made at the discretion of the NIST technical staff by prearrangement. Also offered as

a special test service is the calibration of standard resistors having values equal to the nominal

quantized Hall resistances of 6,453.2 Q or 12,906.4 Q.

3. MEASUREMENT METHODS

To provide a wide-ranging calibration service at NIST for 17 decades of resistance from 10-4Q

to 1012 Q requires the application of three basic methods that are used in seven stand-alone

measurement systems for comparing standard resistors. Listed below are the seven measurement

systems along with their primary resistance measurement levels.

1) Automated current comparator for 1 Q measurements.

2) Automated current comparator for 10 Q and 100 Q measurements.

3) Current comparator for measurements < 1 Q.

4) Automated unbalanced bridge for 1 kQ to 1 MQ measurements.

5) Guarded double-ratio bridge for special 10 kQ measurements.

6) Guarded Wheatstone bridge for 107 Q to 1010Q measurements.

7) Capacitance-discharge (CD) system for 107 Q to 1012Q measurements.

The current comparator systems (#1 to #3), the bridge systems (#4 to #6), and the CD system

(#7) are based on a current-ratio method, a resistance-ratio method, and a loss-of-charge method,

respectively, for the comparison of resistors. Although each method is unique, they share all or

some of the following measurement concepts and techniques:

1) Working Standards - NIST standard resistors, whose values are based on the quantum Hall

effect, existing at each resistance level. The mean value of two or more working standards is

used to assign a value to a resistor under test.

4

----
-- - - - - - -

2) Check Standard -A NISTstandardresistorthat is treatedas an unknownandmeasuredduring

each measurement run. An analysis of the check standard measurement results, over a substantial

period of time and over fluctuating environmental conditions, provides an indication of the

random error of the measurement process. For any given measurement run, the difference

between the measured and predicted values for a check standard indicates whether the

measurement system is operating under statistical control.

3) Dummy Resistor - A resistor, of equal quality to a working standard resistor, that is used in

a bridge or current comparator measurement system. Its absolute value need not be known;

however, it must remain stable or predictable during a measurement run.

4) Transfer Standards - Usually 10 resistors connected permanently in series, of which any

combination of resistors can be connected in a parallel configuration using special connection

fixtures. They are also commonly known as Hamon boxes [6] or build-up resistors, and they are

used at NIST to intercompare working standards at the different resistance levels. NIST transfer

standards provide accurate ratios of 10/1 and 100/1 for extending the 1 Q level in decade

increments up to and including the 1010Q level.

5) Substitution Technique - Since the working standards and test resistors are of the same

nominal value, they can be indirectly compared by substitution in the same positional arm of a

bridge circuit. This technique tends to cancel errors resulting from ratio non-linearity, leakage

currents, and lead and contact resistances.

6) Reversal Technique - A null detector balance is achieved upon reversal of the battery or power

supply connections to the circuit. This eliminates the effect of constant thermal emfs in the

detector circuit. With at least two reversals, the effect of slowly varying thermal emfs also can

be eliminated.

7) Quality Control - One or more check standards are measured during each test run to monitor

the measurement process. In addition, the standard deviation of a test run and the previous

history of the test resistor are examined to determine the quality of the measured value. Also the

measured and predicted differences among NIST working standards are compared.

4. DIRECT CURRENT COMPARATOR SYSTEMS

Direct current comparator (DCC) systems [7,8] are used at NIST to calibrate four-terminal

standard resistors from the 100 ~Q level up to the 1 kQ level. The DCC, because of its high

level of resolution, insensitivity to lead resistances, excellent ratio linearity and ratio stability, has

replaced resistance-ratio instruments such as the Wenner and Kelvin bridges for these resistance

measurements. Another distinguishing feature of the DCC in contrast to resistance-ratio bridges

is that the balance condition is obtained under equal voltage drops across the resistors. For ratios

other than 1/1, this results in the greater power dissipation occurring in the lower-value resistor

which is usually designed to withstand higher currents. The detector in a DCC system is a

photocell galvanometer amplifier (PGA) which exhibits low noise with nanovolt sensitivity at

these impedance levels. The DCC system current noise is 3 ~A or less depending on the model

5
in use. This noise limitation, along with the possibility of errors resulting from leakage currents

in the DCC, limits the practical maximum resistance range to 1 kQ at NIST. Above 1 kQ, the

resistance-ratio bridges with high-impedance electronic detectors are used for standard resistor

calibrations.

In 1969, a DCC potentiometer system replaced the NIST Wenner bridge for the intercomparison

of Thomas-type 1 Q standard resistors. With the improved precision of this system, a correlation

of the change of resistance of a Thomas-type resistor with variations of barometric pressure was

detected. This led to the determination of the pressure coefficients of the NIST set of Thomastype standard resistors in order to correct for this effect. The magnitude of the ambient pressure

is now included in the calibration report for a Thomas-type resistor. This NIST DCC

potentiometer system for the calibration of 1 Q standard resistors was automated in 1982 [9].

In 1984, a second DCC potentiometer was modified for the intercomparison of 10 Q and 100 Q

standard resistors. This system was automated in 1985.

A DCC resistance bridge has been in operation since 1969 for the measurement and scaling of

low-valued, four-terminal standard resistors. Although it is primarily used for calibrating standard

resistors of nominal decade values ranging from 100 /lQ to 100 mn, this bridge has the

capability of measuring four-terminal resistors up to the 1 kQ range. The maximum current level

of this system for the calibration of resistors is 100 A.

4.1 Theory of Operation

In general, the operation of a current comparator is based on Ampere's fundamental law

fH.dl = "'£,1,

where the line integral of the magnetic field H around a closed path dl is equal to the total

current 1 crossing any surface bounded by this path. For an ideal comparator, the total current is

carried by two ratio windings (primary and secondary) and the total number of ampere-turns of

one winding is equal and opposite to that of the other winding; thus,

"'£,1=N 1 - N 1 = 0 p p s s '

where the subscripts p and s refer to the primary and secondary windings, respectively. The

current ratio of the comparator, 1plIs,is therefore equal to the inverse of the turns ratio, Ns/NpTo obtain high ratio accuracies, the ampere-turn balance or zero flux condition is determined by

some type of flux detector system that is only sensitive to the mutual fluxes generated by the

ratio windings.

In practice, a DCC achieves high ratio accuracy and high sensitivity by utilizing highpermeability toroidal cores, magnetic and eddy-current shields, and careful winding procedures.

The main component of a DCC consists of a pair of high-permeability cores, surrounded by a

magnetic shield, over which are the ratio windings that carry the direct currents to be compared.

6
The currents for the ratio windings are supplied by two isolated direct current sources. Around

the cores and within the magnetic shield is wound a modulation-detection winding that is used

to sense the flux condition of the cores. This is achieved by modulating the core permeabilities

and using a second harmonic detector circuit. The presence of dc flux in the cores due to

primary and secondary ampere-turn unbalance is indicated by this detector output both in

magnitude and polarity. The detector output is used in a feedback circuit to adjust the current

in one of the windings automatically to maintain ampere-turn balance.

Demodulator

Q12\ Modulation

;- LrJ Oscillator

Slave

Current

Source

~

4

Rx

Constant

Current

Source

Is

~ . Ip -

Fig. 4.1. Basic circuit of CCC.

The basic circuit of a self-balancing DCC resistance bridge is shown in Fig. 4.1. This bridge

requires two simultaneous balances, an ampere-turn balance and a voltage balance. The slave

current source is continuously adjusted in a feedback mode by the output of the demodulator

circuit so that ampere-turn balance is maintained. Under this condition, the ampere-turn product

of the primary circuit equals that of the secondary circuit, i.e.,

N I =N I

p p s s

(4.1)

The voltage balance is achieved by the adjustment of the number of turns in the primary circuit,

Np until there is a null condition on detector D. Then the voltage drop across the unknown

resistor ~** in the primarycircuitis equalto the voltagedrop acrossthe dummyresistorRdin

the secondary circuit or,

**Romanor upright type is used to denote a component (e.g., R for resistor, C for capacitor)

and italic type is used to represent its physical quantity (e.g., R for resistance, C for capacitance).

7
R I = R d

I r p s

and using eq (4.1), the value of~ can be expressed as

R =(N IN ).R . r p s d (4.2)

Similarly, another measurement with the direct substitution of a known standard resistor ~ of

the same nominal value in the primary circuit and re-balancing the detector by adjusting Np to

a newvalueN; resultsin

I

Rs = (Np INJRd . (4.3)

Combining eqs (4.2 and 4.3) gives

R = (t1.N).R r p s'

where Mp is the difference in the number of primary turns between the two voltage balance

settings.

Thus, the value of an unknown resistor ~ is determined in terms of a standard resistor and the

small difference in turns ratio. The dummy resistor Rd must remain stable during the time

interval the two voltage balances are made; otherwise an error will occur in the measurements.

For the DCC potentiometer systems which include the 1 Q, 10 0, and 100 0 measurements, a

string of resistors are connected in series in the primary circuit. Then each resistor in turn is

compared to the dummy resistor. If more than one working standard resistor is used in this

measurement process, then the value of an unknown resistor is based on the mean value of the

working group.

4.2 Dee Potentiometer System for 1 0 Measurements

4.2.1 Description of System

A schematic diagram of the DCC potentiometer circuit for 1 0 measurements is shown in

Fig. 4.2. Fifteen Thomas-type resistors -five of which comprise the working group, along with

two check standards and eight unknown resistors - are connected in series within the primary

circuit of the DCC. The value of any resistor in the string can be determined by indirectly

comparing its voltage drop to the mean of the voltage drops of the reference group via a stable,

0.5 0 dummy resistor (Rd) in the secondary circuit of the DCC. The resistors are mounted on

a mercury stand that is housed in a constant temperature oil bath controlled at (25.000 :f:

0.003) °C. The voltage balance is made automatic by driving the PGA detector to a null

condition with a feedback current through an auxiliary 10 turn winding. This feedback current,

which is proportional to the difference between the test and dummy resistors, is monitored by

measuring the voltage drop across a 100 0 resistor using a digital voltmeter (DVM). The

feedback circuit is calibrated by inserting an additional unit turn in the primary circuit of the

DCCwhichchangesthevoltagebalanceby exactly500ppm. A personalcomputer(PC)controls

8

-~ --
-- --

the operation of the DVM, resistor selection, current reversal, and the insertion of the feedback

calibration signal. The PC also monitors the oil bath temperature, ambient temperature, ambient

relative humidity, and barometric pressure.

Demodulator

enJ Modulation :-lrJ Oscillator

2000 turn. 1 turn

Ns

Slave

Current

Source Rx

(10)

Constant

Current

Source

lp

+-

Fig. 4.2. Automated DCC potentiometer for 1 0 measurements.

A description of some of the important features of the main components of the system follows:

1. DCC Potentiometer

The DCC is a commercially available unit having an adjustable 2000-turn primary winding, a

1000-turn secondary winding, and a fixed 0.1 A primary current source. The system noise level

is specified by the manufacturer to be less than 1 J.lA.The constant current source is specified

as having a voltage compliance of 30 V, an output resistance of 10 Go, and a stability of

1 ppm/day plus the instability of its standard cell. To automate the system, four major

modifications of the comparator were necessary:

A. The PGA detector was modified to provide an isolated detector output by mounting

a pair of cadmium-sulfide (CdS) photoconductive cells adjacent to the original set of photocells.

Four I kO resistors (one of which is variable) were also mounted within the PGA to complete

an adjustable bridge circuit along with the two CdS photocells (see Fig. 4.3). An external 5.4 V

mercury battery supply energizes the bridge.

B. The push-button current reversing switch was replaced with a DPDT relay. It is

connected to a relay control module interfaced to the PC.

C. A DPDT relay with mercury-wetted contacts was connected to the 1 turn/step switch

9
of the DCC between the "0" and ".1" dial positions. This relay is also connected to the relay

control module. When energized this relay provides a 500 ppm bridge offset.

D. The current divider circuit used for the "standardize" mode of the DCC was

disconnected from its 10 turn winding. This winding is used in the feedback circuit which drives

the PGA detector to a null condition to provide for an automatic voltage balance.

2. Feedback Circuit

The schematic diagram of the isolated detector output and feedback circuits is also shown in Fig.

4.3. The isolated detector output is buffered by an operational amplifier, AI, and then amplified

by a factor of 5 by A2. Since a 1 ppm change of resistance corresponds to a voltage change of

0.1 ~V, the open-loop gain of the system G at this point is equal to 3.35 x 106. Any further

amplification leads to oscillations in the feedback circuit. Amplifier A3 provides a feedback

current If through the 10 turn winding Nf. The current If is monitored by measuring the voltage

drop across a 100 n resistor with a DVM. A 1 ~F capacitor, with PTFE dielectric, is connected

across the 100 n resistor to provide sufficient filtering of electrical noise in the system.

R

0.067 V/ppm

CdS

G = 3.35X108 10 turns

Va= GV.

I, = VaIRa

Fig. 4.3. Feedback circuit for automated DCC system.

3. Resistor Switch Module

A modified crossbar switch selects the appropriate potential terminals of a resistor in the primary

circuit of the DCC whose voltage drop is to be compared to that of the dummy resistor in the

secondary circuit. The switch mechanism is separated from the electromagnetic actuator coils

and placed in a heavy aluminum box. The coils are mounted outside the box and their push rods

are extended by plastic rods. This type of separation reduces heat transfer from coil to switch

point, and the heavy aluminum box effectively eliminates thermal gradients within the box. The

crossbar switch uses beryllium-copper conductors and gold-silver-platinum contacts which are

thermoelectrically matched to each other resulting in thermal emfs of less than 250 nV/K.

10

--
4. Resistance Thermometer Bridge

The temperature of the oil bath, maintained at 25.000 :f: 0.003°C,is monitoredwith a calibrated

platinum resistance thermometer (PRT). The PRT is calibrated in terms of the International

TemperatureScaleof 1990(ITS-90),and its resistanceof ~ 28 Q at the control temperature is

measured using an automated resistance thermometer bridge [10]. The bridge has a range up to

101.1 Q, a resolution of 1 ~Q, and an accuracy limited by the resolution or 0.1 ppm. The bridge

has four input ports and is remotely controlled through an IEEE 488 bus. The bridge is

calibrated prior to each PRT measurement against a known 100 Q resistor. The PRT and resistor

are measured at a current level of 1 mA.

5. Pressure Transducer

The barometric pressure is monitored using a calibrated commercial transducer which measures

pressure as a function of the natural frequency of a thin-wall metal cylinder. Transducer

temperature is determined indirectly by measuring the voltage drop across a calibrated diode that

is mechanically attached to the transducer body. The transducer outputs are measured by a

counter/DVM that is controlled by the PC through the IEEE 488 bus. The barometric pressure

is calculated from the period and voltage measurements. The sensitivity of the transducer is

13.3 Pa (0.1 mm Hg) with an accuracy of 4 Pa (0.3 mm Hg). The accuracy of the transducer is

periodically checked against a calibrated aneroid barometer.

6. Temperature-Humidity Indicator

Ambient temperature and relative humidity are monitored by a commercial digital

thermometer/hygrometer instrument. The instrument has a resolution and reproducibility of

0.1 °C and 0.1% RH. The temperature and relative humidity analog recorder outputs are

measured by a DVM which is interfaced to the PC via the IEEE-488 bus.

7. Personal Computer

The PC is a DOS-based system configured with hard and diskette drives for program and data

storage. It contains the following ports and boards: a printer port, a RS-232 port to communicate

with a central time-sharing computer, a IEEE-488 board, and a parallel I/O board to control the

crossbar switch and DCC.

8. Software

The computer program for operating the system is written in BASIC language using multiple

subroutines to handle the data taking and data processing. A MS-Kermit communications

program is executed to transfer the data file of a test run stored on the PC to the central timesharing computer via the RS-232 ports. The system program "THOMAS.COM" on the central

computer is executed to compute, analyze, and store the results of the test run. This program

adjusts the predicted value of the group mean of the five reference resistors for variations of the

oil bath temperature and ambient pressure from their respective nominal values of25.000 °C and

101,325 Pa (760 mm Hg). This corrected group mean is then used to calculate the values of all

11
of the unknown resistors in the measurement string for the test run including the values of the

check standards. The values of NIST resistors corrected to a temperature of 25.000 °C and a

pressure of 101,325 Pa are stored in individual data files according to their NIST serial number.

The values of the five reference resistors are stored in a single file named "GRPIT.OT". The data

for a customer's resistor is also saved, if a file for it exists. The data in these individual files are

saved in a format so that a linear regression fit of the data vs time can be calculated using

another system program. The "THOMAS.COM" program also provides a check on the results

by flagging the mean value of a resistor if its standard deviation exceeds a predetermined value

(see section 10).

4.3 Dee Potentiometer for 10 nand 100 n Measurements

The design, construction, and operation of this system is similar to that for the automated 1 n

system. The following description and operation sections will emphasize the differences between

the two systems. Similarities between the two systems will be briefly mentioned. For more

details on these similar features, refer to section 4.2 of this report.

4.3.1 Description of System

The DCC potentiometer circuit for IOn and 100 n measurements resembles that shown in Fig.

4.2 for the automated 1 n system. However instead of 15 resistors, the system is designed to

intercompare eight resistors of the same nominal value: two working standards, one check

standard, and five unknown resistors. These resistors are mounted on a mercury stand housed

in a constanttemperatureoil bath controlledat (25.000 :f: 0.003) °C. The resistors for the

secondary circuit are sealed in a heavy aluminum box filled with silicone fluid and the box is

immersed in the oil bath. The DCC is operated at a 2/1 ratio; hence this box contains a 5 n

resistor and a 50 n resistor that are needed for measuring Ion and 100 n resistors in the

primary circuit, respectively.

In similar fashion to the 1 n system, the DCC was modified to provide 1) automatic current

reversal, 2) automatic ratio offset, 3) an external access to a 10 turn winding, and 4) an isolated

detector output circuit. The detector-feedback circuit is identical to the one used in the 1 n

system except that resistor R3in Fig. 4.3 has been increased to 200 n, thus reducing the gain of

the feedback circuit to prevent oscillations from occurring in the system.

The original 50 mA constant current source (CCS) for the primary circuit of the DCC was

modified to provide output currents of 10 mA and 31.6 mA. The two current outputs are needed

in order to limit the power dissipation of the 100 n and Ion resistors to 10m W, respectively.

The excellent stability of the CCS is obtained by sending the load current through a reference

resistor whose voltage drop is connected in series opposition to the reference voltage of a

standard cell. Any difference between these two voltages is detected by a galvanometer. Light

from the galvanometer mirror falls on a pair of phototransistors that provide the feedback signal

to control the load current. The modifications to the current source consisted of changing the

reference resistor and changing the bias conditions of the phototransistors. This was

accomplished by installing a rotary switch in the circuit. Each switch position inserts a different

reference resistor and bias resistor into the circuit. The two critical reference resistors are sealed

12
in a heavy aluminum box filled with silicone fluid and the box is immersed in the oil bath.

A commercial relay scanner is used for automatic selection of the appropriate potential terminals

of any resistor in the primary circuit of the DCC during a test run. The scanner contains

latching-type relays with precious metal contacts for low-thermal emf operation. Shielded twoconductor PTFE-insulated cable is used to make the interconnections between the scanner and

the potential terminals of the resistors. The scanner is controlled by the PC through the IEEE488 bus.

The PC is similar to the one used in the automated 1 0 system with the same number of hard

and diskette drives, ports, and I/O boards. The MS-Kermit communications program is executed

to transfer the data file stored on the PC to the central computer. The system program

"AMPERE.COM" on the main computer is executed to compute, analyze, and store the results

of the test run. This program adjusts the predicted value of the group mean of the two reference

working resistors for variations of the oil bath temperature from the nominal value of 25.000 °C.

The corrected group mean is then used to calculate the values of the resistors in the measurement

string for the test run. The values are stored in individual data files that exist on the main

computer. The program "AMPERE.COM" also provides a check on the results by flagging the

mean value of a resistor if its standard deviation exceeds a predetermined value (see section 10).

4.4 Dee Resistance Bridge

The DCC resistance bridge is used primarily for the calibration of Rosa type 1 0 standard

resistors or their equivalent, and for all four-terminal standard resistors having nominal values

of 0.1 0, 0.010, 0.0010, and 0.0001 O. The bridge is also capable of measuring 10 0, 100 0,

and 1000 0 four-terminal standard resistors.

4.4.1 Description of System

A partial schematic diagram of the DCC resistance bridge is shown in Fig. 4.4. The bridge

consists of an adjustable 0-1000 turn winding in the primary circuit, and a fixed 1000 turn and

adjustable deviation windings in the secondary circuit. The resistor to be measured, ~, is

connected in the primary circuit and a reference resistor, ~, is connected in the secondary circuit.

If the deviation winding is set equal to the correction of resistor ~, the bridge becomes direct

reading in ohms. The resistors are located in a constant temperature oil bath maintained at

(25.000:!: 0.010)°C. The DCCresistancebridgeis balancedby adjustingthe turns ratio for a

null condition on detector D using the reversal balancing procedure.

The adjustable ratio winding in the primary circuit can be replaced by a fixed winding of 100

turns, 10 turns, or 1 turn which will provide additional bridge ratios of 10/1, 100/1, and 1000/1.

For these higher ratios, the adjustable fractional-turn section in the primary side is switched to

the secondary side in order to balance the bridge. The bridge has a resolution of 0.1 ppm for all

ratios; however, it only has a range of 1111.1 ppm for ratios> 1/1. For resistance ratio

measurements of 1/1 and 10/1, a O-to-l A internal power supply is connected in the primary

circuit. When the bridge is used for ratio measurements of 100/1 and 1000/1, the internal power

supply is replaced by an external, adjustable 100 A supply. The 100/1 and 1000/1 ratios have

13
respective maximum current ratings of 20 A and 100 A.

4.4.2 Measurement Parameters and Design

The resolution of a resistance measurement when using this DCC resistance bridge is limited by

the following factors:

1. The smallest incremental ratio adjustment of 0.1 ppm.

2. The detector sensitivity of IOn V.

3. The system noise of 3 1lA.

4. The maximum current ratings of the ratio windings.

5. The maximum power dissipation of the resistors.

1000 T o

IT

f\ o

lOT

o---IYY\---o

lOOT

~

Slave

Current

Source Rs

~

Rx

Constant

Current

Source

~

Is

--+ . IF

~

Fig. 4.4. DCC resistance bridge.

Normally, the power dissipation of a standard resistor is 10m W or less during a measurement.

However, in order to obtain sufficient resolution and, since a lower-value resistor is usually

designed to withstand higher currents, the power dissipation level of a standard resistor below

1 Q is set at 100 mW or less. Table 4.1 gives the measurement parameters for the various

resistance levels when using the DCC resistance bridge.

The value of an unknown resistor can be obtained by two different methods using the DCC

resistance bridge. The first method consists of alternately substituting the unknown resistor and

14
-- - -

a reference working resistor in the primary circuit (substitution technique) along with a dummy

resistor in the secondary circuit. The second method consists of connecting the reference working

resistor in the secondary circuit with the unknown still in the primary circuit. The second method

relies directly on the accuracy of the bridge ratio. Usually, the ratio error of a DCC is negligible

for these measurements.

Table 4.1. Measurement parameters for DCC resistance bridge

Resistance

(0)

Ratio Maximum Current

(A)

0.0001

0.001

0.01

0.1

1

10

1000/1

1000/1

100/1

100/1

1/1

1/1

30

10

3

1

0.3

0.1

5. RESISTANCE-RATIOBRIDGES

Before the development of the DCC, the comparison of standard resistors was done chiefly by

the use of bridges with resistance ratio arms. For many years at NIST, a Wenner bridge [11]

served this purpose for the comparison of multiples and submultiples of the ohm from 100 fJO

to 1 Mil. This bridge, designed in 1918, was a combination Wheatstone bridge and Kelvin

double bridge with ratios of 1/1 or 10/1 having an adjustment range of 5000 ppm. In later years,

it was modified to increase its resolution to 0.01 ppm. The bridge was retired in 1983 because

of the deterioration of its switch contacts and insulation. By this time it had been already

replaced by DCC systems for the comparison of four-terminal standard resistors from 100 fJO

to 1 kO as described in section 4.

During the late 1960's and early 1970's, several resistor manufacturers developed a high-quality,

transportable 10 kO standard resistor in order to establish an additional reference level of

resistance along with the traditional 1 0 level [12]. The 10 kO level was attractive because it

was nearer to the mid scale of precision resistor measurements, and it was expected to provide

a convenient level for comparison with the SI ohm derived from absolute ohm experiments. The

improved 10 kO standard resistor surpasses the Thomas-type resistor in temperature coefficient

of resistance, is about equal to it in transportational effects, but is second to it in time stability.

Nevertheless, it has gained wide acceptance as a primary reference standard and the number of

calibrations of these standards at NIST is second only to that of the Thomas-type resistor

15
calibrations in the dc resistance area. Around 1975, a modified Kelvin-type bridge was

constructed specifically for the comparison of the improved or "special" 10 kO standard resistors.

The bridge employs a guard network to reduce errors caused by possible leakage currents in the

circuit. The bridge has been refined and improved over the years and its latest version is

described in section 5.2.

Prior to 1989, standard resistors having nominal values of 1 kO, 10 kO, 100 kO, and 1 MO were

calibrated at NIST in a Wheatstone bridge circuit using a Direct-Reading Ratio Set (DRRS) that

was operated manually. Generally, these standard resistors are of the Rosa design which are

measured in a mineral-oil bath controlled at a nominal temperature of 25°C. Since 1989 these

standards have been calibrated using an automated system based on an unbalanced-bridge method

[13]. Since this method is unique in that it is not a 4-arm bridge method, it will be described

separately in section 6.

Standard resistors> 1 MQ, specifically resistors with nominal decade values from 10 MO to

1 TO, are calibrated using a specially-designed guarded Wheatstone bridge (section 5.3) or a

teraohmmeter (section 7). The bridge is limited to the calibration of standard resistors that differ

from their nominal value by less than 5000 ppm. For high-value resistors outside of this

tolerance, the teraohmmeter is used as a comparator for calibration. All high-value standard

resistors are calibrated in a temperature-humidity chamber maintained at a temperature of 23°C

and a relative humidity of 35%.

5.1 Theory of Operation

The operation of the resistance measurement systems described in this section for the comparison

of standard resistors are based on variations of two well-known bridge circuits, namely the

Wheatstone bridge and the Kelvin double bridge. The Wheatstone bridge circuits are used for

the measurement of two-terminal resistors, while the Kelvin double bridge circuits are used for

the comparison of four-terminal resistors. In general, the comparison of four-terminal resistors

is done at resistances of 100 0 or less. However, in special cases where higher accuracies are

warranted, e.g., the comparison of special 10 kO resistors, four-terminal measurements are done

at resistances > 100 O.

A schematic diagram of a typical NIST Wheatstone bridge circuit for the comparison of twoterminal resistors is shown in Fig. 5.1. Resistors A and B constitute the two arms of a DRRS.

The 1/1 resistance ratio of a typical DRRS can be adjusted over a range extending from

-5000 ppm to +5000 ppm in increments of 0.1 ppm. Rdis an auxiliary or dummy resistor of the

same nominal value as the test or unknown resistor, ~, and the standard resistor,~. Lead

resistances IJ,12,and 13complete the bridge network. Variability in the contact resistances at the

resistor terminations are negligible for two-terminal resistor comparisons above 100 O. The

substitution technique (see section 3) is used for determining the small difference between the

resistors ~ and~. The bridge equation with ~ in the circuit and the bridge balanced at a

DRRS reading of DJ in ppm is

16
(A/B).(1 +D)oI0-6) =(R" +I)/(Rd +/2 +13),

Similarly for ~ substituted in the circuit, the bridge equation is

(A/B).(1 + D2.1 0-6) =(Rs + I.)/(Rd + 12 + 13) ,

where D2 is the new DRRS reading in ppm after the bridge is re-balanced. The value of ~ can

be representedas

Rs =Rs'(1 + cs.l0-6) ,

where R's is the nominal value of the standard resistor and Csits correction in ppm. Solving for

R" and neglecting 2ndorder and higher terms results in

R" ~ Rs'(1 + (D) -D2).10-6 +csol0-6 + (I/RJ(D) -D2)-10-6) .

Usually the last term in the above equation is negligible for measurements above 100 Q, since

the differences between nominally-equal resistors are within 500 ppm, and for most practical

circuits the ratio l/~ < 10.3. Therefore the equation for R" reduces to

R" ~ Rs'(l + (D) -D2).10-6 +cs.l0-6) .

Rx or Rs RD

11 ~+ 12

A B

D

Fig. 5.1. DRRS bridge circuit.

The difference in the DRRS ratio for the two balances gives the difference between the values

of the two resistors in ppm. For measurements> 1 MQ, a guarding network is added to the

Wheatstone bridge circuit in order to suppress errors caused by leakage currents flowing from

the main bridge arms to ground potential. The guard circuit drives the shields of the bridge

terminations at the proper potentials to confine leakage currents within this network.

17

..- ___u__ _ _________.
Four-terminal resistors are used to avoid uncertainties arising from variations in lead and contact

resistances. A Kelvin double bridge, as shown in Fig. 5.2, is used for the comparison of fourterminal resistors. The fundamental difference between the Kelvin double bridge and the

Wheatstone bridge is the use of a second set of ratio arms a/b. Resistors ~ and ~ are connected

together by a low-resistance link L. The link and battery circuits contain the current lead

resistancesof ~ and~. Potential lead resistances I}, I]>IJ, and 14are eliminated from the final

bridge balance equation by special balancing techniques. When the bridge is balanced, Rr can

be expressed as:

Rr =(A/B).R" +«b.L )/(a + b +L». (A/B - a/b) .

B8

Rx

Rs

L

Fig. 5.2. Kelvin double bridge circuit.

This equation reduces to that for a simple Wheatstone bridge when the last term on the right hand

side is zero. This can be accomplished by adjusting AlB = aIb, irrespective of the value of L.

In practice, the resistance of L is kept small to lessen the importance of any lack of inequality

between the ratios AlB and aIb. For some measurements the nominal ratio of A/B is set equal

to 10/1 in order to reduce the power dissipation in the ~ arm of the bridge. Whenever it is

possible, Rr is determined by the substitution technique which means replacing ~ with a stable

dummy resistor ~.

5.2 Modified Kelvin Bridge for 10 kO Measurements

This measurement system was specifically designed for the comparison of four-terminal 10 kO

standard resistors by the substitution method. Similar to the Kelvin double bridge circuit, it

incorporates inner ratio arms with a link arrangement to eliminate the effects of contact and lead

resistances of one set of current-potential terminals of the resistor under test. Unlike the Kelvin

double bridge, the dummy resistor Rdneed not be connected in a four-terminal arrangement. In

18

-- - -- -.---
---- -

addition, the contact and lead resistances associated with the other set of current-potential

terminals of the resistor under test are measured in a two-step procedure and subtracted from the

final result. The schematic diagram for this measurement system is shown in Fig. 5.3 without

its guard circuit. The A/B ratio arms of the bridge consist of a 100 Q DRRS with additional

10 kQ resistors to increase the resistance of each arm to a nominal value of 10.1 kQ. This

arrangement results in a dial resolution of better than 0.01 ppm/step. It also closely simulates

a square-bridge for optimal circuit operation. This composite DRRS has an adjustment range of

110 ppm. The inner ratio arms aIb consist of two 1 kQ resistors separated by an adjustable

10 turn 100 Q resistor. The removable link L is an amalgamated copper bar approximately 5 cm

in length and 0.4 cm2 in cross section. The battery supply V contains 15 D-size mercury batteries

to provide a bridge excitation current of 1 mA resulting in 10m W of power being dissipated in

each main arm of the bridge. The batteries are mounted in a shielded enclosure and they are

isolated from ground potential using PTFE insulation. The electronic null detector D is

connected to either position A or P using a low-thermal rotary switch. Dummy resistor Rd is an

oil-type, 10 kQ resistor of equal quality as the resistor ~ under test.

Rx L RD

r 1 kO

~v

10ka1000 1000

A

s D

p

Fig. 5.3. Modified Kelvin bridge for 10 kQ measurements.

Two BPO... connector panels are mounted on either side of the bridge ratio arms to provide easeof-use in connecting test resistors into the circuit. Each panel contains 40 connectors attached

to 10 resistors by twin-conductor shielded PTFE insulated cables. One panel is for use with oiltype resistors, while the other panel is for air-type resistors. A temperature lag box houses airtype 10 kQ resistors (two working standards and one check standard) used in the measurement

...BPO is an acronym for British Post Office and refers to a type of coaxial connector

manufactured in Britain. The connectors are con~tructedusing silver-plated conductors and PTFE

insulation. A connector pair has low contact resistance and low thermal emfs.

19
process. This lag box helps to minimize the effect of fluctuations of the ambient temperature on

the measurements. The temperatures of the air-type resistors are measured using a calibrated

digital thermometer with thermistor probes. The resolution of the thermometer is 0.01 °c with

an accuracy of 0.05 °C. If requested by a customer, the resistive temperature sensor mounted in

an air-type resistor can be measured at the time of calibration using a calibrated digital

multimeter. An additional check standard is located in the oil bath along with the oil-type

resistors under test. The oil bath temperature of (25.00:1:0.01) °C is monitored periodically by

a PRT measurement system.

This bridge circuit for the measurement of special 10 kil resistors is guarded (guard circuit not

shown in figure). The guard circuit suppresses the effects of leakage currents flowing to ground

potential or to other parts of the circuit that may cause an error in the measurement.

Unfortunately, the terminations of most resistors under test are not guarded. The shields of the

cables connecting a resistor into the test circuit are driven at a guard potential to complete the

guard circuit as much as possible. However, the NIST-built transfer or series-parallel buildup

standards, as described in section 8.2, contain internal guard networks to take advantage of this

guarded bridge circuit.

5.3 Guarded Wheatstone Bridge

Standard resistors of nominal decade values from 10 Mil to 10 00 are measured using a NISTbuilt guarded Wheatstone bridge. This bridge is limited to the comparison of standard resistors

that have correctionswithin :I: 5000 ppm from nominal. For the measurementof high-value

resistors outside of this tolerance or with nominal decade values extending from 10 Gil to 1 Tn,

a semiautomatic technique using a digital teraohmmeter is used (see section 7).

A simplified diagram of the guarded Wheatstone bridge is shown in Fig. 5.4. The main bridge

arms, drawn with heavy lines, consist of the main ratio arms A and B, the dummy resistor Rd'

and the test resistor~. Drawn with lighter lines and in parallel with the main bridge circuit is

an auxiliary guard network for the purpose of reducing measurement errors caused by leakage

currents. The NIST-built working standards that are used with this measurement system contain

their own internal guard network to take full advantage of this guarding feature. For test resistors

that do not have an internal guard resistor (nearly all of them), an external resistor must be added

in order to complete the guard circuit. The main and guard circuits are energized by a battery

supply V having an output isolation of> 1012il from ground. The bridge circuit is connected to

a single ground point at the guard terminal between guard resistors a and b as shown in Fig. 5.4.

The detector D is an electrometer having a high input impedance of >1016il. Its low end is

connected to the bridge terminal between the main ratio arms A and B which is not grounded but

driven to near ground potential by the guard circuit~i. e., a virtual ground potential.

The test resistor ~ is shown in Fig. 5.4 with leakage resistance paths between its terminals and

case represented by r1 and r2. When the test resistor is measured, its case is connected to ground

potential. Measurement errors caused by terminal leakage resistance r1 is greatly reduced since

it is effectively in parallel with guard resistor a, and unwanted ground currents are intercepted

by the guard circuit and not the main bridge circuit. Terminal leakage resistance r2 is effectively

in parallel with the detector, and it does not contribute to any measurement errors. The test

20
---- --

D

, guardcircuit

" ""

.::r:""

-=

Fig. 5.4. Guarded Wheatstonebridge.

resistor is compared to a working standard in the same arm of the bridge (substitution technique),

and, consequently, any leakage errors associated with Rd are negligible if the leakage resistances

are constant during the time interval of the measurement run.

The A/B ratio arms of the bridge can be connectedin a 1/1 or 10/1 ratio configuration. A more

detailed circuit diagram of the NIST guarded Wheatstone bridge is shown in Fig. 5.5. If the

bridge connections are made at terminals labeled A) and B) or A) and B2, which correspondsto

ratios of 1/1 or 10/1 respectively, the A arm has a nominal value of 1 Mil and the total

adjustment range of the A/B ratio is 1111.10 ppm with a resolution of 0.01 ppm. The A arm

contains an adjustable 5-decade resistor having a maximum resistance of 1111.10 il. If the

bridge connections are made at A) and B) or A) and B2,which again corresponds to ratios of 1/1

or 10/1 respectively, the A arm has a nominal value of 100 kil and the total ratio adjustment is

11111.0 ppm with a resolution of 0.1 ppm. The A/B ratio-arm resistors are suspended in air and

attached to guarded binding posts mounted on a PTFE top plate. This entire assembly is

enclosed in a grounded aluminum box to provide electrostatic shielding.

The resistorundertest~ and the dummy resistor Rd are placedin an environmentalair chamber

with temperature and relative humidity control of (23.0::1:0.1) °C and (35 ::I:5) %, respectively.

The temperature and humidity are continuously monitored by a digital thermometer and an analog

humidity indicator. Electrical access into the air chamber is made via 10 BPO connectors

mounted on a PTFE panel. This provides for the connection of five resistors within the chamber:

usually two working standards, one check standard, one dummy resistor, and a test resistor. Lead

connections between the resistors and the other parts of the bridge are made using shielded,

PTFE-insulated cable with silver-plated copper conductors. The shields of these cables and BPO

connectors are driven at a guard potential by the auxiliary guard network.

21
A .............

B

.~...~~..,.

900kn ,'"

/':

/00,

,~-.- 90kn .....

0~

A. '.Y"~

9 5k 1

"'1 9.5kn

. Q"'!

"'.

0

/.,

,./: ' B . ~ I

..' ..'

10kO :"".:

8118111I~r.uU ~J __I""'1UI1t

Fig. 5.5. Guarded bridge for high resistance measurements.

6. RING METHOD

This automated measurement system, based on an unbalanced-bridge technique, was developed

to replace the manual DRRS system used to calibrate resistors in the resistance range 1 kO to

1 Mo. This technique is referred to as the "ring" method since the resistors are connected in a

ring configuration. The system is specifically designed to measure the differences among six

nominally-equal, four-terminal standard resistors of the Rosa type that are mounted on a mercury

ring stand located in a temperature-controlled oil bath. The system has sufficient switching

capability to operate four six-arm mercury ring stands, usually at the nominal resistance levels

of 1 kO, 10 k.Q, 100 kO, and 1 Mo. The system has the flexibility to accommodate other types

of standard resistors including those operating in a laboratory air environment. Also the system

can be used to compare resistors having lower nominal resistance values of 100 0 or 10 .0. The

resistors mounted on the ring stand are energized at a power level of 10m W or less.

6.1 Theory of Operation

In general, the unbalanced-bridge or "ring" method consists of connecting an even number of six

or more nominally-equal, four-terminal resistors in a ring configuration, i.e., a string of resistors

in a closed electrical circuit where the first and last resistors are interconnected. The number of

resistors equals "2.(n + 2)," where n is an integer ~ 1. A voltage is applied across opposite

22
--- -- --

comers of the hexagonal ring which divides the ring into two branches, each containing "n + 2"

resistors, connected in parallel. Then, a DVM is used to measure voltages between opposite

potential terminals of the resistors that are at nearly equal potentials. Next, the applied voltage

points across the ring are rotated in a clockwise (or counterclockwise) direction to the next pair

of resistor connection points. Again voltage measurements are taken between corresponding

terminals of the resistors that are at nearly equal potentials. This measurement process is

repeated "n + 2" times. From the "n + 2" subsets of voltage measurements, one obtains a set of

"3.(n + 2)" linear equations that can be solved using a least-squares technique. Values of the

resistors can be calculated if the value of at least one of the resistors in the ring is known.

B C

A A'

-4NL

Rs

C' B'

Fig. 6.1. Ring method circuit for six resistors.

The automated measurement system described in this report is based on a ring of six resistors

(n = 1) as shown in Fig. 6.1. Two of the resistors are working standards (R3 and ~), one is a

check standard (R4), and the remaining three are unknowns or resistors under test (R), R2, and

Rs). The three pairs of applied voltage points are designated as AA', BB', and CC'. Three

subsets of voltage measurements are taken to determine the values of the unknown resistors.

6.1.1 First Subset of Voltage Measurements

The positions of the six nominally-equal resistors for the first subset of voltage measurements is

shown in Fig. 6.2a. The supply voltage is applied across points A and A'. The voltage

differences measured by the DVM across opposite potential terminals of the resistors are

designated VIthrough V6. These voltages are the average of measurements for the two directions

of current; this procedure reduces errors caused by thermal emfs in the critical low-voltage

circuits. From this first subset of voltage measurements, one obtains three linear equations of the

form analogous to the equations derived for comparing two voltage dividers [14]. These

equations, neglecting higher order terms, are:

23
\

,

R) R6

(

V2-v) V4-V3

]

-~- 1 + -

R2 Rs V V

R) R6

[

V; -V/ V6-Vs

]

-~- 1 + -

R3 R4 V V

(

" , ,

]

R2 Rs V4 -V3 V6 -Vs -~- 1 + -

R3 R4 V V

where V is the nominal voltage across a resistor (1/3 the applied voltage), and the V:'s (e.g., V'!,

V'2'etc.) are repeated measurements of that particular voltage difference to ensure independence.

The measurements are made in the sequence implied by the above equations to minimize errors

caused by changes in interconnection and lead resistances.

24

RI R2 Rs

-r;"M 6 bWv6 Wv b

A 0--1 VI V2 Vs V, Vs Vs 1--0 A'

m? ?m? ?.

Rs Rs R,

(a)Sub8etl

R2 Rs R4

BQ--/ V7 V8 VB VIO Vu VI2 1--0 B'

w1-

RI Rs Rs

(6)Sub8e12

Rs R4 Rs

6 b"M6 bVlvC0--1 VIS VI' VIS VIS V 17 V 18 1--0 C'

m? ?m? ?mi

R2 RI Rs

(c)Sub8el:l

Fig. 6.2. Subsets of voltage measurements for ring method.
- - - --- -- -- -- - --- - - ---

6.1.2 Second Subset of VoItage Measurements

The positions of the six resistors, after the supply voltage connections are rotated to points B and

B', are shown in Fig. 6.2b. In this figure, the voltage differences measured between opposite

terminals of the resistors are designated V7through V12'The measurement procedure is analogous

to that described in sec. 6.1.1 for obtaining the first subset of voltage measurements. The three

linear equations obtained from the second subset of measurements are:

R2 RI

(

Vs -V7 VIO-V9

) -::::- 1 + - R3 R6 V V

R2 RI

(

Vi -V/ VI2-VII

)

_::::- 1 + -

R4 Rs V V

(

, , , ,

)

R3:::: R6 1 + VIO-V9 _ VI2 -VII

R4 Rs V V

where higher order terms have been neglected.

6.1.3 Third Subset of Voltage Measurements

The positions of the six resistors for the third subset of voltage measurements are shown in Fig.

6.2c. The supply voltage connections are rotated to points C and C. The voltage differences

measured between opposite resistor terminals are designated VJj through V18' The three linear

equations, neglecting higher order terms, obtained from these voltage measurements are:

R3 R2

(

VI4 -V13 VI6 -VIS

]

_::::- 1 + - R4 RI V V

R3 R2

(

VI~ -VI~ VIS-V17

)

_::::- 1 + - Rs R6 V V

(

, , , ,

)

R4 RI VI6 -VIS VIS -V17 _::::- 1 + -

Rs R6 V V

6.2 Data Analysis

From the three subsets of measurements for the different connections of the applied voltage, one

obtains a set of nine linear equations. These equations can be expressed in terms of the resistor

25


resistances above 109 Q [16]. At NIST a commercially-built teraohmmeter is used to measure

high-value standard resistors out of the range of the Wheatstone bridge system (M> 5000 ppm),

or above 1010Q by comparison with NIST working standards. To do this at lOll Q and 1012Q,

the 1011 and 10011 ratios of the teraohmmeter must be used.

7.1 Description of System

A simplified block diagram is shown in Fig. 7.1, where ~ is the test resistor and C is a feedback

capacitor connected across amplifier A to form an integrator. The change in the output voltage,

L\vo'of the integrator over a time interval L\tcan be expressed as

L\vo = -(v; /RxC)L\t

or

Rx = -(1/C)(v; /L\vo )L\t,

where Viis the constant applied voltage across~. Note that a working standard resistor is not

needed to determine ~ as is the case with the Wheatstone bridge system. Only C, L\t,and the

ratio of voltages (vlL\vo) need to be known accurately. In practice, the quantity vlL\vo is

determined by a ratio of low-value resistors in a divider chain that is energized by a constant

current source. The input stage of the teraohmmeter, including capacitor C and switch S along

with the input connectors, are guarded to minimize the effects of leakage paths across these

critical components. A more detailed description and analysis of this circuit is given in ref. [16].

C COUNTER

Vo LEVEL

COMPARATOR

STANDARD

FREQUENCY

SOURCE

~

Fig. 7.1. Block diagram of teraohmmeter.

8. RESISTANCE SCALING

The U.S. representation of the ohm (~IST) is based on the quantum Hall effect. Periodically, the

28

--- - ---------
-- ----

five 1 n working standards are compared to the quantized Hall resistance, usually at the

6453.20 n level (Hall plateau where the integer of the quantum Hall state equals 4) [3]. The

values and/or drift factors of the 1-0 working standards are adjusted if their values in terms of

the quantized Hall resistance differ by more than 0.02 ppm for two or more intercomparisons.

The resistance scale is extended upward in multiple decade values from this 1 0 level, up to and

including the 10100 level, using NIST-built transfer standards or Hamon boxes [6] that provide

accurate ratios of 10/1 and 100/1. Below the 1 0 level, the resistance scale is extended

downward to the 10-40 level in submultiple decade values using current comparator ratios of

10/1, 100/1, and 1000/1. Above 1010Q, the resistance scale is extended upward to the 10120

level using the 10/1 and 100/1 ratios of the teraohmmeter.

8.1 Quantized Hall Resistance Scaling

The quantized Hall resistance, at the 6453.20 0 level, of a Hall device operated at a temperature

below 4 K and in a magnetic flux density around 6 T, is compared to a group of 6453.2 0 wirewound reference resistors using an automated potentiometric measurement system [17]. The

design of these reference resistors is a series-parallel combination of card-type Evanohm resistors,

sealed in a silicone-fluid-filled container, and placed in a portable NIST-built temperatureregulated air bath enclosure. These reference resistors are then used to calibrate the five 1 0

working standards in terms of the quantized Hall resistance. This is done in two stages: the first

stage uses a 6453.20 0 to 100 0 transfer standard designated as HQHA; the second stage uses

a 100 0 to 1 0 transfer standard designated as H10. Figure 8.1 is a block diagram indicating

the steps in scaling from the quantized Hall resistance to the 1 0 working group.

I GS

Fig. 8.1. Resistance scaling from QHR to 1 n.

Transfer standard HQHA containsnine series-connected card-type resistors sealed in an aluminum

box filled with silicone fluid. The first eight resistors have a nominal value of 800 0 each, and

the ninth has a value of 53.20 0 to make the total resistance equal to 6453.20 n. Transfer

29

QUANTIZED HALL RQHA

RESISTANCE

HJ (6453.2Q) 8s8OOQ53.2a

, H8OO-P

H

RIGS

RIO

loa/Step

RIo.P

NIST

OHM

(lQ)
standard HI 0 contains ten series-connected Rosa-type 10 0 resistance elements. These resistance

elements are sealed in brass cans filled with a silicone heat sink compound. Both transfer

standardsare operatedin oil baths,temperaturecontrolledat (25.000 ~ 0.003) °C.

The 6453.20 0 reference resistors, whose values were assigned based on the quantized Hall

resistance, are compared to transfer standard HQHA using a guarded, resistance ratio-arm bridge.

Next, HQHA's eight 800-0 resistors connected in parallel is compared to transfer standard HI0,

connected in its series configuration of 100 0, using the automated 100 0 DCC system. The

53.20 0 section of HQHA is compared to HI0 using either an automatic NIST resistance

thermometer bridge or a DCC resistance bridge. The 53.20 0 measurement is not very critical

since it only represents R:0.82%of the total resistance of HQHA. At this stage, the value of HI 0

is known in terms of the quantized Hall resistance. Finally HI0, connected in its parallel

configuration of 1 0, is compared to the 1 0 working standards using the automated 1 0 DCC

system. The result of these measurements is an assignment of the mean value of the 1 0

working standards based on the quantized Hall resistance.

8.2 Transfer Standards

NIST transfer standards provide accurate ratios of 10/1 and 100/1 for extending the use of ~IST

to higher resistance levels. The main advantage of transfer standards is that they are calibrated

at one resistance level and are then used with equal accuracy at a different resistance level as a

short-term working standard. In a series of measurements using such transfer standards, the ~IST

can be extended in multiple decade values up to 1010n Neither the absolute accuracy nor longterm stability of the resistors in the transfer standards have any effect on the measurement

accuracy. The concerns with the transfer standards are only with the short-term stability required

to complete the measurements. The transfer accuracy is ensured through proper design and

various operational tests.

Fig. 8.2. Diagram of a typical transfer standard.

30

- -- - - -- -
---

Figure 8.2 is a schematic diagram of a typical NIST transfer standard. It consists of 10

nominally-equal resistors connected permanently in series by means of "tetrahedral" junctions

[18]. Each junction has two current and two potential terminations, and the 4-terminal resistance

of each junction is designed to be zero. If necessary, the junctions are adjusted to have a

negligible effect on the transfer accuracy. The degree of adjustment depends on the nominal

value of the main resistors. Figure 8.3 shows the transfer standard connected in a parallel mode

2b

b

Fig. 8.3. Parallel connection for transfer standard.

using special fixtures. The potential circuit of the fixtures contains "fan" resistors for suppressing

connection errors. The series and parallel resistances of a transfer standard are:

Rs =NR(l +c),

and

Rp = (R/N)(l + c +f(c 2» ,

where Rs and Rp are the series and parallel resistances, respectively, N equals the number of

resistors, R is the resistance of a single coil, c is the correction to the nominal value for the series

mode, andf(~) includes negligible higher-order terms. For a transfer standard having 10 main

resistors,

31
R /R =N 2 = 100 . s p

Figure 8.4 shows the transfer standard connected in a series-parallel mode for a 10/1 ratio. In

this configuration only nine of the ten resistors are used. The series-parallel resistance Rsp is

R =R (l +c +O.l (c -c )) , sp sp x

where cspis the correction of the nine resistors in the series-parallel configuration and Cxis the

correction of the tenth resistor. The resistance ratio is

R /R =10(1 +O.l (c -c )) . ~ p ~ x

Figures 8.5 and 8.6 are block diagrams of the NIST scaling process from 1 0 to 1060 and 104

o to 10100 using transfer standards. The "P", "S", and "SP" notation indicates whether the

transfer standard is in the parallel, series, or series-parallel mode, respectively. Arrows indicate

1/1 comparisons made and unless otherwise labelled, boxes represent NIST working standards

at various resistance levels.

2b

Fig. 8.4. Series-parallel connection for transfer standard.

32
Fig. 8.5. Resistance scaling from 1 0 to 1 Mil.

Fig. 8.6. Resistance scaling from 10 kO to lOGO.

33

QUANTJZED NJST HALL OHM 10 RESISTANCE

(In)

lUo.P

HlIl.8 Hl0 Hlo.8P 1000 100

lon/Step

1U0.8

HUr.-P

10110 Hlk-S Hlk Hlk.sP 1110

1 kO/Step

HUr.-S

Jll00k-P

lMO Hl00k-S 1U04Ir. IUOOk-SP 100110

l00kO/Step

10kO

Hl00k-P

,

1U04Ir.

100kO/Step

Hl00k-S

Jll0M-P

l00Mn Hl0M-S H10M Hl0M-SP 10MO

10MO/Step

H1OM-S

,H1G-P

lOGO H1G-8 HlG H1G-8P lGO

1 co/Step
8.3 DCC Ratios

It is difficult to construct accurate transfer standards with single coil resistances < IOn. The

major difficulties are with the adjustment and stability of the resistances associated with the

tetrahedral junctions and fan resistors. Therefore, to extend ~IST below 1 Q, NIST uses DCC

ratios of 1011,100/1, and 1000/1. The high ratio accuracies of the DCC results from the use of

multiple-winding, high-permeability toroidal transformers. The DCC ratio is insensitive to lead

resistances or current level. The ratio accuracy and ratio linearity of a DCC is checked without

the use of any external equipment with a resolution better than 1 part in 107[7]. The ratio

accuracy can also be checked by the use of two higher-valued standard resistors whose values

are based on transfer standards.

8.4 Teraohmmeter Ratios

Resistors with nominal values of 1011 Q and 1012 Q are measured using the teraohmmeter

calibrated against a 1010Q working standard. The uncertainties of the 1011 and 10011 ratios of

the teraohmmeter are less than those associated with transfer standards at the 1011Q and 1012Q

levels. High-resistance, film-type resistors at these resistance levels have large drift rates and

exhibit large TCR's and voltage coefficients of resistance (VCR's).

9. MEASUREMENT UNCERTAINTY

The expanded or overall uncertainty assigned to the measured value of resistance of standard

resistors, as given in a NIST Report of Calibration, is equal to

2 /S2 +"JJu2(i) (9.1)

where s is the estimated Type A standard uncertainty based on the pooled standard deviation

from a large population of individual measurements, and u(i) is the estimated Type B standard

uncertainty for each known component quantified by a standard deviation. The coverage factor

2 used at NIST is consistent with international practice [19]. The method of combining

uncertainties is based on the approach recommended by the International Bureau of Weights and

Measures (BIPM) [20]. The reported expanded uncertainty contains no allowances for the longterm drift of the resistor under test, for the possible effects of transporting the standard resistor

between laboratories, nor for measurement uncertainties in the user's laboratory. As mentioned

in section 1, this reported uncertainty also does not include any allowance for the possible error

between the U.S. representation of the ohm and the ohm as defined by SI. The appendix contains

samples of some NIST Reports of Calibration. Also included in the appendix is a copy of an

information sheet on resistance measurements that is included with each report.

The calibration of a resistor involves the comparison of the test resistor with NIST working

standards using one of several measurement systems previously described. The critical elements

contributing to the measurement uncertainty are the standard resistors (working, transfer, check,

and test), and the measurement systems.

34

- --
---- -

9.1 Model - Standard Resistors

Experimental data indicate that the resistance of a standard resistor is a function of environmental

parameters, time, and load level. To some degree, the environmental parameters can be

controlled and/or measured in order to correct for their influence. Assuming the resistor is not

subjected to mechanical disturbances, the environmental parameters of main concern that

contribute to the measurement uncertainty are temperature, pressure, and humidity.

The change of resistance of a resistor with time cannot be controlled and it is difficult to

measure. This characteristic is inherent in a resistor as a result of its design and construction.

The four major sources of this resistance change are metallurgical processes, oxidation, bending

stresses and strains, and tensile stresses and strains. The combination of these effects results in

a unique stability curve for each resistor. Although such curves may exhibit a shape of an

exponential decay function, evidence indicates that over the short term the stability curves of

resistors can be modeled as linear functions. This evidence includes the results of the absolute

determinations of resistance in SI units and, more recently, the monitoring of resistance by the

quantum Hall effect by NIST and other national laboratories. In addition, the run-sequence plots

of NIST working and check standard resistors over a time span of several years are fitted best

by straight lines having slopes of different signs as well as different magnitudes. It is inferred

that for standard resistors not mechanically disturbed, it is highly likely they will drift linearly,

and with sufficient data their value can be predicted to a high degree of certainty using a linear

least-squares analysis.

The change in resistance of a standard resistor as a function of load level results from: 1) the i2R

or self-heating of a resistor, and/or 2) the voltage dependence of a resistor. The former is

primarily a function of the TCR and the surface area of the resistance material, while the latter

is significant for film-type resistors. Errors caused by loading are negligible for resistor

calibrations from 1 n to 1 Mn since the measurements are done at the same power level of 10

mW. For calibrations below 1 n, the power dissipation in the test resistor may be as large as

100 mW in order to have adequate measurement sensitivity. These low-resistance standards are

designed to dissipate higher power (~1 ppm/W), and consequently, errors caused by loading at

~ 100 mW are negligible. Above 1 MQ, errors due to loading are usually significant for filmtype resistors which exhibit large VCR's. The absolute values of VCR's for film-type resistors

can be as large as 100 ppmN or more.

9.2 Model -Measurement Systems

The model for a measurement system for calibrating resistors is broken down into the following

main components: the ratio instrument; dummy resistor; detector circuit; the operator and/or

computer; procedures and conditions of test; and auxiliary equipment. The measurement

technique is usually that of a 1/1 comparison, in which a test resistor or check standard is

replaced or substituted by a working standard of the same nominal value (substitution technique).

The ratio instrument (dc comparator, resistance-ratio bridge, or teraohmmeter) is then relied upon

to determine only the difference between resistors, and this difference need not be accurately

measured. For example, if the test resistor and working standard differ by 100 ppm, the

difference need only to be determined to 1% to achieve a 1 ppm measurement of the test resistor

35
based on the working standard. The important sources of error to consider are: stability and

linearity of the ratio instrument; stability of the dummy resistor (if used); detector resolution; and

changing thermal emfs in the detector circuit. Of secondary importance are errors resulting from

leakage currents, lead resistances, contact resistances and test conditions which tend to cancel or

are significantly reduced when using the substitution technique. All other sources of error

associated with the operator, the computer (if used), procedures, and auxiliary equipment are

believed to be negligible in the systems currently at use at NIST.

The two most critical measurement systems will be examined in more detail than the others.

They are the 1 Q DCC potentiometer system and the 10 kQ resistance-ratio system. These two

resistance levels are critical because 1 Q and 10 kQ commercial resistors are of the highest

quality, and as a consequence, most NIST resistor calibrations with the smallest NIST

uncertainties are done at these two resistance levels. The first thing to establish is whether or

not the measurement systems are "in statistical control." To determine this the data history of

the measurement processes are examined. Figures 9.1 and 9.2 are the control charts for the NIST

1 Q check standards C84 and C93 from 1982 to 1991. The check standards have significant

changes both in measured values and subsequent drift rates after January 1, 1990 as a result of

implementing the new representation of the ohm (see section 1). The y-axis scales on the right

are offset by -1.69 ppm, which is the change applied to the numerical values of all NIST

reference resistors on January 1, 1990. Note that the scale on the left refers to measurements

made before January 1, 1990, while the scale on the right refers to measurements made after

January 1, 1990. Each filled-circle symbol represents a mean of measurements taken over a

period of one month. The number of monthly measurements varied from a minimum of 4 to a

maximum of 43. The solid line is a fitted least-squares line of the data. The upper and lower

dashedlines aboutthis trendline correspondto confidencelevellimitsof ~ 0.02 ppm or a 95%

confidence interval. The residuals from the linear regression fits for C84 and C93 are plotted in

Fig. 9.3 and Fig. 9.4 as histograms.

The 10 kQ measurement system has one air-type check standard, C1410, and one oil-type check

standard, C1419. Figures 9.5 and 9.6 are control charts of the data during 1990 for C1410 and

C1419, respectively. Each filled-circle symbol represents a single point for a measurement run.

Upperandlowerdashedlinescorrespondingto confidencelevellimitsof ~ 0.02 ppm are shown

about the solid fitted line. Histograms of the residuals from the linear regression fits are shown

in Fig. 9.7 and Fig. 9.8.

9.3 Type A Standard Uncertainty

The Type A standard uncertainty, s, assigned to the value of a standard resistor is based on an

estimate of the standard deviation of the measurement process for that particular resistance level.

The s is calculated from a sampling of at least 15 measurement runs. First, the individual

estimates of the standard deviations of one or more test resistors are calculated from repetitive

measurements taken during a single test run. If more than one test resistor is measured during

a run, a pooled value of the estimate of the standard deviation is obtained for that particular run.

Finally, the pooled values for at least 15 measurement runs, over a several month interval, are

themselves pooled to obtain a realistic estimate of s for the measurement process. The Type A

standard Wlcertaintiesfor the various resistance levels are listed in Tables 9.1 and 9.2.

36
--

Year

Fig. 9.2. Control chart for 1 n check standardC93.

37

28.351

I I I I 126.66

C84 (1 0)

28.30 [

i 26.61

l_____

, .. --. /

28.25 //'------_. 26.56

,..... ,..... co'"'" 28.20 26.51 :$ 0) 0) .... .... --- ---

6 28.15 26.46 6

.5 28.10 26.41 .5

CJ CJ

28.05 26.36

28.00 26.31

27.95 26.26

1982 1984 1986 1988 1990 1992

Year

Fig. 9.1. Control chart for 1 0 check standard C84.

1.50 -0.19

1.45 I- C93 (1 0) -0.24

1.40 I- -0.29

1.35 I- -I -0.34

,..... 1.30 co -0.39 S '"'" 0) 0)

.... 1.25 -0.44 --- ---

6 1.20 -0.49 6

1.15 -0.54

.5 .5 CJ 1.10 -0.59 CJ

1.05 I- -I -0.64

1.00 l- I

I -I -0.69

0.95 II -0.74 I

0.90 -0.79

1982 1984 1986 1988 1990 1992
o c:::::J

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Residuals (ppm)

Fig. 9.3. Histogram for 1 n check standard C84.

10

5

o I I

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Residuals (ppm)

Fig. 9.4. Histogram for 1 n check standard C93.

38

50

45 L C84 (1 0)

40

35

30 lot

CD

.c 25

EI

=s

z 20

15

10

5

50

45 L C93 (1 0)

40

35

30 lot

CD

.c 25 EI

=s

z 20

15
- ----

-0.50

C1410 (10 kO)

//

//

//

//

//

//

//

" " //

"..-,," //

//

//

//

//

//

//

//

"",,_.... ,," .. /

.

//////'/'//

~"...

../

,/////

..

95% Confidence Interval

-0.70

J J

1990

Fig. 9.5. Control chart for 10 kO check standard C1410.

F M A M J A SON D

1.00

C1419 (10 kO) '-

/

/ / / / / / / / / / / / / / /

/ ~/

. /// . //

/////./ //

///'/ //

// /

""

.

95% Confidence Intervol

0.80

J J A SON D

1990

Fig. 9.6. Control chart for 10 kO check standard C1419.

F M A M J

39

-0.55

S

0.. 0.. -0.60

.5

()

-0.65

0.95

S

0..

0.. 0.90

.5

()

0.85
o I I I

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Residuals (ppm)

Fig. 9.7. Histogram for 10 kQ check standard C1410.

70

65 ~ C1419 (10 kO)

60

55

50

45

... 40 CD

.0 35 a

::s 30

:z;

25

20

15

10

5

o L....-

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Residuals (ppm)

Fig. 9.8. Histogram for 10 kQ check standard C1419.

40

60

55 C1410 (10 kO)

50

45

40

... 35

CD .0 30 a

::s 25 :z;

20

15

10

5
9.4 Type B Standard Uncertainty

The Type B standard uncertainty, u, assigned to the value of a standard resistor is determined by

combining in quadrature (root-sum-square or RSS) the estimated standard uncertainties from each

known individual component of the measurement process for that particular resistance level.

Each Type B standard uncertainty evaluated is either equal to 1/~3 times an estimated bound for

a uniform distribution, or an estimate by the experimenter. For analysis, the sources of error for

the Type B standard uncertainties are separated into two main categories: 1) those associated with

the standard resistors, and 2) those associated with the measurement systems. Tables 9.3 and 9.4

list the estimates of the Type B standard uncertainties for the various resistance levels along with

the RSS subtotal for each level.

9.4.1 Standard Resistors

This category includes the sources of error associated with the Type B standard uncertainties

assigned to the values of the working standards. These sources of error are subdivided into three

main areas: a) maintaining the working NIST ohm in terms of the quantized Hall resistance, b)

scaling from the NIST ohm to other resistance levels using transfer standards, and c) the

environmental and drift factors of the working standards themselves.

a) NIST Ohm - The 1 Q working group of five Thomas-type resistors preserves the NIST ohm

between QHR comparisons. Since 1986 the combined standard uncertainty of comparing this

working group with the QHR has been within 0.02 ppm. Reference [3] lists in detail the Type

A and Type B standard uncertainties for this process.

b) Transfer Standards - As described in section 8.2, transfer standards provide accurate ratios of

1011and 10011for extending the use of !4.ISTat the 1 Q level to higher resistance levels. One

of the components under this listing in Tables 9.3 and 9.4 includes the combined standard

uncertainty of the transfer standard used to assign a value, based on !4.!ST'to a particular transfer

standard. For example (see Figs. 8.5 and 8.6), the Type B uncertainties for transfer standards

H1k, H100k, H10M and H1G include the combined standard uncertainties of transfer standards

H10, H1k, H100k, and H10M, respectively.

Also included in the Type B uncertainties under this listing in Tables 9.3 and 9.4 are estimates

of the ratio errors of the various transfer standards. An estimate of the ratio error of a particular

transfer standard can be calculated from measurements of: 1) the differences among the main

resistors, 2) the finite resistances of the 4-terminal junctions, and 3) the resistances of the

paralleling fixtures including fan resistors. Additional checks are made by using paralleling

fixtureshaving differentvaluesof fan resistors. If loadingerrors are small,the 1011ratio can

be verified by comparing the results obtained from the series-parallel measurements as described

in section 8.2 against the mean value of the main resistors obtained by measuring each individual

resistor. Leakage resistances within transfer standards of high resistance can cause significant

ratio errors. Surface leakage is eliminated by guarding the terminations of these transfer

standards. Internal leakage, mainly caused by the properties of the fluid sealed in the box

(mineral oil or silicone fluid), is monitored to determine if it is within acceptable limits.

41
An independent check of the 10011ratio of HI 0 was made against the 10011ratio of a cryogenic

current comparator (CCC). CCC's [21] utilize superconducting shields and SQUID's to provide

current ratios with accuracies of better than 1 part in 109,orders of magnitude better than roomtemperature DCC's. An automated CCC resistance bridge [22] using low-noise and stable current

sources [23] was used to verify that the 100/1 ratio of HI0 is exact to within 0.01 ppm.

c) Working Standards - A set of working standards exists at each decade resistance level. The

Type B standard uncertainty assigned to a particular set of working standards is based, primarily,

on a combination of errors associated with not knowing exactly the temperature, humidity,

pressure, and drift effects of that particular set of standards during a measurement run.

9.4.2 Measurement Systems

Listed in Tables 9.3 and 9.4 are the estimated Type B standard uncertainties for the various

sources of systematic error associated with the seven measurement systems for each resistance

level. The sources of error are subdivided into six classifications as follows:

a) Ratio -These include the errors caused by the instability and non-linearity of the turns ratio

of a dc comparator or the ratio arms of a resistance bridge. Usually, the short-term ratio

instability results from changes in the test or environmental conditions during a measurement run,

and this can be monitored, to some extent, by measuring a check standard at the beginning and

at the end of the run. For most systems the ratio linearity can be determined and corrections

applied if the errors are significant.

Of greater significance are ratio errors for measurement systems that use ratios greater than unity.

This is the circumstance for measurements < 1 Q using the 1011,100/1, and 100011ratios of the

dc comparator bridge and/or for measurements> 1010Q using the 1011and 10011ratios of the

teraohmmeter. The dc comparator bridge has provisions for self-calibrating its 1011,100/1, and

100011ratios. The accuracy of these ratios has also been verified by comparison to resistance

ratios previously checked against transfer standards, e.g., 100/1 Q, 1000/1 Q, and 1000 0/1 Q.

b) Stability - This includes the error caused by the short-term instability of a dummy resistor in

a bridge or DCC measurement system. In the DCC systems it also includes an estimate of the

instabilities of the constant current sources that may occur during a measurement run.

c) Detector - The error in the detector circuit is associated with the stability of the zero setting

of the detector, the stability of the thermal emfs in the circuit, and the resolution of the detector

system. For the automated dc comparator potentiometer systems, it also includes the errors

caused by the non-linearity of the detector and feedback circuits.

d) Ambient - This category contains: 1) the estimated error of the temperature of the customer's

resistor from the indicated temperature of a particular bath, 2) the estimated error of knowing the

bath temperature from the true temperature as derived from the ITS-90, 3) the estimated error of

the pressure measurement for a Thomas-type 1 Q or air-type 10 kQ measurement, and 4) the

estimated error of the humidity measurement for the high resistance measurements. The critical

temperature measurements are made using a calibrated PRT. The secondary temperature

42
measurements are made with digital thermistor thermometers that are calibrated against a PRT.

e) Connection - This includes the estimated errors associated with: 1) the change in the lead

resistances of a resistance-ratio bridge network during a test run, 2) the location of the potential

points for a Rosa-type standard resistor, and 3) the variation in resistance of the mercury contacts

on two-terminal measurements. The resistivity of the terminal arms of a commercial Rosa-type

standard resistor is :::::3.5J.101cm.The maximum error of positioning a potential lead to a screwtype terminal is about 0.5 cm for each arm. Therefore, an uncertainty of 3.5 J.10is allotted for

this systematic error. The maximum day-to-day variations in a normal (surfaces slightly askew)

mercurycontactis estimatedto be :::::5J.10.

f) Leakage - This uncertainty results from the possible deterioration of the insulating

properties of the mineral oil and/or resistor headers. The insulation of the mineral oil in the baths

is checked periodically and the oil is changed if it falls below 5 x 1013n.

43

Table 9.1. Standard uncertainties in ppm

Resistance TYM.A meB RSS Total

(0) (s) (u)

I(T) 0.008 0.021 0.022

104(S) 0.008 0.037 0.038

10-4 1.5 5.2 5.4

10-3 1.0 2.1 2.3

10-2 0.5 1.2 1.3

10-1 0.1 0.5 0.5

1 0.05 0.44 0.44

10 0.01 0.44 0.44

102 0.01 0.22 0.22

103 0.02 0.24 0.24

104 0.02 0.24 0.24

lOs 0.04 0.85 0.85

106 0.04 1.44 1.44
Table 9.2. Standard uncertainties in ppm

44

- -

Resistance Type A fueB RSS Total

(n) (8) (u)

107(WB) 4 5 6

107(T) 40 33 52

108(WB) 4 12 13

108(T) 40 104 111

109(WB) 40 37 54

109(T) 80 206 221

1010(T) 200 256 325

101l(T) 200 256 325

1012(T) 200 532 568

WB -Wheatstone Bridge

T -Teraohmmeter
Table 9.3. Type B standard uncertainties in ppm

Resistance Standards .system

ill) Q(NIST) Transfer Working Ratio Stability Detector Ambient Connection Leakage

I(T) 0.020 0 0.005 0.002 0.002 0.002 0.004 0.002 0.001

104(S) I 0.020 0.020 0.020 I 0.005 0.005 0.005 0.005 0.005 0.005

10,4 0.02 5 1 0.1 0.4 1 0.5 0.1 0

.j:::o.

VI 10'3 0.02 2 0.6 0.1 0.2 0.2 0.4 0.1 0

10-2 0.02 1 0.4 0.1 0.2 0.2 0.4 0.1 0

10'1 0.02 0.1 0.2 0.1 0.2 0.2 0.3 0.1 0

1 0.02 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0

10 0.02 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0

102 0.02 0.05 0.1 0.05 0.1 0.1 0.1 0.05 0

103 0.02 0.1 0.1 0.05 0.1 0.1 0.1 0.05 0

104 0.02 0.1 0.1 0.05 0.1 0.1 0.1 0.05 0.05

105 0.02 0.8 0.1 0.05 0.2 0.1 0.1 0.05 0.1

106 0.02 1 0.1 0.05 0.2 0.1 0.1 0.05 1
Table 9.4. Type B standard uncertainties in ppm

Resistance Standards System

ill) Q(NIST) Transfer Working Ratio Stability Detector Ambient Connection Leakage

107(WB) 0.02 3 2 1 2 2 1 0 2

107(T) 0.02 3 2 10 20 10 10 0 20

108(WB) 0.02 5 2 1 2 2 1 0 10

.j::..

108(T) 0\ 0.02 5 2 10 20 10 10 0 100

109(WB) 0.02 10 20 1 20 2 10 0 20

109(T) 0.02 10 20 10 40 10 10 0 200

1010(T) 0.02 50 20 100 50 100 10 0 200

10II (T) 0.02 50 20 100 50 100 10 0 200

1012(T) 0.02 100 20 100 50 100 10 0 500

WB - Wheatstone Bridge

T - Teraohmmeter
---

47

Table 9.5. Resistance expanded uncertainties

SP-250 [4] Resistance Power Uncertainty

Test No. ill} (mW) Umml

51130C I(T) 10 0.05

51131C 104(S) 10 0.15

51132C 10-4 100 11

51133C 10-3 100 5

51134C 10-2 100 3

51135C 10-1 100 2

51136C 1 50 1

51137C 10 50 1

51138C 102 10 0.5

51139C 103 10 0.5

51140C 104 10 0.5

51141C 105 10 2

51142C 106 10 3

51143C 107(WB)

* 14

107(T)

* 140

51145C 108(WB)

* 40

108(T)

* 400

51147C 109(WB)

* 140

109(T)

* 700

51149C 1010(T)

* 700

51151C 101\(T)

* 700

51153C 1012(T)

* 1400

*Customer specified voltages

WB - Wheatstone Bridge

T - Teraohmmeter
9.5 Reported Uncertainties

Table 9.5 lists the expanded or overall uncertainties for the various resistance levels that are

given in a NIST Report of Calibration. These uncertainties are based on calculations using

eq (9.1) with a coverage factor of 2 and the estimated Type A and Type B standard uncertainties

listed in Tables 9.1 through 9.4. In most cases the reported uncertainties have been

conservatively rounded upward. Table 9.5 lists the maximum power dissipation of a test resistor

during calibration, except for resistances of 107n or above where the customer specifies the test

voltage. Also listed in this table are the test numbers for each of the resistance levels.

10. QUALITY CONTROL

It is important that procedures be established to determine whether or not a measurement process

is and remains in a state of control if the uncertainty that NIST assigns to the value of a standard

resistor is to be meaningful. Three factors are examined for each calibration performed in order

to insure the quality of the measurement value that is assigned to a standard resistor:

1. Standard deviations of the measurement run.

2. Control charts of check standards.

3. Data history of the standard resistor under test.

The computer hardcopy of the data analysis/results of a measurement run contains the individual

standard deviations, calculated from repeated measurements during the run, for each resistor. If

any standard deviation for a resistor exceeds the Type A standard uncertainty as listed in Tables

9.1 or 9.2, for that particular resistance level by a factor of 2, the measurement process is

considered out of control, and appropriate steps are taken to correct the situation. Usually, the

explanation for this out-of-control condition is an error on the part of the observer in recording

or entering data, or a malfunction in a piece of equipment. The problem is corrected and the

measurement test is repeated.

The computer hardcopy also lists the difference between the measured value and the predicted

value for each of the check standards. The predicted value is calculated from a drift factor that

is derived from a previous least-squares analysis of a linear fit for that check standard. If this

difference or residual exceeds the Type A standard uncertainty by a factor of 2, it is flagged by

an asterisk. It indicates that a potential problem may exist and that the other control indicators

should be scrutinized. The over range of the residual may be caused by a lack of knowledge of

the resistor model. The listing of the residual, in effect, is examining a point on the control chart

for that check standard to determine if it is within acceptable limits. If necessary, a linear

regression analysis computer program is run to generate the control chart for the particular check

standard in question.

Finally, the data history of the standard resistor under test is examined if more than two

measurement points exist. If the new value appears unreasonable (on the order of three times the

residual standard deviation from a linear fit), it is considered an outlier and the source of the

discrepancy is investigated. Additional tests are run to determine the stability of the resistor, and

the customer is apprised of the situation.

48

-----
--

11. ONGOING PROJECTS

Projects are underway in several areas of resistance measurements to improve the maintenance

and disseminationof ~IST , to extend NIST calibration services to 1014Q, and to develop a new

calibration service for ac resistors. These projects include the following.

1) A QHR standard has been installed in the resistance calibration laboratory. It will become the

national standard and replace the one kept in the QHR research facility. This will provide for

more frequent monitoring of working standards, and also reduce the uncertainties associated with

maintaining the ohm representation by eliminating the need to transfer resistors between

laboratories as in the present procedure.

2) Two CCC resistance bridges have been constructed and are being used to verify Hamon-type

resistance techniques from 1 0 to 100 Q, 1 kO, 6453.20 0, and 10 kO [24]. Measurements

comparing the 10/1,64.532/1, and 100/1 ratios ofCCC's to that of Hamon transfer ratios indicate

agreement to ~ 0.01 ppm, the practical limit of accuracy using Hamon transfer standards with

conventional resistance bridges. The higher ratio accuracies and sensitivities of CCC bridges will

make it possible to lower the uncertainties associated with resistance scaling.

3) Near completion is the evaluation of a prototype system that is an automated version of a

capacitance discharge method for the measurement of high-value resistors. This system will

providea new calibrationservicefor resistancestandardsfrom 1012 0 to 1014 0 or higher.

4) The design of an automated system for the measurement of special Evanohm 10 kO standard

resistors has been completed, and a prototype system is under construction. The system will

feature a guarded ratio bridge, and automatic switching of resistors using BPO connectors.

5) The design of a guarded scanner to be used with the ring method for calibrating resistors

~ 100 kO is underway. This should reduce the leakage errors at these resistance levels, and

therefore reduce the respective calibration uncertainties. A guarded scanner would also be used

to completely automate the teraohmmeter system for high-resistance measurements.

6) Under development is an automated ac Kelvin bridge for measuring the frequency dependence

and phase angle of precision resistors from 1 0 to the 1 MO level over the frequency range

10 Hz to 10 kHz [25]. The main ratio arms consist of 30-bit binary inductive voltage dividers.

12. ACKNOWLEDGMENTS

The authors wish to express their appreciation to our group leader, Norm Belecki, for his

continued support and guidance in this area. We also would like to acknowledge our calibration

coordinator, Denise Prather, for the many tasks she does in coordinating resistor calibrations with

our customers and keeping this measurement service running smoothly. Finally, but not least,

we would like to thank our secretary, Sharon Fromm, for performing the many secretarial duties

that make our work easier.

49
13.REFERENCES

[1] K. v. Klitzing, G. Dorda, and M. Pepper, "New method for high-accuracy

determinationof thefine-structure constant based on quantized Hall resistance,"

Phys. Rev. LeU., vol.45, pp. 494-497, Aug. 1980.

[2] N. B. Belecki, R. F. Dziuba, B. F. Field, and B. N. Taylor, "Guidelines for

implementing the new representations of the volt and ohm effective January 1,

1990," Natl. Inst. Stand. Technol. Technical Note 1263, June 1989.

[3] M. E. Cage, R. F. Dziuba, C. T. Van Degrift, and D. Yu, "Determination of

the time dependence of Q(NBS) using the quantized Hall resistance," IEEE

Trans. Instrum. Meas., IM-38, pp.263-269, Apr. 1989.

[4] "NIST calibration services users guide," Natl. Inst. Stand. Technol. Special

Publication 250, for sale by the Superintendent of Documents, U. S. Government

Printing Office, Washington, DC 20402.

[5] C. Croarkin, "Measurement Assurance Programs, Part II: Development and

Implementation," NBS Special Publ. 676-11,April 1984.

[6] B. V. Hamon, "A 1-100 Q build-up resistor for the calibration of standard

resistors," 1. Sci. Instr., vol. 31, pp. 450-453, Dec. 1954.

[7] M. P. MacMartin and N. L. Kusters, "A direct-current-comparator ratio bridge

for four-terminal resistance measurements," IEEE Trans. Instrum. Meas., IM-15,

pp. 212-220, Dec. 1966.

[8] M. P. MacMartin and N. L. Kusters, "The application of the direct current

comparator to a seven-decade potentiometer," IEEE Trans. Instrum. Meas., IM-l7,

pp. 263-268, Dec. 1968.

[9] K. R. Baker and R. F. Dziuba, "Automated NBS 1 Q measurement system," IEEE

Trans. Instrum. Meas., IM-32, pp. 154-158, Mar. 1983.

[10] R. D. Cutkosky, "An automated resistance thermometer bridge," IEEE Trans.

In strum. Meas., IM-29, pp. 330-333, Dec. 1980.

[11] F. W. Wenner, "Methods, apparatus and procedures for the comparison of

precision standard resistors," Natl. Bur. Stand. (u. S.) 1. Res., RP1323, vol. 25,

pp. 229-294, Aug. 1940.

[12] G. D. Vincent and R. M. Pailthorp, "Experimental verification of the fiveterminal ten-kilohm resistor as a device for dissemination of the ohm," IEEE

Trans. Instrum. Meas., IM-17, pp. 239-244, Dec. 1968.

50

- --
-- --

[13] R. F. Dziuba, D. G. Jarrett, and 1. D. Neal, "Wide-range automated system for

measuring standard resistors," 1988 Conference on Precision Electromagnetic

Measurements, IEEE CPEM'88 Digest, pp. 158-159, June 7-10, 1988.

[14] B. L. Dunfee, "Method for calibrating a standard volt box," Natl. Bur. Stand. (U S.)

1. Res., vol. 67C, pp. 1-13, March 1963.

[15] 1. M. Cameron, M. C. Croarkin, and R. C. Raybold, "Designs for the calibration of

standards of mass," Natl. Bur. Stand. (U S.) Technical Note 952, June 1977.

[16] S. Hoi Tsao, "An accurate, semiautomatic technique of measuring high

resistances," IEEE Trans. Instrum. Meas., IM-16, pp. 220-225, Sept. 1967.

[17] G. M. Reedtz and M. E. Cage, "An automated potentiometric system for

precision measurement of the quantized Hall resistance," Nat!. Bur. Stand. (U S.)

1. Res., vol. 92, pp. 303-310, Sept.-Oct. 1987.

[18] 1. C. Riley, "The accuracy of series and parallel connections of four-terminal

resistors," IEEE Int. Conv. Record, Pt. II, pp. 136-146, March, 1965.

[19] B. N. Taylor and C. E. Kuyatt, "Guidelines for evaluating and expressing the

uncertainty of NIST measurement results," Natl. Inst. Stand. Technol. Technical

Note 1297, 1992.

[20] International Bureau of Weights and Measures (BIPM) Working Group on the

Statement of Uncertainties, Metrologia, vol. 17, pp. 73-74, 1981.

[21] R. F. Dziuba and D. B. Sullivan, "Cryogenic direct current comparators and their

applications," IEEE Trans. Mag., MAG-II, pp. 716-719, Mar. 1975.

[22] R. F. Dziuba and 1. Kinoshita, "Automated cryogenic current comparator

resistance bridge," CPEM'86 Digest, IEEE Cat. No. 86CH2267-3, June 1986.

[23] R. E. Elmquist and R. F. Dziuba, "Isolated ramping current sources for a

cryogenic current comparator bridge," Rev. Sci. Instr., vol. 62, pp. 2457-2460,

Oct. 1991.

[24] R. F. Dziuba and R. E. Elmquist, "Improvements in resistance scaling at NIST using

cryogenic current comparators," CPEM'92 Digest, pp. 284-285, June 1992.

[25] D. G. Jarrett and R. F. Dziuba, "Automated ac bridge for the measurement of resistors

over the frequency range 10 Hz to 10 kHz," CPEM'92 Digest, pp. 87-88, June 1992.

51
14. BIBLIOGRAPHY

7

[1] Precision Measurement and Calibration: Electricity and Electronics, Natl. Bur.

Stand. (u. S.) Handbook 77, vol. I, Feb. 1961.

[2] Precision Measurement and Calibration: Electricity-Low Frequency, Ed. by F. L.

Hermach and R. F. Dziuba, Natl. Bur. Stand. (u. S.) Spec. Publ. 300, vol. 3,

Dec. 1968.

[3] Precision Measurement and Calibration: Electricity, Ed. by A. O. McCoubrey, Natl.

Bur. Stand. (u. S.) Spec. Publ. 705, Oct. 1985.

[4] Electrical Measurements, F. K. Harris, John Wiley & Sons, New York, NY, 1952.

[5] Precision DC Measurements and Standards, D. S. Luppold, Addison-Wesley,

Reading, MA, 1969.

[6] The Current Comparator, W. 1. M. Moore and P. N. Miljanic, Peter Peregrinus Ltd.,

London, UK, 1988.

52
- - -----

15. APPENDIX

15.1 Typical Report of Calibration

15.2 Report for a 1 Q Standard Resistor

15.3 Report for a 10 kQ Standard Resistor

15.4 Report for a High-Value Standard Resisto.'

15.5 Information Sheet on Standard Resistors

53
.,."v.'o,C'~ I ~ 'to~

'11: \. . ~ . \.~,tl ~"'r..tiI

UNITED STATES DEPARTMENT DF CDMMERCE

Net:lonel Inat:lt:ut:e of St:enderda end Technology

Gaitharsburg. Maryland 20899

REPORT OF CALIBRATION

STANDARD RESISTOR

Model , SIN

Submitted by

This standard resistor was calibrated on January 1, 1993 and its value of resistance is based on

the results of measurements between this standard and those of NIST working standards

calibrated in terms of the quantum Hall effect used to maintain the U. S. ohm.

Temperature Resistance Uncertainty

25.0 °c 0.999 987 6 Q 1 ppm

The expanded uncertainty given above is based on the approach recommended by the

International Bureau of Weights and Measures (BIPM) and is equal to

2 /S2 + E u2(z) ,

where s is the estimated Type A standard uncertainty based on the pooled standard deviation

from a large population of individual measurements, and u(i) is the estimated Type B standard

uncertainty for each known component quantified by a standard deviation. The coverage factor

2 used by NIST is consistent with international practice. Detailed information is given in NIST

Technical Note 1298 which lists all uncertainty components and describes the method used to

calculate this expanded uncertainty. This reported uncertainty contains no allowances for the

long-term drift of the standard under test or for the possible effects of transporting this standard

between laboratories.

For the Director,

Norman B. Belecki, Group Leader

Electricity Division

Test No.

Reference:

Date:

54
-- ----

..., 0, C'~ I''''~ '10"

·~1I \.

1!J

* #.,,",.- .:.. .

\, ~ '\ . ~..

· "'<4'11 of ,.,

UNITED STATES DEPARTMENT DF CDMMERCE

Nat:lonal Inat:lt:ut:a of St:andarda and Technology

Gaithersl::1urg. Maryland 20899

REPORT OF CALIBRATION

STANDARD RESISTOR

Model , SIN

Submitted by

This standard resistor was calibrated on January 1, 1993 and its value of resistance is based on

the results of measurements between this standard and those of NIST working standards

calibrated in terms of the quantum Hall effect used to maintain the U. S. ohm.

Temperature Pressure Resistance Uncertainty

25.00 °c 101.660 kPa 0.999 998 76 (2 0.05 ppm

The expanded uncertainty given above is based on the approach recommended by the

International Bureau of Weights and Measures (BIPM) and is equal to

2 /S2 +}J u2(z) ,

where s is the estimated Type A standard uncertainty based on the pooled standard deviation

from a large population of individual measurements, and u(i) is the estimated Type B standard

uncertainty for each known component quantified by a standard deviation. The coverage factor

2 used by NIST is consistent with international practice. Detailed information is given in NIST

Technical Note 1298 which lists all uncertainty components and describes the method used to

calculate this expanded uncertainty. This reported uncertainty contains no allowances for the

long-term drift of the standard under test or for the possible effects of transporting this standard

between laboratories.

For the Director,

Norman B. Belecki, Group Leader

Electricity Division

Test No.

Reference:

Date:

55
<#>~y(f0' C', /v\

. ~ . \.~~l .'<4,1Sof

UNITED STATES DEPARTMENT OF COMMERCE

Netolonel In.toltoutoe of Stoenderel. end Technology

Gaitharsburg. Maryland e0899

REPORT OF CALIBRATION

STANDARD RESISTOR

Model , SIN

Submitted by

This standard resistor was calibrated on January 1, 1993 and its value of resistance is based on

the results of measurements between this standard and those of NIST working standards

calibrated in terms of the quantum Hall effect used to maintain the U. S. ohm.

Temperature

23.0 °C

Pressure Resistance Uncertainty

101.660 kPa 10 000.012 3 Q 0.15 ppm

The expanded uncertainty given above is based on the approach recommended by the

International Bureau of Weights and Measures (BIPM) and is equal to

2vs2+'1Ju2(i) ,

where s is the estimated Type A standard uncertainty based on the pooled standard deviation

from a large population of individual measurements, and u(i) is the estimated Type B standard

uncertainty for each known component quantified by a standard deviation. The coverage factor

2 used by NIST is consistent with international practice. Detailed information is given in NIST

Technical Note 1298 which lists all uncertainty components and describes the method used to

calculate this expanded uncertainty. This reported uncertainty contains no allowances for the

long-term drift of the standard under test or for the possible effects of transporting this standard

between laboratories.

For the Director,

Norman B. Belecki, Group Leader

Electricity Division

Test No.

Reference:

Date:

56

- - - ----
---

~..~o. ('~ I''''~ ...~ ·~ .111: ~

~

t;t". .

: ~ \ .. ",.

· r..ofp11'

UNITED STATES DEPARTMENTDF CDMMERCE

Net:lanel In.t:lt:ut:e at St:enderd. end Teahnalagy

Gaitharsburg,Maryland 20888

REPORT OF CALIBRATION

STANDARD RESISTOR

Model , SIN

Submitted by

This standard resistor was calibrated on January 1, 1993 and its value of resistance is based on

the results of measurements between this standard and those of NIST working standards

calibrated in terms of the quantum Hall effect used to maintain the U. S. ohm.

23.0 °C

Humidity

35 % 0.998 76 x 108 Q

0.998 65 x 108 Q

Temperature

23.0 °C 35 %

Voltage

1 V

10 V

Resistance Uncertainty

40 ppm

40 ppm

The expanded uncertainty given above is based on the approach recommended by the

International Bureau of Weights and Measures (BIPM) and is equal to

2/s2+~U2(i) ,

where s is the estimated Type A standard uncertainty based on the pooled standard deviation

from a large population of individual measurements, and u(i) is the estimated Type B standard

uncertainty for each known component quantified by a standard deviation. The coverage factor

2 used by NIST is consistent with international practice. Detailed information is given in NIST

Technical Note 1298 which lists all uncertainty components and describes the method used to

calculate this expanded uncertainty. This reported uncertainty contains no allowances for the

long-term drift of the standard under test or for the possible effects of transporting this standard

between laboratories.

For the Director,

Norman B. Belecki, Group Leader

Electricity Division

Test No.

Reference:

Date:

57
GENERAL INFORMATION ON STANDARD RESISTORS

1. Representation of the SI Unit of Resistance

The International System of Units, abbreviated SI, is

the unit system used throughout the world. In the SI,

the unit of resistance (R) is the ohm (0). In practice,

the ohm, which sometimes is referred to as the

"absolute ohm", is realized at NIST by means of the

NIST calculable capacitor. However, commercial,

industrial, and scientific requirements for the longterm repeatability and worldwide consistency of

measurements of resistance often exceed the accuracy

with which the SI unit for such measurements can be

realized. To meet these severe demands, it has

become necessary to establish a representation of the

ohm that has superior long-term reproducibility and

constancy than the present direct realizations of the

ohm itself.

From January 1, 1948until January 1, 1990,the U. S.

representation of the ohm as maintained at NIST had

been based on the mean resistance of reference

groups of Thomas-type 1 0 resistors whose mean

values were thought to be constant with time. The

discovery of the quantum Hall effect in 1980 by

Klaus von Klitzing led to a method for basing a

representation of the ohm on invariant fundamental

constants. Quantized Hall resistance measurements at

NIST indicated that the U. S. representation of the

ohm was drifting at a rate of (0.0529 :!:: 0.0040)

ppm/year. To eliminate this drift, starting on January

1, 1990, the U. S. representation of the ohm has been

based on the quantum Hall effect in which a

resistance is related to the fundamental constants hle1.

The quantized Hall resistance, RH,is defined as the

quotient of the Hall voltage VHof the ilbplateau to

the current I in the Hall device and is given by

RH(i) = VH(J)/I = RKli,

where RK, the von Klitzing constant, is equal to hle1,

and j is an integer. The value of the U. S.

representation of the ohm is consistent with the

internationally accepted conventional value of the von

Klitzing constant, i.e.,

RK-90 = 25 812.807 {)

exactly. This conventional value is believed to be

consistent with the true SI value to within a 0.005 0

assigned combined standard uncertainty which

corresponds to a relative uncertainty of 0.2 ppm.

Because this uncertainty is the same for all national

laboratories and is not relevant for traceability to

national standards, it is not included in the

uncertainties given in NIST Reports of Calibration.

However, its existence must be taken into account

when the utmost consistency between electrical and

nonelectrical measurements of the same physical

quantity is required.

As a result of adopting the internationally accepted

value for the von Klitzing constant, on January 1,

1990, the numerical values of all NIST reference

resistors were decreased by 1.69 ppm. Likewise the

assigned values of all standard resistors, based on

NIST calibrations before January 1, 1990, should

have been decreased by 1.69 ppm on January 1,

1990. For more information on the change in the

U. S. ohm representation consult NIST Technical

Note 1263 entitled "Guidelines for Implementing the

New Representations of the Volt and Ohm Effective

January 1, 1990."

2. Calibration

NIST provides calibration services for primary

standard resistors of nominal decade values in the

range between 10-4 0 and 1012n. In addition,

Measurement Assurance Program (MAP) services for

resistance are offered at the 1 .0. and 10 kO levels.

Special resistance measurements are undertaken if

they require the unique capabilities at NIST. Consult

the latest edition of the NIST Calibration Services

Users Guide (SP250) for detailed descriptions of the

currently available NIST calibration services for

resistance measurements.

Resistors are usually calibrated against standard

resistors maintained at NIST in a manual or an

automated comparison measurement system using a

resistive ratio-arm bridge, a flux-balancing type of

current comparator, or a capacitance-discharge

method. The specific equipment used depends upon

the value of the resistor being calibrated and on the

accuracy required or warranted. NIST procedures

follow well-recognized dc measurement practices

such as current reversal, minimum power dissipation

consistent with desired resolution and accuracy, and

the use of check standards and data analysis

techniques to monitor the operation of the

measurement system.

Resistors ranging in value from 1 0 to 1 MQ are

usually calibrated at a temperature of 25°C while

58
- ------

totally immersed in a well-regulated oil bath with a

power dissipation in the resistor not exceeding

10 mW. Resistors of value less than 1 .Qdown to a

resistance of 0.0001 .Q are also usually calibrated

immersed in a 25 °C oil bath except the power

dissipation may be as great as 100 mW. The highgrade mineral oil used in oil baths is frequently

checked, and changed, if necessary, to ensure that its

conductivity will not cause a significant error in the

measurement process. Resistors having values greater

than 1 M.a, or resistors not designed for oil

immersion, are calibrated in air at an approximate

temperature of 23 °C and a relative humidity not

exceeding 45%. In all cases environmental

conditions known to have an effect on the value of

the resistor are reported, and where possible,

controlled.

3. Reported Uncertainty

The expanded uncertainty of the value of resistance

given in a NIST Report of Calibration is equal to

2 ';S2 + 1:,u2(i)

where s is the estimated Type A standard uncertainty

based on data from a large population of individual

calibrations, and u(i) is the estimated Type B standard

uncertainty for each known component quantified by

a standard deviation. The coverage factor 2 used by

NIST is consistent with international practice.

Detailed information is given in NIST Technical Note

1298 entitled "NIST Measurement Service for DC

Standard Resistors," which lists all uncertainty

components and describes the method used to

calculate this expanded uncertainty. The reported

uncertainty contains no allowances for the long-term

drift of the resistor under test or for the possible

effects of transporting the standard resistor between

laboratories. As previously mentioned, the reported

uncertainty does not include the possible error

between the U. S. representation of the ohm and the

ohm as defined by SI.

4. Potential Terminals

The resistance of a standard resistor having separate

pairs of current and potential terminals will, unless

otherwise specified, be the four-terminal resistance

between the branch points defined by the potential

terminals. When there are more than one pair of

potential terminals, the innermost pair will be used to

define the resistance. For resistors of the Rosa type,

where the potential terminals are ill-defined, the

----

potential connections are made by placing straight

pieces of wire under the inner sides of the innermost

screw connections on the heavy copper arms of the

resistor. Resistors having only one pair of terminals

will be measured as two-terminal resistors.

For Rosa-type resistors the difference between the

four-terminal value and the two-terminal value of

resistances defined by the mercury-wetted surfaces is

usually on the order of 50 !l.Q. This difference is

0.05 ppm or less for resistors of nominal values

~1 k.Q,and for most measurements, this difference is

negligible.

5. Mercury Connections

The contact surfaces, on the terminals of standard

resistors, designed to be mercury-wetted are cleaned

and amalgamated with mercury before the resistors

are calibrated. Users should periodically check the

condition of these contact surfaces and, if necessary,

recondition them exercising care so that the surfaces

remain smooth and flat. Because mercury is

poisonous, it should be used in accordance with

prescribed safety regulations.

6. Stability

Studies indicate that the stability with time of

standard resistors depends upon many factors such as:

the basic design of the resistor, the resistance alloy

used and its heat-treatment history, the detailed

construction of the resistor, and subsequent handling

of the resistor in the laboratory and during

transportation. In the final analysis each laboratory

must determine the stability of its standard resistors

based on measurements over a long period of time

and, especially, measurements before and after the

resistors are transported.

7. Temperature Coefficients

The resistance-temperature curve for resistors over the

interval 20 °C to 30 °C can be represented by

R(t) ~ R'[t + «(t - tT) + P(t - tTi] ,

where R(t) is the resistance at temperature t, R' is the

resistance at a reference temperature tr,a. is the slope

of the curve at tr, and fJ determines the curvature at

any temperature. The reference temperature t, is

usually 25 °C for oil-type resistors and 23 °C for airtype resistors. The coefficients a. and fJ do not

change appreciably with time and need only be

59
detennined once. Resistor manufacturers usually can

supply infonnation on the temperature coefficients

pertaining to their standards.

8. Pressure Coefficient

Some standard resistors (Thomas-type 1 nand airtype 10 ill), because of their thin-walled

construction, exhibit small changes of resistance with

changes in pressure. From a study of a small number

of these resistors it appears that the effect of pressure

on resistance is linear over the range of barometric

pressures and can be expressed as

R(P) '" Ro[1 + y(P - Po)] ,

where R(P) is the resistance at pressure P, Ro is the

resistance at a reference pressure Po, and y is the

pressure coefficient. The reference pressure is usually

taken to be one standard atmosphere or 101.325 kPa.

Typically, the pressure coefficients of commercial

Thomas-type resistors range from +0.0002 x lO-6/hPa

to +0.0025 x lO-6/hPa. For a user located at an

altitude of one mile above sea level, the resistance of

this type of resistor can be as much as 0.5 ppm less

than the value at the altitude of the NIST

Gaithersburg Laboratory.

Besides the barometric or surface pressure one has to

consider the additional pressure effect on the resistor

due to its depth of immersion in the oil bath. As an

example, for mineral oil with a specific gravity of

0.086 the value of P increases 8.48 Pa for each

millimeter descent below the surface of the oil. At

NIST the reference position of the resistor is taken to

be at the level of the surfaces of the amalgamated

current tenninals of the resistor. The value of

pressure given in a NIST Report of Calibration for a

Thomas-type resistor is the sum of the ambient

barometric pressure at the time of calibration plus the

pressure resulting from the depth of the resistor below

the surface of the oil.

9. Load Effects

Current. Standard resistors are calibrated at NIST at

low power dissipations so that the change in

resistance resulting from the effect of i2Rheating is

neglgible. Standard resistors of nominal values ~l n

are calibrated at power dissipations of 10m W or less.

For standard resistors of nominal values < 1 n, the

power level may be as large as 100 mW in order to

have sufficient resolution in the measurement system.

Voltage. Thin-film standard resistors of nominal

values ~ 1 Mn usually exhibit a significant change in

resistance with applied voltage. Typically these

voltage coefficients of resistance can vary from 0 to

-0.03%/volt. Hence, the magnitude of the test voltage

should be specified by the customer when a resistor

of this type is submitted for calibration.

10. Selected References

1. N. B. Belecki, R. F. Dziuba, B. F. Field, and B. N.

Taylor, "Guidelines for Implementing the New

Representations of the Volt and Ohm Effective

January 1, 1990," Natl. Inst. Stand. Technol.

Technical Note 1263, June 1989.

2. "NIST Calibration Services Users Guide," Natl.

Inst. Stand. Technol. Spec. Pub. 250.

3. Precision Measurement and Calibration: Electricity

and Electronics, Natl. Bur. Stand. (D. S.) Handbook

77, vol. I, Feb. 1961.

4. Precision Measurement and Calibration: Electricitv

- Low Frequency, Ed. by F. L. Hennach and R. F.

Dziuba, Natl. Bur. Stand. (D. S.) Spec. Pub. 300, vol.

3, Dec. 1968.

5. PrecisionMeasurement andCalibration: Electricitv,

Ed. by A. O. McCoubrey, Natl. Bur. Stand. (D. S.)

Spec. Pub. 705, Oct. 1985.

6. F. W. Wenner, "Methods, Apparatus and

Procedures for the Comparison of Precision Standard

Resistors," Natl. Bur. Stand. (D. S.) J. Res., RP1323,

vol. 25, pp. 229 - 294, Aug. 1940. Reprinted in

reference 3.

7. J. L. Thomas, "Precision Resistors and their

Measurements," Natl. Bur. Stand. (D. S.) Circular

470, Oct. 1948. Reprinted in references 3 and 4.

8. Paul P. B. Brooks, "Calibration Procedures for

Direct Current Resistance Apparatus, Natl. Bur.

Stand. (D. S.) Monograph 39, Mar. 1962.

9. R. F. Dziuba, P. B. Boynton, R. E. Elmquist, D. G.

Jarrett, T. P. Moore, and J. D. Neal, "NIST

Measurement Service for DC Standard Resistors,"

Natl. Inst. Stand. Technol. Technical Note 1298,Nov.

1992.

60
----

ELECTRONICFORM *U.S. G.P.O. :1992-341-832:60377

NIST-114A U.S. DEPARTMENT OF COMMERCE 1. PUBUCATION OR REPORT NUMBER

.(REV. 3-90) NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY NIST/TN-1298

2. PERFORMING ORGANIZATION REPORT NUMBER

BIBLIOGRAPHIC DATA SHEET 3- PUBUCATIONDATE

November 1992

4. TITLE AND SUBTITLE

NIST Measurement Service for DC Standard Resistors

5. AUTHOR(S)

Ronald F. Dziuba, Paul A. Boynton, Randolph E. Elmquist, Dean G. Jarrett, Theodore P. Moore,

and Jack D. Neal

s. PERFORMING ORGANIZATION (I' "'OINT OR OTHER THAN NIST, SEE INSTRUCTIONS) 7. CONTRACT/GRANT NUMBER

U.S. DEPARTMENT 0' COMMERCE

NATIONALINSTITUTE 0' STANDARDS AND TECHNOLOGY .. TYPE 0' REPORT AND PERIOD COVERED ERSBURG,MD Final

9. SPONSORINGORGANIZATIONNAMEANDCOMPLETEADDRESS(STREET,CITY,STATE,ZIp)

Same as item #6

10. SUPPLEMENTARYNOTES

11. ABSTRACT(A2QO.WORDORLESSFACTUALSUMMARYOFMOSTSIGNIFICANTINFORMATION.IFDOCUMENTINCLUDESA SIGNIFICANTBIBUOGRAPHYOR UTERATURESURVEY,MENTIONITHERE.)

At the National Institute of Standards and Technology (NIST), the U.S. representation of the

ohm is based on the quantum Hall effect, and it is maintained and dissemminated at various

resistance levels by working reference groups of standards. This document describes the

measurement systems and procedures used to calibrate standard resistors of nominal decade

values in the resistance range from 10-4 n to 1012 n. Resistance scaling techniques used to

assign values to the working standards are discussed. Also included is an assessment of the

calibration uncertainties at each resistance level.

12. KEYWORDS(8TO 12 ENTRIES;ALPHABmCALORDER;CAPITALIZEONLYPROPERNAMES;ANDSEPARATEKEYWORDSBYSEMICOLONS)

calibration; current comparators; quantized Hall resistance; resistance bridges;

resistance measurements; resistors

13. AVAILABIUTY 14. NUMBEROFPRINTEDPAGES

rx- - UNUMITED

65 - FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONALTECHNICAL INFORMATION SERVICE (NTIS).

X ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE,

15. PRICE

WASHINGTON, DC 20402.

ORDER FROM NATIONALTECHNICAL INFORMATION SERVICE INTIS" SPRINGFIELD, VA 22181.


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