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NBS TECHNICAL NOTE 1182

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

AC Voltage Calibrations

for the 0.1 Hz to 10 Hz

Frequency Range

•QC

100

.115753

no, 1182

1933 -
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities2 — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

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provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

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THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234.

! Some divisions within the center are located at Boulder, CO 80303.
ATiUKAL BUJUk&«

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AC Voltage Calibrations for the 0.1 Hz ^

to 10 Hz Frequency Range &a<>*

no ttZ>

Howard K. Schoenwetter ->v;

Electrosystems Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

N£6> iioU^^adi wokSponsored in part by:

Calibration Coordination Group of the

Department of Defense

•^aeAu o*

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued Sept. 1983
-

-

National Bureau of Standards Technical Note 1182

Natl. Bur. Stand. (U.S.)Jech. Note 1182, 58 pages (Sept. 1983)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1983

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $4.25

(Add 25 percent for other than U.S. mailing)
TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract 1

1. INTRODUCTION 1

2. A METHOD FOR INFRASONIC VOLTAGE MEASUREMENTS 3

3. CALIBRATION OF NBS AC VOLTMETER/ CALIBRATOR 5

3.1 Calibration of AC Voltage Calibrator 6

3.1.1 Frequency Response Calibration of AC Calibrator 6

3.1.2 Voltage Calibration of AC Calibrator 11 3.2 Calibration of the Standard Cells 15

3.3 Calibration of the DC Calibrator 15

3.4 AC-DC Difference Calibration of RMS/DC Converter ... 17

3.5 Summary of Calibration Errors of AC Voltage

Calibrator 17

3.6 Frequency Response of the RMS Voltmeter 19

4. CALIBRATIONS OF VOLTMETERS 26

5. CALIBRATIONS OF VOLTAGE STANDARDS 27

5.1 Voltage Calibrations 27

5.2 Frequency Response Calibrations 28

6. ACKNOWLEDGMENTS 28

7. REFERENCES 29

APPENDIX A. Calibration Forms A-l

APPENDIX B. Detailed Design of Voltage Calibrator B-l

APPENDIX C. Shipping and Fee Information C-l

n i
LIST OF FIGURES

Page

Figure 1. New method for supporting ac voltage measurements

at frequencies below 10 Hz 4

Figure 2. Front panel view of NBS AC Voltmeter/ Cal ibrator ... 7

Figure 3. Controls and connectors on rear, top, and side

panels of AC Voltmeter/ Calibrator 8

Figure 4. AC calibrator frequency response calibrations from

average-value measurements. Calibrator voltages, Vf,

at 5, 2 Hz are compared with 10 Hz value. If

(Vf - V^g) exceeds ±10 ppm for any frequency,

adjustment is made to minimize value 12

Figure 5. Drift (ppm) between calibrations of ac and dc

calibrator references and buffer amplifier gain

(X10 range). The ac voltage reference is not

readjusted unless its drift exceeds ±20 ppm 14

Figure 6. Plot of DVM frequency response, using equations

1 and 2 21

Figure 7. Section of input amplifier used to compensate for

decrease in DVM response at low frequencies 22

Figure 8. Transfer characteristic of input amplifier with

DVM FREQ RESPONSE circuit switched in (see fig. 7) . 24

Figure 9. Theoretical DVM response with input amplifier

frequency compensated 25

Figure B-l . Voltage calibrator. The 1 VAC reference is shown

in figure B-2 B-2

Figure B-2. AC (sine-wave) reference B-3

IV
AC VOLTAGE CALIBRATIONS FOR THE 0.1 Hz TO 10 Hz

FREQUENCY RANGE

Howard K. Schoenwetter

The development of voltmeters to meet the need for rms voltage measurements in the infrasonic frequency range is

discussed as well as the need to trace these measurements to

the U.S. legal unit of voltage. A new method for supporting

voltage measurements in the 0.1 Hz - 10 Hz range was described

in a 1979 paper and is discussed further. The principles of

the method are embodied in detailed procedures given for

calibrating sine-wave voltage standards and rms voltmeters

over the 0.1 Hz - 10 Hz frequency range, using the NBS AC

Voltmeter/Calibrator. The sine-wave calibrator of this

instrument, used for these calibrations, has an accuracy of

0.020 percent over the 0.5 mV - 7 V range.

Key words: ac voltage calibrations; ac voltage calibrators;

ac voltage standards; infrasonic voltage measurements;

low-frequency voltage measurements; rms voltmeters.

1. INTRODUCTION

Calibrated vibration transducers are required in laboratories

and test facilities to determine the acceleration of vibration exciters,

tables, and fixtures. They are also used to measure the vibrations

in many other types of machines and structures, including prototype

models of military, space, and commercial vehicles undergoing qualification

testing. In past years, calibrations of these transducers at frequencies

below 2 Hz were either omitted or performed with uncertain accuracy.

This was because the voltmeters available for measuring the transducer

outputs at these frequencies had questionable accuracy and excessively

long response times (15 to 20 periods of the measured voltage).

In 1976, an rms digital voltmeter (DVM) was developed at the

National Bureau of Standards (NBS) to support vibration measurements

over the 0.1 Hz - 50 Hz range. 1 It was designed to measure voltages

from 2 mV to 10 V with an uncertainty of approximately 0.1 percent

of reading. The maximum response time of 40 seconds corresponds to

four periods of the lowest frequency signal that can be measured.

Since the means for calibrating the voltmeter to the required accuracy

did not exist, a voltage calibrator was developed and incorporated

'•This work was supported, in part, by the DC and Low Frequency

Calibration Coordination Working Group of the Department of Defense.
into the same instrument. This calibrator, providing bipolar dc voltages

and sine-wave voltages at frequencies of 0.1, 0.2, 0.5, 1, 2, 10, and

50 Hz, was intended not only for calibration of the companion voltmeter

but also for the calibration of other low-frequency voltmeters.

During the 1976-77 period, the NBS AC Voltmeter/Calibrator was

used at the Metrology and Calibration Centers of Redstone Arsenal (Army)

and Newark Air Force Base, as well as the Vibration Section at NBS,

to measure vibration transducer outputs and to calibrate other ac voltmeters [1]^. Except for the need of a 5-Hz calibration frequency,

3

the instrument met all present and expected future requirements for

support of voltage measurements at very low frequencies. ^ Consequently,

a detailed instruction manual and an archival paper were written to

facilitate reproduction of the instrument [2]. A commercial instrument

based on the NBS design later became unfeasible because the ac voltmeter

portion utilizes a multi -junction thermal converter (MJTC), which

has been available only in limited quantities from one manufacturer.

Subsequent to the development of the NBS AC Voltmeter/Calibrator, at

least two other instruments have been developed which can measure

voltages at infrasonic frequencies. NBS has developed a Low Frequency

AC Samping Voltmeter which has approximately 0.1 percent uncertainty

and a nominal maximum response time of two periods of the lowest

frequency signal (0.1 Hz) that can be measured [3,4], 5 Also, a large instrumentation manufacturer has developed a multimeter with a sampling voltmeter, operable down to 0.1 Hz or lower. However, the

accuracy and response time of the voltmeter depend upon the frequency

of the measured voltage.

As the number of ac voltage measurements in the 0.1 Hz - 10 Hz

range increases, because of the greater availability of suitable

voltmeters, the need increases for tracing these measurements to the

U.S. legal unit of voltage. Selecting the best method for effecting

this traceability is discussed next.

^Numbers in brackets refer to the literature references listed at

the end of this report.

^This calibration frequency was added later.

^Commercial voltage calibrators operate at frequencies down to 10 Hz

and can be calibrated using conventional ac-dc transfer measurements.

Also, a number of commercial voltmeters function satisfactorily above

10 Hz; therefore, the voltage measurement and calibrator capability

above 10 Hz were not considered vital.

5 Six of these units have been made by NBS, and supplied to each of

the DoD metrology laboratories. They were calibrated by using the

NBS AC Voltmeter/Calibrator as a reference standard.
2. A METHOD FOR INFRASONIC VOLTAGE MEASUREMENTS

Standards laboratories calibrate ac voltage standards against

dc voltage standards, using thermal voltage converters (TVCs) to make

the ac-dc voltage comparisons. Calibrations of the dc voltage

standards and TVCs are traceable to reference standards maintained

by NBS. Theoretical and practical limitations arise in calibrating

TVCs (measuring their ac-dc difference), and employing them to make

calibrations at the lower infrasonic frequencies [5].° These

limitations cause the calibrations to be slow, costly, and inaccurate,

particularly at frequencies below ~2 Hz. For these reasons, a new method was proposed in [5] for supporting ac voltage measurements

below 10 Hz, which supplements the existing method as shown in figure 1.

The primary objective of the new procedure is to make it feasible to

equip standards laboratories with easily calibrated multi-range sine-wave

standards, which operate at frequencies of 0.1, 0.2, 0.5, 1, 2, 5,

and 10 Hz. These voltage sources would be used mostly to calibrate

voltmeters at these frequencies over the voltage range of approximately

0.5 mV - 7 V rms. 7

The proposed equipment and procedures for testing a multi-range

voltage source are described in sections IV and V of [5]. Central

to the method is a single voltage level sine-wave reference source with frequencies of 0.1, 0.2, 0.5, 1, 2, 5, and 10 Hz, whose amplitude

variation with frequency (frequency response) is calibrated and has

excellent long-term stability. This unit serves as a voltage transfer

standard. By adjusting the output of the multi -range source to be

approximately the same as the voltage level of the reference, the

frequency response of the source can be determined from ac-ac comparisons, using an rms transfer voltmeter. Following this step,

the voltage level at each frequency is established by calibrating

the unit at 10 Hz, using a dc voltage standard and a TVC to make an ac-dc transfer measurement.

Except for the rms voltmeter contained in the NBS AC

Voltmeter/Calibrator, existing rms voltmeters do not have the necessary

high resolution and small differential nonlinearity to make ac-ac comparisons for calibration work.^ Until rms voltmeters suitable

6For convenience, reference 5 is included at the end of this report.

^Present commercial ac voltage calibrators either have insufficient

accuracy over this voltage range or only operate above 10 Hz.

fy\ transfer voltmeter must be able to measure voltage differences as small as 20 ppm of the measured value, both voltages being of the same frequency. The ac-dc difference and accuracy of the voltmeter

are not critical, however.
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for this work become available, calibration of multi-range sine-wave

voltage sources 9 and rms voltmeters will be performed at NBS.

Procedures for these calibrations are discussed in sections 4 and 5.

Since the ac calibrator portion of the NBS AC Voltmeter/Calibrator

(see fig. 1) would be a suitable multi -range voltage standard for use

by standards laboratories, the detailed design of this circuit is

given in appendix B. The methods used to calibrate the unit are included in the calibration procedure described in the next section.

3. CALIBRATION OF NBS AC VOLTMETER/CALIBRATOR

As described in [2] and [5], the NBS AC Voltmeter/Calibrator

consists of an rms digital voltmeter and a calibrated voltage source which can function as either a dc or ac voltage calibrator. The rms voltmeter consists of an input amplifier, rms/dc converter, and dc DVM.

The ac voltage calibrator is used to calibrate ac voltmeters and

is used in conjunction with the rms voltmeter to calibrate ac voltage

sources. The procedure used to calibrate the ac voltage calibrator

is shown in figure 4 of [5]. To perform this calibration, the

frequency response of the ac calibrator and the ac-dc difference

of the rms/dc converter must be known from prior measurements. All

of these calibrations are listed below and are discussed in this

section.

(1) Frequency response and voltage calibrations of the ac voltage

cali brator.

(2) Calibration of the laboratory dc voltage standard (standard cell)

(3) Calibration of the dc calibrator.

(4) AC-DC difference calibration of the rms/dc converter.

The errors associated with the items listed above all contribute to

the estimated uncertainty assigned to the ac calibrator voltage and

will be summarized after these calibrations have been described.

Several refinements were made recently to simplify the task of

calibrating the AC Voltmeter/Calibrator and to improve its overall

performance. These changes are also discussed in this section.

^Assuming that the voltage standards employ a D/A converter for the

sine-wave generation, a frequency response (relative voltage) calibration

is preferable to a conventional voltage calibration.
3.1 Calibration of AC Voltage Calibrator

Calibration of the ac voltage calibrator consists of two

calibrations: (1) a frequency response calibration in which the

calibrator voltages at 5, 2, 1, 0.5, 0.2, and 0.1 Hz are compared

with the voltage at 10 Hz, and (2) a voltage calibration at 10 Hz.

3.1.1 Frequency Response Calibration of AC Calibrator

The frequency response of the ac calibrator was originally

determined using peak-to-peak and rms measurements, the latter being

made with the rms voltmeter and limited to the 1 Hz - 10 Hz range [2].

Average-value measurements were later combined with the above results [5].

Since the peak-to-peak method uses a storage oscilloscope to exhibit

the voltage peaks, the measurements are somewhat subjective and are considered less reliable than the average-value measurements; therefore,

only the latter (along with limited rms measurements) are now used

for the frequency response calibrations. The precision rectifier-filter

circuit used for these measurements is represented by figure 5 of [5].

This circuit and associated power supply are contained in a separate

shielded enclosure. The justification for basing the rms frequency

response of the ac voltage calibrator on average-value (or peak-to-peak)

measurements is given in [5].

Figure 2 shows the front panel operating controls of the NBS AC

Voltmeter/Calibrator. The 5 Hz and 0.1 Hz frequencies are selected

with the CAL FREQ switch in the 10 Hz and 0.2 Hz positions, respectively,

using the rear panel "5 Hz-10 Hz" and "0.1 Hz-0.2 Hz" switches (see fig. 3)

For average-value measurements, the precision rectifier circuit is

connected between the CAL OUT terminals and the AVE. VOLT. IN terminals

(rear panel) with the PREC RECT-INTERNAL switch in the PREC RECT

position. In this switch position, the rms/dc converter is disconnected

and the output of the precision rectifier is connected to the input

(point o) of the voltmeter's low pass filter (see fig. 2 of [5]).

A dc voltage level of 5 V (nominal) at this terminal corresponds

to a full-scale indication of the voltmeter. Therefore, the full-scale

voltmeter reading is normalized to whatever range is selected by the

V-RANGE-MV switch. Since full-scale readings of 10000.0, 5000.0,

2000.0, 1000.00, —- result from range selections of 10, 5, 2,

1, — volts, it is seen that the best resolution is obtained with

the 10, 1, 0.1 or 0.01 V ranges. (Unless indicated otherwise, the

PERIOD is set to 10 for all measurements.) The 10 V range has been

arbitrarily selected for the frequency response measurements. Because

the rms/average ratio for a sinewave is ~1.11, the ac calibrator

should be set to approximately 5.55 V to yield a full-scale output

of 5 V from the rectifier-filter circuit. (The "t!00" attenuator

switch, not shown in fig. 2, should be kept in the OUT position.

Also, the FUNCTION switch should be in the MEAS position.)
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DVM FREQ RESPONSE ® <€> ©

IN OUT K-V

LEFT SIDE PANEL

Figure 3. Controls and connectors on rear, top, and side

panels of AC Voltmeter/Calibrator.
The dc DVM employed in the rms voltmeter of the NBS AC

Voltmeter/Calibrator (fig. 2 of [5]) consists of a V/F converter

and a counter-timer which counts the output pulses from the V/F

converter over periods of 1 s or 10 s (PERIOD set to 1 or 10),

determined by a crystal -control led oscillator. An integrating

voltmeter was used to effectively reduce the ripple in the output

voltage from the low-pass filter, to minimize fluctuations in the

displayed voltage. The frequency of the ripple voltage in the outputs

of both the rms/dc converter and the precision rectifier circuit is

twice the frequency of the input voltage to these circuits. If the

counter period (integration period) includes an integral number of

ripple periods, the ripple in the dc voltage applied to the dc DVM

will integrate to zero [2]J0 Therefore, fluctuations in the indicated

voltage from ripple are zero for frequencies of 0.05, 0.1, 0.15, — Hz,

which include the nominal values of the calibrator frequencies. (An

integration period of 10 s must be used for frequencies of 0.5 Hz

and less.) To allow for some deviation from these frequencies by

the AC Voltage Calibrator, ripple filtering in the low-pass filter

and rms/dc converter can be increased (with respect to the original

design) using the HEAVY FILTERING switch on the rear panel of the

AC Voltmeter/Calibrator.

The effect of this filtering on rms measurements will be discussed

later. When the precision rectifier is used, the additional filtering

limits the measured peak-to-peak ripple voltage to ±0.30 percent of

the dc voltage applied to the dc DVM when the input frequency is near

0.1 Hz. (The ripple voltage is much less near the higher calibrator

frequencies.) The computed maximum peak-to-peak fluctuation in the DVM

readings is approximately ±30 ppm for each percent deviation in frequency

from 0.1 Hz. For all calibration work, the calibrator frequencies should

be held within ±0.05 percent of their nominal values so that the effect

of ripple on DVM readings is negligible (±1.5 ppm or less, based on the

preceding statements). The calibrator frequencies are at their nominal

values when the clock frequency, from which they are derived, is 6400 Hz.

The clock frequency is easily held with ±0.05 percent of 6400 Hz, since

observed daily frequency variations are usually less than ±2 Hz (±0.03%).

The frequency can be adjusted by the CLK ADJ pot and is displayed by the

counter-timer when the CO0NTER switch is in the CLK position (see fig. 3).

Worst-case DVM reading errors caused by ripple voltage can be

avoided by using the average of several successive readings instead

of a single reading, since the ripple integrations in the dc DVM will

vary in size and usually are of both polarities. Therefore, the

average value is more accurate than the worst-case single reading

"^In other words, the ripple voltage integrates to zero if a time

interval equal to two counter periods includes an integral number of

input signal periods.
value. Unless indicated otherwise, maximum filtering (FILTER FREQ

switch in position L and the HEAVY FILTERING switch on) should be

used for all calibration work. With maximum filtering, the DVM

settling time to within 5 ppm is about 2 minutes. This response time

must be considered when devising the measurement procedure for

determining the calibrator frequency response.

Table 1 shows a typical set of average-value measurements which

was used to evaluate the frequency response of the ac calibrator.

The DVM readings are represented by Vf or V-j q , where the subscripts

denote the frequency of the voltage being measured. Calibrator

frequencies are switched approximately every 3 minutes, allowing

2 minutes for voltmeter settling and 1 minute for recording six readings.

If the first-recorded value is not repeated, it should be discarded,

since this probably indicates lack of complete settling by the DVM.

Successive numbers represent the least significant digit of successive

DVM readings. The 0.5, 0.2, and 0.1 Hz measurements are compared with

the succeeding 10 Hz measurement to minimize the time periods between

readings that are compared, thus minimizing the effect of voltmeter drift.

Table 1. Typical set of average-value measurements used to

evaluate the frequency response, Vf - V-jq, of the

ac voltage calibrator. The nominal value of

Vf and \I\q is normalized to 10U0 units.

Elapsed

time (mi n

)

Frequency (f) DVM reading(V

f

) a Mean

value V f

V 10

10 Hz 1000.47,8,8,8,8,7 1000.477

3 5 1000.48,8,8,8,8,8 1000.480 +0.003

6 2 1000.48,8,8,8,8,8 1000.480 +0.U03

9 1 1000.48,8,8,7,8,8 1000.478 +0.001

12 0.5 1000.48,8,9,8,9,8 1000.483 +0.005

15 0.2 1000.48,8,8,9,8,8 1000.482 +0.004

18 0.1 1000.48,7,7,7,8,8 1000.475 -0.003

21 10 1000.48,8,7,8,8,8 1000.478

Successive numbers represent the least significant digit of successive

readings.

10
For routine cal ibrations of the frequency response, it is planned

to use the averages (Vf - V-jq) from two sets of measurements like those

shown in table 1. In order to hold the magnitude of (Vf - V-|q) near

zero, freq uency response adjustments have been added recently. If

(Vf - V

-J q ) exceeds ±10 ppm for any frequency, the appropriate CAL

FREQ RESPONSE pot should be adjusted to minimize the voltage difference

(see fig. 3).

The estimated standard deviation of the measurement process is based

on 15 sets of measurements, divided evenly among three groups. One group

of measurements was made after the frequency response adjustments were

added. A second group was made before the adjustments were provided.

The third group of sets was obtained from the Naval Air Test Center,

Patuxent River, MD (NATC) calibrator, which is based on the NBS

design without frequency response adjustments. The maximum magnitude

of (Vf - V]q) was approximately 5, 27, and 12 ppm, respectively, for

the first, second, and third groups of sets. Although the statistical

populations corresponding to the three groups have different values

of (Vf - V-j o ) » their standard deviations should be approximately

equal, since all three calibrators had nearly identical electrical

and mechanical designs. Therefore, a worst-case pooled estimate of

the standard deviation (Sp), based on these three groups (15 sets)

of measurements, will be used as the estimated standard deviation of

a (Vf - V-jq) measurement. The largest pooled estimate of the

standard deviation is 4.4 ppm and occurs for a frequency equal to

0.5 Hz.

The estimated imprecision in (Vf - Vio7» obtained from N sets of

measurements, can be expressed by (s

p //N)t, where t is Student's t,

based on 2 d egrees o f freedom and a selected confidence level of

0.99. If (Vf - V-|q ) is determined from two sets of measurements, the

calculated imprecision is approximate ly 10 ppm. As mentioned

previously, Vf will be readjusted if (Vf - V-jq) is larger than

±10 ppm. A control chart (fjkj^ 4) will be kept showing calibration

dates and the value of (Vf - V-j q7 before being reset.

3.1.2 Voltage Calibration of AC Calibrator

The voltage level of the ac voltage calibrator is established by

comparing the ac calibrator voltage at 10 Hz with the dc calibrator

voltage, using the rms voltmeter as a transfer standard. For these

ac-dc comparisons, the PREC RECT-INTERNAL switch is set to the

INTERNAL position, HEAVY FILTERING is switched to OFF, and the FILTER

FREQ switch set to L. Also, the PERIOD is set to 10 to yield maximum

voltmeter resolution, and the DVM FREQ RESPONSE switch should be in

the OUT position.

Before making ac-dc comparisons, the dc offset voltage of the

calibrator buffer amplifier should be adjusted to a minimum value as follows. Set the CAL VOLTS dial to all zeros, the RANGE switch to 1 and the FUNCTION switch to INT AC CAL. Then, using a sensitive null

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detector, adjust the XI OFFSET for a minimum voltage (<1 yV) at

the CAL OUT terminals. With the RANGE at 10, adjust the X10 OFFSET

for a minimum voltage (<10 yV). Following these adjustments, set

the CAL FREQ to 10 Hz, CAL VOLTS to 5.000000, and the V-RANGE-MV switch

to 10 V. Also, connect the CAL OUT terminals to the TE INPUT terminals

with a coaxial cable and set the TE switch to EXT. Compare the ac calibrator voltage with the dc calibrator voltage (average of both

polarities) as shown in table 2.

Table 2. A comparison between ac and dc calibrator voltages,

applied directly to the rms/dc converter (TE INPUT).

The FUNCTION and CAL columns are switch positions on the AC Voltmeter/Calibrator. The averages of ac and

dc mean values are used for V ac and V^. The nominal

value of the DVM readings is normalized to 1000 units.

Elasped FUNCTION Mean

time (mi n) INT CAL CAL DVM readings value V ac

- V dc

AC 1006.64,4,4,4,3,4 1006.638

0.6365-0.6236

DC + 1006.64,4,4,4,3,3 1006.637 = 0.013

6 DC 1006.61,1,1,1,1,1 1006.610

9 AC 1006.64,3,4,3,4,3 1006.635

For rou tine ac-dc difference calibrations, it is planned to use the average (V ar

- V^~) from three comparisons like the one shown

in table 2. If (V d? - V dc ) exceeds ±20 ppm, the AC REF GAIN should

be adjusted for a minimum difference. The estimated standard deviation s, of a comparison, is 7.0 ppm, obtained from 13 compa risons. Us ing the

expression (s//N")t to calculate the imprecision of (V ac

- V dc ) yields approximately 12 ppm, where N is 3 and Student s t is based on

12 degrees of freedom and a confidence level of 0.99. Since (V ac

- V dc ) will be readjusted if it is larger than ±20 ppm, the maximum estimated

systematic error is ±20 ppm. A control chart (fig. 5) will be kept

showing calibration dates and the value of the ac-dc difference before

the AC REF GAIN is readjusted.

The dc offset of the function generator used in the sine-wave

reference should be checked approximately every three years. It can

be measured at pin 11 of the function generator with the DPDT switch

in the ZERO position (see fig. B-2). The switch and offset adjustment

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(R21 ) are accessed by removing the top panel. Adjustment of the offset

is non-critical and is seldom required. Measurements show that an offset

as large as ±200 y

V contributes less than ±1 ppm to the rms value

of the 1 V ac reference. A dc offset has a much larger effect on the

average value of a sine wave; however, an offset voltage affects all

calibrator frequencies the same and has no affect on frequency response

measurements.

The measured temperature coefficient of the ac voltage reference

is approximately +3 ppm/°C. Therefore, the imprecision for a 2°C range

is ±6 ppm.

3.2 Calibration of the Standard Cells

The basic laboratory voltage standard to be used for calibrating the

dc voltage calibrator is a set of four saturated standard cells,

housed in a temperature-controlled standard cell enclosure and located

near the AC Voltmeter/Calibrator. The cell voltages are fed to the

NBS Volt Facility via a cable to facilitate in situ calibration. It

is planned to calibrate the cells at least once a year. Calibrations

performed in January and November of 1982 show a maximum drift of

0.4 ppm for this 10-month period.

3.3 Calibration of the DC Calibrator

The voltage of one of the calibrated standard cells (approx.

1.01815 V) is transferred to a "working" reference, using a null detector for the voltage comparison. A stable, 10 V laboratory

reference with seven decade resolution (1 yV) is suitable for the

working reference. The null detector should have approximately 140 dB common mode rejection and at least 1 Mn input impedance. The

detector is used for all voltage comparisons and offset voltage (zero)

measurements described in this section.

A laboratory Kel vin-Varley (K-V) divider is used to "step" the

reference voltage to the appropriate level for calibrating the dc

reference, buffer amplifier, and ^1 00 attenuator of the calibrator.

The K-V divider should have seven-digit resolution and a linearity

of 0.1 ppm of input for dial settings between 1.0 and 0.1.

To calibrate the dc reference and buffer amplifier gain, set the

CAL VOLTS dial to 0000000 and the FUNCTION switch to INT AC CAL.

With the RANGE at 1, adjust the XI OFFSET for minimum voltage

(<1 yV) at the CAL OUT terminals. With the RANGE at 10, adjust

the X10 OFFSET for minimum CAL OUT voltage (<10 yV). Return the

RANGE to 1 and set the FUNCTION switch at INT DC CAL, CAL at + and

CAL VOLTS at .99999910 (last digit set to 10). Set the K-V divider

to the reciprocal of the standard cell voltage (approx. .9821700) and

connect its input to the laboratory reference. Then, adjust the DC

REF pot so that the calibrator voltage equals the K-V divider output

15
voltage. The gain of the buffer amplifier is adjusted with RANGE at

10, CAL VOLTS at 5.000000, and the K-V divider set to the ratio of the

standard cell voltage to 5 V (approx. .2036300). With the K-V divider

input connected to the CAL OUT terminals, adjust the X10 GAIN so that

the divider output voltage equals the laboratory reference voltage.

In order to minimize errors in the ac and dc calibrator voltages

at small signal levels (< 50 mV) caused by extraneous signal and

noise pickup, voltage offsets and Kel vin-Varley divider (see fig. 2 [5])

nonlinearity , an attenuator has been provided which attenuates

both ranges of the dialed voltage by a factor of 100. This precision

resistive attenuator has a 50 q output impedance and is inserted

between the buffer amplifier output and the CAL OUT terminals when

the attenuator switch is in the "-=-100" position. When calibrator

voltages larger than 50 mV are desired, this switch should be in the

OUT position. If required, calibration of the VI 00 attenuator

should immediately follow the preceding calibrations. The calibrator

control positions are not changed, except for putting the attenuator

in the -=-100 position. The laboratory K-V divider input is connected

to the laboratory reference and set to the ratio of 0.05 V to the

standard cell voltage (approx. .0491090). The i-l 00 pot is then

adjusted so that the calibrator voltage equals the K-V divider output

voltage.

The uncertainty in transferring the standard cell voltage to the

laboratory voltage reference at the 1.01815 V level is less than

±2 ppm. The uncertainties in stepping the reference voltage

down to 1.000000 V (calibration of dc reference) and up to 5.000000 V are 4 and 10 ppm, respectively. These uncertainties are caused

mostly by varying thermal voltages at connectors, circuit noise, and

lack of resolution in adjustments. The 10 ppm uncertainty includes

1 ppm systematic error, caused by the nonlinearity of the laboratory

K-V divider. The measured temperature coefficients of the dc reference

and buffer amplifier (on X10 range) are -6 ppm/°C and +2 ppm/°C,

respectively. The corresponding imprecisions for a 2°C range are

±1 2 ppm and ±4 ppm.

The expected maximum temperature coefficient for the attenuator is

±3 ppm/°C (±6 ppm uncertainty for a 2°C range). Tests show

that thermal voltages up to ±0.7 y

V are generated at the CAL OUT

terminals when the voltage applied to the -=-100 attenuator is zero.

This corresponds to ±14 ppm of the 50 mV output from the attenuator

when it is being calibrated. Also, the nonlinearity of the laboratory

K-V divider at the .0491090 setting may contribute 2 or 3 ppm error to

the calibration of the attenuator. Finally, the adjustment of the

attenuator has an uncertainty of about 2 ppm. Therefore, a systematic

error of 3 ppm (from K-V divider) and an imprecision of 22 ppm have

been assigned to the -=-100 attenuator calibration.

16
Based on a linearity comparison with the laboratory K-V divider,

the K-V divider employed in the calibrator can cause up to 25 ppm error in the ac calibrator voltage (V

c

). It is planned to check this

unit against the laboratory standard approximately once a year.

Control charts (fig. 5) will be kept which show the changes in

the ac and dc reference voltages and the buffer amplifier gain that occur between calibrations. Based on measurements and manufacturer's

specifications, the yearly drift rates of the standard cell, -=-100 attenuator, and the K-V divider are expected to be less than 2, 2,

and 3 ppm, respectively. Since these systematic errors are very small

compared with the expected uncertainty of the ac calibrator voltage,

no control charts are planned for these components.

3.4 AC-DC Difference Calibration of RMS/DC Converter

The ac-dc difference of the rms/dc converter used in the rms voltmeter was calibrated at NBS in April 1981. The reference thermal

voltage converter (TVC), employed in the calibration test set,

consisted of model FE reference thermal element and model F.10V (#1)

multiplier range resistor. This thermal element, consisting of four

single junction thermal elements in series, was designed to have

negligible ac-dc difference for frequencies down to 10 Hz or below.

Ten comparisons were made between the rms/dc converter and reference

TVC involving four measurements each (ac, dc, dc reverse, ac), yielding

an average ac-dc difference of ±0.25 ppm. The standard deviation

of a comparison was 5.83 ppm, so that the standard error of the mean

was 1.84 ppm. If the selected confidence level is 0.99, Student's t is 3.3 and the imprecision in the calculated ac-dc difference is

±6 ppm.

The only known source of systematic error in the ac-dc calibration

is the uncertainty in the ac-dc difference of the reference TVC.

This unit has been intercompared with several other reference TVCs,

with an ac-dc difference of less than 1 ppm [6]. These units are maintained at NBS and are believed to have zero ac-dc difference to

within 1 or 2 ppm for frequencies as low as 10 Hz. If ±2 ,ppm

uncertainty is allowed for the reference TVC, the estimated ac-dc

difference of the rms/dc converter is ±8 ppm.

It is recommended that multi -junction thermal converters (MJTCs)

be re-calibrated every five years. This re-calibration interval should

also apply to the rms/dc converter, since its ac-dc difference is

determined by the ac-dc difference of the MJTC employed.

3.5 Summary of Calibration Errors of AC Voltage Calibrator

Table 3 lists the estimated uncertainties which limit the

calibration accuracy of the ac calibrator. Item 9 of this

table 3 shows that, following a frequency response calibration, the

(Vf-V-jQ = 0) with an uncertainty of ±20 ppm. It should be emphasized

17
Table 3. Estimated systematic error and imprecision components

of the uncertainties which limit calibration accuracy

of ac voltage calibrator. Estimated components of

uncertainties less than 0.5 ppm are rounded to zero.

Systematic

error Imprecision

2 ppm ppm

2

4

1 9

12

20 12

(1) Standard cell uncertainty

(2) Standard cell lab reference transfer

(3) Step-down to 1 V level in dc reference

(4) Step-up to 5 V level in dc calibrator

(5) Temperature coefficient of dc reference

(-6 ppm/°C) for a 2°C range

(6) AC/DC comparisons (calibration of ac calibrator at 10 Hz)

(7) AC-DC difference uncertainty of

rms/dc converter 2 6

(8) Temperature coefficient of ac reference

(+3 ppm/°C) for a 2°C range 6

(9) Calibration of (V f -V 10 ) 10 10

(10) Maximum error from calibrator K-V divider 25

(11) Maximum K-V drift between calibrations 3

(12) Temperature coefficient of buffer

amplifier on XI range

(+2 ppm/°C) for a 2°C range 4

(13) Calibration of the -100 attenuator 3 22

(14) Maximum attenuator drift between

calibrations 2

Sub-totals 68 33 (rss)

Total uncertainty of ac calibrator voltage V c ±101 ppm
that when frequency response calibrations are made of a customer's

voltage source or voltmeter, only the uncertainty of (Vf-V-jg) needs

to be known. Table 3 also shows that the estimated uncertainty of

the ac calibrator voltage V

c is ±101 ppm, following a complete

calibration of the dc and ac calibrator circuits.

Although periodic calibration intervals cannot be established for

these circuits until control chart data are available, it is believed

that a specified maximum uncertainty of ±200 ppm for the ac calibrator

will allow calibration intervals approaching one year for the dc

reference voltage, buffer amplifier gain, and (Vf-V-jg). A somewhat

shorter calibration interval is expected for the ac reference. The

corresponding error budget for (Vf-V-|g) alone is ±35 ppm. Therefore,

the calibration intervals will be chosen to ensure that the maximum

uncertainties of ( V^-V-jq ) and V

c are less than ±35 ppm and

±200 ppm (0.020%), respectively.

Although considerable reliance will be placed on control chart

data to anticipate future drifts in calibrator circuits, accurate

checks on circuit performance can be made at any time using shortened

procedures. Using only one set of measurements as shown in table 1 to determine (Vf-V]g), instead of the average of two sets, decreases

the measurement time from 48 minutes to 24 minutes. The imprecision

increases from ±10 ppm to ±14 ppm and the allowable value of

(Vf-V-jg) should be increased from ±10 ppm to ±14 ppm before being

readjusted. Using one set of measurements as shown in table 2 to determine

(V ac-V

cj c

), instead of the average of three sets, decreases the measurement

time from 36 minutes to 12 minutes. The imprecision increases from

±12 ppm to ±21 ppm and the allowable value of (V ac-V ^J should

be increased from ±20 ppm to ±35 ppm before being readjusted.

Substituting these values into table 3 (items 6 and 9) yields maximum

uncertainties of ±28 ppm and ±125 ppm for (Vf-V-jg) and V

c , respectively. The time required to calibrate the dc reference, buffer

amplifier gain, and -flOO attenuator is 13 minutes. (These procedures

cannot be shortened.) Therefore, the total calibration time of the

dc and ac calibrators, using the shortened procedures, is approximately

50 minutes.

3.6 Frequency Response of the RMS Voltmeter

The ac calibrator can be used to calibrate voltage standards at

frequencies other than the nominal calibrator frequencies, if the

frequency response of the rms voltmeter (DVM) is known. The response

of the DVM decreases as the frequency of the input signal is decreased

below ~2 Hz, because of increasing ripple voltage in the rms/dc

converter and lack of square law response by the MJTC of this circuit [2j.

The effect from ripple is minimized, however, by the HEAVY FILTERING

circuit which is used for most calibration work (see sec. 3.1.1).

Five ( V-p-V

-J q) comparisons were made using the ac calibrator voltage as the input signal. The mean values of these comparisons and the

standard deviation of a comparison for each frequency are shown in

table 4.

19
Table 4. Frequency response of the rms voltmeter with corrections

applied for variations in the ac calibrator voltage,

used for the input signal. The mean values and standard

deviation, Sf, were obtained from five (Vf-V-jg) DVM

comparisons.

Frequency (f) (Vf-Vio)DVM Sf

5 Hz ppm 6.1 ppm

2 -2 6.5

1 -13 4.5

0.5 -49 6.5

0.2 -109 5.5

0.1 -208 2.7

The voltmeter response as a function of input signal frequency can

be approximate d by sec ond degree equations of curves that pass through

the values of (V^-V-jq)dVM at frequencies of 2, 1, 0.5 Hz and at

0.5, 0.2, and 0.1 Hz. The equation that is applicable to the 0.5 to

2 Hz range is

(Vf -V10 ) DVM = -105.33 + 133. OOf - 40.67f2

. (1)

The equation for the 0.5 to 0.1 Hz range is

(V

f

-V 10 ) DVM

= -346.50 + 1582. 50f - 1975. 00f 2

. (2)

These equations are used to plot the curves in figure 6.

As indicated previously, the lack of flatness in the DVM response

is attributed to the rms/dc converter response. Since applying

corrections from the curves in figure 6 or the preceding equations is

quite tedius, an effort was made to improve the DVM frequency response

sufficiently so that corrections usually are not necessary. This was accomplished by employing frequency-dependent negative feedback

circuits in a section of the input amplifier, as shown in figure 7.

With these circuits, the amplifier response approximately complements

the rms/dc converter response. Components Rl, CI, and R2, C2 provide

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high-frequency attenuations of approximately 250 and 30 ppm,

respectively. The corresponding corner frequencies are 0.14 and

0.71 Hz. The frequency response of the circuit which has the higher

attenuation is adjustable over a small range by the DVM FREQ RESPONSE

pot. Figure 8 is a plot of the amplifier transfer characteristic

with the DVM FREQ RESPONSE circuit switched in (switch S closed).

Resistances r-| and ri were arbitrarily assigned the value of 100 k^;

however, measurements show that the frequency response is essentially

independent of the values of r-| and r^ selected by the V-RANGE-MV

switch (see fig. 2).

The frequency response of the circuit shown in figure 7 was combined with the responses of eqs. 1 and 2 and plotted in figure 9.

This response curve shows that the maximum values of (Vf-Vio)DVM occur at 0.5 Hz and approximately 0.14 Hz. A good estimate of the

outside limits of (Vf-V"|o)DVM can be obtained by measuring this

quantity at 0.1, 0.2, and 0.5 Hz, using the ac calibrator. Table 5 shows the DVM response at the lowest four calibrator frequencies,

obtained from 13 measurements. Corrections were made for the measured

frequency response of the calibrator (systematic error), leaving

only the imprecision of these measurements (±6.0 ppm) as the

uncertainty of the calibrator voltages. (The frequency response and

estimated standard deviation of the ac calibrator were based on 5 and 13 measurements, respectively - see section 3.1.1.) Using the

maximum estimated standard deviation of the measurement process

represented by table 5 (6.4 ppm) and a confidence level of 0.99, the

imprecision of these measurements is 5.4 ppm. Combining this

imprecision with the calibrator imprecision gives ±8.1 ppm as the maximum uncertainty of (Vf-V"|o)DVM* Therefore, the outside

limits of (Vf-V-|o)DVM> measured at 0.1, 0.2, 0.5, and 1 Hz, are approximately +20 and -19 ppm.

Table 5. Measured DVM frequency response with input amplifier

compensated. The average values of (Vf-V"io)DVM and

estimated standard deviations, Sf, are based on

13 measurements.

Frequency (f) (Vf-Vlo)DVM s f

1 Hz +1 ppm 3.0 ppm

0.5 -11 4.2

0.2 +12 6.4

0.1 -7 5.0

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These limits result from using 5 and 13 measurements to establish

the frequency response of the calibrator and DVM, respectively. For

routine calibrations of the DVM frequency response, it is planned to

use three measurements. Assuming that the calibrator response is also

obtained from three measurements, the DVM and calibrator imprecisions

will be 11.3 and 7.8 ppm, respectively. Combining these quantities

gives 13.7 ppm, an increase of 5.6 ppm over the imprecision applicable

to the frequency response values in table 5. To obtain the maximum

expected values of (Vf-V-|o)DVM> us "i n 9 three DVM and three calibrator

measurements, the maximum frequency response values in figure 5 should be increased by 5.6 ppm, yielding +17.6 and -16.6 ppm. Adding

the corresponding imprecision to these quantities gives estimated

uncertainty limits of +31.3 and -30.3 ppm to (Vf-V"|o)DVM* ^he

response curve in figure 9 indicates that ( Vf -V -j q)dVM 1S approximately

4 ppm larger at 0.14 Hz than at 0.2 Hz. Also, any uncertainty in

the difference between (

a ] 4~V-|

g

)dvm anc' (^.2~^10)dVM in figure 6

carries over to figure 9. The computed value of this difference is

approximately 55 ppm. It is believed that the uncertainty in this

difference should not exceed 10 percent or 6 ppm. Adding this

uncertainty and the 4 ppm difference mentioned above to the uncertainty

limits for the measured frequency response yields +41.3 and -30.3 ppm

as the uncertainty limits of ( V-^-V

-| o)d\/M f° r any frequency. Since the

attenuation caused by the feedback circuits of the input amplifier

is small at 0.1 Hz but increases with frequency, the DVM response

curve (fig. 9) can be effectively rotated about the 0.1 Hz point of

the curve by adjusting the DVM FREQ RESPONSE pot. Therefore, this

control can be used to adjust the +41.3 and -30.3 limits to approximately

±36 ppm. Drift in ( V-p-V

-j q )qvm tnat cannot De removed by adjusting

the DVM FREQ RESPONSE pot, estimated to be less than 2 ppm in five

years, can be compensated by trimming the values of R2 and C2 in

figure 7. However, to obviate the trimming, the frequency response

will be specified as ±40 ppm to allow some margin for drift of

this type.

It is useful to estimate the uncertainty that the DVM response

causes if two voltages are compared which have frequencies differing

by no more than 5 percent. Figure 9 shows that the maximum rate of

change of ( V-p-V

-| o)DVM with frequency occurs over the frequency range

of 0.1 Hz to 0.14 Hz, approximately. Assuming that (Vf-V-jo)DVM changes

by no more than two-thirds of the specified limits of ±40 ppm over

this frequency range (a 40% change in frequency), a 5 percent uncertainty

in frequency corresponds to a maximum uncertainty in (Vf-V^DVM of

approximately ±7 ppm.

4. CALIBRATIONS OF VOLTMETERS

Calibrations are performed on rms-responding ac voltmeters using the

ac voltage calibrator of the NBS AC Voltmeter/Calibrator. AC voltmeters

can be calibrated at frequencies of 10, 5, 2, 1, 0.5, 0.2, and 0.1 Hz at

any voltage level between 0.5 mV and 7 V.

26
The total uncertainty of a calibration is ±( Ec + er ), where

e c is the uncertainty of the ac voltage calibrator voltage and £r

is the imprecision of the calibration process. The estimated uncertainty

of the ac voltage calibrator is ±0.020 percent, as described in section

3.5. The imprecision for a given calibration point is ts//N", where t

is Student's t for the selected confidence level, s is the standard

deviation for a measurement, and N is the number of measurements (test

runs) used to obtain the mean values of the measured quantities (voltmeter

readings ).

Unless otherwise requested by the customer, a single accuracy of

calibration will be given for the corrections to the calibration points,

based on a confidence level of 0.98 and the largest standard deviation

encountered. It is expected that the value of N, requested by the

customer, will generally be 3, 4, or 5. Assuming a selected confidence

level of 0.98, values of t corresponding to N equal 3, 4, and 5 are approximately 7.0, 4.5, and 3.7, respectively.

5. CALIBRATIONS OF VOLTAGE STANDARDS

Voltage calibrations are performed on precision ac sources using the

ac voltage calibrator and rms voltmeter of the NBS Voltmeter/Calibrator.

The rms voltmeter is used as a transfer voltmeter to compare the voltages

(of the same nominal level) from the test unit and the ac calibrator.

Voltage calibrations can be made at any frequency in the 10 Hz to 0.1 Hz

range and are usually made near the full-scale level of the DVM ranges

(2, 5, 10, 20, 50 mV, and 0.1, 0.2, 0.5, 1, 2, 5 V).

If the voltage standard is of a design which has inherently stable

voltage with respect to frequency, a frequency response (relative voltage)

calibration may be preferable to a conventional voltage calibration. The user then establishes the voltage levels by calibrating the voltage at

10 Hz. Since the rms voltmeter has a frequency response that is flat to

within ±40 ppm, it is used to determine the frequency response of

voltage sources. Frequency response calibrations can be made at any

frequency in the 10 Hz to 0.1 Hz range and are usually made near the

full-scale level of the DVM ranges (2, 5, 10, 20, 50 mV, and 0.1, 0.2,

0.5, 1, 2, 5, 10 V).

5.1 Voltage Calibrations

For each calibration point, the rms voltmeter (DVM) is used to

compare the voltage Vy from the standard under test with the voltage

V c of the same nominal level from the ac voltage calibrator, choosing

the calibrator frequency closest to that o f the vol tage being measured.

After the test runs are made, the average (V

c ^~Vy) is formed for

each calibration point, yielding corrections to the nominal voltage

values of the test unit.

27
If the uncertainty of the calibrator voltage and the uncertainty

caused by the DVM frequency response are denoted by e c and em, respectively, the total uncertainty of a calibration point is given by

±(e c + e m

+ ts/y/N"), where s is the standard deviation of a (V c

- Vj) comparison and N is the number of comparisons (test runs).

If the frequencies of the voltages being compared are within 5 percent

of each other, e m

is ±7 ppm. If the frequency difference is

larger, the worst case value of e m, ±40 ppm, is used. The value

assigned to e c is ±200 ppm (±0.02%); however, if the highest

calibration accuracy is required by the customer, e c can be decreased

to ±125 ppm by a special calibration of the NBS instrument.

Unless otherwise requested by the customer, a single accuracy of

calibration will be given for the corrections to the calibration points,

based on a confidence level of 0.98 and the largest standard deviation

encountered. It is expected that the value of N, requested by the

customer, will be 3, 4, or 5.

5.2 Frequency Response Calibrations

These calibrations are made using the DVM to compare test unit

voltages of frequency f w ith the 10 Hz value. After N comparisons,

the quantities (Vf - V-jq) are computed for each test frequency, yielding

the frequency response. The uncertainty of these calibration points

is ±(e m

+ ts//TT), where e m

is ±40 ppm, the frequency response

of the DVM, and s is the standard deviation of a comparison.

Unless otherwise requested by the customer, a single accuracy of

calibration will be given for the frequency response, based on a confidence level of 0.98 and the largest standard deviation encountered.

It is expected that the value of N, requested by the customer,

will be 3, 4, or 5.

6. ACKNOWLEDGMENTS

The author is grateful for the valuable suggestions made by

Barry A. Bell, Group Leader for Electronic Instrumentation and

Metrology, and the CALC0M subcommittee members who reviewed this

document. The members of this subcommittee were: David W. Berning,

Ronald F. Dziuba, Dr. James A. Lechner, and John D. Ramboz. Special

thanks are due Mr. Ramboz, who served as chairman of the CALC0M

subcommittee, and Dr. Lechner, who provided assistance on the

statistical aspects of the measurements. The very helpful suggestions

by Jenny Pal 1 a, the typing of Bonnie L. Smith, and the editorial

assistance of Betty A. Oravec, in preparing this manuscript, are also

gratefully acknowledged.

28
7. REFERENCES

[1] AC Voltmeter/Calibrator Developed, NBS DIMENSIONS, Dec. 1977.

[2] H. K. Schoenwetter, "An RMS Digital Voltmeter/Calibrator for

Very Low Frequencies," IEEE Trans. Instrum. Meas., Vol. IM-27,

pp. 259-268, Sept. 1978.

[3] B. F. Field, "A Fast Response Low-Frequency Voltmeter," IEEE Trans.

Instrum. Meas., Vol. IM-27, pp 368-372, Dec. 1978.

R] B. A. Bell, B. F. Field, and T. H. Kibalo, "A Fast Response Low

Frequency Voltmeter," Nat. Bur. Stand. (U.S.) Tech Note 1159

(Aug. 1982).

[5] H. K. Schoenwetter, "NBS Provides Voltage Calibration Service in

0.1 - 10 Hz Range Using AC Voltmeter/Calibrator," IEEE Trans.

Instrum. Meas., Vol. IM-28, pp. 327-331, Dec. 1979.

(This paper is included at the end of this report.)

[6] F. L. Hermach, "An Investigation of Multi junction Thermal Converters,"

IEEE Trans. Instrum. Meas., Vol. IM-25, pp. 524-528, Dec. 1976.

29
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979 327 NBS Provides Voltage Calibration Service

in 0.1-10-Hz Range Using AC

Voltmeter/Calibrator

HOWARD K. SCHOENWETTER, senior member, ieee

Abstract—Prompted by the need to support vibration and pressure measurements at frequencies down to 0.5 Hz (with expected future needs to 0.1 Hz), NBS now offers a calibration service for voltage standards and rms voltmeters in the range of 0.1-10 Hz. The means

for the service is an "ac Voltmeter/Calibrator," an NBS-developed

instrument containing an rms digital voltmeter and ac and dc voltage

calibrators. The methods used to calibrate the ac voltage calibrator are discussed; also, application of the ac Voltmeter/Calibrator to the calibration of customers' voltage and voltmeter standards is described. Finally, a multifrequency voltage reference source with frequency-independent amplitude is proposed as a more suitable transfer standard than thermal voltage converters (TVC's) for the 0.1-10-Hz range.

I. Introduction

THE National Bureau of Standards (NBS) supports ac

voltage measurements in standards laboratories by

calibrating the ac-dc difference of thermal voltage converter (TVC) reference standards. 1 TVC working standards, cal- ibrated from the reference standards, are then used to

transfer the accuracy of dc voltage standards to ac voltage

standards and ac voltmeters. NBS routinely calibrates

TVC's from the megahertz region down to 20 Hz. In special

cases, calibrations have been made down to 5 Hz and a few

times down to 2 Hz. Voltage measurement support is now

required at still lower frequencies. Vibration and pressure measurements used in the test of land, sea, air, and space

vehicles as well as in other applications now require the measurement of output voltages from vibration and press- ure transducers at frequencies down to 0.5 Hz, with ex- pected future requirements as low as 0.1 Hz.

Theoretical and practical limitations arise in calibrating

TVC's, and employing them to make calibrations, at the

lower infrasonic frequencies. Below ~ 2 Hz, significant

cyclic temperature variation of the TC heater occurs. This

improper integration, indicated by ripple in the output

voltage, presents the following measurement problems.

1) Large ripple filter time constants are required to reduce

fluctuations to an acceptable level in the indicating instru- ment (galvanometer, digital voltmeter (DVM), etc.), causing

Manuscript received May 15, 1979; revised June 29, 1979. The author is with the Electrosystems Division, National Bureau of Standards, Washington, DC 20234.

1 Thermal converters (TC's) and thermal voltage converters (TVC's)

are described in [1]. The reference also includes an extensive bibliography on ac-dc comparators for LF measurements.

slow tedious measurements. 2) The ac-dc difference of the

TVC increases as the square of the output ripple before

external filtering is applied, because of its lack ofsquare-law

response [2]. Thus below 2 Hz, the ac-dc difference can be

significant and must be determined at a number of

frequencies.

Since TVC calibrations below 2 Hz are slow and costly, it appears that a precision sine-wave voltage source with

nominally equal outputs at several discrete frequencies in the 0.1-10-Hz range is a more appropriate transfer standard

than a TVC for this frequency range. If the variation in rms

voltage level with frequency of the voltage standard is known from a calibration, the absolute voltage at each

frequency can then be established by calibrating the sine- wave standard at 10 Hz using a dc voltage standard and

conventional TVC transfer circuits.

2 NBS proposes to support voltage measurements in the

0.1-10-Hz range primarily by accurately determining the rms frequency response of single-voltage-level sine-wave

voltage standards such as described above. However, cali- bration of multirange sine-wave voltage standards and rms

voltmeters is also offered. The equipment for making these

calibrations is described in the following sections.

II. Voltage Calibration Methods

for 0.1-10-Hz Range

A. Description of NBS AC Voltmeter/Calibrator

The means for calibrating voltage standards and rms

voltmeters in the 0.1-10-Hz range is an rms digital

voltmeter/calibrator (Fig. 1) described in an earlier paper

[2] . A brief discussion of the circuit (Fig. 2 ) will be given here

to describe its application to calibrations. The voltage

calibrator shown in the lower part of the figure can function

as either a dc or ac calibrator. It basically consists of a 7-digit

Kelvin-Varley (K-V) divider fed by a reference voltage of 1 V (sine wave, +dc, or — dc) and buffered at its output by a

voltage follower with selectable gains of 1 or 10. The

sine-wave reference is shown in Fig. 3. The sine wave is synthesized by a 7-bit counter read-only memory (ROM)

digital-to-analog converter (DAC) circuit so that 128 input

pulses are required per sine-wave cycle. The necessary input

2 An rms voltmeter with small ac-dc difference at 10 Hz may be used

instead of the TVC circuits.

U.S. Government work not protected by U.S. copyright.

30
328 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979

Fig. 1. AC Voltmeter/Calibrator. The rms voltmeter and voltage calibra- tor operate at dc and over the 0.1-50-Hz range.

I MEASURE l ex-

( l~m~| ° fcITl riNTAq] o

I I INT DC| Q

4ri

INPUT M AMPl, RMS/DC CONV

LOW PASS

FILTER

DC DVM £

a Eo «M

| CAL V0LTS~1

CD i&D

SINE WAVE

REFERENCE

ED

rcAn--

1 voc

REF

1 K-V DIVIDER

S BUFFER AMPL c~CAL OUT |

Fig. 2. Simplified block diagram of ac Voltmeter/Calibrator. Instru- ment contains an rms digital voltmeter and ac and dc voltage

calibrators.

frequencies to the circuit are obtained using a fixed clock

frequency and scaling it to obtain output frequencies of 0.1,

0.2, 0.5, 1.0, 2.0, 10, and 50 Hz. The amplifier is designed to have an output of 1-V rms and sufficient filtering to reduce

the contribution to the rms value of the output of all harmonics generated by the DAC to a few parts per million

(ppm). The ac calibration voltages, available at the CAL

OUT terminal (Fig. 2), are applied to the voltmeter input

when the FUNCTION switch is in the CAL INT AC

position. The CAL INT DC position selects dc calibration

voltages. The dc calibrator serves as the basic reference for the AC Voltmeter/Calibrator. Calibration of the dc and ac

calibrators and their resulting accuracies are discussed in Section III. The rms digital voltmeter, shown functionally in the upper part of Fig. 2, was designed to serve three measure- ment functions: 1) direct rms measurement of voltages, 2)

ac-dc transfer measurements so that the dc calibrator can be

employed to calibrate the ac calibrator, and 3) ac-ac transfer measurements so that ac voltage sources can be calibrated

using the ac calibrator. The accuracy with which these

CLOCK COUNTERS

6 6 6 6 6 6

I | CAL FREQ

9 9 9 9 9 9 9 lliL^[i[^S]_0[c5_

C, C b C c C d C e cTcJ

I—•—•--•—•—1—

1 VAC

Fig. 3. Sine-wave reference used in the calibrator.

measurements can be made largely depends upon the rms-dc converter design and the methods used to filter ripple in the converter and succeeding circuits. The ripple in the converter's output voltage E is filtered by the low-pass

filter and dc DVM, a voltmeter with integration periods of 1 and 10 s. Use of these integration periods yields voltmeter

resolutions of 4 and 5 digits, respectively, aftd makes it possible to obtain perfect filtering (zero fluctuations of the indicated voltage) at all calibration frequencies. The importance of these characteristics in making very accurate ac-dc

and ac-ac transfer measurements is discussed in the Appendix.

The rms voltmeter employs a multijunction thermal

converter (MJTC) as the sensing element in its rms-dc

converter. It is shown in [2] that the converter and, therefore, the voltmeter have true rms response. Selection ofan MJTC

with small deviation from square law response resulted in an rms voltmeter with an ac-dc difference of about 10 ppm at 1 31
schoenwetter: nbs provides calibration service in 0.1-10-hz range 329

AC

CALIBRATOR

0.1 HZ-50 HZ

tJ

DC CALIBRATOR

RMS VOLTMETER

DC & 0.1 HZ-50 HZa AC

VOLTMETER/

CALIBRATOR

Fig. 4. Calibration of the ac calibrator in the ac Voltmeter/Calibrator.

After calibration against the dc lab standard, the dc calibrator is employed to calibrate the ac calibrator, using the rms voltmeter as a

transfer instrument.

Hz, decreasing to ~ ppm at 10 Hz. The ac-dc difference increases below 1 Hz and is ~500 ppm at 0.1 Hz. Thus

accurate ac-dc comparisons, such as are used in calibrating the ac calibrator, are limited to frequencies in the 1-10-Hz

range. However, accurate ac-ac comparisons are feasible down to 0.1 Hz if the voltages being compared have

approximately the same frequency.

B. Calibration of AC Voltmeters and Voltage Standards

The ac calibrator may be used to calibrate ac voltmeters at any of the above-mentioned frequencies for voltage levels ranging from 0.2-mV to 7-V rms. The rms voltmeter accuracy ranges from 0.1-0.2 percent

of reading, depending upon frequency and voltage level, and

is not sufficient to calibrate ac voltage standards. On the other hand, when the voltmeter used as a transfer instrument

and ac calibrator are employed to make ac-ac transfer measurements, measurement accuracy is limited only by the

calibrator accuracy and voltmeter resolution. For example,

if e,(r), a voltage to be measured, is applied to the rms

voltmeter, its correct rms value Et is

£, = £;(i- e ) (i)

(or,£';~ E,{1 + e)), where E\ is the voltmeter reading and e is the voltmeter error in proportional parts. If E\ is dialed into the calibrator, the voltmeter reading is, approximately,

£>£;(i + 4 (2) Solving for £, from (1) and (2) gives

Et ^ 1E\ - E'c. (3) AC voltage standards may be calibrated at any frequency

from 0.1 to 10 Hz over the voltage range of0.2-mV-7-V rms.

III. Calibration of the AC Voltmeter/Calibrator

The dc calibrator is calibrated against laboratory stan- dards as shown in Fig. 4. Calibrations are made at the 1-V

and 5-V levels to set the voltage level of the 1-V dc reference and the gain of the buffer amplifier on the x 10 range (see. Fig. 2). The resulting dc calibrator accuracy at 23 ± 1°C is ± 50 ppm, based on the average of both polarities.

As mentioned previously, the ac calibrator voltages may

be accurately measured at any frequency in the 1-10-Hz

range, using the rms voltmeter to compare ac and dc

calibrator voltages. Calibration of the ac calibrator is performed at 10 Hz and consists of adjusting the ac reference so

that the ac and dc calibrator voltages are equal at the 5-V

level. Following calibration, the uncertainty of the calibra- tor voltage at 10 Hz is ±90 ppm and consists of the dc

calibrator uncertainty plus twice the voltmeter resolution. The uncertainty of the ac calibrator voltage at the other

frequencies is somewhat larger than ± 90 ppm because the calibrator amplitude varies slightly with frequency. A conservative figure for the overall calibrator uncertainty may be

obtained by adding the amplitude variation over the

0. 1-10-Hz frequency range to the calibrator voltage uncertainty at 10 Hz. The estimated amplitude variation, based on

measurements described in the Appendix, is 61 ppm. Adding

this quantity to the calibrator accuracy at 10 Hz, and

including the measured temperature coefficient of the ac

calibrator (± 50 ppm/°C), yields an overall ac calibrator accuracy of ± 0.02 percent at 23 ± 1°C. 3 Following calibration, the ac calibrator is then employed to adjust and

calibrate the rms voltmeter.

IV. Equipment Needed for

0.1-10-Hz Voltage Calibrations

In general, the following equipment is needed in a stan- dards laboratory for voltage calibrations in the 0. 1-10-Hz

frequency range.

1

)

A laboratory multirange dc voltage standard.

2) A TVC and associated equipment for ac-dc transfer measurements at or near 10 Hz. Item 5 may also be suitable

for this purpose.

3) A single voltage level, multifrequency4 sine-wave vol- tage standard, whose amplitude variation with frequency

(frequency response) is calibrated and has excellent long- term stability. This unit serves as a voltage transfer standard.

4) A multifrequency multirange sine-wave standard.

5) An rms transfer voltmeter with good short-term stability, including periodic fluctuations, and sufficient resolution

to make accurate ac-ac voltage comparisons. The voltages

being compared must be of approximately the same freq- uency, unless the frequency response is accurately known.

Good voltmeter accuracy is not required since only small

voltage differences will be measured ; however, the differential nonlinearity must be small.

6) A calibrated resistive voltage divider, whose ratios are frequency-independent up to at least 10 Hz (e.g., a low

impedance K-V divider). Items 1 and 2 serve to calibrate the voltage level ofitem 3. Item 6 is then used to step the voltage of item 3 up or down,

as required, to the nominal value of the voltage being

calibrated in item 4. Item 5 is used for the ac-ac comparison

and calibration. After calibration, the multirange sine-wave

standard is then the means for calibrating rms voltmeters. 5 If items 1, 3, 4, and 6 are not already available as separate

3 For calibrator voltages below 2 mV, the accuracy decreases with decreasing voltage to 0.2 percent at 0.2 mV.

4 The following discrete frequencies are desired: 0.1, 0.2, 0.5, 1.0, 2.0 5.0, and 10 Hz.

5 NBS has also developed a sampling voltmeter for frequencies down to

0.1 Hz [3]. 32
330 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979

entities, they may be quite easily and economically

combined into one circuit as shown in the lower part of Fig.

2. As mentioned previously, NBS proposes to support vol- tage measurements in the 0.1-10-Hz range primarily by

performing the calibration on item 3 ; however, calibration

of multirange sine-wave voltage standards6 and rms volt- meters is also being offered.

V. Proposed Voltage Transfer Standard for

0.1-10-Hz Range

A sine-wave generator based on the design of Fig. 3 is proposed as a voltage transfer standard for the 0.1-10-Hz

range.

7 This circuit has the following characteristics, important for a sine-wave reference standard.

1) The calibrator voltage is nearly independent of the

selected frequency. As indicated previously, the measured

amplitude variation is approximately 60 ppm.

2) Temperature effects are essentially the same for all frequencies, if the temperature coefficients for the filter capacitors are approximately the same or quite small. The

measured variation in amplitude temperature coefficients is < 2 ppm/°C over the 20-25°C range.

8

3) Amplitude drift with time is nearly the same for all frequencies. The measured amplitude variation drifted ap- proximately 8 ppm during 16 months of use.

9

4) A small clock frequency drift has the same amplitude

effect for all frequencies.

5) The phase and magnitude of the harmonics are essentially the same for all frequencies; therefore, average and

peak-to-peak measures of amplitude variation versus frequency are good approximations, in fractional terms, to the rms differences. 6) Maximum drift of the dc output level with temperature

change is primarily determined by the temperature

coefficients ofthe DAC bipolar offset and the amplifier offset and is easily limited to 15 ppm/°C. This has a negligible effect on the rms value of the sine-wave output.

7) The circuit is easy and relatively inexpensive to implement.

8) Lower operating frequencies are feasible, should the need arise.

Appendix A

Effect of Voltmeter Resolution on Transfer

Accuracy

The rms digital voltmeter's lack of resolution ("voltmeter

resolution") contributes significantly to the uncertainty of a measurement. For example, if a 5-V signal is measured with

6A calibration of amplitude variation with frequency for a given level within each voltage range is preferred over actual individual amplitude

calibrations.

7 An operating frequency of 5 Hz instead of 50 Hz is recommended and

will be implemented in the NBS instrument. Also, a larger output voltage than 1 V should be considered. Voltage levels up to 7-V rms can be

calibrated at NBS.

8,9 Peak-to-peak values of amplitudes were measured.

AC IN

Fig. 5. Precision rectifier-filter circuit used to measure the average value

of ac calibrator voltages.

5-digit resolution (10-s integration period), voltmeter res- olution contributes ± 20 ppm to the uncertainty of a single

measurement or ±40 ppm to an ac-ac transfer, involving

two measurements. The same uncertainty also applies to an

ac-dc comparison, since two measurements are effectively

required—one ac measurement and the average of two dc

measurements (one for each polarity). Fluctuations in the indicated voltage have the effect of further decreasing a

voltmeter's resolution; therefore, careful filtering of the

ripple generated in the rms-dc converter is necessary if the rms voltmeter is to be used for accurate transfer measurements.

If the rms voltmeter's integration period is denoted by Th perfect filtering of the ripple occurs for input frequencies of

/= n/27j, where n = 1, 2, 3, , and includes all ac calibrator

frequencies [2]. Minimum filtering occurs for/ = (n + \)/2Tt and causes a worst case peak fluctuation in the indicated

voltage of 0.05 percent at/= 0.125 Hz.

Appendix B

Measurement of Calibrator Voltage Versus

Frequency

As indicated in Section III, the variation of rms voltage

level with frequency must be determined to establish the maximum uncertainty of the ac calibrator voltage. Since

measurements using the rms voltmeter have insufficient accuracy at frequencies below ~ 1 Hz, the rms amplitude

variation versus frequency was determined from a combination of peak-to-peak and average value measurements over

the entire frequency range of 0.1-10 Hz and rms measure- ments over the 1-10-Hz range. Based on these measurements, the estimated rms amplitude variation is 61 ppm.

The method of making the peak-to-peak measurements is described in [2]. The average value of the ac voltage

variation with frequency was measured using the precision

rectifier-filter circuit shown in Fig. 5. 10 This circuit, an

average-responding ac-dc converter, uses" chopperstabilized amplifiers and very stable passive components to

insure good dc stability. In order to provide additional

ripple filtering without increasing the response time unduly,

the dc voltage output at node P was fed to node o of the ac voltmeter of Fig. 2 with the rms/dc converter disconnected

and the readings taken from the dc DVM.

Basing differences between the rms values of voltages versus frequency on the differences between average values

10 This type of circuit is described in [4].

33
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 4, DECEMBER 1979 331

(and peak-to-peak values) versus frequency appears to be

valid since all necessary precautions were taken to insure

that the waveshape is the same for all frequencies. For

example, capacitances Ca

, Cb, are chosen so that the product of capacitance and frequency is constant within 0.2 percent. Therefore, attenuation of the fundamental and

harmonic components and the phase shifts ofthe harmonics

relative to the fundamental remain constant for all calibra- tion frequencies.

References

[1] F. L. Hermach, "Ac-dc comparators for audio-frequency current and

voltage measurements of high accuracy," IEEE Trans. Instrum. Meas., vol. IM-25, pp. 489-494, Dec. 1976.

[2] H. K. Schoenwetter, "An rms digital voltmeter/Calibrator for very-low

frequencies," IEEE Trans. Instrum. Mcas.. vol. IM-27, pp. 259-268,

Sept. 1978.

[3] B. F. Field, "A fast response low-frequency voltmeter," IEEE Trans.

Instrum. Meas., vol. IM-27, pp. 368-372, Dec. 1978.

[4] P. Richman, "A new absolute ac voltage standard," in IEEE Int. Conv. Rec, ot. 5, pp. 170-183, Mar. 1963.

34
APPENDIX A

Calibration Forms

Several forms have been prepared to facilitate the calibrations of

rms voltmeters and the voltage and frequency response calibrations of ac voltage standards. These are:

(1) LOG SHEET

(2) WORK SHEET

(3) TABLE OF CALIBRATIONS

(4) REPORT OF TEST

These forms, as well as a brief description of the calibration

procedure, are given in the following sections for each type of calibration

Items 3 and 4 and the summarized calibration procedure are sent to the

customer, following a calibration.

ADepartment of Commerce VOLTMETER CALIBRATIONS USING NBS AC VOLTMETER/CALIBRATOR

National Bureau

of Standards Equipment Mf.r.

LOG SHEET Submitted by:

Date Test No. , . Mo(jcl No> Ser _ No>

Time Frequency

Voltage

range Voltmeter readings (Vm ) Mean value

Aai "o u It C IS\ 4-> ai 3

-a c

•t- i— o

»- 01 t- c > o O 01 z CJ >—

J_ >,

+> *""* 0) c s_ to * « •£ M 1 +J U O (- u 1 0£ t- 01 «— O o +» I— 3 1 et

OCCO

»—1

>» _1 £ w

<c •a*-' ^

CJ 1- o

01 >• ai u

UJ

I— o c <t- =3 O

UJ z s c

1— t— o

_i ai '^ O "O > o ii w 1 o s £ v

§"«-

<£CO

COz o u»o> o »- c^- 1 z oi ••- z

-O T3—• —1 e <o 1 CO =1 01 3 Z C

CO 1 z 1 o c

-a o | 1 1—4 u-^

(— IO •J'"* e£ a « <A a: « >

CO +J 01 1—«

t/> -o —1 c

ac o

*- E I UJ *J. >

1— <-*» 1 UJ >I

ai i o 1 -j s: JO CJ 1 o 1 > •#-> TJ 1 c <D

ai

M ! E +J a .o

•r— E > 3 JO 1 i a 3

UJ CO . I 1 l» 1 <DO

J-a)E 3 E <o o o <U 1/) z 01en 01 O J- -c1 m en 3 J. »-> 4-> C

c>- co

aj 10 i— «o o (- 1 O "C) a> >

t— c »—

+J »o «j 1- c: c +

<D

O

C> u > ujj E •- 3 >. 1 1 +J 4-> <+ c5 uc

01 1 J- ra c> ra z 2*i <!J 3

a.

Q: •-> or

01 QJ C> <o a 3: a u.

J 1

A- 3
Calibration of Voltmeters

Calibrations are performed on rms-responding ac voltmeters using

the ac voltage calibrator of the NBS AC Voltmeter/Calibrator. AC

voltmeters can be calibrated at frequencies of 10, 5, 2, 1, 0.5, 0.2,

and 0.1 Hz at any voltage level between 0.5 mV and 7 V.

The total uncertainty of a calibration is ±(eC + er)» where

e c is the uncertainty of the ac calibrator voltage and £r is

the imprecision of the calibration process. The estimated maximum

uncertainty of the ac voltage calibrator is ±0.020 percent. The

imprecision for a given calibration point is ts//IT, where t is

Student's t for the selected confidence level, s is the standard

deviation for a measurement, and N is the number of measurements

(test runs) used to obtain the mean values of the measured quantities

(voltmeter readings).

Unless otherwise requested by the customer, a single accuracy of

calibration will be given for the corrections to the calibration

points, based on a confidence level of 0.98 and the largest standard

deviation encountered.

ADepartment of Commerce

National Bureau

of Standards

TABLE OF CALIBRATIONS

Date Test No.

VOLTMETER CALIBRATIONS USING NBS AC VOLTMETER/CALIBRATOR

Equipment Mfr.

Submitted by:

Model No. Ser. No.

Frequency

Voltage

range

Average of voltmeter

readings

"vm

Correction

to VTM

Number of readings

(N) Total uncertainty

Confidence

level used

for t

AFOftM NM-2M

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OP «TANDA«D»

WASHINGTON. D.C. 20294

REPORT OF TEST

LOW FREQUENCY VOLTMETER

Manufacturer

Model No.

Serial No.

Submitted by

This voltmeter was tested using the ac voltage calibrator of the NBS AC

Voltmeter/Calibrator at a room temperature of 23 ±1 °C.

The test points, average voltmeter readings, corrections, and total uncertainty

are shown in the attached TABLE OF CALIBRATIONS. Also shown is the confidence

level upon which the imprecision is based. The ac calibrator voltage

uncertainty is treated totally as a systematic error. Unless otherwise

indicated, the total uncertainty is based on the largest standard deviation

encountered for any of the test points. Measurements on the test unit were

made over a period of time which was too short to yield long-term stability

information.

For the Director

National Engineering Laboratory

Barry A. Bell, Group Leader

Electronic Instrumentation and Metrology

Electrosystems Division

Test No. 722/

Order No.

Date:

Attn:

A6
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A- 8
Calibration of Voltage Standards

For each calibration point, the rms voltmeter (DVM) is used to

compare the voltage Vj from the standard under test with the voltage

V c of the same nominal level from the ac voltage calibrator, choosing

the calibrator frequency closest to that of the vol tage being measured,

After the test runs are made, the average (V

c

- Vj) is formed for

each calibration point, yielding corrections to the nominal voltage

values of the test unit.

If the uncertainty of the calibrator voltage and the uncertainty

caused by the DVM frequency response are denoted by e c and em, respectively, the total uncertainty of a calibration point is given

by ±(e c + e m

+ ts//N), where s is the standard deviation of a (Vc - Vf) comP ar "i son an d N is the number of comparisons (test runs).

If the frequencies of the voltages being compared are within

5 percent of each other, e m

is ±7 ppm. If the frequency difference

is larger, the worst case value of e m, ±40 ppm, is used. The

value assigned to £m is ±200 ppm (±0.02%); however, if the highest

calibration accuracy is required by the customer, e c can be decreased

to ±125 ppm by a special calibration of the NBS instrument.

Unless otherwise requested by the customer, a single accuracy of

calibration will be given for the corrections to the calibration

points, based on a confidence level of 0.98 and the largest standard

deviation encountered.

ADepartment of Commerce

National Bureau

of Standards

TABLE OF CALIBRATIONS

Date Test No.

CALIBRATIONS OF VOLTAGE STANDARD USING NBS

AC VOLTMETER/CALIBRATOR

Equipment Mfr.

Submitted by:

Model No. Ser. No.

Nominal voltage of standard

Frequency of standard

Correction to

nominal voltage

Number of comparisons

(N) Total uncertainty

Confidence

level used

for t

'"

.:—,—

A-10
FOftM NM-2S9

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON. D.C. 20234

REPORT OF TEST

LOW FREQUENCY VOLTAGE STANDARD

Manufacturer

Model No.

Serial No.

Submitted by

This voltage standard was tested using the ac voltage calibrator and rms voltmeter (DVM) of the NBS AC Voltmeter/Calibrator at a room temperature of

23 ±1°C.

The test points (nominal voltage and frequency), corrections, and total

uncertainty are shown in the attached TABLE OF CALIBRATIONS. Also shown

is the confidence level upon which the imprecision is based. The uncertainty

of the ac calibrator voltage and the uncertainty caused by the DVM frequency

response are treated as systematic errors. Unless otherwise indicated, the

total uncertainty is based on the largest standard deviation encountered for

any of the test points. Measurements on the test unit were made over a period

of time which was too short to yield long-term stability information.

For the Director

National Engineering Laboratory

Barry A. Bell, Group Leader

Electronic Instrumentation and Metrology

Electrosystems Division

Test No. 722/

Order No.

Date

Attn:

A- 11
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A-13
Frequency Response Calibrations

These calibrations are made using the DVM to compare test unit

voltages of freq uency f w ith the 10 Hz value. After N comparisons,

the quantities fVf - V-j q ) are computed for each test frequency,

yielding the frequency response. The uncertainty of these calibration

points is ±(c m

+ ts//N), where e m

is ±40 ppm, the frequency response

of the DVM, and s is the standard deviation of a comparison.

Unless otherwise requested by the customer, a single accuracy of

calibration will be given for the frequency response, based on a confidence level of 0.98 and the largest standard deviation encountered,

A-14
Department of Commerce

National Bureau

of Standards

TABLE OF CALIBRATIONS

Date Test No.

FREQUENCY RESPONSE CALIBRATIONS OF VOLTAGE STANDARD

USING NBS AC VOLTMETER/CALIBRATOR

Equipment Mfr.

Submitted by:

Model No. Ser. No.

Nominal voltage Frequency

Frequency response

(Vf-Vio)

Number of comparisons

(N) Total uncertainty

Confidence

level used

for t

A-15
fommNH-3M

(>-M>

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON. D.C. 20294

REPORT OF TEST

LOW FREQUENCY VOLTAGE STANDARD

Manufacturer

Model No. '_ Serial No.

Submitted by

This voltage standard was tested for frequency response using the rms voltmeter (DVM) of the NBS AC Voltmeter/Calibrator at a room temperature

of 23 ±1°C.

The test points (nominal voltage and frequency), corrections, and total

uncertainty are shown in the attached TABLE OF CALIBRATIONS. Also shown

is the confidence level upon which the imprecision is based. The uncertainty

caused by the DVM frequency response is treated as a systematic error. Unless otherwise indicated, the total uncertainty is based on the largest

standard deviation encountered for any of the test points. Measurements

on the test unit were made over a period of time which was too short to

yield long-term stability information.

For the Director

National Engineering Laboratory

Barry A. Bell, Group Leader

Electronic Instrumentation and Metrology

Elect rosystems Division

Test No. 722/

Order No.

Date

Attn:

A- 16
APPENDIX B

Detailed Design of Voltage Calibrator

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B-3
Description of Components Used in Voltage Calibrator

Amplifiers AR1 and AR2 are Analog Devices Type 52K. 1

Capacitors CI and C2 are 5 percent silver mica types. Capacitor

C2, or associated timing components, may need trimming to yield the

desired clock frequency. The capacitors associated with AR2 should

be trimmed so that (capacitance) (cal ibrator frequency) = constant,

to within ±0.2 percent. Nominal values ( yF ) are: C

a

= 0.025,

C b

= 0.05, Cc= 0.125, C d= 0.25, Ce= 0.5, C f= 1.25, and C

g

= 2.5.

These polycarbonate capacitors have a rating of 100 V, 5% tolerance

and ±0.1%/°C temperature coefficient. They were shunted with

smaller capacitors (mica or polycarbonate) to obtain the desired

capacitance ratios.

The function generator (U8) is Micro Networks Corporation Type

MN350.

The dc reference ( PS 1 ) should have a dc stability of better than

±5 ppm/year.

Resistors R12 and R13 are 1W precision wirewound resistors with

±0.01% tolerance and temperature coefficients matched to within 2 ppm/°C.

Two parallel 100 q resistors may be used for R13. All trimpots are

1W, 25 turn, panel mount type with ±150 ppm/°C temperature coefficient.

Resistors Rl - R4, R8, R14 - R16, R23 - R25 and R28 - R30 are Vishay

Resistive Systems Group Type 51 02 C. A non-inductive wirewound resistor

was used for R17. R27 is a sensistor from Texas Instruments, whose

value is determined from temperature tests. R7 is a general resistance

Type DV-4007A K-V divider.

Switches SI - S4 should have plastic sleeves on their handles to

minimize thermal voltage generation at the switch contacts.

1 Certain commercial equipment, instruments or materials are identified

in this report in order to adequately specify procedures or special

circuits. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply

that the material or equipmment identified is necessarily the most

suitable for the purpose.

B-4
APPENDIX C

Shipping and Fee Information

General shipping instructions are given in the latest issue of

NBS Special Publication 250, "Calibration and Related Measurement

Services of the National Bureau of Standards." Shipments of voltmeters

and voltage sources 'for calibrations should be directed to

National Bureau of Standards

Electrosystems Division, MET B162

Rt. 270 and Quince Orchard Road

Gaithersburg, MD 20878 .

Current information on calibration fees is given in the NBS Special

Publication 250 Appendix, which is updated every six months.

C-l
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN 1182

2. Performing Organ. Report NoJ 3. Publication Date Sept. 1983

4. TITLE AND SUBTITLE

AC VOLTAGE CALIBRATIONS FOR THE 0.1 Hz to 10 Hz FREQUENCY RANGE

5. AUTHOR(S)

Howard K. Schoenwetter

6. PERFORMING ORGANIZATION (If joint or other than N&S, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Sponsored in part by the

Calibration Coordination Group of the

Department of Defense

10. SUPPLEMENTARY NOTES

2] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

The development of voltmeters to meet the need for rms voltage measurements in the infrasonic frequency range is

discussed as well as the need to trace these measurements to

the U.S. legal unit of voltage. A new method for supporting

voltage measurements in the 0.1 Hz - 10 Hz range was described

in a 1979 paper and is discussed further. The principles of

the method are embodied in detailed procedures given for

calibrating sine-wave voltage standards and rms voltmeters

over the 0.1 Hz - 10 Hz frequency range, using the NBS AC

Voltmeter/Calibrator. The sine-wave calibrator of this

instrument, used for these calibrations, has an accuracy of

0.020 percent over the 0.5 mV - 7 V range.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons) ac voltage calibrations; ac voltage calibrators; ac voltage standards;

infrasonic voltage measurements; low-frequency voltage measurements;

rms voltmeters

13. AVAILABILITY

|X I Unlimited

| | For Official Distribution. Do Not Release to NTIS

[X~1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

3) Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

58

15. Price $4.25

USCOMM-DC 6043-P80

it U.S. GOVERNMENT PRINTING OFFICE : 1983 O—380-997 (5178)
NBS TECHNICAL PUBLICATIONS

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