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Time and Frequency from A to Z: A to Al


A440 (sometimes called A4) is the 440 Hz tone that serves as the internationally recognized standard for
musical pitch. A440 is the musical note A above middle C. Since 1939, it has served as the audio
frequency reference for the calibration of pianos, violins, and other musical instruments.

Tuning a piano is an example of a simple frequency calibration that is actually done with the human ear.
The piano tuner listens to a standard musical pitch and compares it to the same note on the piano
keyboard. The piano is then adjusted (by tightening or loosening strings), until it agrees with the audio
standard. What is the smallest frequency offset that a piano tuner can hear? It depends on lots of factors,
including the sound volume, the duration of the tone, the suddenness of the frequency change, and the
musical training of the listener. However, the just noticeable difference is often defined as 5 cents, where 1
cent is 1/100 of the ratio between two adjacent tones on the piano’s keyboard. Since there are 12 tones in
a piano’s octave, the ratio for a frequency change of 1 cent is the 1200th root of 2. Therefore, to raise a
musical pitch by 1 cent, you would multiply by the 1200th root of 2, or 1.000577790. If you do this 5 times
starting with 440 Hz, you’ll see that 5 cents high is about 441.3 Hz, or high in frequency by 1.3 Hz.

NIST (then called the National Bureau of Standards) began broadcasting A440 from radio station WWV in
1936, several years before A440 was officially recognized as an audio frequency standard. The tones can
currently be heard during minute 2 of each hour on WWV, and during minute 1 on WWVH. The 440 Hz tone
is omitted, however, during the first hour of each UTC day.

Accuracy is the degree of conformity of a measured or calculated value to its definition. Accuracy is
related to the offset from an ideal value. In the world of time and frequency, accuracy is used to refer to
the time offset or frequency offset of a device. For example, time offset is the difference between a
measured on-time pulse and an ideal on-time pulse that coincides exactly with UTC. Frequency offset is
the difference between a measured frequency and an ideal frequency with zero uncertainty. This ideal
frequency is called the nominal frequency. The relationship between accuracy and stability is illustrated

In recent years, the term uncertainty has been given preference over accuracy when a quantitative
measure is stated. Accuracy is often used in a qualitative sense. For example, we might say that a time
measurement has an uncertainty of 1 microsecond, and that the accuracy of the measurement is very

Active Frequency Standard
An atomic oscillator, usually a hydrogen maser, whose output signal is derived from the radiation emitted
by the atom. Most commercially available atomic oscillators are passive frequency standards.

A change in frequency with time due to internal changes in an oscillator. Aging is usually a nearly linear
change in the resonance frequency that can be either positive or negative, and occasionally, a reversal in
direction of aging occurs. Aging occurs even when factors external to the oscillator, such as environment
and power supply, are kept constant. Aging has many possible causes, including a buildup of foreign
material on the crystal, changes in the oscillator circuitry, or changes in the quartz material or crystal
structure. A high quality OCXO might age at a rate of < 5 x 10-9 per year, while a TCXO might age 100
times faster.

Allan Deviation
A non-classical statistic used to estimate stability. This statistic is sometimes called the Allan variance, but
since it is the square root of the variance, its proper name is the Allan deviation. The equation for the Allan
deviation is

where yi is a set of frequency offset measurements that consists of individual measurements, y1, y2, y3,
and so on; M is the number of values in the yi series, and the data are equally spaced in segments
seconds long. Or

where xi is a series of phase measurements in time units that consists of individual measurements, x1, x2,
x3, and so on, N is the number of values in the xi series, and the data are equally spaced in segments
seconds long.

A graph of Allan deviation is shown below. It shows the stability of the device improving as the averaging
period ( ) gets longer, since some noise types can be removed by averaging. At some point, however,
more averaging no longer improves the results. This point is called the noise floor, or the point where the
remaining noise consists of nonstationary processes such as aging or random walk. The device in the
graph has a noise floor of about 5 x 10-11 at = 100 s.

The Allan deviation is also used to identify types of oscillator and measurement system noise. The slope of
the Allan deviation line can identify the amount of averaging needed to remove these noise types, as
shown in the graph below. Note that the Allan deviation does not distinguish between white phase noise
and flicker phase noise.

The properties of something that allow it to have more than one possible meaning. For example, if a clock
based on a 12-hour system displays 6 hours and 43 minutes, it could be morning or night. This means the
clock is ambiguous to the hour, since 6 hours can represent two different times of day.

An item which has been well characterized for value, stability, environment, handling, and other conditions
important when used as a standard to transfer or correlate measurement results between laboratories or
within a laboratory.

Atomic Clock
A clock referenced to an atomic oscillator. In the truest sense, only clocks with an internal atomic oscillator
qualify as atomic clocks. However, the term is sometimes used to refer to radio clocks that receive a
signal referenced to an atomic oscillator at a remote location.

Atomic Oscillator
An oscillator that uses the quantized energy levels in atoms or molecules as the source of its resonance.
The laws of quantum mechanics dictate that the energies of a bound system, such as an atom, have
certain discrete values. An electromagnetic field at a particular frequency can boost an atom from one
energy level to a higher one. Or, an atom at a high energy level can drop to a lower level by emitting
energy. The resonance frequency (f) of an atomic oscillator is the difference between the two energy
levels divided by Planck’s constant (h):

The principle underlying the atomic oscillator is that since all atoms of a specific element are identical, they
should produce exactly the same frequency when they absorb or release energy. In theory, the atom is a
perfect “pendulum” whose oscillations are counted to measure time interval. The first atomic oscillator was
developed at NIST (then NBS) in 1949, and is shown in the photo below. Its resonance frequency was
derived from an absorption line in the ammonia molecule. The national frequency standards developed by
NIST derive their resonance frequency from the cesium atom, and use cesium beam or cesium fountain
technology. NIST researchers have used several other atoms to build experimental atomic oscillators,
including mercury and calcium. Rubidium oscillators are the lowest priced and most common atomic
oscillators, but cesium beam and hydrogen maser atomic oscillators are also sold commercially.

Atomic Time Scale (TA)
A time scale based on an atomic definition of the second. Elapsed time is measured by counting cycles of a
frequency locked to an atomic or molecular transition. Atomic time scales differ from the earlier
astronomical time scales, which define the second based on the rotation of the Earth on its axis.
Coordinated Universal Time (UTC) is an atomic time scale, since it defines the second based on the
transitions of the cesium atom.

Automated Computer Time Service (ACTS)
A telephone service operated by the NIST Time and Frequency Division that synchronizes computer clocks
to UTC(NIST). Client computers can connect to the ACTS time servers using an analog modem and an
ordinary telephone line. The phone number is 303-494-4774. For detailed information about the service,
visit the ACTS home page.

The range of frequencies that an electronic signal occupies on a given transmission medium. Any digital or
analog signal has a bandwidth. In digital systems, bandwidth is often expressed as data speed in bits per
second. In analog systems, bandwidth is expressed in terms of the difference between the
highest-frequency signal component and the lowest-frequency signal component. For example, a typical
voice signal on an analog telephone line has a bandwidth of about 3 kHz. An analog television (TV)
broadcast video signal has a bandwidth of 6 MHz, some 2,000 times as wide as the telephone signal. As a
general rule, systems with more bandwidth can carry more information.

Beat Frequency
The frequency produced when two signals are mixed or combined. The beat frequency equals the
difference or offset between the two frequencies. Audible beat frequencies, often called beat notes, are
used for simple frequency calibrations. For example, an amateur radio operator might calibrate a receiver
dial by mixing the incoming signal from WWV with the signal from the receiver’s beat frequency oscillator
(BFO). This produces a beat note that sounds like a low frequency whistle. The receiver is tuned to the
station, and the dial is moved up or down until the whistle completely goes away, a condition known as
zero beat. Usually, headphones are used to listen for zero beat, since the receiver’s speaker might not be
able to produce the low frequency beat note signals. Since a person with average hearing can hear tones
down to 20 or 30 Hz, an audio zero beat can resolve frequency within 2 or 3 parts in 106 at 10 MHz.

The Bureau International des Poids et Mesures (International Bureau of Weights and Measures) located
near Paris, France. The task of the BIPM is to ensure worldwide uniformity of measurements and their
traceability to the International System of Units (SI). The BIPM averages data from about 50 laboratories
(including NIST) to produce a time scale called International Atomic Time (TAI). When corrected for leap
seconds, TAI becomes Coordinated Universal Time (UTC), or the true international time scale. The BIPM
publishes the time offset or difference of each laboratory’s version of UTC relative to the international
average. For example, the BIPM publishes the time offset between UTC and UTC(NIST). The work of the
BIPM makes it possible for NIST and the other laboratories to adjust their standards so that they agree as
closely as possible with the rest of the world. For more information, visit the BIPM web site.

A comparison between a device under test and an established standard, such as UTC(NIST). When the
calibration is finished it should be possible to state the estimated time offset and/or frequency offset of the
device under test with respect to the standard, as well as the measurement uncertainty.

Carrier Frequency
The base frequency of a transmitted electromagnetic pulse or wave on which information can be imposed
by varying the signal strength, varying the base frequency, varying the wave phase, or other means. This
variation is called modulation. If the carrier frequency is derived from a cesium oscillator, the received
signal can be used to calibrate other frequency sources. The table belows lists the carrier frequencies of
several radio transmissions commonly used as frequency standards. In metrology, an unmodulated signal
from an oscillator (such as a 10 MHz sine wave) is also sometimes referred to as a carrier frequency.

Radio Signal Carrier Frequency
60 kHz

100 kHz

2.5, 5, 10, 15, 20 MHz

2.5, 5, 10, 15 MHz

Global Positioning System (GPS)
1575.42 MHz, 1227.6 MHz

Carrier Phase Measurements
A type of calibration that uses the carrier frequency of a radio transmission as a measurement reference.
Carrier phase measurements have been made for many years using low frequency radio signals from
WWVB or LORAN-C. However, the carrier phase measurements with the smallest uncertainties are made
using GPS satellite signals. For more information, visit the GPS carrier-phase measurement page.

Cesium Beam Oscillator
Cesium oscillators can be primary frequency standards since the SI second is defined from the resonance
frequency of the cesium atom (133Cs), which is 9,192,631,770 Hz. A properly working cesium oscillator
should be close to its nominal frequency without adjustment, and there should be no change in frequency
due to aging. However, environmental conditions (motion, vibration, magnetic fields, and so on) do cause
small frequency shifts.

Commercially available oscillators use cesium beam technology. Inside a cesium oscillator, 133Cs atoms
are heated to a gaseous state in an oven. Atoms from the gas leave the oven in a high-velocity beam that
travels through a vacuum tube toward a pair of magnets. The magnets serve as a gate that allows only
atoms of a particular magnetic energy state to pass through a gate into a microwave cavity, where they
are exposed to a microwave frequency derived from a quartz oscillator. If the microwave frequency
matches the resonance frequency of cesium, the cesium atoms change their magnetic energy state.

The atomic beam then passes through another magnetic gate near the end of the tube. Only those atoms
that changed their energy state while passing through the microwave cavity are allowed to proceed to a
detector at the end of the tube. Atoms that did not change state are deflected away from the detector. The
detector produces a feedback signal that continually tunes the quartz oscillator in a way that maximizes
the number of state changes so that the greatest number of atoms reaches the detector. Standard output
frequencies are derived from the locked quartz oscillator as shown in the figure.

The Q of a commercial cesium standard is a few parts in 108. The beam tube is typically less than 0.5 m in
length, and the atoms travel at velocities of greater than 100 meters per second inside the tube. This limits
the observation time to a few milliseconds, and the resonance width to a few hundred hertz. Stability is
typically 5 x 10-12, and reaches a noise floor near 1 x 10-14 at about one day, extending out to weeks or
months. The frequency offset is typically near 1 x 10-12 after a warm-up period of 30 minutes.

Cesium Fountain Oscillator
The current state-of-the-art in cesium oscillator technology, the cesium fountain oscillator is named after
its fountain-like movement of cesium atoms. A cesium fountain named NIST-F1 serves as the primary
standard of time interval and frequency for the United States.

A cesium fountain works by releasing a gas of cesium atoms into a vacuum chamber. Six infrared laser
beams are directed at right angles to each other at the center of the chamber. The lasers gently push the
cesium atoms together into a ball. In the process of creating this ball, the lasers slow down the movement
of the atoms and cool them to temperatures a few millionths of a degree above absolute zero. This
reduces their thermal velocity to a few centimeters per second.

Vertical laser beams gently toss the ball upward and then all of the lasers are turned off. This little push is
just enough to loft the ball about a meter high through a microwave-filled cavity. Under the influence of
gravity, the ball then stops and falls back down through the microwave cavity. The round trip up and down
through the microwave cavity lasts for about 1 second, and is limited only by the force of gravity pulling
the atoms downward. During the trip, the atomic states of the atoms might or might not be altered as they
interact with the microwave signal. When their trip is finished, another laser is pointed at the atoms. Those
atoms whose states were altered by the microwave signal emit photons (a state known as fluorescence)
that are counted by a detector. This process is repeated many times while the microwave signal in the
cavity is tuned to different frequencies. Eventually, a microwave frequency is found that alters the states
of most of the cesium atoms and maximizes their fluorescence. This frequency is the cesium resonance.

The Q of a cesium fountain is about 1010, or about 100 times higher than a traditional cesium beam.
Although the resonance frequency is the same, the resonance width is much narrower (< 1 Hz), due to the
longer observation times made possible by the combination of laser cooling and the fountain design. The
combined frequency uncertainty of NIST-F1 is estimated as less than 1 x 10-15.

An extended test of the performance characteristics of a clock or oscillator. A characterization is more
involved than a calibration. The device under test is usually measured for a long period of time (days or
weeks), and sometimes a series of measurements is made under different environmental conditions. A
characterization is often used to determine the types of noise that limit the uncertainty of the
measurement, and the sensitivity of the device to environmental changes.

A device that generates periodic, accurately spaced signals used for timing applications. A clock consists of
at least three parts: an oscillator, a device that counts the oscillations and converts them to units of time
interval (such as seconds, minutes, hours, and days), and a means of displaying or recording the results.

A measurement technique used to compare two clocks or oscillators at remote locations. The
common-view method involves a single reference transmitter (R) and two receivers (A and B). The
transmitter is in common view of both receivers. Both receivers compare the simultaneously received
signal to their local clock and record the data. Receiver A receives the signal over the path dra and
compares the reference to its local clock (R - Clock A). Receiver B receives the signal over the path drb
and records (R - Clock B). The two receivers then exchange and difference the data as shown in the

Common-view directly compares two clocks or oscillators to each other. Errors from the two paths dra and
drb ) that are common to the reference cancel out, and the uncertainty caused by path delay is nearly
eliminated. The result of the measurement is (Clock A - Clock B) - (dra - drb ).

Common-view measurements were made for many years using land based transmitters as the reference.
Today, nearly all common-view measurements use a GPS satellite as the reference transmitter, as
illustrated below. This enables clocks to be compared over transcontinental distances, with uncertainties of
just a few nanoseconds.

Coordinated Universal Time (UTC)
The international atomic time scale that serves as the basis for timekeeping for most of the world. UTC is
a 24-hour timekeeping system. The hours, minutes, and seconds expressed by UTC represent the
time-of-day at the Earth's prime meridian (0° longitude) located near Greenwich, England.

UTC is calculated by the Bureau International des Poids et Measures (BIPM) in Sevres, France. The BIPM
averages data collected from more than 200 atomic time and frequency standards located at about 50
laboratories, including the National Institute of Standards and Technology (NIST). As a result of this
averaging, the BIPM generates two time scales, International Atomic Time (TAI), and Coordinated
Universal Time (UTC). These time scales realize the SI second as closely as possible.

UTC runs at the same frequency as TAI. However, it differs from TAI by an integral number of seconds.
This difference increases when leap seconds occur. When necessary, leap seconds are added to UTC on
either June 30 or December 31. The purpose of adding leap seconds is to keep atomic time (UTC) within
±0.9 s of an older time scale called UT1, which is based on the rotational rate of the Earth. Leap seconds
have been added to UTC at a rate averaging about 8 every 10 years, beginning in 1972.

Keep in mind that the BIPM maintains TAI and UTC as “paper” time scales. The major metrology
laboratories use the published data from the BIPM to steer their clocks and oscillators and generate
real-time versions of UTC, such as UTC(NIST). You can think of UTC as the ultimate standard for
time-of-day, time interval, and frequency. Clocks synchronized to UTC display the same hour, minute, and
second all over the world (and remain within one second of UT1). Oscillators syntonized to UTC generate
signals that serve as reference standards for time interval and frequency.

Cycle Slip
A change in the signal tracking point of a carrier frequency that occurs during a measurement. Cycle slips
introduce phase shifts equal (in time units) to the period of the carrier frequency, or to a multiple of its
period. For example, if a WWVB receiver changes its signal tracking point during a measurement, a phase
shift equal to a multiple of 16.67 microseconds (the period of 60 kHz) will result. Most cycle slips are
caused by a temporary loss of lock due to a weak or noisy signal.

A number or series of numbers used to identify a given day with the least possible ambiguity. The date is
usually expressed as the month, day of month, and year. However, integer numbers such as the Julian
Date are also used to express the date.

Daylight Saving Time
The part of the year when clocks are advanced by one hour, effectively moving an hour of daylight from
the morning to the evening. Daylight Saving Time begins in the United States at 2 a.m. on the first Sunday
of April. Time reverts to standard time at 2 a.m. on the last Sunday of October. In the European Union, it
starts at 1 am the last Sunday in March, and ends the last Sunday in October.

Daylight Saving Time, for the U.S. and its territories, is not observed in Hawaii, American Samoa, Guam,
Puerto Rico, the Virgin Islands, the Eastern Time Zone portion of the State of Indiana, and the state of
Arizona (not including the Navajo Indian Reservation, which does observe). For more information, visit the
exhibit on daylight saving time.

Daytime Protocol
A time code protocol used to distribute time over the Internet. The daytime protocol is described in the
RFC-867 document, and is implemented by the NIST Internet Time Service.

Dead Time
The time that elapses between the end of one measurement and the start of the next measurement. This
time interval is generally called dead time only if information is lost. For example, when making
measurements with a time interval counter, the minimum amount of dead time is the elapsed time from
when a stop pulse is received to the arrival of the next start pulse. If a counter is fast enough to measure
every pulse (if it can sample at a rate of 1 kHz, for instance, and the input signals are at 100 Hz), we can
say there is no dead time between measurements.

Disciplined Oscillator (DO)
An oscillator whose output frequency is continuously steered (often through the use of a phase locked
loop) to agree with an external reference. For example, a GPS disciplined oscillator (GPSDO) usually
consists of a quartz or rubidium oscillator whose output frequency is continuously steered to agree with
signals broadcast by the GPS satellites.

Doppler Shift
The apparent change of frequency caused by the motion of the frequency source (transmitter) relative to
the destination (receiver). If the distance between the transmitter and receiver is increasing the frequency
apparently decreases. If the distance between the transmitter and receiver is decreasing, the frequency
apparently increases. To illustrate this, listen to the sound of a train whistle as a train comes closer to you
(the pitch gets higher), or as it moves further away (the pitch gets lower). As you do so, keep in mind that
the frequency of the sound produced at the source has not changed.

Drift (frequency)
The linear (first order) component of a systematic change in frequency of an oscillator over time. Drift is
caused by aging, by changes in the environment, and by other factors external to the oscillator.

The current difference between UTC and to the astronomical time scale UT1. It is always a number ranging
from -0.8 to +0.8 seconds, with a resolution of 0.1 seconds. This number is broadcast by WWV, WWVH,
WWVB, GOES, and ACTS, and can be added to UTC to obtain UT1. The current DUT1 correction is
available here.

A group of clocks or oscillators whose outputs are averaged to create a time scale. Typically, the relative
value of each clock is weighted, so that the best clocks contribute the most to the average. NIST uses an
ensemble of clocks to produce UTC(NIST).

Ephemeris Time (ET)
An obsolete time scale based on the ephemeris second, which served as the SI second from 1956 to 1967.
The ephemeris second was a fraction of the tropical year, or the interval between the annual vernal
equinoxes, which occur on or about March 21. The tropical year was defined as 31,556,925.9747
ephemeris seconds. Determining the precise instant of the equinox is difficult, and this limited the
uncertainty of Ephemeris Time (ET) to +/- 50 ms over a 9-year interval. ET was used mainly by
astronomers, and was replaced by Terrestial Time (TT) in 1984.

The beginning of an era (or event) or the reference date for a system of measurements.

Femtosecond (fs)
One quadrillionth of a second (10-15 s).

Flicker Noise
A type of low frequency noise where the power spectral density is inversely proportional to the frequency.
For this reason, it is sometimes referred to as 1/f noise.

The rate of a repetitive event. If T is the period of a repetitive event, then the frequency f is its reciprocal,
1/T. Conversely, the period is the reciprocal of the frequency, T = 1/f. Since the period is a time interval
expressed in seconds (s), it is easy to see the close relationship between time interval and frequency. The
standard unit for frequency is the hertz (Hz), defined as the number of events or cycles per second. The
frequency of electrical signals is often measured in multiples of hertz, including kilohertz (kHz), megahertz
(MHz), or gigahertz (GHz).

Frequency Accuracy
The degree of conformity of a measured or calculated frequency to its definition. Since accuracy is related
to the offset from an ideal value, frequency accuracy is usually stated in terms of the frequency offset.

Frequency Counter
An electronic instrument or circuit that displays the frequency of an incoming signal. The frequency is
determined by comparing the signal to the counter's time base oscillator. Some frequency counters (often
called "universal counters") measure other parameters in addition to frequency, such as time interval and

Frequency Divider
An electronic instrument or circuit that converts an incoming signal to a lower frequency by removing a
fixed number of cycles or pulses from the signal. For example, a circuit that divides by 1000 could accept
a 1 MHz signal as an input, and produce a 1 kHz signal as an output. Dividers are commonly used to
convert the standard output of a frequency standard (often 5 or 10 MHz) to a 1 Hz signal that can be
synchronized to UTC for timing applications.

Frequency Domain
The measurement domain where voltage and power are measured as functions of frequency. A spectrum
analyzer is often used to analyze signals in the frequency domain. It does so by separating signals into
their frequency components and displaying the power level at each frequency. An ideal sine wave (perfect
frequency) appears as a spectral line of zero bandwidth in the frequency domain. Real sine wave outputs
are always noisy, so the spectral lines have a finite bandwidth, as shown in the graphic. Noise is usually
present over a wide band of frequencies. The total power (or voltage) measured by a spectrum analyzer
depends on the bandwidth used.

Frequency Drift
An undesired progressive change in frequency with time. Frequency drift can be caused by component
aging and environmental changes. Frequency drift may be in either direction (higher or lower frequency)
and is not necessarily linear.

Frequency Mixer
An electronic instrument or circuit that accepts two input signals at two different frequencies, and produces
an output frequency (called the beat frequency or difference frequency) equal to the difference of the two
inputs. Frequency mixers are commonly employed in frequency measurement systems (as shown in the
graphic below), to convert a high frequency to a low frequency, and to obtain more measurement
resolution. For example, a 5 MHz signal might be mixed with a 5,000,010 Hz signal. Measuring the 10 Hz
beat frequency with a frequency counter (as opposed to the 5 MHz) allows the detection of smaller
frequency changes.

Frequency Multiplier
An electronic instrument or circuit that converts an incoming signal to a higher frequency by adding a fixed
multiple of cycles or pulses to the signal. For example, a circuit that multiplies by 10 could accept a 1 MHz
signal as an input, and produce a 10 MHz signal as an output.

Frequency Offset
The difference between a measured frequency and an ideal frequency with zero uncertainty. This ideal
frequency is called the nominal frequency.

Frequency offset can be measured in either the frequency domain or the time domain. A simple frequency
domain measurement involves directly counting and displaying the output frequency of the device under
test with a frequency counter. The frequency offset is calculated as:

where fmeasured is the reading from the frequency counter, and fnominal is the specified output
frequency of the device under test.

Frequency offset measurements in the time domain involve measuring the time difference between the
device under test and the reference. The time interval measurements can be made with an oscilloscope or
a time interval counter. If at least two time interval measurements are made, we can estimate frequency
offset as follows:

where is the difference between time interval measurements (phase difference), and T is the
measurement period.

Frequency offset values are usually expressed as dimensionless numbers such as 1 x 10-10, since the
quantities being measured are typically quite small. Using dimensionless values does not require
knowledge of the nominal frequency. However, they can be converted to units of frequency (Hz) if the
nominal frequency is known. To illustrate this, consider a device with a nominal frequency of 5 MHz and a
frequency offset of +1.16 x 10-11. To find the frequency offset in hertz, multiply the nominal frequency by
the offset:

(5 x 106) (+1.16 x 10-11) = 5.80 x 10-5 = +0.0000580 Hz
Then, add the frequency offset to the nominal frequency to get the actual frequency:

5,000,000 Hz + 0.0000580 Hz = 5,000,000.0000580 Hz

Frequency Shift
A sudden change in the frequency of a signal.

Frequency Stability
The degree to which an oscillating signal produces the same frequency for a specified interval of time. It is
important to note the time interval; some devices have good short-term stability, others have good
long-term stability. Stability doesn't tell us whether the frequency of a signal is right or wrong, it only
indicates whether that frequency stays the same. The graphic below shows two oscillating sine waves: one
stable, the other unstable.

Frequency Standard
An oscillator (usually an atomic oscillator) that is used as a reference source for frequency measurements.
The current frequency standard for the United States is a cesium fountain oscillator named NIST-F1.

Frequency Synthesizer
An electronic device or circuit that can produce a wide range of user selectable output frequencies. In
order to produce a wide range of frequencies, frequency synthesizers typically contain several
components, including frequency dividers, frequency multipliers, and phase locked loops.

Gigahertz (GHz)
One billion cycles per second (109 Hz).

Global Positioning System (GPS)
A constellation of satellites controlled and operated by the United States Department of Defense (USDOD).
The constellation includes at least 24 satellites that orbit the Earth at a height of 20,200 km in six fixed
planes inclined 55° from the equator. The orbital period is 11 h 58 m, which means that a satellite will orbit
the earth twice per day. By processing signals received from the satellites, a GPS receiver can determine
its own position with an uncertainty of < 10 m.

The GPS satellites broadcast on two carrier frequencies: L1, at 1575.42 MHz, and L2, at 1227.6 MHz. Each
satellite broadcasts a spread-spectrum waveform, called a pseudo-random noise (PRN) code on L1 and L2,
and each satellite is identified by the PRN code it transmits. There are two types of PRN codes. The first
type is a coarse acquisition (C/A) code with a chip rate of 1023 chips per millisecond. The second type is a
precision (P) code with a chip rate of 10230 chips per millisecond. The C/A code is broadcast on L1, and
the P code is broadcast on both L1 and L2. GPS reception is line-of-sight, which means that the antenna
must have a clear view of the sky. The signals can be received nearly anywhere on Earth where a clear
sky view is available.

The primary purpose of GPS is to serve as a radionavigation system, but it has also become perhaps the
dominant system for the distribution of time and frequency. Each satellite carries either rubidium or
cesium oscillators, or a combination of both. The on-board oscillators provide the reference for both the
carrier and code broadcasts. They are steered from USDOD ground stations and are referenced to
Coordinated Universal Time (UTC) maintained by the United States Naval Observatory (USNO). By mutual
agreement UTC(USNO) and UTC(NIST) are maintained within 100 ns of each other, and the frequency
difference between the two time scales is < 1 x 10-13.

There are several types of time and frequency measurements that involve GPS, including one-way,
common-view, and carrier-phase measurements. To view one-way GPS data received at Boulder and
compared to UTC(NIST), please visit the GPS data archive.

The Global Navigation Satellite System operated by the Soviet Federation as a space-based navigation
system. GLONASS is similar in some ways to GPS, and is sometimes used as a reference or common-view
source for time and frequency measurements. The GLONASS satellites use two frequency bands:
1602.5625 to 1615.5 MHz and 1240 to 1260 MHz. The satellites carry on-board cesium oscillators.

An acronym for the Geostationary Operational Environmental Satellites operated by the National Oceanic
and Atmospheric Agency (NOAA). These satellites were used to broadcast a NIST time code from 1974
until December 31, 2004, when the service was discontinued.

Greenwich Mean Time (GMT)
A 24-hour time keeping system whose hours, minutes, and seconds represent the time-of-day at the
Earth's prime meridian (0° longitude) located near Greenwich, England. Technically speaking, GMT no
longer exists, since it was replaced by other astronomical time scales many years ago, and those
astronomical times scales were subsequently replaced by the atomic time scale UTC. However, the term
GMT is still incorrectly used by the general public. When heard today, it should be considered as a
synonym for UTC.

In radio transmission, a wave that propagates close to the surface of the Earth. Groundwave propagation
is a characteristic of low frequency (LF) radio signals. Since the propagation or path delay of a
groundwave signal remains relatively constant, LF signals tend to be a better time and frequency
reference than high frequency (HF) signals, which are often dominated by skywave.

The standard unit of frequency, equivalent to one event, or cycle per second. The abbreviation for hertz is

A technique that generates new frequencies by mixing two or more signals together. For example, a
superheterodyne radio receiver converts any selected incoming radio frequency by heterodyne action to a
common intermediate frequency (such as the 455 kHz frequency used by many AM radios). The
heterodyne technique is also used to increase the resolution of some time and frequency measurement
systems, by converting the incoming signal from the device under test to a lower frequency.

High Frequency (HF)
The part of the radio spectrum ranging from 3 to 30 MHz, commonly known as shortwave. The carrier
frequencies of 5, 10, and 15 MHz within this spectrum are internationally allocated for time and frequency
broadcasts, and are used by a number of stations, including NIST radio stations WWV and WWVH.

Hydrogen Maser
The hydrogen maser is the most elaborate and expensive commercially available frequency standard. The
word maser is an acronym that stands for microwave amplification by stimulated emission of radiation.
Masers operate at the resonance frequency of the hydrogen atom, which is 1,420,405,752 Hz.

A hydrogen maser works by sending hydrogen gas through a magnetic gate that only allows atoms in
certain energy states to pass through. The atoms that make it through the gate enter a storage bulb
surrounded by a tuned, resonant cavity. Once inside the bulb, some atoms drop to a lower energy level,
releasing photons of microwave frequency. These photons stimulate other atoms to drop their energy
level, and they in turn release additional photons. In this manner, a self-sustaining microwave field builds
up in the bulb. The tuned cavity around the bulb helps to redirect photons back into the system to keep the
oscillation going. The result is a microwave signal that is locked to the resonance frequency of the
hydrogen atom and that is continually emitted as long as new atoms are fed into the system. This signal
keeps a quartz oscillator in step with the resonance frequency of hydrogen, as shown in the figure.

The resonance frequency of hydrogen is much lower than that of cesium, but the resonance width of a
hydrogen maser is usually just a few hertz. Therefore, the Q is about 109, or at least one order of
magnitude better than that of a commercial cesium standard. As a result, the short-term stability is better
than that of a cesium standard for periods out to a few days - typically < 1 x 10-12 and reaching a noise
floor of appoximately 1 x 10-15 after about 1 day. However, when measured for more than a few days or
weeks, a hydrogen maser might fall below a cesium oscillator’s performance. The stability decreases
because of changes in the cavity’s resonance frequency over time.

International Atomic Time (TAI)
A time scale maintained internally by the the BIPM, but seldom used by the general public. TAI realizes the
SI second as closely as possible, and runs at the same frequency as Coordinated Universal Time (UTC).
However, TAI differs from UTC by an integral number of seconds. This difference increases when leap
seconds occur.

International Date Line
The line on the Earth, generally located at 180° longitude, that separates two consecutive calendar days.
The date in the Eastern hemisphere, to the left of the line, is always one day ahead of the date in the
Western hemisphere. The International Date Line passes through an area covered mainly by empty ocean,
and most of the line is located exactly halfway around the world from the prime meridian (0° longitude)
that passes near Greenwich, England. However, there are a few zigs and zags in the date line to allow for
local circumstances.

Internet Time Service (ITS)
A popular NIST service that allows client computers to synchronize their clock via the Internet to
UTC(NIST). The service responds to time requests from any Internet client by sending time codes in
several formats defined by the Daytime, Time, and NTP protocols. The ITS handles hundreds of millions of
timing requests every day. For more information, visit the ITS home page.

Intrinsic Standard
A standard (such as a frequency standard) based on an inherent physical constant or an inherent or
sufficiently stable physical property. Technically, all atomic oscillators are intrinsic standards. In practice,
however, only cesium oscillators are considered as intrinsic time and frequency standards, because the SI
definition of the second is based on a physical property of cesium.

Ion Trap
A device that allows ions to be trapped for long periods of time, during which the ions can be interrogated
and their state changes observed. Since the ions are nearly motionless during the observation period, an
ion trap can provide the basis for highly stable and accurate atomic oscillators that should eventually
replace today's frequency standards. For more information, visit the Ion Storage Group web site.

IRIG Time Codes
The time codes originally developed by the Inter-Range Instrumentation Group (IRIG), now used in
government, military and commercial fields. There are many formats and several modulation schemes,
but they are typically amplitude modulated on an audio sine wave carrier. The most common version is
probably IRIG-B, which sends day of year, hour, minute, and second data on a 1 kHz carrier frequency,
with an update rate of once per second.

The abrupt and unwanted variations of one or more signal characteristics, such as the interval between
successive pulses, the amplitude of successive cycles, or the frequency or phase of successive cycles.
Although widely used in fields such as telecommunications, the term jitter is seldom used in time and
frequency metrology, since terms such as phase noise are more descriptive.

Julian Day or Julian Date (JD)
An integer day number obtained by counting days from the starting point of noon on 1 January 4713 B.C.
(Julian Day zero). One way of telling what day it is with the least possible ambiguity. The Modified Julian
Date (MJD) has a starting point of midnight on November 17, 1858. You can obtain the MJD by subtracting
exactly 2 400 000.5 days from the JD.

Kilohertz (kHz)
One thousand cycles per second (103 Hz).

Laser Cooling
A technique that uses laser beams to slow down the motion of atoms and cool them to temperatures a few
millionths of a degree above absolute zero. This technique is used to improve the performance of NIST-F1
and other standards, since it increases the interrogation and observation time of the atoms. For more
information, visit the Ion Storage Group web site.

Leap Day
The extra day added to a year to make it have 366 days. Leap days are added on February 29th during
leap years.

Leap Second
A second added to Coordinated Universal Time (UTC) to make it agree with astronomical time to within 0.9
second. UTC is an atomic time scale, based on the performance of atomic clocks. Astronomical time is
based on the rotational rate of the Earth. Since atomic clocks are more stable than the rate at which the
Earth rotates, leap seconds are needed to keep the two time scales in agreement.

The first leap second was added on June 30, 1972. Since then, leap seconds have occurred at an average
rate of less than one per year. Leap seconds are announced at least several months in advance and are
implemented on either June 30th or December 31st. Although it is possible to have a negative leap second
(a second removed from UTC), so far all leap seconds have been positive (a second has been added to
UTC). Based on what we know about the Earth's rotation, it is unlikely that we will ever have a negative
leap second. For more information and a table of leap seconds, visit the NIST Time Scale Data Archive.

Leap Year
Leap years are years with 366 days, instead of the usual 365. Leap years are necessary because the
actual length of a year is about 365.242 days, not 365 days, as commonly stated. Basically, leap years
occur every 4 years, and years that are evenly divisible by 4 (2004, for example) have 366 days. This
extra day is added to the calendar on February 29th.

However, there is one exception to the leap year rule involving century years, such as the year 1900.
Since the year is slightly less than 365.25 days long, adding an extra day every 4 years results in about 3
extra days being added over a period of 400 years. For this reason, only 1 out of every 4 century years is
considered as a leap year. Century years are considered as leap years only if they are evenly divisible by
400. Therefore, 1700, 1800, 1900 were not leap years, and 2100 will not be a leap year. But 1600 and
2000 were leap years, because those year numbers are evenly divisible by 400.

Line Width
Another name for resonance width. The term line width is generally used to refer to the resonance width of
an atomic oscillator.

Long-Term Stability
The stability of a time or frequency signal over a long measurement interval, usually of at least 100
seconds. In most cases, long-term stability is used to refer to measurement intervals of more than one

A ground based radionavigation system that operates in the LF radio spectrum at a carrier frequency of
100 kHz, with a bandwidth from 90 to 110 kHz. LORAN-C broadcasts are referenced to cesium oscillators
and are widely used as a standard for frequency calibrations. It is also possible to synchronize a LORAN-C
receiver so that it produces an on-time UTC pulse. However, the broadcast does not contain a time code,
so time-of-day cannot be recovered using LORAN-C. NIST continuosly monitors the broadcasts from three
LORAN-C stations and publishes the results in the LORAN-C data archive.

Low Frequency (LF)
The part of the radio spectrum ranging from 30 to 300 kHz. A number of standard time and frequency
signals are broadcast in this region, including the 60 kHz signal from NIST Radio Station WWVB, and the
100 kHz LORAN-C signals.

An acronym that stands for Microwave Amplification by Stimulated Emission of Radiation. In the field of
time and frequency, the term is generally associated with the hydrogen maser.

Maximum Time Interval Error (MTIE)
A statistical test used to measure the largest peak-to-peak variation in a digital signal. MTIE can help
detect sudden frequency or phase changes that cause data loss on a communications channel.

Megahertz (MHz)
One million cycles per second (106 Hz).

An acronym for Microcomputer-Compensated Crystal Oscillator. An MCXO is a quartz oscillator that uses
digital techniques to observe the frequency drift, and compensates for this drift through digital-to-analog
conversion to a tuning port in the circuit. The stability of a MCXO is generally better than that of a TCXO,
but worse than that of an OCXO.

Mean Solar Time
An astronomical time scale that is based on the average length of the day, called the mean solar day. The
length of an average day is different from a true or apparent solar day, due to daily variations, over the
span of a year, in the Sun's apparent angular speed across the sky when viewed by an observer on Earth.
For example, in a true apparent solar time scale, noon is the instant when the Sun transits the local
meridian and reaches its highest point in the sky. However, the Sun is at this point at a different time each
day, varying over the course of a year from 14.2 minutes ahead of noon to 16.3 minutes behind it. Thus,
the length of an average or mean solar day is used for a more uniform system of timekeeping.

One millionth of a second (10-6 s).

Millisecond (ms)
One thousandth of a second (10-3 s).

Modified Allan Deviation (MDEV)
A modified version of the Allan deviation statistic, which has the advantage of being able to distinguish
between white and flicker phase noise. This makes it more suitable for estimating short-term stability than
the normal Allan Deviation.

Nanosecond (ns)
One billionth of a second (10-9 s).

Network Time Protocol (NTP)
A standard protocol used to send a time code over the Internet. The Network Time Protocol (NTP) was
created at the University of Delaware, and is defined by the RFC-1305 document. The 64-bit time code
contains the time in UTC seconds since January 1, 1900 with a resolution of 200 picoseconds. The NTP
format is supported by the NIST Internet Time Service.

Nominal Frequency
An ideal frequency with zero uncertainty. The nominal frequency is the frequency labeled on an oscillator's
output. For this reason, it is sometimes called the nameplate frequency. For example, an oscillator whose
nameplate or label reads 5 MHz has a nominal frequency of 5 MHz. The difference between the nominal
frequency and the actual output frequency of the oscillator is the frequency offset.

The interval between two frequencies having a ratio of 2 to 1. Starting from a fundamental frequency, one
octave higher is twice that frequency; one octave lower is half that frequency. The concept of an octave is
most widely known and most easily illustrated with musical notes. For example, a piano keyboard has a
range of over seven octaves from the lowest frequency to the highest frequency note. There are eight
keys on a piano that play the musical note A. Each musical note A has a frequency twice as high as the
note in the previous octave, as shown in the table.

Musical Note Frequency (Hz)








An acronymn for Oven Controlled Crystal Oscillator. A type of quartz oscillator design that reduces
environmental problems by enclosing the crystal in a temperature-controlled chamber called an oven.
When an OCXO is turned on, it goes through a "warm-up" period while the temperatures of the crystal
resonator and its oven stabilize. During this time, the performance of the oscillator continuously changes
until it reaches its normal operating temperature. The temperature within the oven then remains constant,
even when the outside temperature varies.

Since the environment is carefully controlled, OCXOs have excellent short-term stability. A typical OCXO
might be stable to 1 x 10-12. The limitations in short-term stability are mainly due to noise from electronic
components in the oscillator circuits. Long term stability is limited by aging.

One Way Time and Frequency Transfer
A measurement technique used to transfer time and frequency information from one location to another.
As shown in the figure, the reference source, A, simply sends a time signal to the user, B, through a
transmission medium.

The delay, d, over a transmission path is at least 3.3 microseconds per kilometer. If high accuracy time
transfer is desired in a one-way system the physical locations (coordinates) of the two clocks must be
known so that the path delay can be calculated. For frequency transfer, only the variability of the delay
(the path stability) is important. For a more detailed description, please visit the One-Way GPS Time
Transfer page.

On Time Marker (OTM)
The part of a time code that is synchronized (at the time of transmission) to the UTC second.

Optical Frequency Standard
A frequency standard based on the optical transitions in ions and neutral atoms. These standards have a
much higher resonance frequency than atomic oscillators based on microwave transitions, a much higher
Q, and potentially a much higher stability. Although optical frequency standards are currently used for
experimental purposes only, the research being conducted in this area could lead to the next generation of
atomic oscillators. For information about current research, visit the NIST Optical Frequency Measurements
Group web site.

An electronic device used to generate an oscillating signal. The oscillation is based on a periodic event that
repeats at a constant rate. The device that controls this event is called a resonator. The resonator needs
an energy source so it can sustain oscillation. Taken together, the energy source and resonator form an
oscillator. Although many simple types of oscillators (both mechanical and electronic) exist, the two types
of oscillators primary used for time and frequency measurements are quartz oscillators and atomic

Overtone Frequency
A multiple of the fundamental resonance frequency of a quartz oscillator that is used as the oscillator's
output frequency. Most high stability quartz oscillators output either the third or fifth overtone frequency to
achieve a high Q. Overtones higher than fifth are rarely used because they make it harder to tune the
device to the desired frequency.

Passive Frequency Standard
An atomic oscillator whose output signal is derived from an oscillator frequency locked to the atomic
resonance frequency, instead of being directly output by the atoms. Unlike active frequency standards, the
cavity where the atomic transitions take place does not sustain self-oscillation. Most commercially
available atomic oscillators are passive frequency standards.

Path Delay
The signal delay between a transmitter and a receiver. Path delay is often the largest contributor to time
transfer uncertainty. For example, consider a radio signal broadcast over a 1000 km path. Since radio
signals travel at the speed of light (with a delay of about 3.3 microseconds/km), we can calibrate the 1000
km path by estimating the path delay as 3.3 ms, and applying a 3.3 ms correction to our measurement.
The more sophisticated time transfer systems are self-calibrating, and automatically correct for path
delay. Path delay is not important to frequency transfer systems, since on-time pulses are not required.
However, variations in path delay do limit the frequency uncertainty.

The period T is the reciprocal of a frequency, T = 1/f. The period of a waveform is the time required for
one complete cycle of the wave to occur. The relationship between period, frequency, and amplitude for a
sine wave is illustrated in the graphic below. In time and frequency metrology knowing the period of a
frequency is necessary, since it helps to identify when cycle slips occur.


The position of a point in time (instant) on a waveform cycle. A complete cycle is defined as the interval
required for the waveform to reattain its arbitrary initial value. The graphic above shows how 1 cycle
constitutes 360° of phase. The graphic also shows how phase is sometimes expressed in radians, where
one radian of phase equals approximately 57.3°. Phase can also be an expression of relative displacement
between two corresponding features (for example, peaks or zero crossings) of two waveforms having the
same frequency.

When comparing two waveforms, their phase difference or phase angle, is typically expressed in degrees
as a number greater than -180°, and less than or equal to +180°. Leading phase refers to a wave that
occurs "ahead" of another wave of the same frequency. Lagging phase refers to a wave that occurs
"behind" another wave of the same frequency. When two waves differ in phase by -90° or +90°, they are
said to be in phase quadrature. When two waves differ in phase by 180° (-180° is technically the same as
+180°), they are said to be in phase opposition.

In time and frequency metrology, the phase difference is usually stated in units of time, rather than in
units of phase angle. The time interval for 1° of phase is inversely proportional to the frequency. If the
frequency of a signal is given by f, then the time tdeg (in seconds) corresponding to 1° of phase is:

tdeg = 1 / (360f) = T / 360
Therefore, a 1° phase shift on a 5 MHz signal corresponds to a time shift of 555 picoseconds. This same
answer can be obtained by taking the period of 5 MHz (200 nanoseconds) and dividing by 360.

Phase Comparison

A comparison of the phase of two waveforms, usually of the same nominal frequency. In time and
frequency metrology, the purpose of a phase comparison is generally to determine the frequency offset of
a device under test (DUT) with respect to a reference.

A phase comparison can be made by connecting two signals to a two-channel oscilloscope. The
oscilloscope will display two sine waves, as shown in the graphic. The top sine wave is the test frequency,
and the bottom sine wave represents a signal from the reference. If the two frequencies were exactly the
same, their phase relationship would not change and both would appear to be stationary on the
oscilloscope display. Since the two frequencies are not exactly the same, the reference appears to be
stationary and the test signal moves. By measuring the rate of motion of the test signal we can determine
its frequency offset. Vertical lines have been drawn through the points where each sine wave passes
through zero. The bottom of the figure shows bars whose width represents the phase difference between
the signals. In this case the phase difference is increasing, indicating that the test signal is lower in
frequency than the reference.

Phase Locked Loop (PLL)
An electronic circuit with a voltage- or current-driven oscillator that is constantly adjusted to match in
phase (and thus lock on) the frequency of an input signal. A PLL has many applications in time and
frequency. It can be used to generate a signal, modulate or demodulate a signal, reconstitute a signal with
less noise, or multiply or divide a frequency.

A typical PLL consists of a voltage-controlled oscillator (VCO) that is tuned using a varactor. The VCO is
initially tuned to a frequency close to the desired frequency. A circuit called a phase comparator causes
the VCO to seek and lock onto a reference frequency. This works by means of a feedback scheme. If the
VCO frequency departs from the reference frequency, the phase comparator produces an error voltage
that is applied to the varactor, bringing the VCO frequency back into agreement with the reference

Phase Noise
The rapid, short-term, random fluctuations in the phase of a wave. To a large extent, phase noise can be
removed by averaging. The unit used to describe phase noise is dBc/Hz (dB below the carrier per Hz of
bandwidth). Reports of phase noise measurement results should include both the bandwidth and the
carrier frequency.

Phase Shift

The change in phase of a periodic signal with respect to a reference.

Phase Signature

An intentional phase shift in a signal used to identify that signal. For example, WWVB identifies itself by
advancing the phase of its carrier frequency 45° at 10 minutes after the hour and returning to normal
phase at 15 minutes after the hour. This signature can be seen on a phase plot as an approximate 2
microsecond step, as shown in the figure below.

Picosecond (ps)
One trillionth of a second (10-12 s).

The term precision is somewhat ambiguous, and has several meanings in time and frequency metrology.
Due to its ambiguity, it is not often used in a quantitative sense. Normally, it refers to the degree of mutual
agreement among a series of individual measurements, values, or results. In this case, precision is
analogous to standard deviation. Precision might also be used to refer to the ability of a device to produce,
repeatedly and without adjustments, the same value or result, given the same input conditions and
operating in the same environment. This use of precision makes it analogous to repeatability,
reproducibility, or even stability. In other instances, precision is used as a measure of a computer's ability
to to distinguish between nearly equal values. For example, a compiler or spreadsheet might have 32-bit
precision when doing calculations with floating point numbers. In this case, precision is analogous to

Primary Standard
A standard that is designated or widely acknowledged as having the highest metrological qualities and
whose value is accepted without reference to other standards of the same quantity. For example, NIST-F1
is recognized as a primary standard for time and frequency. A true primary standard like NIST-F1
establishes maximum levels for the frequency shifts caused by environmental factors. By summing or
combining the effects of these frequency shifts, it is possible to estimate the uncertainty of a primary
standard without comparing it to other standards.

In the time and frequency field, the term primary standard is sometimes used to refer to any cesium
oscillator, since the SI definition of the second is based on the physical properties of the cesium atom. The
term primary standard is also commonly used, at least in a local sense, to refer to the best standard
available at a given laboratory or facility.

Quality Factor, Q
An inherent characteristic of an oscillator that influences its stability. The quality factor, Q, of an oscillator
is defined as its resonance frequency divided by its resonance width. Obviously a high resonance
frequency and a narrow resonance width are both advantages when seeking a high Q. Generally speaking,
the higher the Q, the more stable the oscillator, since a high Q means that an oscillator will stay close to its
natural resonance frequency. The table shows some approximate Q values for several different types of

Oscillator Type Quality Factor, Q
Tuning Fork 103
Quartz Wristwatch 104
OCXO 106
Rubidium 107
Cesium Beam 108
Hydrogen Maser 109
Cesium Fountain 1010
Mercury Ion Optical Standard 1014

Quartz Oscillator
The most common source of time and frequency signals. More than two billion (2 x 109) quartz oscillators
are manufactured annually. Most are small devices built for wristwatches, clocks, and electronic circuits.
However, quartz oscillators are also found inside test and measurement equipment, such as counters,
signal generators, and oscilloscopes; and interestingly enough, inside every atomic oscillator.

A quartz crystal inside the oscillator is the resonator. It could be made of either natural or synthetic
quartz, but all modern devices use synthetic quartz. The crystal strains (expands or contracts) when an
electrical voltage is applied. When the voltage is reversed, the strain is reversed. This is known as the
piezoelectric effect. Oscillation is sustained by taking a voltage signal from the resonator, amplifying it,
and feeding it back to the resonator. The rate of expansion and contraction is the resonance frequency,
and is determined by the cut and size of the crystal. The output frequency of a quartz oscillator is either
the fundamental resonance or a multiple of the resonance, called an overtone frequency. A typical Q for a
quartz oscillator ranges from 104 to 106. The maximum Q for a high stability quartz oscillator can be
estimated as Q = 1.6 x 107/f, where f is the resonance frequency in MHz.

Environmental changes of temperature, humidity, pressure, and vibration can change the resonance
frequency of a quartz crystal, but there are several designs that reduce these environmental effects.
These include the TCXO, MCXO, and OCXO. These designs (particulary the OCXO) often produce devices
with excellent short-term stability. The limitations in short-term stability are due mainly to noise from
electronic components in the oscillator circuits. Long term stability is limited by aging. Due to aging and
environmental factors such as temperature and vibration, it is hard to keep even the best quartz
oscillators within 1 x 10-10 of their nominal frequency without constant adjustment. For this reason, atomic
oscillators are used for applications that require better long-term stability and accuracy.

Radio Clock
A clock that automatically synchronizes to a signal received by radio. The most common radio clocks in
the United States receive signals from NIST radio station WWVB.

Random Walk
A type of oscillator noise caused by environmental factors such as mechanical shock, vibration and
temperature fluctuations which cause random shifts in frequency. As a general rule, random walk noise
cannot be removed by averaging.

Ramsey Cavity
The microwave cavity typically found inside atomic frequency standards where the atoms are subjected to
radiation near their resonance frequency. The cavity is part of an electronic circuit tuned to match the
atomic resonance frequency as closely as possible. Named after Norman Ramsey, who was awarded the
Nobel Prize in physics in 1989.

The ability of a device or measurement to produce, repeatedly and without adjustments, the same value
or result, given the same input conditions and operating in the same environment.

The degree to which a measurement can be determined. For example, if a time interval counter has a
resolution of 10 ns, it could produce a reading of 3340 ns or 3350 ns but not a reading of 3345 ns. This is
because 10 ns is the smallest significant difference the instrument can measure. Any finer measurement
would require more resolution. The specification for an instrument usually lists the resolution of a single
measurement, sometimes called the single shot resolution. It is usually possible to obtain more resolution
by averaging.

Resonance Frequency
The natural frequency of an oscillator. The resonance frequency is usually either divided or multiplied to
produce the output frequency of the oscillator. The table below shows the resonance frequency for several
types of oscillators. A high resonance frequency leads to a higher Q, and generally improves the stability.

Oscillator Type Resonance
Frequency (Hz)
Pendulum 1
Quartz Wristwatch 32 768
Hydrogen Maser 1 420 405 752
Rubidium 6 834 682 608
Cesium 9 192 631 770

Resonance Width
The range of possible frequencies where a resonator can resonate. Narrowing the resonance width of an
oscillator leads to a higher Q, and generally improves the stability. For example, if a resonator has a line
width of 1 Hz, it will resonate only if it is within 1 Hz of the correct frequency.

Rubidium Oscillator
The lowest priced members of the atomic oscillator family, rubidium oscillators operate at 6,834,682,608
Hz, the resonance frequency of the rubidium atom (87Rb), and use the rubidium frequency to control the
frequency of a quartz oscillator. The optical beam from the rubidium lamp pumps the 87Rb buffer gas
atoms into a particular energy state. Microwaves from the frequency synthesizer induce transitions to a
different energy state. This increase the absorption of the optical beam by the 87Rb buffer gas. A photo
cell detector measures how much of the beam is absorbed and its output is used to tune a quartz oscillator
to a frequency that maximizes the amount of light absorption. The quartz oscillator is then locked to the
resonance frequency of rubidium, and standard frequencies are derived from the quartz oscillator and
provided as outputs as shown in the figure.

Rubidium oscillators continue to become smaller and less expensive, and offer perhaps the best price to
performance ratio of any oscillator. Their long-term stability is much better than that of a quartz oscillator
and they are also smaller, more reliable, and less expensive than cesium oscillators.

The Q of a rubidium oscillator is about 107. Undesirable shifts in the resonance frequency are due mainly
to collisions of the rubidium atoms with other gas molecules and aging effects in the lamp system. These
shifts limit the long-term stability. Stability is typically 1 x 10-11, and about 1 x 10-12 at one day. The
frequency offset of a rubidium oscillator ranges from 5 x 10-10 to 5 x 10-12 after a warm-up period of a
few minutes or hours, so they meet the accuracy requirements of most applications without adjustment.

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. The definition was added to the International
System (SI) of units in 1967.

Short-Term Stability
The stability of a time or frequency signal over a short measurement interval, usually of 100 seconds or

Sidereal time
An astronomical time scale that is based on the Earth's rate of rotation measured relative to the fixed
stars. Thus a sidereal day is the time interval during which the Earth completes one rotation on its axis and
some chosen star appears to transit twice consecutively on the observer's local meridian. Because the
Earth moves in its orbit about the Sun, a mean solar day is about 4 minutes longer than a sidereal day.
Thus, a given star appears to rise 4 minutes earlier each night, relative to solar time, and different stars
are visible at different times of the year.

A radio wave that bounces off the ionosphere and returns back to Earth. Skywave propagation is a
characteristic of HF radio signals, such as those transmitted by WWV. Since the path delay of a skywave
signal is constantly changing, skywaves are not as suitable for time and frequency measurements as
groundwave or satellite signals.

Solar Day
The day defined as one revolution of the Earth on its axis with respect to the Sun. Since the Earth's
rotational period (one day) rate is much more variable than its period of revolution about the Sun (one
year), the mean solar day is more useful for timekeeping, since it averages the length of the day over the
course of a year.

Solar Time
An astronomical time scale that is based on the Earth's rate of rotation, measured with respect to either
the "ficticious" mean Sun, or of the "true" apparent Sun. In the apparent solar time scale, noon is the
instant when the Sun transits, i.e., crosses the local meridian and reaches its highest point in the sky,
called Local Apparent Noon (LAN). Over the course of the year, the Sun has considerably different daily
high points, lowest in the winter and highest in the summer, due to the tilt in the Earth's axis of about 27.5
degrees. The daily variation, over the course of a year, in the Sun's apparent angular speed across the
sky causes LAN to occur at a slightly different time each day. The variance in the apparent angular speed
is due to a daily change in the Earth's distance from the Sun. In the late fall and early winter months,
when the Earth is closer to the Sun (near or at perihelion), the Sun appears to travel faster (a greater
angle per unit of time), than during the late spring and early summer months, when the Sun is farther
away (near or at aphelion).

The difference between apparent and mean solar time is known as the "equation of time" and is a
measure of the apparent Sun preceding or following the mean Sun by an interval than can be as much as
16 minutes. Therefore, mean solar time (based on the length of an average day) is more useful for
uniform timekeeping than apparent solar time. In addition, since the Earth is much closer to the Sun than
to other stars, one complete rotation of the Earth relative to the Sun (mean solar day) requires about four
more minutes than one sideral day.

An inherent characteristic of an oscillator that determines how well it can produce the same frequency
over a given time interval. Stability doesn't indicate whether the frequency is right or wrong, but only
whether it stays the same. The stability of an oscillator doesn't necessarily change when the frequency
offset changes. You can adjust an oscillator and move its frequency either further away from or closer to
its nominal frequency without changing its stability at all. The graphic below illustrates this by displaying
two oscillating signals that are of the same frequency between t1 and t2. However, it’s clear that signal 1 is
unstable and is fluctuating in frequency between t2 and t3.

The stability of an oscillator is usually specified by a statistic such as the Allan deviation that estimates the
frequency fluctuations of the device over a given time interval. Some devices, such as an OCXO, have
good short-term stability and poor long-term stability. Other devices, such as a GPS disciplined oscillator
(GPSDO), typically have poor short-term stability and good long-term stability. Specification sheets for
quartz oscillators seldom quote stability numbers for intervals longer than 100 seconds. Conversely, a
specification sheet for an atomic oscillator or a GPSDO might quote stability estimates for intervals ranging
from one second to more than one day.

A device or signal used as the comparison reference for a measurement. A standard is used to measure
or calibrate other devices. NIST is responsible for developing, maintaining and disseminating national
standards for the United States for the basic measurement quantities (such as time interval), and for many
derived measurement quantities (such as frequency).

Stop Watch
A device (usually a handheld device) used to measure time interval. Most stop watches are manually
operated, a button is pushed to start and stop the measurement. The measurement is made using a quartz
or mechanical time base. Stop watches are used for simple time interval measurements and calibrations.
Their resolution is very coarse compared to a time interval counter, with 10 millisecond resolution being

Stratum clocks
A clock in a telecommunications system or network that is assigned a number that indicates its quality and
position in the timing hierarchy. The highest quality clocks, called stratum 1 clocks, have a frequency
offset of 1 x 10-11 or less, which means that they can keep time to within about one microsecond per day.
The formal specifications are given in the ANSI standards T1.101-1999 and T1.105.09-1997. Only stratum
1 clocks may operate independently; other clocks are synchronized directly or indirectly to a stratum 1

The process of setting two or more clocks to the same time.

The process of setting two or more oscillators to the same frequency.

A temperature-compensated crystal oscillator. A TCXO is a type of quartz oscillator that compensates for
temperature changes to improve stability. In a TCXO, the signal from a temperature sensor is used to
generate a correction voltage that is applied to a voltage-variable reactance, or varactor. The varactor
then produces a frequency change equal and opposite to the frequency change produced by temperature.
This technique does not work as well as the oven control used by an OCXO, but is less expensive.
Therefore, TCXOs are used when high stability over a wide temperature range is not required.

Terahertz (THz)
One trillion cycles per second (1012 Hz).

Terrestrial Time (TT)
An astromonical time scale which equals TAI + 32.184 s. The uncertainty of TT is +/- 10 microseconds. It
replaced the now obsolete Ephemeris Time scale in 1984.

Test Uncertainty Ratio (TUR)
A measurement or calibration compares a device under test (DUT) to a standard or reference. The
standard should outperform the DUT by a specified ratio, called the Test Uncertainty Ratio (TUR). Ideally,
the TUR should be 10:1 or higher. The higher the ratio, the less averaging is required to get valid
measurement results.

The designation of an instant on a selected time scale, used in the sense of time of day; or the interval
between two events or the duration of an event, used in the sense of time interval.

Time Base
An oscillator found inside an electronic instrument that serves as a reference for all of the time and
frequency functions performed by that instrument. The time base oscillator in most instruments is a quartz
oscillator, often an OCXO. However, some instruments now use rubidium oscillators as their time base.

Time Code
A code (usually digital) that contains enough information to synchronize a clock to the correct time-of-day.
Most time codes contain the UTC hour, minute, and second; the month, day, and year; and advance
warning of daylight saving time and leap seconds. NIST time codes can be obtained from the WWV,
WWVH, WWVB, ACTS, and Internet Time Services. The format of the WWV/WWVH time code is shown in
the graphic below.

Time Deviation
A statistic used to estimate time stability, based on the Modified Allan deviation. The time deviation is
particularly useful for analyzing time transfer data, such as the results of a GPS common-view

Time Domain
The measurement domain where voltage and power are measured as functions of time. Instruments such
as oscilloscopes and time interval counters are often used to analyze signals in the time domain.

Time Interval
The elapsed time between two events. In time and frequency metrology, time interval is usually measured
in small fractions of a second, such as milliseconds, microseconds, or nanoseconds. Coarse time interval
measurements can be made with a stop watch. Higher resolution time interval measurements are often
made with a time interval counter.

Time Interval Counter
An instrument used to measure the time interval between two signals. A time interval counter (TIC) has
inputs for two electrical signals. One signal starts the counter and the other signal stops it.

TIC's differ in specification and design, but they all contain several basic parts known as the time base, the
main gate, and the counting assembly. The time base provides evenly spaced pulses used to measure
time interval. The time base is usually an internal quartz oscillator that can often be phase locked to an
external reference. It must be stable because time base errors will directly affect the measurements. The
main gate controls the time at which the count begins and ends. Pulses passing through the gate are
routed to the counting assembly, where they are displayed on the TIC's front panel or read by computer.
The counter can then be reset (or armed) to begin another measurement. The stop and start inputs are
usually provided with level controls that set the amplitude limit (or trigger level) at which the counter
responds to input signals. If the trigger levels are set improperly, a TIC might stop or start when it detects
noise or other unwanted signals and produce invalid measurements.

The graphic below illustrates how a TIC measures the interval between two signals. The TIC begins
measuring a time interval when the start signal reaches its trigger level and stops measuring when the
stop signal reaches its trigger level. The time interval between the start and stop signals is measured by
counting cycles from the time base. The measurements produced by a TIC are in time units such as
microseconds or nanoseconds. These measurements assign a time value to the phase difference between
the reference and the test signal.

The most important specification of a TIC is resolution. In traditional TIC designs, the resolution is limited
to the period of the TIC’s time base frequency. For example, a TIC with a 10 MHz time base would be
limited to a resolution of 100 ns. This is because traditional TIC designs count whole time base cycles to
measure time interval and cannot resolve time intervals smaller than the period of one cycle. To improve
this situation, some TIC designers have multiplied the time base frequency to get more cycles and thus
more resolution. For example, multiplying the time base frequency to 100 MHz makes 10 ns resolution
possible, and 1 ns counters have even been built using a 1 GHz time base. However, a more common way
to increase resolution is to detect parts of a time base cycle through interpolation and not be limited by the
number of whole cycles. Interpolation has made 1 ns TICs commonplace, and even 20 picosecond TICs
are available.

Time of Day
The information displayed by a clock or calendar, usually including the hour, minute, second, month, day,
and year. Time codes derived from a reference source such as UTC(NIST) are often used to synchronize
clocks to the correct time of day.

Time Offset
The difference between a measured on-time pulse or signal, and a reference on-time pulse or signal, such
as UTC(NIST). Time offset measurements are usually made with a time interval counter. The
measurement result is usually reported in fractions of a second, such as milliseconds, microseconds, or

Time Protocol
An Internet time code protocol defined by the RFC-868 document and supported by the NIST Internet
Time Service. The time code is sent as a 32-bit unformatted binary number that represents the time in
UTC seconds since January 1, 1900. The server listens for Time Protocol requests on port 37, and
responds in either TCP/IP or UDP/IP formats. Conversion from UTC to local time (if necessary) is the
responsibility of the client program. The 32-bit binary format can represent times over a span of about 136
years with a resolution of 1 second. There is no provision for increasing the resolution or increasing the
range of years.

Time Scale
An agreed upon system for keeping time. All time scales use a frequency source to define the length of
the second, which is the standard unit of time interval. Seconds are then counted to measure longer units
of time interval, such as minutes, hours, and days. Modern time scales such as UTC define the second
based on an atomic property of the cesium atom, and thus standard seconds are produced by cesium
oscillators. Earlier time scales (including earlier versions of Universal Time) were based on astronomical
observations that measured the frequency of the Earth's rotation.

Time Standard
A device that produces an on-time pulse that is used as a reference for time interval measurements, or a
device that produces a time code used as a time-of-day reference.

Time Transfer
A measurement technique used to send a reference time or frequency from a source to a remote location.
Time transfer involves the transmission of an on-time marker or a time code. The most common time
transfer techniques are one-way, common-view, and two-way time transfer.

Time Zone
A geographical region that maintains a local time that usually differs by an integral number of hours from
UTC. Time zones were initially instituted by the railroads in the United States and Canada during the
1880's to standardize timekeeping. Within several years the use of time zones had expanded

Ideally, the world would be divided into 24 time zones of equal width. Each zone would have an east-west
dimension of 15° of longitude centered upon a central meridian. This central meridian for a zone is defined
in terms of its position relative to a universal reference, the prime meridian (often called the zero
meridian) located at 0° longitude. In other words, the central meridian of each zone has a longitude
divisible by 15°. When the sun is directly above this central meridian, local time at all points within that
time zone would be noon. In practice, the boundaries between time zones are often modified to
accommodate political boundaries in the various countries. A few countries use a local time that differs by
one half hour from that of the central meridian.

Converting UTC to local time, or vice versa, requires knowing the number of time zones between the
prime meridian and your local time zone. It is also necessary to know whether Daylight Saving Time
(DST) is in effect, since UTC does not observe DST. The table below shows the difference between UTC
and local time for the major United States time zones.

Time Zone Difference from UTC During Standard Time Difference from UTC During Daylight Time
Pacific -8 hours -7 hours
Mountain -7 hours -6 hours
Central -6 hours -5 hours
Eastern -5 hours -4 hours

Total Deviation
A statistic used to estimate oscillator stability. Total deviation reduces the estimation errors of the Allan
deviation at long averaging times, and thus is well suited for estimating long-term stability.

The property of a result of a measurement or the value of a standard whereby it can be related to stated
references, usually national or international standards, through an unbroken chain of comparisons all
having stated uncertainties.

For general information about traceability, visit the NIST Traceability web site. For information specific to
time and frequency metrology, visit the NIST Frequency Measurement Service page.

Tuning Fork
A metal two-pronged fork that, when struck, produces an almost pure tone of a predetermined frequency.
Tuning forks are used for simple frequency calibrations, such as tuning musical instruments, and
calibrating radar guns used by law enforcement agencies.

Two Way Time and Frequency Transfer
A measurement technique used to compare two clocks or oscillators at remote locations. The two-way
method involves signals that travel both ways between the two clocks or oscillators that are being
compared, as shown in the graphic below.

A half-duplex channel is a one-way system that is “turned around” to retransmit a signal in the opposite
direction. In this method, the one-way delay between the transmitter and receiver is estimated as one-half
of the measured round trip delay. The delay estimate can be sent to the user and applied as a correction,
or the transmitter can advance the signal so that it arrives at the user's site on time. The latter is how the
NIST Automated Computer Time Service (ACTS) system works. Internet time transfers using the Network
Time Protocol (NTP) also use a half-duplex technique.

A full-duplex system uses one-way signals transmitted simultaneously in both directions, often through a
communications satellite. In this case data must be exchanged in both directions so that the two data sets
can be differenced. For more information, visit the NIST Two Way Transfer web page.

Parameter, associated with the result of a measurement, that characterizes the dispersion of values that
could reasonably be attributed to the measurand. By convention, two standard deviations are normally
used for uncertainty numbers.

United States Naval Observatory (USNO)
Established in 1830, the USNO is one of the oldest scientific agencies in the United States. The USNO
determines and distributes the timing and astronomical data required for accurate navigation and
fundamental astronomy. It maintains a UTC time scale that is (by mutual agreement) within 100
nanoseconds of UTC(NIST). Both NIST and the USNO can be considered official sources of time and
frequency in the United States.

Universal Time (UT) Family
Before the acceptance of atomic time scales such as TAI and UTC in the 1960s, astronomical time scales
were used for everyday timekeeping. These time scales are still used today, but mostly for applications
related to astronomy. They are based on mean solar time. The mean solar second is defined as 1/86,400
of the mean solar day, where 86,400 is the number of seconds in the mean solar day. This mean solar
second provides the basis for Universal Time (UT). Several variations of UT have been defined:

UT0 - The original mean solar time scale, based on the rotation of the Earth on its axis. UT0 was first kept
by pendulum clocks. As better clocks based on quartz oscillators became available, astronomers noticed
errors in UT0 due to polar motion, which led to the UT1 time scale.

UT1 - The most widely used astronomical time scale, UT1 is an improved version of UT0 that corrects for
the shift in longitude of the observing station due to polar motion. Since the Earth’s rate of rotation is not
uniform, UT1 is not completely predictable, and has an uncertainty of +/- 3 milliseconds per day.

UT2 - Mostly of historical interest, UT2 is a smoothed version of UT1 that corrects for known deviations in
the Earth’s rotation caused by angular momenta of the Earth’s core, mantle, oceans, and atmosphere.

The distance between identical points in the adjacent cycles of a waveform that is traveling in free space
or in a guide structure such as a coaxial cable. The wavelength of radio signals is usually specified in
meters, centimeters, or millimeters. In the case of infrared, visible light, ultraviolet, and gamma radiation,
the wavelength is more often specified in nanometers (units of 10-9 meter) or Angstrom units (units of
10-10 meter). The wavelengths of the various frequency bands in the radio spectrum are shown in the

Wavelength is inversely related to frequency. The higher the frequency of the signal, the shorter the
wavelength. If f is the frequency of the signal as measured in megahertz, and w is the wavelength as
measured in meters, then

w = 300/f

and conversely

f = 300/w

The table shows the frequency and wavelength ranges for the frequency bands in the radio spectrum.

Band Description Frequency Wavelength
VLF Very Low 3 to 30 kHz 100 to 10 km
LF Low 30 to 300 kHz 10 to 1 km
MF Medium 300 to 3000 kHz 1 km to 100 m
HF High 3 to 30 MHz 100 to 10 m
VHF Very High 30 to 300 MHz 10 to 1 m
UHF Ultra High 300 to 3000 MHz 1 m to 10 cm
SHF Super High 3 to 30 GHz 10 to 1 cm
EHF Extremely High 30 to 300 GHz 1 cm to 1 mm

White Noise
Noise having a frequency spectrum that is continuous and uniform over a specified frequency band. White
noise is independent of frequency, and its spectrum looks flat on a spectrum analyzer's display. It has
equal power per hertz over the specified frequency band.

The NIST radio station located near Fort Collins, Colorado. WWV broadcasts time and frequency
information 24 hours per day, 7 days per week to millions of listeners worldwide on carrier frequencies of
2.5, 5, 10, 15, and 20 MHz. Please visit the WWV web pages for a complete description of the station.

The NIST radio station located on the same site as WWV near Ft. Collins, Colorado. WWVB broadcasts on
a carrier frequency of 60 kHz. The WWVB broadcasts are used by millions of people throughout North
America to synchronize consumer electronic products such as wall clocks, clock radios, and wristwatches.
In addition, WWVB is used for high level applications such as network time synchronization and frequency
calibrations. Please visit the WWVB web pages for a complete description of the station.

The NIST radio station located on the Island of Kauai, Hawaii. WWVH broadcasts time and frequency
information 24 hours per day, 7 days per week to listeners worldwide on carrier frequencies of 2.5, 5, 10,
and 15 MHz. Please visit the WWVH web pages for a complete description of the station.

An acronym for a quartz crystal oscillator. It usually refers to the simplest types of quartz oscillators that
have no compensation for the effects of temperature.

Zero Beat
The condition reached during a measurement or calibration when the beat frequency between two input
signals is no longer detectable. Zero beat is often associated with audio frequency calibrations (such as the
tuning of musical instruments), when the person performing the measurement can no longer hear the beat
frequency or beat note.

A term sometimes used in the military and in navigation as a synonym for Coordinated Universal Time
(UTC). In military shorthand, the letter Z follows a time expressed in UTC. Zulu is not an official time
scale. The term originated because the word zulu is the radio transmission articulation for the letter Z, and
the time zone located on the prime meridian is designated on many time zone maps by the letter Z .



Active Frequency Standard


Allan Deviation



Atomic Clock

Atomic Oscillator

Atomic Time Scale

Automated Computer Time Service (ACTS)


Beat Frequency



Carrier Frequency

Carrier Phase Measurements

Cesium Beam Oscillator

Cesium Fountain Oscillator




Coordinated Universal Time (UTC)

Cycle Slip


Daylight Saving Time

Daytime Protocol

Dead Time

Disciplined Oscillator (DO)

Doppler Shift

Drift (frequency)



Ephemeris Time (ET)


Femtosecond (fs)

Flicker Noise


Frequency Accuracy

Frequency Counter

Frequency Divider

Frequency Domain

Frequency Drift

Frequency Mixer

Frequency Multiplier

Frequency Offset

Frequency Shift

Frequency Stability

Frequency Standard

Frequency Synthesizer

Gigahertz (GHz)

Global Positioning System (GPS)



Greenwich Mean Time (GMT)




High Frequency (HF)

Hydrogen Maser

International Atomic Time (TAI)

International Date Line

Internet Time Service (ITS)

Intrinsic Standard

Ion Trap

IRIG Time Codes


Julian Day

Kilohertz (kHz)

Laser Cooling

Leap Day

Leap Second

Leap Year

Line Width

Long-Term Stability


Low Frequency (LF)


Maximum Time Interval Error (MTIE)

Megahertz (MHz)


Mean Solar Time



Modified Allan Deviation (MDEV)

Nanosecond (ns)

Network Time Protocol (NTP)

Nominal Frequency



One Way Time and Frequency Transfer

On Time Marker (OTM)

Optical Frequency Standard


Overtone Frequency

Passive Frequency Standard

Path Delay



Phase Comparison

Phase Locked Loop (PLL)

Phase Noise

Phase Shift

Phase Signature

Picosecond (ps)


Primary Standard

Quality Factor, Q

Quartz Oscillator

Radio Clock

Random Walk

Ramsey Cavity



Resonance Frequency

Resonance Width

Rubidium Oscillator


Short-Term Stability

Sidereal time


Solar Day

Solar Time



Stop Watch

Stratum clocks




Terahertz (THz)

Terrestrial Time (TT)

Test Uncertainty Ratio (TUR)


Time Base

Time Code

Time Deviation

Time Domain

Time Interval

Time Interval Counter

Time of Day

Time Offset

Time Protocol

Time Scale

Time Standard

Time Transfer

Time Zone

Total Deviation


Tuning Fork

Two Way Time and Frequency Transfer


United States Naval Observatory (USNO)

Universal Time (UT) Family


White Noise





Zero Beat


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