Frequency Standards and Clocks: >ARTMENT of 0MMERC

NBS TECHNICAL NOTE 616 U.S. Frequency Standards and Clocks: >ARTMENT OF 0MMERC. A Tutorial Introduction National of 00 Js snss £2 a NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress 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 consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and Technology, and the Office for Information Programs. 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THE CENTER FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improv- ing cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment; and serves as the principal focus within the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Center consists of the following offices and divisions: Information Processing Standards—Computer Information—Computer Services —Systems Development—Information Processing Technology. THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum accessibility to the scientific information of the world, and directs the public information activities of the Bureau. The Office consists of the following organizational units: Office of Standard Reference Data—Office of Technical Information and Publications—Library—Office of International Relations. 1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washing- ton, DC. 20234. - Part of the Center for Radiation Research. ! Located at Boulder, Colorado 80302. UNITED STATES DEPARTMENT OF COMMERCE Peter G. Peterson, Secretary y'<5- NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director N8S TECHNICAL NOTE 616 ISSUED APRIL 1972 Nat. Bur. Stand. (U.S.), Tech. Note 616, 69 pages (April 1972) CODEN: NBTNA Frequency Standards and Clocks: A Tutorial Introduction Helmut Hellwig Time and Frequency Division Institute for Basic Standards National Bureau of Standards Boulder, Colorado 80302 NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be listed or referred to in the open literature. This paper is provided as partial fulfillment of Contract EIIIM-6 to Richards-Gebaur AFB, Missouri 64030. For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. 013.46:616), Price 70 cents CONTENTS Page 1. INTRODUCTION 1 2. BASIC CONCEPTS 6 2. 1 Accuracy, Reproducibility, Stability 6 2. 2 Time Accuracy 10 2.3 Clocks 12 3. FREQUENCY STANDARDS, GENERAL ASPECTS 12 3. 1 Resonators 12 3.2 Primary and Secondary Standards . 18 4. QUARTZ CRYSTAL DEVICES 18 4. 1 Quartz Crystal Resonator 18 4. 2 Effects on the Crystal Resonator Frequency 24 4. 3 Quartz Crystal Oscillator Performance 29 5. ATOMIC RESONANCE DEVICES 32 5. 1 Atomic Resonators 32 5. 2 State Selection 33 5. 3 Interrogation of the Atoms 3 5 5.4 Signal Detection 37 5. 5 Atomic Frequency Standard 40 5.6 Effects on the Atomic Resonator Frequency 43 6. AVAILABLE ATOMIC FREQUENCY STANDARDS 46 6. 1 Cesium Beam Frequency Standard 46 6.2 Rubidium Gas Cell Frequency Standard 50 6. 3 Atomic Hydrogen Maser 53 7. SUMMARY AND COMPARISON OF AVAILABLE FREQUENCY STANDARDS 57 8. TRENDS 61 9. LITERATURE 6 3 in LIST OF FIGURES Page Fig. 1. Definition of time and frequency. 3 Fig. 2. Frequency standard and clock. 5 Fig. 3. Relationships between clock accuracy, frequency stability, 11 and frequency offset. Example (dashed line): for At = 10 ns, resynchronization every 1 hour is needed, if the frequency stability for 1 hour sampling time is 5 X 10 . The frequency ""12 offset is assumed to be less than 5X10 Fig. Example of a clock system (frequency values arbitrarily chosen). 13 Fig- Examples of resonators. 14 Fig. Decay time, linewidth, and Q-value of a resonator. 16 Fig. Hierarchy of frequency standards. 19 Fig. 8 The piezoelectric effect. 21 Fig. 9 Principal vibrational modes of quartz crystals. 22 Fig. 10 Typical quartz crystal mount. 23 Fig. 11 Quartz crystal oscillator. The block diagram shown is not 2 5 necessarily the one giving optimum performance of the crystal oscillator. Fig. 12. Fundamental and overtone resonance frequencies; example: 26 violin string. (In acoustics, the numbering of the overtones is done differently: their first overtone 'would be our second, their second our third, etc. ) Fig. 13. Frequency stability of the better quartz crystal oscillators. 30 Fig. 14. Spatial state selection. 34 Fig. 15. Optical state selection. 36 Fig. 16. Atom detection. 38 Fig. 17. Optical detection. 39 Fig. 18. Microwave detection. 41 Fig. 19. Atomic frequency standard. 42 Fig. 20. Cesium beam frequency standard. 47 Fig. 21. Frequency stability of commercial cesium beam frequency 48 standards (dashed = performance of improved models in 1971) IV Fig. 22. Rubidium gas cell frequency standard. 51 Fig. 23. Frequency stability of commercial rubidium gas cell frequency 52 standards. Fig. 24. Hydrogen maser oscillator. 55 Fig. 25. Frequency stability of a hydrogen maser oscillator with 56 automatic cavity tuning. LIST OF TABLES 1. Summary and Comparison of Available Frequency Standards 57-60 2. Additional Promising Items Under Investigation 62 FREQUENCY STANDARDS AND CLOCKS: A TUTORIAL INTRODUCTION 1 Helmut Hellwig Atomic Frequency and Time Standards Section National Bureau of Standards Boulder, Colorado 80302 USA The topic of frequency standards and clocks is treated in a tutorial and non -mathematical way. The concepts of time, frequency, frequency stability, and accuracy are introduced. The general physical principles and design features of frequency standards and clopks are described. The design, performance, and limitations of quartz crystal oscillators and atomic devices (cesium, hydrogen, rubidium) are discussed in detail and critically compared for laboratory devices as well as for devices intended for field usage. Key Words: Cesium beam; Clocks (atomic); Crystal oscillator; Frequency accuracy; Frequency stability; Fre- quency standards; Hydrogen maser; Quartz crystal; Rubidium gas cell; Timekeeping. 1. INTRODUCTION Frequency standards and clocks: what do they have in common? A more complete answer will be given later. We note for the moment that most clocks and in particular the very accurate and precise ones are

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