(source: Electronics World, Aug. 1964)
Examination of our National Standards, their derivation, maintenance,
and accuracies, and an assessment of the present state of the art.
By FOREST K. HARRIS [Chief, Absolute Electrical Measurements Section
National Bureau of Standards]
IF we wish to say how large some physical quantity is, our description
of its size has two partsa unit and a number. The unit is a defined
reference amount of the quantity; and, if our statement is to be understood,
everyone who is concerned must agree on the size of the unit. The number,
which completes our statement, tells how much bigger or smaller is the
quantity we are discussing than the defined unit quantity. The size of
the unit can be fixed by definition, quite independently of any measurement,
and therefore can be exact. We can arrive at the numerical part of our
statement only through measurementthis number is subject to the errors
of the measuring process by which we obtain it, and therefore can never
be exact.
 The practical standard for d.c. voltage is provided in this
country by saturated standard cells forming National Reference Standards.
These cells are extremely stable, but sensitive to change in temperature.
Both the reference cells and cells sent to the Bureau for calibration
are kept in a circulating oil bath whose temperature is electrically
controlled to within a few thousandths of one degree of 28 degrees centigrade.
Thus if a statement of quantity is to have meaning, there must first
be agreement on the size of the unit. Next, there must be acceptable
reference standards to represent the physical embodiment of the defined
unit or some multiple of it; and it is through such reference standards
that measurement errors are controlled.
Reference standards form the basis for the calibration of measuring
devices and systems; and, to the extent that their assignment derives
from National or International Standards, they can also serve to coordinate
measurements made at different times and places. It will be the purpose
of this article to examine our National Standards of electrical measure,
their derivation and maintenance, and, in addition to these items, to
assess the present state of the art in just a few of the important areas
of electrical measurements.
History of the Electrical Units
In the years following the promulgation of Ohm's Law (1827) many suggestions
were made regarding a standard (and unit) of resistance. Examples were:
(1) a foot of copper wire weighing 100 grains; (2) an English mile of
No. 16 copper wire; (3) a kilometer of iron wire 4 mm. in diameter; and
(4) a column of mercury 100 cm. long and 1 mm. in crosssection at 0
°C. The last of these units was used for a time in Germany, and was known
as the Siemens unit. It is interesting to note that it differs from today's
resistance unit by a little more than 6 %. During this same period the
e.m.f. of the Daniell (zinccopper) cell was widely used as the unit
of voltage.
By the middle of the 19th century the work of Gauss and Weber had shown
that electric and magnetic quantities could be measured in terms of mechanical
units. Then in 1861, the British Association for the Advancement of Science
formed a Committee on Electrical Units and Standards with Maxwell as
chairman. This committee realized the value of a correlated system of
electrical and mechanical units based on the metric systemwhich was
already familiar to scientific workers through the world; and in 1863
(just over a century ago) the committee recommended a set of "absolute
practical" units
that were decimal multiples of the centimetergramsecond electromagnetic
units. By "absolute" was meant that the unit was defined directly
in terms of mechanical units; and "practical" signified that
the unit was of a convenient size for practical engineering measurements.
The following is a list of the British Association recommendations:
Absolute practical unit
1 coulomb 1 ampere 1 volt 1 ohm 1 joule 1 watt
Equivalent in c.g.s. electromagnetic units
0.1 c.g.s. unit of charge
0.1 c.g.s. unit of current
10^8 c.g.s. units of potential difference
= 10^9 c.g.s. units of resistance 10^7 ergs
10^7 ergs per second
These units were accepted on an international basis in 1881 by the Paris
Electrical Congress and have been formally recognized as the electrical
units in the United States by Congressional acts. (The most recent such
act is Public Law 617 of the 81st Congress.) The choice of 109 as the
conversion factor between ohms and c.g.s. units of resistance brought
the size of the new unit close to that of the existing German unit (the
Siemens unit, smaller than the ohm by about 6 %). Similarly, with 108
chosen as the factor between the volt and the c.g.s. unit of e.m.f.,
the new unit did not differ greatly from the Daniellcell unit ( within
about 20 %) . Having fixed the values of these two conversion factors,
the others are all fixed by the simple relationssuch as Ohm's Lawthat
exist between the units.
The wisdom of the BA committee's choice will be seen when we consider
that if the e.m.f. of the Daniell cell had been chosen as an electrical
unit together with one of the suggested units of resistance (a mile of
No. 16 copper wire), the electrical and mechanical units of power and
energy would have differed by a factor of about 25, whereas with the
chosen units they are identical.
The BA committee sponsored "absolute" experiments that resulted
in the assignment of values to a number of wire standards that were distributed
to various laboratories in the interest of international agreement. These
standards were not completely stable, and the assigned value of one was
found by Rowland in 1878 to differ by 1.5% from its intended absolute
value.
At that time there were no national laboratories where standards could
be checked; and there was a need for "reproducible" standards
that could be set up in any laboratory to duplicate the units. In 1893
the Chicago Electrical Congress fixed on a mercury column 106.3 cm. long
aril with a crosssection of 1 sq. mm. to represent the ohm at 0° C.
In 1892 the British Association adopted as a "reproducible" ampere,
the current that would deposit silver from a silver nitrate solution
under specified conditions at the rate of 0.001118 gram per second. The
apparatus used for this measurement was called a "voltameter."
Fig. 1. Present absolute electrical units, used since 1948.
Fig. 2. Available accuracy of various standard resistors.
National Laboratories
During the closing years of the 19th century and the beginning of the
20th, national laboratories were organized in a number of countries including
the United States, to preserve and disseminate the units of measure;
and in 1910 representatives of the national laboratories of Germany,
France, Great Britain, and the United States met in Washington to compare
standard resistors and standard cells whose values had been assigned
in terms of their national units, and to resolve differences among the
various silver voltameters. As a result of this meeting each representative
returned to his own national laboratory with a group of resistors and
standard cells whose values were assigned in terms of a mutually acceptable "International" ohm and volt, realized through the "reproducible" units.
During the next four decades, the various national laboratories maintained
their electrical units more or less in terms of these groups of resistors
and cells; but by 1930 it was quite generally argued that the mercury
ohm and silver ampere, on which the "International" system
of units was based, were not reproducible with sufficient accuracy for
scientific and technological purposesin short, the techniques of measurement
were outgrowing them; and also, unacceptably large discrepancies were
showing up in comparisons between the national standards of some countries.
So it was agreed that "absolute" ohm and ampere experiments
would be performed at some of the national laboratories, and that the
results of these experiments would be used to reassign the various national
units on an "absolute" basis. At an international meeting in
1935 it was hoped that the transition to the "absolute" units
could be made on January 1, 1940; but the outbreak of war in the summer
of 1939 interfered with this plan.
Fig. 3. Present voltage and voltageratio accuracies.
The transition was finally made on January 1, 1948, with changes amounting
to a few hundredths of a percent. For example, the "International" ohm
as then maintained at the National Bureau of Standards was stated to
be 1.000495 absolute ohms, and the "International" volt, 1.000330
absolute volts. Conversion factors for the remaining electrical units
can be derived in terms of these two factors and the simple relations
that exist between the units.
It should be noted that if the meter, kilogram, and second are used
in place of the centimeter, gram, and second as mechanical units, and
if the permeability of free space is assigned the value 107, the absolute
system of electrical units becomes identical with the practical system.
Alternatively, since four arbitrarily chosen quantities can be used to
define a system of electrical units, it has been suggested that the meter,
kilogram, second, and ampere be used as the basis of the defined system
of units, the m.k.s.a. system.
This was adopted by the General Conference of Weights and Measures in
1960 as a part of the general system to be known as the Systeme International
d' Unites (which is commonly abbreviated SI).
Experimental Realization of Units
Section 12 of the Public Law that defines the electrical units contains
the following statement: "It shall be the duty of the National Bureau
of Standards to establish the values of the primary electrical units
in absolute measure; and the legal values for these units shall be those
represented or derived from National reference standards maintained by
the National Bureau of Standards." Two types of "absolute" measurements
have been used in assigning numerical values to our basic electrical
standards in terms of the mechanical units. The ohm is evaluated in terms
of length and time; the ampere in terms of length, mass, and time. (See
Fig. 1.)
The absoluteohm determinations on which our "legal" ohm are
based were performed in the National Bureau of Standards and in the national
laboratories of other countries. These determinations have involved an
inductor (either self or mutual) of such construction that its value
can be computed from its measured dimensions together with the conventionally
assigned permeability of the space around it. This inductance is supplied
with a periodically varying current and its reactance at the known frequency
is, in effect, compared with the resistance of a standard resistor.
A similar experiment could involve the comparison of a capacitive reactance
and a resistance; and such a determination would have the advantage that
the electrical field of a capacitor can be completely confined by a shield
so that the capacitance value is independent of anything outside the
shield, whereas the magnetic field of an inductor cannot be limited to
be free from proximity effects. However, it is only within the past few
years that a practical capacitor geometry capable of simple measurement
and computation has been described in terms of a new theorem in electrostaticsthe
ThompsonLampard theorem. The value of such a capacitor can be assigned
with sufficient accuracy to make attractive an absoluteohm determination
in terms of capacitance; and such determinations have been made, although
their results have not yet (1964) been incorporated into the "legal" ohm.
In an absoluteampere determination, a pair of coils is arranged so
that the force between them when they carry current can be measured in
terms of the force of gravity acting on a known massthus the units of
measure are length, mass, and time. The current, measured in absolute
amperes, is passed through a standard resistor whose value is known in
absolute ohms. The resulting voltage drop is compared to the electromotive
force of a standard cell, and its value is assigned in terms of absolute
volts.
"Legal" Electrical Units
The absolute measurements on which are based the assignment of the National
reference standards are time consuming and require great care and skill.
Their occasional repetition, to maintain surveillance on the constancy
of the national standard, is desirable. But for the purpose of providing
a continuing measurement capability, groups of wirewound resistors
and of standard cells constitute the National reference standards and
form the basis of the "legal" electrical units.
The National reference standard of resistance for the United States
is a group of ten 1ohm resistors of special construction. Their values
were assigned on January 1, 1948, in terms of an international agreement
based on the results of the various absoluteohm determinations. The "legal" unit
of resistance is preserved in terms of their group average, which is
assumed not to have changed since the 1948 assignment. The resistors
of the group are regularly intercompared to about a part in 107. In
addition, our national standard is compared at regular intervals, through
measurements made at the International Bureau of Weights and Measures
in Sevres, France, with the standards maintained by National laboratories
of other countries.
 Overall view of the NBS helicalcoil balance. In the center
of the coil (bottom) is a small movable coil which is attached to the
arm of the precision balance. This arrangement measures change in force
on the small currentcarrying coil when current in the two parts of the
outer coil is reversed. From the change in force and the dimensions of
the coils, the exact current value in amperes is found.
This large, doublewalled standard 1ohm resistor is used
to maintain the standard unit of resistance .
The 100ohmperstep dial of a universal ratio set is being
checked against one of the group of 100ohm reference standards.
The maximum net change in any of the group with respect to the group
average has been a little over 2 ppm (parts per million) in the 30 years
that have elapsed since the group was first set up. In the international
comparisons over the past decade, the differences between our unit of
resistance and that maintained by the International Bureau have never
been greater than 1 ppm; and in only one instance was the difference
greater than 0.4 ppm. It is believed very unlikely that the "legal" ohmmaintained
in terms of the average of this group of ten resistorsdiffers from the
defined absolute ohm by as much as 4 ppm; and there is evidence in terms
of recent absoluteohm determinations (capacitive) that the difference
is no more than 1 ppm (Fig. 2).
The National reference standard of e.m.f. is a group of 44 saturated
standard cells (commonly referred to as Weston cells), maintained continuously
at a temperature of 28 ±0.01° C, and held at 28 ±0.001 degr. C during
intercomparisons. Eleven of the cells have been in the reference group
since 1906; of the remainder, 7 made in 1932 and 26 made in 1949 were
added to the group in 1955. New cells are made periodically of carefully
purified materials, and are kept under the same conditions as the reference
group and compared with it regularly. Thus a cell having a known history
of constancy is always available for replacement, if one of the National
reference group fails. The cells of the reference group are intercompared
regularly and their average value is assumed to be constant. It is in
terms of this group average The 100ohmperstep dial of a universal
ratio set is being checked against one of the group of 100ohm reference
standards of this group of ten resistorsdiffers from the defined absolute
ohm by as much as 4 ppm; and there is evidence in terms of recent absoluteohm
determinations (capacitive) that the difference is no more than 1 ppm
(Fig. 2).
Fig. 4. Present current and currentratio accuracies.
Fig. 5. The accuracy of capacitance measurements.
Fig. 6. The attainable accuracy of inductance measurements.
 Improved standard of capacitance. This design, based on a recently
discovered theorem in electrostatics, allows capacitance value to be
calculated directly in terms of length.
The National reference standard of e.m.f. is a group of 44 saturated
standard cells (commonly referred to as Weston cells), maintained continuously
at a temperature of 28 ±0.01° C, and held at 28 ±0.001 degr. C during
intercomparisons. Eleven of the cells have been in the reference group
since 1906; of the remainder, 7 made in 1932 and 26 made in 1949 were
added to the group in 1955. New cells are made periodically of carefully
purified materials, and are kept under the same conditions as the reference
group and compared with it regularly. Thus a cell having a known history
of constancy is always available for replacement, if one of the National
reference group fails. The cells of the reference group are intercompared
regularly and their average value is assumed to be constant. It is in
terms of this group average and its 1948 assignment that the “legal" volt
is maintained.
This unit is regularly compared with those of other countries at the
International Bureau. Over the past decade the differences between our
unit and the one maintained by the International Bureau have generally
been less than 2 ppm, although on one occasion (1953) the difference
amounted to about 3 ppm (Fig. 3) . Recently an additional means of checking
the constancy of our National electrical units has become available by
using a natural physical constantthe gyromagnetic ratio of protons in
a sample of pure water. These elementary charged particles are continually
spinning like miniature tops. Because of this spin and their electric
charge, they behave like magnets and tend to align their spin axis in
the direction of the ambient magnetic field. When they are thus oriented
and then disturbed, they precess about the direction of the magnetic
field, just as does a spinning top or gyroscope in the earth's gravitational
field. This precession frequency, which we can measure very accurately,
can be used to measure the strength of the field.
In our experiment, the field is set up within a precisely made solenoid
and can be computed from the coil dimensions and the measured current
in the coil. This current is measured by comparing the voltage drop it
produces in a standard resistor to the e.m.f. of a standard cell. If
the measured precession frequency is constant we know that the current
has not changed and therefore that the ratio of the National volt to
the ohm has not changedstrong evidence that neither has changed, since
it is quite unlikely that they would both drift in such a way that their
ratio would remain constant.
A series of measurements over the past four years indicate that the
Bureau's ampere has been constant over that interval, the maximum departure
from the mean value being 0.4 ppm (Fig. 4). While all available data
indicate constancy of the National reference standard of e.m.f., there
is evidenceboth from absoluteampere determinations and from consideration
of internal consistency of the assigned values of various atomic constantsthat
the "legal" volt (maintained in terms of the National reference
standard) differs from the defined absolute volt by about 10 ppm. Certainly
there is need for further absolute measurements, and there is now under
consideration an absolutecolt determination directly in terms of the
amount of force that is associated with a potential difference between
the electrodes of a capacitor.
Capacitance and Inductance
There are no national reference standards for capacitance and inductance
in the pattern used for the National reference standards of resistance
and e.m.f. However, the 1pf computable capacitor used in the absoluteohm
determination can be set up and measured without great difficulty; and
the assignment of its value is believed to be correct within 12 ppm
in terms of the defined absolute unit. Studies are in progress to develop
stable capacitance standards in the range 1 10^3 pf.; and in this range,
the values of "ideal" capacitors can be compared within 12
parts in 10^7. In this context, the term "ideal" means a standard
which is completely stable and whose value is independent of ambient
conditions. For values of capacitance greater than 10^3 pf., the attainable
measurement accuracy falls off, and is less by a factor of about 10 at
the 1u.f. level of capacitance ( Fig. 5) . Inductances are regularly
measured at low frequencies in terns of capacitance and resistance, for
example in a MaxwellWien bridge. In the middle range of inductance (1100
millihenries) and at a frequency of 1 kc., an "ideal" inductor
can be measured in terms of real capacitors and resistors to about 0.01%.
Measurement accuracy falls off at higher and lower values. In fact, if
one were to plot measurement accuracy for any kind of quantity against
magnitude, the typical shape of the curve would be a triangle with its
apex (the region of best accuracy) in the intermediate range of values
(Fig. 6).
Accuracy of Measurement
For resistance and voltage measurements, where a national reference
standard is maintained, the apex of the "accuracy triangle" coincides
with the value at which the standard is maintained. That this must be
so is apparent when one considers that at this value onetoone comparison
or substitution methods are available for measurement, with only small
differences involved. As one departs from the reference value, measurement
techniques grow more involved and complicated; and the additional sources
of error are present. For example, the accuracy with which a ratio can
be established may need to be considered as part of the problem. Thus,
whereas 1ohm standards can be compared to 12 parts in 10^7, when we
reach 10^7 ohm on one side of our accuracy triangle and 10" ohms
on the other side, stateofart accuracy has fallen off to perhaps 4
5 ppm, somewhat more than a factor of 10.
Using potentiometers and appropriate voltagedivider techniques, direct
voltages can be measured within 10 ppm between 10^2 and 10 volts, and
standard cells (at the 1volt level) can be compared within 1 2 parts
in 10'. Direct currents can be established at the 1ampere level within
a few parts in 10^7, and within 10 ppm for lower values down to perhaps
10^4 ampere. In the higher current range (above 1 ampere) where measurement
is complicated by the heating effect of power that must be dissipated
in the measuring equipment, measurement accuracy is somewhat lessperhaps
a few parts in 10^7 up to 10^4 amperes.
In transferring from direct to alternating voltage, an additional uncertainty
is involved, amounting to perhaps 10 ppm in stateofart voltage transfers
up to 20 kc. between 1 to 500 volts. In current transfer over the same
frequency span, the stateofart transfer uncertainty is about the same,
10 ppm, in the 510 milliampere range where no shunts are required. The
use of shunts or other circuit elements designed to carry currents of
higher magnitude, involve further uncertainties because of their inductance.
The total transfer uncertainty, up to about 20 amperes, need not amount
to more than 0.01%. In this article, we have described and examined our
National Standards of electrical measure. We have covered their derivation
and maintenance, as well as assessed the present state of the art regarding
measurement accuracy.
