accuracy charts for rf measurements

1056 mocmmcs OF THE EEE, VOL. 55, NO. 6, JUNE 1967

plotters), as well as in newly developed relatively high- quality spectrum analyzers. The x-y plotter gives a perma- nent record and can be arranged to provide for automatic comparison with specification limits. Standards for the design and use of such devices do not now exist and are un- doubtedly needed. Considerable thought should be given to the ways in which accuracy and completeness of data should be exchanged for data acquisition cost.

The large systems studies have been begun by various groups to provide methods of arriving at the solution of specific problems in this area of endeavor, and it seems inevitable that a sophisticated application of statistical techniques will be essential, as well as the establishment of accurate scientific bases for control of unnecessary radiation and for the planning of the use of the radio-frequency spectrum in order to maximize the use of this valuable resource. Problems exist in the maintenance of accurate and elaborate data bases for use in computer calculation of large system compatibility. Measurement techniques of the future must be compatible with the formats used in these procedures.

REFERENCE [ l ] F. D. Lewis and R. A. Soderman, “Radio frequency standardization

activities,” this issue. See Table 11. [2] Amendment to Section 15.75(b)(4) of the Rules and Regulations of

the Federal Communications Commission, dated October 18, 1 9 6 6 . [3] Private communication. [4] V. G . Price, “Measurement of harmonic power generated by micro-

wave transmitters,” IRE Trans. on Microwave Theory and Techniques, vol. MTT-7, pp. 116-120, January 1959.

[5] M. P. Farrer and K. Tomiyasu, “Determination of high order propa- gating modes in waveguide systems,”/. Appl. Phys., vol. 29, pp. 1040- 1045, July 1958.

[6] C. M. Knop and S . I . Cohn, “A multiple probe method for the mea-

surements of reflected and transmitted power in coaxial waveguides,” 6th Con$ on Radio Interference Reduction and Electronic .Cornpati- bility, pp. 52S541, October 1960.

[7] V. G. Price, “Harmonic calorimeter for power measurements in a multimode waveguide,” I R E Nat’l Conv. Rec., pt. 3, pp. 136144, 1 9 6 0 .

[8] E. D. Sharp and E. M. T. Jones, “A sampling technique for the measurement of multimode harmonic power,” 3rd Nat’l Symp. on Radio Frequency Interference, pp. 3 9 4 1 , June 1961.

[9] D. J. Lewis, “Mode couplers and multimode measurement techniques,” IRE Tram. on Microwave Theory and Techniques, vol. MlT-7, pp. 1 IC1 16, January 1959.

[IO] D. J. Lewis and J. Oliver, “Interference studies,” Institute for Cooper- ative Research, University of Pennsylvania, Philadelphia, Final Rept.,Task 1,vol. I, AD 148 812, April 15, 1958.

[I 1 ] J. J. Taub, “A new technique for multimode power measurement,” IRE Trans. on Microwave Theory and Techniques, vol. MTT-IO, pp. 49&505, November 1962.

[I21 0. F. Hinckelmann, R. L. Sleven, and L. F. Moses, “Equipment for measurement of spurious emissions in waveguide,” IEEE Trans. on Electromagnetic Compatibility, vol. EMC-6, pp. %37, October 1964.

[I31 Imtruction Manual for Filters, Tunable Rejection, Types F-643- (XN-1)JURM to F-659(XN-I)/URM and Radio-Frequency Trans- mitter Spectrum Characteristics, Measurement ox Navy Department, Bureau of Ships, December 31,1962.

[I41 W. W. Cowles, “Implementation of Poynting vector measurements,” The Moore School of Electrical Engineering, University of Penn- sylvania, Philadelphia, Final Rept. AD 640 990, August 31, 1966, available through CFSTI.

[I51 A. M. Vural and D. K. Cheng, “A light-modulated scattering technique for diffraction field measurements,” /. Res. NBS (Radio Science)/USNC-URSI, vol. 68D, pp. 355-362, April 1964.

[I61 R. R. Bowman and R. M. Green, this issue. [I71 W. E. Pakala and R. M. Showers, “Principles and application of

radio interference measurements,” IRE Trans. on Instrumentation, vol. !-7, pp. 297-303, December 1958.

[I81 F. Haber and R. M. Showers, “Instrumentation for radio interference measurements,” Electronic I d . , p. 1 IO, March 1%1.

[I91 “Measurement of radio frequency spectrum characteristics,” MIL- STD49C. March I , 1965.

Accuracy Charts for RF Measurements WILLIAM A. WILDHACK, H. L. MASON, AND ROBERT S. POWERS, JR.

A DEQUATE accuracy in measurement is essential for uniformity and interchangeability of goods and technical data, for the satisfactory fabrication, test-

ing, and operation of manufactured products, and for the quantitative description of natural phenomena.

Manuscript received March 29, 1967. The authors are with the National Bureau of Standards, Washington,

D. C. 20234

To provide sustained accuracy at the point of measurement, the measuring instruments or test equipment must be checked or calibrated periodically by other instruments or devices serving as standards. These, in turn, must be checked or calibrated periodically by yet other standards of still higher accuracy, and so on to standards that embody, or realize, the internationally defined units for mass (kilogram), length (meter), time (second), temperature (degree Kelvin), electric current (ampere), or luminous intensity (candela). These are the six physical quantities for which independent units have been defined by actions of the General Con- ference of Weights and Measures (CGPM) to serve as the base for a consistent International System of Units. The units are defined as follows [ 1 1.

WILDHACK ET AL.: ACCURACY CHARTS 1057

Kilogram-The 3rd CGPM, 1901, has declared : The kilogram is the unit of mass; it is represented by the mass

of the International Prototype Kilogram (a particular cylinder of platinum-iridium alloy preserved in a valult at Sevres, France, by the Internation Bureau of Weights and Measures).

Meter-The 1 1 th CGPM, 1960 has adopted the following : The meter is the length equal to 1 650 763.73 wavelengths in

vacuum of the radiation corresponding to the unperturbed transition between the levels 2P,, and Sd, of the atom of krypton-86.

Second-The 12th CGPM, 1964, considering that, in spite of the results obtained in the use of cesium as an atomic frequency standard, the time has not yet come for the General Conference to adopt a new definition of the second, a fundamental unit of the International System of Units, because of the new and important progress which may arise from current researches, and considering also that it is not possible to wait any longer to base physical measurements of time on atomic or molecular frequency standards, empowered the International Committee on Weights and Measures to designate the atomic or molecular standards of frequency to be used temporarily. The International Committee then acquainted the CGPM with the following declaration: The standard to be used is the transition between the hyperfine levels F=4, m=O and F = 3 , m=O of the fundamentai state ’S, of the cesium-133 atom unperturbed by external fields. The value 9 192 631 770 hertz is assigned to the frequency of this transition.

Degree Kelvin-The 10th CGPM, 1954, has adopted the following :

The 10th General Conference on Weights and Measures decides to define the thermodynami‘c scale of temperature by means of the triple-point of water as a fixed fundamental point, attributing to it the temperature 273.16 degrees Kelvin, exactly.

Ampere-The 9th CGPM, 1948, has adopted the following: The ampere is the constant current that, if maintained in two

straight parallel conductors that are of in6nite length and negligible cross section and are separated from each other by a distance of 1 meter in a vacuum would produce between these conductors a force equal to 2 x IO- ’ newton per meter of length.

Candela-The 9th CGPM, 1948, has adopted the following: The magnitude of the candela (unit of luminous intensity) is

such that the luminance of a blackbody radiator at the freezing temperature of platinum is 60 candelas per square centimeter.

It will be noted from the preceding definitions that a kilogram mass standard can be calibrated only through a series of comparisons, starting from the International Prototype. The units for the other five base quantities, and all quantities derived from them, are in principle independently realizable in many laboratories. In practice, however, the realization of these units involves extensive theoretical study and extreme care in design and use of experimental equipment. It should be noted that the units are defined in terms of the physical phenomena, not in terms of apparatus. Inevitable differences among the various principles, instruments, environments, and operators are bound to lead to discrepancies between the units as realized in various laboratories. For measurements of high accuracy, compatibility among national and international standards laboratories

requires the periodic comparison of standards and the resolution of these discrepancies.

The National Bureau of Standards periodically makes intercomparisons of U. S . standards with those of other countries through the International Bureau of Weights and Measures. (See Selby [ 2 ] for several such instances.) The operations of the International Bureau are supervised by the General Conference of Weights and Measures, to which U. S . delegates are appointed by the Department of State. (In the case of time and frequency, intercomparisons are studied by the International Bureau of the Hour and the International Consultative Committee on Radio.)

Within the United States, the National Bureau of Stan- dards consults with the major industrial and governmental standards laboratories and cooperates with the Department of Defense and the National Conference of Standards Laboratories in conducting measurement agreement comparisons [3], [4].

All other physical quantities are functionally related to two or more of the six base quantities listed. Therefore, the uncertainty with which any of these other quantities may be measured (or their units realized) is, at best, a combination of the uncertainties associated with the functionally related base quantities. The term uncertainty, as applied to measurement or calibration processes, is used here in a general sense as a measure (estimate) of the range of possible discrepancies between the results from an actual measurement or calibration, and those that might have been obtained by “ideal” (error-free) measurement techniques and standards.

The uncertainty in any practical measurement of products, performance, or phenomena is a summation of uncertainties associated with each of the successive standards, calibrations, and measuring instruments intervening in the calibration chain between international or national standards and the ultimate measurement. Part of the uncertainty at any stage of the succession of calibrations and measurement involves the repeatability (precision) of the measurement or comparison; another part involves bias arising from unsuspected sources or from imperfectly corrected errors from recognized sources (such as environmental effects); another part is due to uncertainties in the numerical values of natural physical constants or the properties of matter or materials that enter into the calculated performance results. Of course, some part results from the uncertainty associated with the (prior) calibration of the calibrating standard at the previous stage.

Estimates of precision at any stage may be obtained from repeated measurements of a known value at that stage. The other elements of uncertainty must be estimated separately, on the basis of critical analysis at that stage, and combined in appropriate ways with the estimated uncertainty in the calibration at the previous stage [ 5 ] .

The generalized chart of Fig. 1 illustrates the “uncertainty” or “accuracy” relationships for some imaginary but typical physical quantity. The magnitude of the quantity is plotted along the abscissa to a logarithmic scale. The range over which comparison with NBS standards is needed may extend above and below the unit magnitude by many powers

1058 PROCEEDINGS OF THE IEEE, JUNE 1%7

part In

one 1 I I I I 1 I

IO’ - A Standard -

lo-’ io-’ I IO‘ IO’ Magnitude -

Needs for better product accuracy NBS projects underway - - - Needs for improved calibration services - - -

Fig. 1. A generalized “accuracy chart,” showing the uncertainty in measurement for various echelons, expressed as a fraction of the magnitude.

of ten. The relative uncertainty is the ordinate, likewise on a logarithmic scale, and extending over as many decades as appropriate.

In the lower part of the useful range of most measurement techniques, the uncertainty is frequently limited by a relatively constant error (e.g., minimum reading error). In this range, the uncertainty in measurement increases (accuracy decreases) linearly as indicated by the slope of the curves in this region. Over much of the range, the residual uncertainty in measurement may be largely due to environmental or inherent factors affecting the readings by some multiply- ing factor. This results in a fairly constant relative (or per- centage) uncertainty. At the upper end of the range, the characteristics of the measuring instrument may be af- fected by the magnitude of the measured quantity, causing a decline in accuracy. No single instrument is generally useful over the the extreme ranges of interest; the curves shown would represent the envelope of the best accuracy char- acteristic of the various types available to cover the range.

The curve marked “Industry RefeF\ence” is intended to show the difference (or ratio) between NBS calibration accuracy and that of the standards in a typical industrial standards laboratory. This ratio is seldom 10 to 1 ; for the best equipped industrial standards laboratories it may be nearer to 2 to 1 for some quantities, and indeed, may be reversed, as shown on the right, when NBS standards become out- dated before appropriate improvements are achieved.

The triangle symbol on the chart indicates that the NBS standard realizes the unit for this particular quantity with an estimated uncertainty of 1 part in lo6 with respect to the “exact” value defined by the base units of the International System. Electrical quantities can be compared more pre- cisely than the units can be realized in terms of the Interna- tional System definitions. Hence, in the United States the

national standards for electrical quantities are those maintained by the National Bureau of Standards. Appropriate NBS reports of calibration call attention to this fact, for the few who have occasion to compare with foreign standards.

The starred points indicate the demands of industry for improved range and accuracy of NBS calibrations; the dashed line, the best service available by special effort; the dot-dash lines, the objectives of NBS projects; and the round dots, the tighter tolerances sometimes needed for accuracy in measurement in production or operations.

Curves representing the 3 or more calibrating echelons between the National Bureau of Standards and product are not shown on the chart of Fig. 1 , nor on the other charts, but should be kept in mind by the reader [6], [7]. This complex area, involving changing industrial practices and availabil- ity of new types of instruments, is the subject of studies by an IEEE Committee on Electromagnetic Measurements- State-of-the-Art and its various subcommittees [8].

The ultimate objective of NBS calibrations and of all other intervening calibrations is the support of adequate accuracy at the product or operations level. While not ap- pearing in Fig. 1, families of curves may be shown for associated parameters, as is done for frequency ranges on many of the other charts.

The remaining charts, Figs. 2 through 25, provide an in- dication of the estimated uncertainty (with respect to the National Bureau of Standards or international standards) in the Bureau’s calibrations or measurements on electrical and radio-frequency standards or instruments. The uncertainties shown cover both imprecision and systematic (bias) error, generally as plus or minus three standard deviations of the mean added to an allowance for the bias error. For most radio-frequency quantities the imprecision is negligible in comparison with the latter. On the other hand, Figs. 19 and 20 show imprecision only, and should not be read as implying bounds of error. The solid lines, blacked circles, and boxes with solid borders pertain to the values regularly obtained in the calibration of commercially available standards using established methods and published fees [9]. The dashed lines, open circles, and boxes with dashed borders indicate the minimum uncertainty possibly obtainable by special arrangement and at higher cost. In most of these charts, the stated uncertainties apply only to standards equipped with precision connectors.

These charts (Figs. 2 through 25) have just been updated and supersede the versions of 1965 and earlier [lo]. It is expected that they will appear later in 1967 with additional background material, and with similar charts for other electrical, mechanical, optical, thermal, and radiation quantities, when [l 1 ] is revised.

The task of estimating the overall uncertainties has been carried out by the project leaders and specialists in the particular measurement areas.

Beyond the foregoing introduction, the function of the present editors has been primarily that of coordination.


In vacuum

0 c - L

-

- Length in inches

IO+ , 10-2 , I , IO' , , IO'

10-1 10-4 10-2 I IO' Length in meters

Fig. 2. NBS calibrations for length and diameter.

Standard-A

\Frequency Stabiilty

Q o f Oscillators

Analysis of Oscillators

(Cavity Wavemeters)

Frequency in Hertz

Fig. 3. NBS calibrations for frequency.

1 d ' ~ ~ ~ I l l ~ l l l l ' l l

- .E 10"- c L O a

Y

WWV, WWVB, WWVL

Time Interval in Seconds Fig. 4. NBS time interval broadcasts and standards.

.r 10' 60 Hz J

Frequency Range: 30kHz - 4 GHz

/

Power in Watts Fig. 5. NBS calibrations for CW high-frequency power

in coaxial waveguide systems.

t - Frequency Range

1

Io' c lo-' lo'' IO0

Power in Watts Fig. 6 . NBS cahbrations for CW microwave power


Established service, with precision connectors - m s i . Possibly obtainable on special arrangement - - 0 m.

1060 PROCEEDINGS OF THE IEEE, JUNE 1967

Frequency Ronge 2.6-26.5 GHz

lo" 1 6 ' w' Power in Watts

Fig. 7. NBS calibrations for CW microwave power in uniconductor waveguide systems.

Q)

C W Source 2 IO' '

h c c ._ 0 . c L

Minimum Duty Rotio: 0.002

E Frequency Ronge: 250 - 500 and

3 950- 1200 MHz

IO' I I I I I I 1 a-' to-* IO+ Id IO' IO' IO' IO'

Peak Pulse Power in Watts

Fig. 8. NBS calibrations for high-frequency peak pulse power in coaxial waveguide systems.

Comportson of Std. Cells

I O ' t

1

1

Frequency Ronge: 8.2 - 18.0 GHZ

Effective Noise Temperature in Degrees Kelvin

Fig. 9. NBS calibrations for microwave noise in uniconductor waveguide systems.

, Inductive Dividers 50 Hz to IO kHz

by AC-Ck TronsfwStds. 5HZ to 50 kHz

Volts e \

Tmnskrmers

18400Hz

I" lo-' a-l I 10 0' IO' lo' IO1 IO' AC voltage in volts

Fig. 1 1. NBS calibrations for low-frequency voltage. For ratio standards, the chart shows the uncertainty in V/V,,,; Vrcr= 100 volts.

Established service, with precision connectors - Possibly obtainable on special arrangement - -

. ESm. 0 E m .


IOS l ~ I l , I l l , / i I I I l 1:106 for Std. Cells t

+Micropot +TVC,ATVM{ I Volts

Fig. 12. NBS calibrations for CW high-frequency voltage in coaxial waveguide systems. Frequency range for thermal voltage converters, 30 kHz to 100 MHz; attenuator thermoelement voltmeters, 10 MHz to 10oO MHz; micropotentiometers, 50 kHz to 900 MHz.

Minimum Pulse Width 0.3 Nanosecond ( 5 - 100 V I 30 Nanosecond (100- IOOOVI

'"loo IO1 IO' IO' Pulsed d c Vol tage In Volts

Fig. 13. NBS calibrations for peak pulse voltage in coaxial waveguide systems.

lo5 1:IO'at 1592 H z t , ,

- Calculable .c 1 0 ' - Standard

Capwitonce in Farads Fig. 15. NBS calibrations for @&-frequency capacitance

of low-loss capacitors.

.- = I IO'

Antenna Coefficient of LOOPS 3 0 H ~ - 3 0 M H z >

c

aJ Antenna Cwff icient 1 C of Dlpoles

30- 1,OOOMHz

Frequency in Hertz

Fig. 14. NBS calibrations for high-frequency field strength.

via Wenner Bridge c ' ." OBridge

0 a * . * *

via Capacitance Discharge - I I I I I i I I I 1

10-4 10-2 I 102 10' IO' 10' IOIO 10" DC resistance R in ohms

Fig. 16. NBS calibrations for dc resistance.

0

I o 0

0. I %

I O h

Established service, with precision connectors - EssJ. Possibly obtainable on special arrangement - - 0 E z z .

1062 PROCEEDINGS OF THE IEEE, JUNE 1967

IOS t 10' a t DC

n lo' t Frequency Range 0.03-250 M H z

Resistance in Ohms Fig. 17. NBS calibrations for high-frequency resistance of low-phase

angle resistors. Standards are referenced to calculable standard capacitor; see Fig. 15.

c Frequency Range 50 kHz - 45 MHz

c

e Io'

3 ': t 1 0 ' 1 10'" IO'"

Effective Resonating Copacltance In Farads

Fig. 20. NBS calibrations for effective resonating capacitance of Q standards. Uncertainty shown is for three-sigma reproducibility.

Frequency Range: 5 O k H z - 4 5 M H Z

Io' ' IO' IO'

Effective Q Fig. 19. NBS calibrations for effective Q of Q standards.

Uncertainty shown is for three-sigma reproducibility.

L 0 n g IO'

s IO'

0 - equency Range:

.-

Attenuation in dB Fig. 2 1. NBS calibrations for insertion loss or attenuation difference


Established senice, with precision connectors - lssss4. Possibly obtainable on special arrangement - - 0 z z z .


Frequency Ranges 8.2- 18.0 GHz 2.6 - 40 GHz

l o ” lo-’ IOD IO1 I O Z IO’ 10‘

Frequency Range: I- 18,000 MHz

-I

Attenuatlon In dB Phase Shift in Degrees Fig. 22. NBS calibrations for insertion loss or attenuation difference Fig. 23. NBS calibrations for high-frequency phase shift

in uniconductor waveguide systems. in two-port coaxial devices.

- C ._ c

lo‘- 1-4 GHz Frequwy Range:

(via Reflectometer c - > + .c I 0 IO - c E 3

1 0 0 10.‘ IO” lo-z 10-I IO’

Magnitude of Reflection Coefficient

Fig. 24. NBS calibrations for magnitude of microwave reflection coefficient in coaxial waveguide systems.

1 1 I IO‘ 10-1 lo-* lo-’ IO’

Magnitude of Reflection Coefficient

Fig. 25. NBS calibrations for magnitude of microwave reflection coefficient in uniconductor waveguide systems.

Established service, with precision connectors - EsxY. Possibly obtainable on special arrangement - - 0 Z B Z .

[ 1 ] ‘“IEEE recommended practices for units in published scientific and technical work,” ZEEESpectrum, vol. 3, pp. 169-173, March 1966.

121 M. C. Selby, “Intercomparison of HF and Ihicrowave electromagnetic quantities,” this issue.

[3] W. J. Youden, “Measurement agreement comparisons,” Proc. 1962 Standards Lab. Conf., NBS Mix. Publ. 248, pp. 147-151, 1963. (Available from Supt. of Documents, U.S. GPO, Washington, D. C. 20402, $1.75.)

[4] S. C. Richardson, “The NCSL 196546 measurement agreement comparison,” Proc. 1966 Standards Lab. Conf, NBS Misc. Publ. 291,

[5] C. Eisenhart, “Realistic evaluation of the precision and accuracy of in press.

instrument calibration systems,” J . Research NES, vol. 67C, pp. 161-187, April-June 1963. This paper also appears in [lo].

[6] A. G. McNish and J. M. Cameron, “Propagation of error in a chain of standards,” IRE Trans. Znstnunentatwn, vol. 1-9, pp. 101-104, September 1960.

[7] E. L. Crow, “Optimum allocation of calibration errors,” Industr. Quality Control, vol. 23, pp. 215-218, November 1966. An earlier discussion of this problem is given in E. L. Crow, “An analysis of the accumulated error in a hierarchy of calibration,” IRE Trans. Znstru- mentatwn, vol. 1-9, pp. 105-114, September 1960.

[8] “IRE technical committee report on the state-of-the-art of measuring sine-wave unbalanced RF voltage,” Proc. ZEEE, vol. 51, pp. 576-580, April 1963.

[9] “Calibration and test services of the National Bureau of Standards,” NBS Misc. Publ. 250, 1965. (Available from Supt. of Documents, U. S. GPO, Washington, D. C. 20402, $1.00.)

[lo] Proc. 1962 Standrds Lab. Con$ NBS Misc. Publ. 248, 1963. (Avail- able from Supt. of Documents, U. S. GPO, Washington, D. C. 20402, $1.75.)

[ l l ] W. A. Wildhack, R. C. Powell, and H. L. Mason, “Accuracy in measurements and calibrations, 1965,” NBS Tech. Note 262, 1965. Also, R. C. Powell, “Accuracy in electrical and radio measurements and calibration, 1965,” NBS Tech. Note 262-A (excerpt from TN 262), 1965. (Both available from Supt. of Documents, U. S. GPO, Washington, D. C. 20402, $1.00 and SO$, respectively.)