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General Concepts of Time and Frequency Metrology. Michael Lombardi lombardi@nist.gov. NIST Boulder Laboratories. Date and Time-of-Day records when an event happened Time Interval duration between two events Frequency rate of a repetitive event.
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General Concepts of Time and FrequencyMetrology Michael Lombardi lombardi@nist.gov
Date and Time-of-Day records when an event happened Time Interval duration between two events Frequency rate of a repetitive event Types of Time and Frequency Information
Second (s) standard unit for time interval one of 7 base SI units Hertz (Hz) standard unit for frequency (s-1) events per second one of 21 SI units derived from base units Two units of measurement in the International System (SI) apply to time and frequency metrology
The relationship between frequency and time We can measure frequency to get time interval, and vice versa, because the relationship between frequency and time interval is known. Frequency is the reciprocal of time interval: Where T is the period of the signal in seconds, and f is the frequency in hertz. We can also express this as f = s-1(the notation used to define the hertz in the SI).
The period is the reciprocal of the frequency, and vice versa. Period is expressed in units of time. Period
second (s) millisecond (ms), 10-3 s microsecond (s), 10-6 s nanosecond (ns), 10-9 s picosecond (ps), 10-12 s femtosecond (fs), 10-15 s Units of Time Interval
hertz (Hz), 1 event per second kilohertz (kHz), 103 Hz megahertz (MHz), 106 Hz gigahertz (GHz), 109 Hz Units of Frequency
The wavelength is the length of one complete wave cycle. Wavelength is expressed in units of length. wavelength in meters = 300 / frequency in MHz Wavelength
We Use a Wide Range of Frequencies“Everyday” frequencies in time and frequency metrology
A clock is a device that counts cycles of a frequency and records units of time interval, such as seconds, minutes, hours, and days. A clock consists of a frequency source, a counter, and a output device. The frequency source is known as an oscillator. A good example is a wristwatch. Most wristwatches contain an oscillator that generates 32768 cycles per second. After a watch counts 32768 cycles, it can record that one second has elapsed. A oscillator is a device that produces a periodic event that repeats at a nearly constant rate. This rate is called the resonance frequency. Since the best clocks contain the best oscillators, the evolution of timekeeping has been a continual quest to find better and better oscillators. Clocks and Oscillators
Synchronization is the process of setting two or more clocks to the same time. Syntonization is the process of setting two or more oscillators to the same frequency. Synchronization & Syntonization
The performance of time and frequency standards has improved by about 13 orders of magnitude in the past 700 years, and by about 9 orders of magnitude (a factor of a billion) in the past 100 years. Clocks and oscillators keep getting better and better
Quartz Oscillators • Mechanical oscillators that resonate based on the piezoelectric properties of synthetic quartz. • Excellent short term stability, but poor long term accuracy stability due to frequency drift and aging. • Highly sensitive to environmental parameters such as temperature and vibration. • A simple quartz oscillator (like those is a stopwatch) is known as an XO. Test equipment usually contains either a TCXO (temperature controlled quartz oscillator), or an OCXO (oven controlled crystal oscillators). An OCXO offers the best performance.
Rubidium Oscillators • The lowest priced atomic oscillator. • A good laboratory standard. Their long-term accuracy and stability is much better than an OCXO, and they cost much less than a cesium oscillator. • Rubidium oscillators do not always have a guaranteed accuracy specification, but most are accurate to about 5 10-10 after a short warm up. However, their frequency often changes due to aging by parts in 1011 per month, so they will require periodic adjustment to get the best possible accuracy.
Cesium Oscillators • Cesium oscillators are the primary standard for time and frequency measurements and the basis for atomic time, because the second is defined with respect to energy transitions of the cesium atom. • Cesium oscillators are accurate to better than 1 10-12 after a short warm-up period, and have excellent long-term stability. • However, cesium oscillators are expensive (usually $30,000 or more USD), and have relatively high maintenance cost. The cesium beam tube is subject to depletion after a period of 5 to 10 years, and replacement costs are high.
An agreed upon system for keeping time, based on a common definition of the second. Seconds are then counted to form longer time intervals like minutes, hours, days, and years. Time scales serve as a reference for time-of-day, time interval, and frequency. What is a Time Scale?
Pendulums or quartz oscillators were never used to define the second. We went directly from astronomical to atomic time. Before 1956, the second was defined based on the length of the mean solar day. Called the mean solar second. From 1956 to 1967, the second was defined based on a fraction of the tropical year. Called the ephemeris second. Since 1967, the second has been defined based on oscillations of the cesium atom. Called the atomic second, or cesium second. The change to the cesium second in 1967 officially began the era of atomic timekeeping. Prior to 1967, time was kept by astronomical observations. How is the SI second defined?
The duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. => Defined by Markowitz/Hall (USNO) & Essen/Parry (NPL), 1958. => Ratified by the SI in 1967. SI Definition of the Second
UTC is an internationally recognized atomic time scale based on the SI definition of the second. The average value of UTC is computed by the International Bureau of Weights and Measures (BIPM) in France. They collect data from over 250 atomic oscillators located at nearly 60 national metrology institutes. UTC is a paper time scale, computed by the BIPM after the data is collected. Therefore, no one can distribute or broadcast the “real” UTC. Fortunately, national labs like NIST, CENAM, NRC, CENAMEP, and ONRJ maintain real-time versions of UTC that they do distribute and broadcast as a measurement reference. Most of the real-time versions of UTC are usually within 100 nanoseconds of the post processed UTC time scale. Coordinated Universal Time (UTC)
UTC is the Official Reference for Time-Of-Day Clocks synchronized to UTC display the same second (and normally the same minute) all over the world. However, since UTC is used internationally, it ignores local conventions like time zones and daylight saving time (DST). The UTC hour refers to the hour at the Prime Meridian which passes through Greenwich, England. California time, for example, will differ from UTC by either 7 or 8 hours, depending upon whether or not DST is in effect.
UTC is the Official Reference for Time Interval • Time interval is the duration between two events. In time and frequency metrology, it is normally expressed in seconds or sub-seconds (milliseconds, microseconds, nanoseconds, picoseconds). • Since UTC is based on the SI definition of the second, all time interval measurements are referenced to its one second pulses. By counting the pulses, time is kept. • Timing systems are synchronized to UTC by using an On-Time Marker (OTM), consisting of a pulse or signal that coincides as closely as possible with the arrival of the Coordinated Universal Time (UTC) second. The uncertainty of the OTM indicates the time interval between its arrival and the UTC second
UTC is the Official Reference for Frequency • UTC runs at an extremely stable rate with an uncertainty measured in parts in 1015. Therefore, it serves as the international reference for all frequency measurements
Units of measurements SI Base Units Electric Current ampere Luminous Intensity candela Amount of Substance mole Temperature kelvin Length meter Time second Mass kilogram m s kg A K cd mol S Coordinated Time international atomic time TAI K Celsius Temperature 0Celsius 0C cd sr Luminous Flux lumen lm SI Derived Units s-1 Frequency hertz Hz kg m s-2 Force newton N m-2cd sr Illuminance lux lx kg m-1s-2 Pressure pascal Pa S A Electric charge coulomb C kg m2s-2 Energy joule J kg m s-3 Power watt W kg m2s-3A-2 Resistance ohm kg m2s-3 A-1 Electric Potential volt V Non-SI units recognized for use with SI day: 1 d = 86400 s hour: 1 h = 3600 s minute: 1 min = 60 s liter: 1 l = 10-3 m3 ton: 1 t = 103 kg degree: 10 = (/180) rad minute: 1’ = (/10800)rad second: 1” = (/648000)rad electronvolt: 1 eV 1.602177 x 10-19 J unified atomic mass unit: 1 u 1.660540 x 10-27 kg sr: the steradian is the supplementary SI unit of solid angle (dimensionless) rad: the radian is the supplementary SI unit of plane angle (dimensionless) s-1 Activity becquerel Bq kg m2s-2A-1 Magnetic Flux weber Wb kg-1 m2s4 A2 Capacitance farad F m2s-1 Absorbed Dose gray Gy kg m2s-2A-2 Inductance henry H kg-1 m2s3 A2 Conductance siemens S m2s-2 Dose Equivalent sievert Sv kg s-2 A-1 Conductance siemens S Electromagnetic measurement units Health related measurement units
If the kilogram is replaced by a Watt balance, mass would be ultimately defined by the second, like the meter and other units. This would leave only the Kelvin and the amount of substance as base units that do not depend on the second. The second can be measured with more resolution and less uncertainty than any other quantity. NIST can measure the second with an uncertainty of about 4 x 10-16. Time is the ultimate measurement!
Where the SI second is not needed SI Base Units Amount of Substance mole Temperature kelvin Mass kilogram kg K mol K Celsius Temperature 0Celsius 0C SI Derived Units sr: the steradian is the supplementary SI unit of solid angle (dimensionless) rad: the radian is the supplementary SI unit of plane angle (dimensionless) Non-SI units recognized for use with SI ton: 1 t = 103 kg degree: 10 = (/180) rad minute: 1’ = (/10800)rad second: 1” = (/648000)rad unified atomic mass unit: 1 u 1.660540 x 10-27 kg
Where the SI second is not needed SI Base Units Amount of Substance mole Temperature kelvin K mol K Celsius Temperature 0Celsius 0C SI Derived Units sr: the steradian is the supplementary SI unit of solid angle (dimensionless) rad: the radian is the supplementary SI unit of plane angle (dimensionless) Non-SI units recognized for use with SI ton: 1 t = 103 kg degree: 10 = (/180) rad minute: 1’ = (/10800)rad second: 1” = (/648000)rad unified atomic mass unit: 1 u 1.660540 x 10-27 kg
TAI and UTC are both atomic time scales based on the cesium definition of the second. International Atomic Time (TAI) TAI runs at the same frequency as UTC (this frequency is determined by the BIPM), but is not corrected for leap seconds. TAI is seldom used by the general public. It is an “internal” time scale used by the BIPM and national laboratories like NIST. Coordinated Universal Time (UTC) UTC is TAI corrected for leap seconds so that it stays within 0.9 seconds of UT1. Atomic Time Scales
An integer second added to atomic time (UTC) to keep it within 0.9 seconds of the most widely used astronomical time scale (UT1). Leap seconds usually occur on June 30th or December 31st. On average, about 7 are needed every 10 years, suggesting that the long term frequency offset of the Earth is about 2 x 10-8. However, the Earth both speeds up and slows down, making the occurrence of leap seconds cyclical. No leap seconds were needed in 1999 to 2004, but there was a leap second on December 31, 2005. The biggest reason that so many leap seconds have been needed is that the atomic second (cesium) was defined relative to the ephemeris second (which served as the SI second in 1958), and not the mean solar second. Leap Seconds
When a leap second occurs, one minute has 61 seconds. This effectively stops UTC for one second so that UT1 can catch up. The sequence is: 23 hours, 59 minutes, 59 seconds 23 hours, 59 minutes, 60 seconds 0 hours, 0 minutes, 0 seconds Implementation of Leap Seconds
The SI second is central to metrology. It is a truly independent unit which is defined in term of physics without the need for another unit. It is the basis for most other units. Unlike mass, it does not depend on the history of an artifact (Sèvres Grand K is measured once every 40 years or so). The place of time in metrology
Device Under Test (DUT) Can be a tuning fork or a stopwatch or timer Can be a quartz, rubidium, or cesium oscillator Traceable References (transfer standards like WWV, WWVB, LORAN, GPS, or any reference that provides a link back to the SI) Calibration Method (measurement system and procedure used to collect data) Uncertainty Analysis (statistics and data reduction) Four Parts of a Calibration
Calibration Comparison between a reference and a device under test (DUT) that is conducted by collecting measurement data. Calibration results should include a statement of measurement uncertainty, and should establish a traceability chain back to the International System of Units (SI).
