NBS TECHNICAL NOTE 616

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Frequency Standards and Clocks:

A Tutorial Introduction
NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMMERCE

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y'<5- NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

N8S TECHNICAL NOTE 616

ISSUED APRIL 1972

Nat. Bur. Stand. (U.S.), Tech. Note 616, 69 pages (April 1972) CODEN: NBTNA

Frequency Standards and Clocks:

A Tutorial Introduction

Helmut Hellwig

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

This paper is provided as partial fulfillment of Contract EIIIM-6 to Richards-Gebaur AFB, Missouri 64030.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. 013.46:616), Price 70 cents

CONTENTS

Page

1. INTRODUCTION 1

2. BASIC CONCEPTS 6

2. 1 Accuracy, Reproducibility, Stability 6

2. 2 Time Accuracy 10

2.3 Clocks 12

3. FREQUENCY STANDARDS, GENERAL ASPECTS 12

3. 1 Resonators 12

3.2 Primary and Secondary Standards . 18

4. QUARTZ CRYSTAL DEVICES 18

4. 1 Quartz Crystal Resonator 18

4. 2 Effects on the Crystal Resonator Frequency 24

4. 3 Quartz Crystal Oscillator Performance 29

5. ATOMIC RESONANCE DEVICES 32

5. 1 Atomic Resonators 32

5. 2 State Selection 33

5. 3 Interrogation of the Atoms 3 5 5.4 Signal Detection 37

5. 5 Atomic Frequency Standard 40

5.6 Effects on the Atomic Resonator Frequency 43

6. AVAILABLE ATOMIC FREQUENCY STANDARDS 46

6. 1 Cesium Beam Frequency Standard 46

6.2 Rubidium Gas Cell Frequency Standard 50

6. 3 Atomic Hydrogen Maser 53

7. SUMMARY AND COMPARISON OF AVAILABLE

FREQUENCY STANDARDS 57

8. TRENDS 61

9. LITERATURE 6 3

in
Fig. 1. Fig. 2. Fig. 3.

Fig.

FigFig.

Fig.

Fig. 8 Fig. 9 Fig. 10

Fig. 11

Fig. 12.

Fig. 13. Fig. 14. Fig. 15. Fig. 16. Fig. 17. Fig. 18. Fig. 19. Fig. 20.

Fig. 21.

LIST OF FIGURES

Definition of time and frequency.

Frequency standard and clock.

Page

3

5 Relationships between clock accuracy, frequency stability, 11 and frequency offset. Example (dashed line): for At = 10 ns, resynchronization every 1 hour is needed, if the frequency

stability for 1 hour sampling time is 5 X 10 . The frequency

""12 offset is assumed to be less than 5X10

Example of a clock system (frequency values arbitrarily chosen).

Examples of resonators. 14

Decay time, linewidth, and Q-value of a resonator. 16

Hierarchy of frequency standards. 19

The piezoelectric effect. 21

Principal vibrational modes of quartz crystals. 22

Typical quartz crystal mount. 23

Quartz crystal oscillator. The block diagram shown is not 2 5 necessarily the one giving optimum performance of the crystal

oscillator.

Fundamental and overtone resonance frequencies; example:

violin string. (In acoustics, the numbering of the overtones

is done differently: their first overtone 'would be our second,

their second our third, etc. ) Frequency stability of the better quartz crystal oscillators.

Spatial state selection.

Optical state selection.

Atom detection.

Optical detection.

Microwave detection.

Atomic frequency standard.

Cesium beam frequency standard.

Frequency stability of commercial cesium beam frequency

standards (dashed = performance of improved models in 1971)

26

30

34

36

38

39

41

42

47

48

13

IV
Fig. 22. Rubidium gas cell frequency standard. 51

Fig. 23. Frequency stability of commercial rubidium gas cell frequency 52

standards.

Fig. 24. Hydrogen maser oscillator. 55

Fig. 25. Frequency stability of a hydrogen maser oscillator with 56

automatic cavity tuning.

LIST OF TABLES

1. Summary and Comparison of Available Frequency Standards 57-60

2. Additional Promising Items Under Investigation 62

FREQUENCY STANDARDS AND CLOCKS:

A TUTORIAL INTRODUCTION 1

Helmut Hellwig

Atomic Frequency and Time Standards Section

National Bureau of Standards

Boulder, Colorado 80302 USA

The topic of frequency standards and clocks is treated in a tutorial and non -mathematical way. The concepts of time,

frequency, frequency stability, and accuracy are introduced.

The general physical principles and design features of frequency

standards and clopks are described. The design, performance,

and limitations of quartz crystal oscillators and atomic devices

(cesium, hydrogen, rubidium) are discussed in detail and critically

compared for laboratory devices as well as for devices intended

for field usage.

Key Words: Cesium beam; Clocks (atomic); Crystal oscillator;

Frequency accuracy; Frequency stability; Frequency standards; Hydrogen maser; Quartz crystal;

Rubidium gas cell; Timekeeping.

1. INTRODUCTION

Frequency standards and clocks: what do they have in common?

A more complete answer will be given later. We note for the moment

that most clocks and in particular the very accurate and precise ones

are based on frequency standards. The reason for this is the intimate

relationship between frequency (symbol V, "nu") and time (symbol t).

If we look at a series of events which are occurring in a somewhat

regular fashion, e. g. , the rise of the sun every morning, we can

state how many of these events occur in a given time period: this

number would be the frequency of this series of events. In our example

we could say that the frequency of sunrises is V = 7 events per week

This paper was originally prepared for inclusion in a handbook on time

and frequency for the Air Force.
or V - 365 events per year. "Events per week" or "events per year"

would be called the unit which we used for our frequency number;

this frequency number is different for different units. In our example we assumed that we know somehow what a week or a year

is, i. e. , we relied on some external definition for our unit of time.

We can now ask, what is the time between the events? The

answer for our example is simple, one sunrise succeeds the other

after t = — week or t = year where we used "week" and "year"

7 36 5 as two possible choices for our unit of time. We can rely on the

regularity and precision of the occurrence of the events, in other

words, on their precise periodicity. Hence, we could define:

the unit of time is one 'week; one week is the time elapsed at the

seventh sunrise following an initial sunrise.

We learned two things: (a) For periodic events, the time

between the events t is related to the frequency V of them occurring

in the following simple way

v-\ (1)

and (b) that periodic events can be used to define time, i. e. , the

generator of the periodic events - the frequency standard - can be

used for a clock. The frequency standard becomes a clock by the

addition of a counting mechanism for the events.

In our example above, the frequency standard is the rotating

earth. The time between recurring events is one day. This frequency standard served mankind for thousands of years and remained

until very recently the source for the definition of time. The counting

mechanism which made it a clock was the recording of years and days.
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The needs to interpolate time from day to day, to get along

for many days -without celestial observations, and to more precisely

measure time-intervals which are very much shorter than a day brought

about the invention of clocks. Although there are other types of clocks

like the sand-clock or the decay in radiation intensity of a radioactive

substance, we shall confine ourselves to the discussion of clocks based

on frequency standards.

The first clocks based on a frequency standard (a pendulum) were

invented about 400 years ago. This type of clock is still most widely

used today. The pendulum may be a suspended weight (gravitational

pendulum) like in "grandfather" clocks or the balance (torsion pendulum)

of modern wristwatches. The objects of our discussion in this report

are today's most advanced frequency standards and clocks; however,

a close look at our traditional clocks will show all the essential features which we will recognize again in our later discussion of quartz

crystal and atomic clocks.

The pendulum in our clock is the frequency determining element.

In order to arrive at a frequency standard the pendulum has to be set

in motion and kept in motion: A source of energy is necessary together

with means to transfer this energy to the frequency determining element.

In a wristwatch this source of energy is typically the winding spring,

and the energy is transferred by mechanical means which are controlled

by the pendulum itself (feedback) in order to cause energy transfer in

the proper amount at the proper time in synchronism with the movement

of the pendulum. We now have a frequency standard; the tick frequency of

its pendulum could be picked up acoustically, for example, and used as a standard frequency. This is actually being done commercially when

adjusting the rate of a clock: the tick-frequency is compared to some

(better) standard frequency. In order to arrive at a clock, a read-out

mechanism is necessary which counts and accumulates the ticks (more
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set of gears and the moving hands on the clockface.

The unit of time today is the second (symbol s). Very much in

analogy to our sunrise example, the second is defined in reference to a frequency determining element. Since 1967 by international agreement this "natural pendulum" is the cesium atom. One second is defined in the official wording as the duration of 9192 631 770 periods

of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium- 133 atom". Accordingly,

the frequency of the cesium pendulum is 9192 631 770 events per

second (the cesium atom is a very rapidly oscillating pendulum).

Following our eq (1) the unit of frequency is then defined as hertz (symbol Hz) which means the repetitive occurrence of one event

per second (the use of "hertz" is preferred to the older term "cycle

per second", cps).

2. BASIC CONCEPTS

2. 1 Accuracy, Reproducibility, Stability

The performance of frequency standards is usually described in

terms of accuracy, reproducibility, and stability. We "will use these

terms in the sense of the following definitions:

Accuracy: the degree of conformity of a measured and/ or calculated value to some specified value or definition.

Reproducibility: the degree of agreement across a set of independent

devices of the same design after adjustment of appropriate specified

parameters in each device.
Stability: the frequency and/or time domain behavior of a process. In the time domain (i. e. , the sampling time is the varied

quantity) a frequently used measure of stability is the Allan variance

(to be explained later) or its square root.

It is obvious from these definitions that frequency accuracy

will be largely of interest in scientific measurements and in the

evaluation and intercomparison of the most advanced devices, but

of little or no interest to the average user of frequency standards.

A good reproducibility is an asset in applications where it is

of importance to rely on some degree of conformity of the output

frequency of several devices. The characterization of the stability

of a frequency standard is usually the most important information

to the user. The frequency stability (symbol cr, "sigma") of a frequency standard will depend on a variety of physical and electronic

influences both internal and external to the device which cause

frequency fluctuations. The frequency stability depends also on

the exact measurement procedure which was used to measure the

stability. We shall explain this in the following. Frequency stability can be measured by taking a reasonably large number of successive

readings of an electronic counter which counts the frequency of the

device to be evaluated. Each counter reading (in hertz) is obtained

by sampling the counted frequency for some specified time, the sampling

time (symbol T, "tau"). This sampling time can usually be chosen by

simply adjusting a knob on the counter; for example, a sampling time of

0. Is or Is or 10s may be chosen.

3 In this paper, for tutorial purposes, only the time domain stability is used.

We note, however, that for many scientific applications the frequency

domain stability measure is more useful.
Everyone has had the experience that fluctuations tend to average out

if observed long enough; however, this is not always so. Sigma

will therefore usually depend on the sampling time of the measurement and tends to get smaller with longer sampling times; again,

there are many exceptions to this.

It may be that the fluctuations at some later time are partially

caused by, or depend to some degree on, the previous fluctuations.

In this case, the actual value of a will also depend on the particular

way in 'which the many counter readings are averaged and evaluated.

Also, it will be of influence whether the counter starts counting

again immediately after completion of the preceeding count or

if some time elapses ("dead-time") before counting commences

again.

Finally, electronic circuits will have a finite response time,

e. g. , they cannot follow fluctuations faster than some given rate. For example, our eye can not register light fluctuations which occur

fester than about every — of a second; using eq (1), we

say that the eye has a frequency response of 10 Hz, or that its bandwidth is only 10 Hz, i. e. the eye can not follow frequencies higher

than 10 Hz. In order to measure frequency stabilities for sampling

times larger than some value T, we have to provide for an electronic

frequency bandwidth which is larger than — . We summarize: a recommended way of properly measuring

and describing frequency stability is the following: (a) make sure

that the frequency bandwidth of the total measuring set-up is larger

than— where T mi n

is the smallest desired sampling time; (b) T min

use a counter with a dead-time as small as possible ; (c) take a

sufficiently large number of readings at a given sampling time

which is held constant and compute

2 The dead-time should be less than the reciprocal bandwidth; if not,

computation procedures exist to account for larger dead-times.

8
/ addition of the squares of the differences between successive readings

v 2 X total number of differences used

(in the scientific literature this CT is called the square root of the twosample Allan variance); (d) repeat (c) at other sampling times T and

tabulate or plot CT as it depends on T. Commonly, CT will be given as a fractional value, i. e. , the value

obtained for the frequency stability is divided by the carrier frequency.

For example, if a frequency stability of OV =10 Hz were measured at

a carrier frequency of V = 5 MHz (MHz = megahertz = million Hz) then

the fractional frequency stability would be

CT. . = 2 X 10"6. 5v/v

We denote the kind of CT by a subscript, 6y ("delta nu") referring to 6v

frequency fluctuation (measured in Hz) or — referring to fractional

frequency fluctuations (dimensionless). A stability of one part in a million is thus

CT R , = 1 X 10"S

,

and one part in a trillion is written as %/^ 1X10 "12

-

The common usage of the fractional frequency stability cr. , instead of the frequency stability CTc (given in Hz) has its good

reasons. In almost all applications of frequency standards their

nominal output frequency will be multiplied or divided, i.e. , the

standard frequency will be used to synthesize other frequencies. Also,

frequency standards themselves will already synthesize several output

frequencies, and different frequency standards will offer different output frequencies. In such a usage of frequency standards as well as in

4 The counter readings can be taken in Hz; CT will then have the

dimension of Hz.
the comparison of their performances it would be extremely inconvenient

to state Cr» because this number (in Hz) will change with any alteration

in frequency due to synthesis. This will not be so with Cj. because

6v as well as V -will change in the same way in synthesizing procedures.

Of course, we assume here that synthesis does not cause additional

instabilities, an assumption which is mostly valid with today's electronic

capabilities.

2.2 Time Accuracy

In clocks, time accuracy is of importance. In accordance with

the definition for accuracy at the beginning of this section, the accuracy

of a clock is the conformity of its reading (the date shown) with the

reading of a standard time scale (a standard or reference date). A

clock can be initially set (synchronized) with respect to a reference

clock with some accuracy At . Its reading will then gradually deviate

by an amount At ("delta t") from the reading of the reference clock.

This deviation, i.e., the accuracy of the clock, depends on the stability

performance CT of the frequency standard in the clock and on the

bkV 5 fractional frequency offset —— of the clock with respect to the reference

clock via

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(r = t) + At

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, (2)

where OV (T = t) means the fractional frequency stability evaluated

for a sampling time T equal to the time t which elapsed after the last

setting of the clock. For example, a clock with a fractional frequency

stability of CT. =10 for sampling times of 1 seconds (about 1 day)

would be accurate to At = ± 10 X 10 =±1 microsecond per day if Ay is assumed to be zero. The same clock with a fractional frequency offset

of t^VjV - 10 would be accurate to At = (100 ± 1) microseconds after 1 day.

5 The frequency offset Al^ is the frequency difference, measured in hertz,

be ween the frequency standard (clock) and the reference.

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2. 3 Clocks

In the Introduction we discussed that the addition to a frequency

standard of a mechanism, which counts and accumulates and possibly

displays the result, creates a clock.

This task can be performed by a frequency divider which, for

example, derives a frequency of 60 Hz directly from a 5 MHz crystal

oscillator. The 60 Hz voltage can be used to drive an electric clock

similar to those driven by the 60 Hz power line frequency which we use

at home or at work. Or, an additional electric pulse generator may be

used which generates one very sharp electrical pulse per second. The

time interval of 1 second between the pulses (corresponding to a frequency

of 1 Hz) is directly derived from the output of our frequency standard.

The pulses can be directly used in time comparisons with those of other,

similar clocks; or a counter/accumulator can be driven by them.

3. FREQUENCY STANDARDS, GENERAL ASPECTS

3. 1 Resonators

The performance of a frequency standard is to a considerable

degree, but not exclusively, given by its frequency determining element.

It determines the frequency by its resonance behavior. Some examples

for resonance phenomena are (a) a rod, clamped only at one end, which can

vibrate, (b) a block of solid material which can contract and expand

and thus vibrate, (c) a capacitor -coil combination (tank circuit) in which the electric energy can oscillate back and forth between these

two elements, (d) an antenna (a dipole) where the distribution of electric

charges can oscillate back and forth, and (e) a coil in which an electric

current can create a magnetic field which can oscillate between its two

possible polarities (a magnetic dipole). All these devices have in

common that they can vibrate or oscillate if they are excited. The

method of excitation may be a mechanical pulse for (a) and (b) or an

electrical pulse for (c) or a sudden surge of an electric field for (d) or of a magnetic field for (e). The devices exhibit a resonance, i.e.,

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they are resonators with a well-defined frequency which is characteristic

of the physical dimensions of the device: the length of the rod, the

thickness of the block, the size of the capacitor and coil, the length of

the antennas. Once excited, the oscillations will die out gradually

with a decay time which is determined by the losses of the resonator.

Some of these losses are internal friction as in our cases (a) and (b), and electrical resistance for (c) through(e); in any case, the oscillation

energy is ultimately transformed into heat. If there were no losses, the

oscillations would never stop; we would have an ideal resonator. The

more losses, the faster the oscillations will decay and the resonance

will be less pronounced. It is now obvious that we could use the decay

time of the oscillations (symbol T) to describe the quality of our resonator. The larger T, the better the resonator.

An alternate way of measuring the resonance behavior is to use an external oscillator, to couple it to the resonator, and to sweep slowly

the frequency of the external oscillator across the resonance. We will

find again a resonance frequency at which the resonator will oscillate

most pronounced, i.e., with the greatest intensity. On both sides of

the resonance frequency, the response of the resonator will lessen until

it ceases to respond. We can define a frequency interval around resonance

in 'which the resonator response is relatively strong; we call it the resonance linewidth (symbol W). There is a simple relationship between

W and T

W=~. (3)

Again, as in the case of (7, it is of advantage to state the linewidth

W

in a fractional way. The fractional linewidth would be —— where the symbol V is used for the resonance frequency. More widely used is

the quality factor of the resonance (symbol Q) which is defined as the

6 Equation (3) is only an approximation. Depending on the particular

shape of the resonance curve we would have to insert a factor into

this equation; however, this factor is never far from unity.

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In frequency standards we obviously like to have large values for

the Q of the frequency determining element. As an example, if Q = 10 , then a fractional accuracy of 1 would imply that we can determine

the center of our resonance curve to a small fraction (10 or one hundredth of a percent) of its width. In the same example, a stability

of 10 ~ for some sampling time would correspond to an ability to keep

the frequency to within 10 (one millionth) of the resonance linewidth

around a given value. It is clear, therefore, that the frequency stability

and accuracy of a frequency standard may be expected to become the

better the higher the Q-value of the frequency determining element.

Many kinds of frequency determining elements have been and are

being used in frequency standards. They can be grouped into three

classes

:

mechanical resonators;

electronic resonators;

atomic resonators.

As far as mechanical resonators are concerned we will only

discuss one group in detail, the quartz crystals. Other mechanical

resonators like the pendulum and the tuning fork are of no importance

in today's high performance frequency standards although they have been

historically very important and are still widely used in low performance

devices (e.g., in watches). For similar reasons we will also omit the

discussion of electronic resonators like the tank circuits (our device (c)

of above) and microwave cavities. Atomic resonators form the heart

of our most accurate frequency standards and clocks and will, therefore,

be extensively discussed.

17
3.2 Primary and Secondary Standards

At this point, we should briefly discuss the frequently used terms

"primary frequency standard" and "secondary frequency standard".

These terms should refer to the systems -use of the devices; any frequency standard, regardless of its accuracy or stability, can be a * primary frequency standard, if it is used as the sole calibration reference

for other frequency sources. A secondary frequency standard is a device

which is occasionally calibrated against a primary frequency standard

but operationally serves as the working reference for other frequency

sources. The use of the terms "primary" and "secondary" to describe

the performance and/or the design of a frequency standard itself is discouraged. These aspects can be described adequately and accurately

by stating accuracy, reproducibility, and design features.

One class of frequency standards can be separated from the rest. We call those the evaluable frequency standards, which, by virtue of

their basic physical operation as well as their design, allow the experimental evaluation of all known influences which might alter the output

frequency. The accuracy of the evaluable frequency standard can thus

be stated for the single device without reference to any other frequency

standard. We will discuss it in more detail later in connection with

cesium beam frequency standards.

4. QUARTZ CRYSTAL DEVICES

4. 1 Quartz Crystal Resonator

The quartz crystal is a mechanical resonator much like our examples (a) and (b) of section 3. 1. The resonator's oscillations have

to be excited and sensed externally. In the case of a quartz crystal this

is done by taking advantage of its piezoelectric properties. The piezoelectric effect is a special property of a certain class of crystals.
Q

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19
Compression or dilatation of the crystal generates a voltage across the

crystal, and conversely, the application of an external voltage across

the crystal causes the crystal to expand or contract depending on the

polarity of the voltage. A crystal is not a homogeneous medium but has

certain preferred directions; thus, the piezoelectric effect has a directional

dependence with respect to the orientation of the crystal. In order to

take advantage of the piezoelectric effect one has to cut the crystal

resonator from the crystal block in a well defined way with respect

to the crystallographic directions. The raw material today is both

natural quartz and synthetic quartz. The crystal is cut out of the

raw crystal in the desired orientation with the aid of optical techniques which allow the determination of the crystallographic axes. The high precision final orientation of the cut and the tuning to the

desired frequency is then done by grinding and etching under control

of x-ray methods.

The quartz crystal can be cut and electrically excited in a variety of ways. The most common types of vibrations (modes)

are the longitudinal and thickness modes, the flexure (bending)

mode, the torsional mode, and the shear mode. In order to use the

piezoelectric effect, electrodes have to be put on some of the crystal surfaces such that the desired mode is excited. The electrodes are typically created as extremely thin metallic coatings by vacuum

evaporation of metals. Electric leads are attached to the electrodes,

(e.g., by soldering), which usually also serve as the mounting support thus freely suspending the quartz crystal. In order to least

perturb the mechanical vibrations of the crystal, the electrode

support leads are attached at points where no vibrational motion

occurs (nodes). The crystal is usually encased and the enclosure

is sometimes filled with a protective gas or is evacuated.

20
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23
A frequency standard can now be built by adding an electronic

amplifier (energy transfer), feedback, and a power supply. We call

such a device a quartz crystal oscillator. Its output frequency is determined by the quartz crystal resonator whose frequency in turn is

determined by the physical dimensions of the crystal together with the

.1. properties of crystalline quartz. The resonance frequency thus depends

on the orientation of the cut, the particular mode, and the dimensions

of the crystal. As an example, we find that the resonance frequency

for a longitudinal mode of vibration is approximately given by

V = 2.7 X lCf X \ , (5) o £ where & is the length of the crystal. Equation (5) is 'written such that the use of meters to express & will give the resonance frequency V in hertz.

Equation (5) allows us to estimate the size of crystals. For example,

a 100 kHz crystal will have a length which is of the order of a few centimeters and a 10 MHz crystal will have a length (thickness) of just a few

tenths of a millimeter. We see from this that the production of quartz

crystals with resonance frequencies much above 10 MHz is hardly possible.

However, one can excite resonators not only in their so-called fundamental

mode (which we discussed so far) but also at multiples (overtones) of this

fundamental resonance frequency. The best example for this is the violin

string which also can be caused to oscillate at frequencies which are

multiples of the fundamental frequency; the violinist depends on this.

Quartz crystals which are designed for the excitation of multiples of

their fundamental resonance are called overtone crystals.

4.2 Effects on the Crystal Resonator Frequency

Two-deleterious effects, among others, are important in the design

of crystals and crystal oscillators and limit their usefulness. The first

is the temperature dependence of the quartz crystal resonance frequency,

the second is a slow change of the resonance frequency as time goes on

(drift).

24
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FUNDAMENTAL

2nd OVERTONE

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The temperature dependence is caused by a slight change in the

elastic properties of the crystal with temperature. This can easily be

imagined from the general behavior of matter that the packing density

of atoms increases with lowering the temperature. However, certain

cuts, i.e., certain crystallographic orientations of the crystal, minimize

this effect over a rather wide range of temperatures, most notably the

so-called "AT" and "GT" cuts. Temperature coefficients of less than one part in 100 million per degree (celsius or kelvin) are possible, in

_g other words, the fractional frequency change will be less than 10 with

one degree of temperature change. Nevertheless, this effect demands

certain precautions in the design of a crystal oscillator if very high

frequency stabilities over longer times (hours or days) are desired

and/or if large environmental temperature fluctuations are to be

tolerated. Hence, crystals are enclosed in electronically regulated ovens which maintain a constant temperature; in certain crystal oscillators this is done to better than of a degree.

A different solution to the temperature problem is the so-called

temperature compensated crystal oscillator or TCXO. An additional

frequency determining element in the oscillator, which can essentially

be just a small capacitor (see our example (c) of sec. 3. 1), gives

the opportunity to tune the oscillator over a limited range by varying this

additional element. If a temperature sensor is added which causes a change in this capacitor one can adjust the response in such a way that

the change in resonance frequency of the crystal resonator is just

compensated by a suitable adjustment of the added capacitor. Bimetal

springs have been used which mechanically change the setting of the

capacitor much in the same way as the automobile choke in many automobiles works. Today, capacitors whose value changes with an applied

voltage (varactors) are used; the applied voltage is derived from a temperature sensing circuit. The TCXO thus does not necessarily

27
require further temperature control by an oven. However, we see the

drawback of this approach. In adding a further frequency determining

element, the crystal resonator has to relinquish a corresponding part

of its control on the output frequency of the whole oscillator. We,

therefore, realize that the stability performance of a TCXO will degrade

the more, the wider the temperature range of compensation is made.

The long-term stability (days) of TCXO's is therefore below that of

crystals with a good oven control. We find TCXO's in small, usually

portable units of relatively low performance, e.g., for applications

where frequency stabilities from day to day and frequency changes over some tens of degrees of temperature of not better than 10 are needed.

The drift, or aging, is a common behavior of all crystal oscillators.

It is a nearly linear (uniform) change in resonance frequency with time,

which is almost always negative, i.e., the resonance frequency decreases.

This decrease could be interpreted as an increase in the crystal size

according to eq (5). Many physical mechanisms have been considered as the cause: contamination of the surfaces (deposition of foreign material); changes in the electrodes or the metallic plating;

reformation of loose (from grinding and etching) surface material;

changes in the internal crystal structure; etc. ; all of this possibly caused

or enhanced by the vibrating motion of the oscillating crystal. Careful

fabrication and electrode design combined with clean vacuum enclosures

have led over the years to a reduction of the aging to about 10 per day

and better for the best crystals. This aging corresponds to 10 fractional

thickness change, as we can see from eq (5). For a 5 MHz crystal

with a thickness of a little less than a millimeter this aging corresponds

to an absolute thickness change of only 10 of a millimeter or less than — of one percent of the diameter of an atom. It seems surprising that

mechanical resonators can be built which change their dimension by so

little.

28
Two more effects on crystal resonators are to be considered.

One is its relative sensitivity to gravitational forces and acceleration:

frequency changes will occur because of the stresses in the crystal

caused by these forces. This influence depends on the direction of the

force relative to the crystallographic axes and thus can be minimized

for certain orientations. The magnitude of the effect is typically of the

order of 10 for accelerations corresponding to the earth's gravitation.

The other effect is related to intermittent operation. If a crystal

oscillator is turned off and, after some time, put back into operation

it will not oscillate immediately at the original frequency but will exhibit

first a "warm-up" due to temperature stabilization of the crystal

resonator and its oven and then for some time (as long as many days)

it will exhibit a large but decreasing drift until it reaches its previous

aging performance. The frequency at which it will then operate might

also be substantially different (as compared to its stability and aging

performance) from its frequency before the interruption.

4. 3 Quartz Crystal Oscillator Performance

Crystal resonators have Q-values which are typically in the range

from Q = 10 to almost Q = 10 . These are very high Q-values as compared to most other resonators except, most notably, atomic resonators.

These high Q-values are an essential prerequisite for the excellent

stability performance of crystal oscillators. The best presently available

devices show stabilities of a few parts in 10 for sampling times from one second to a day. There is some experimental evidence that the stability

is limited not by the crystal resonator but by noise in the electronic

components in the oscillator circuits. This noise (flicker noise) may

possibly be reduced by a special selection of low noise components

(transistors, capacitors, etc. ) and by some special circuit design. Thus

there is a reasonable chance that the stability may reach values of better

29
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30
than 10 for sampling times of seconds to hours. For times of about

one millisecond or less, the stability is often determined by additive

noise in the output amplifiers and can then be reduced by a (crystal)

filter in the output. The long-term stability beyond several hours

sampling time is determined by the aging and by external influences

such as line voltage variations, temperature fluctuations, etc. A specification of accuracy is not very well possible with crystal oscillators.

Without any frequency calibration they possibly can be fabricated via

thickness -determination (not very practical) to about 10 frequency

accuracy. If they are calibrated against a high accuracy frequency

standard they maintain this calibration (accuracy) according to their

long-term stability performance, e.g., a crystal with the low aging of

10 per day will be accurate to a few parts in 10 for the duration of a year.

We realize, therefore, that crystal oscillators require calibration,

which may be rather frequent depending on the requirements. The frequency adjustments are being made with a small added capacitor in much

the same way as we discussed before in connection with the TCXO. The

most stable ones with the lowest aging rate cost approximately $2000,

have a volume of a few thousand cubic centimeters, and require a power

of about 10 watts. They have an elaborate crystal oven for temperature

control, well-designed electronics, and usually several output frequencies

which are derived from the oscillator frequency with the aid of frequency

dividers and multipliers. These high performance devices presently use

5 -MHz or 2. 5 -MHz crystal resonators with Q-values of a few million.

31
Crystal oscillators which are cheaper and/or smaller are available

in an immense variety of designs at certain sacrifices in frequency

stability and/or environmental insensitivity . Costs can go down to below $100, sizes to a few cubic centimeters, and power requirements

to less than 0. 1 watt. The reliability of crystal oscillators is usually

not limited by the crystal, the mean time between failure (MTBF) being

that of any electronic circuit of equivalent sophistication.

5. ATOMIC RESONANCE DEVICES

5. 1 Atomic Resonators

The basis of commercially available atomic frequency standards are resonances in atoms at microwave frequencies (range 1 to 100 GHz,

GHz = gigahertz = billion hertz). Resonances in molecules and resonances

at higher frequencies in the infrared and visible regions have been studied

for frequency standard applications but have not yet led to practical

devices; however, their potential is highly promising (see sec. 8).

We will confine ourselves, therefore, to the discussion of microwave

resonances in atoms. We may picture such a resonance as a little magnetic

dipole antenna as was discussed in our example (e) in section 3. 1. We

will typically deal with a great many of these dipole antennas (atomic

resonators), and we can separate them into two kinds : (1) receiving

antennas, which will absorb energy from a field at their resonance

frequency, much like our TV antenna at home, and (2) transmitting

antennas which will radiate energy at their resonance frequency in a fashion analogous to the action of the transmitting antenna of a broadcasting station. A physicist might say that the atoms which act like

a receiving antenna are in the "lower state" and those acting like a

7 Of course, this is a simplification.

32
transmitting antenna are in the "upper state" . In a natural ensemble

of a great many atoms (a gas), we will find that the total number of

upper state atoms is nearly equal to the total number of lower state atoms. This has an important consequence: if this gas is placed in an external magnetic field, which oscillates at the atomic resonance

frequency, all atoms may resonate; however, nearly half of the atoms

receive (absorb) energy from the field, the other half emit (add) energy

of an equivalent amount to the field. It is obvious that the net effect is almost zero; the gas as a whole acts as if it has almost no resonance

although the individual atoms each may resonate. From this we see

that in order to observe the atomic resonance we have to change somehow the relative amounts of the two kinds of atoms; the upper or the

lower state has to be in the majority. The way in which this is done

determines the design of an atomic resonance device, which is the

frequency determining element in our atomic frequency standard.

5. 2 State Selection < We will now discuss the two most important methods to accomplish

what is called state selection: the change in the relative numbers of the

two kinds of atoms.

(a) Spatial state selection : This method relies on an actual sorting

procedure where the two atomic states are sorted into different directions

in space. One of the states can then be used, the other is discarded.

As an example, an actual system may produce an atomic gas by heating

the substance in an oven to a suitable temperature. The atoms leave the oven through a hole and form an atomic beam in an adjacent vacuum

chamber. The atomic beam is then passed through a rather strong magnet

8 There is a peculiarity with atoms: an atom changes from the upper

to the lower state upon emission of a well-defined amount of energy,

and, correspondingly, an atom changes from the lower to the upper

state after receiving an equal amount of energy at the atomic resonance

frequency.

33
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34
which causes the separation of the beam into two beams, each of them

containing only one kind of atoms. We remember that our picture of an atom is that of a little magnetic dipole antenna. The magnet exerts

a force on these magnetic dipoles, which point in opposite directions

for the two different atomic states (we note this without further explanation).

(b) Optical state selection : This technique takes advantage of the fact

that the atoms have more than just one resonance. Other resonances

typically correspond to infrared or visible (light) frequencies. We can

excite one of these resonances by shining intense light of the corresponding

frequency on the atoms. If the light is filtered carefully, very monochromatic (one color, i.e., a very well-defined frequency) light is obtained. If the light frequency is chosen properly, only one kind of the

atoms will resonate. At the same time, this light frequency is too

far away from the corresponding light resonance of the other kind of

atoms. The light resonance can thus "remove" one kind of the atoms

and provide for the desired majority of the other kind.

5. 3 Interrogation of the Atoms

We are now almost in a position to assemble our atomic frequency

standard. We still need some means to observe the atomic resonance. A microwave cavity is typically used. Such a cavity has microwave

resonances which are determined by its physical size. The (electrical)

losses of this cavity are given by the electrical conductivity of the cavity

material. Such a cavity may have the shape of a cylinder or that of a box. It resonates in a way quite similar to the working of an organpipe in the case of acoustic waves. The best known example of a microwave cavity is the microwave oven where food is cooked or fried by placing it into the resonance field of a cavity. In order to observe the atomic

resonance we have to place the state selected atoms inside of this cavity

35
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and subject them for some specified time to a microwave signal at their resonance frequency. The microwave signal will change the relative

number of atoms in the two states, e.g., if all atoms were initially in

the upper state we find some in the lower state after the microwave

signal acted upon them for some time (see footnote 8). If the frequency

of the external microwave signal is exactly at the atomic resonance

frequency, this transfer of atoms from one state to the other reaches a maximum. The center of the atomic resonance is thus found by monitoring the number of atoms in one of the two states and by varying the

microwave frequency until the number of atoms in the lower state reaches

a maximum, or the number of atoms in the upper state a minimum. A

proportional electric signal can be derived which is fed back to the

oscillator generating the microwave signal. Thus an automatic servo

can be built which keeps the oscillator (usually a crystal oscillator)

locked to the atomic resonance.

5.4 Signal Detection

The detection of the effect of the microwave signal on the atoms

can be done in basically three ways, two of which relate to the two

methods of state selection.

(a) Atom detection : The atoms which leave the cavity as an atomic beam

are passed through the field of a magnet which spatially sorts the two

states. An atom detector is placed to intercept one of these states. The output of the detector thus indicates the number of atoms in the

upper (or lower) state.

(b) Optical detection : If the atoms are optically state selected, a detector

for light (photo-detector) can be placed in a position such that the light

which has interacted with the atoms is detected. Since the light removes

atoms from one of the states, its intensity will change if atoms which

resonate at the light frequency are added. Such an addition takes place

37
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as a result of the microwave signal which, in effect, transfers atoms

from one state (with no light interaction) to the other (taking part in the

light resonance). The light at the photo -detector therefore is a measure

of the r rnber of atoms in one of the states.

(c) Microwave detection : In this type of detection, the microwave signal

is transmitted through the cavity to a microwave detector. Since the

atoms will either add energy to the signal (if initially in the upper state) or subtract energy (if initially in the lower state), the microwave power

level at the detector is a measure of the number of atoms changing state.

5. 5 Atomic Frequency Standard

The analogy to our mechanical frequency standard, the wrist watch,

which we discussed in section 1, may now be drawn: the frequency

determining element is the atomic resonator which consists of a cavity

containing the state selected atoms, and some means of detecting the

change in the number of atoms in the two states. A control signal,

related to the number of atoms which changed their state due to the action

of the microwave signal, is fed back to the (crystal) oscillator. The

oscillator and the associated frequency multiplier or synthesizer

correspond to the energy transferring means in our wrist watch (see

sec. 1).Some power supply has to provide for the energy necessary to drive the oscillator, multiplier, and possibly the atom state selector.

Very high Q-values can be achieved with atomic resonators. To understand this, we have to recall our eqs (3) and (4).

As we discussed before, good crystal oscillators are available at frequencies of several MHz; the atomic resonances are at GHz

frequencies. The crystal oscillator frequency therefore has to be

multiplied by a factor of about 1000.

40
STATE SELECTED

ATOMIC BEAM •»««

MICROWAVE SIGNAL

(OF ATOMIC RESONANCE

FREQUENCY)

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41
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The Q is related to the time T, which describes the average

duration of oscillations of the resonator. In atomic resonators we find

two chief causes for the termination of oscillations. The first one is

collisions of the resonating atoms with each other and with surrounding

walls; each collision usually terminates the oscillation. The second

one is a rather obvious cause: the atoms may simply leave the region

of microwave signal interaction. In an atomic beam apparatus, the

atoms enter the cavity, traverse the cavity in a certain time, and then

leave the cavity. As an example, let us assume that we have a cavity

of 1 meter length which is traversed by atoms with an average speed of

100 meters per second (a typical value). We assume an atomic resonance

frequency of 10 GHz. The interaction time T is then second, the

linewidth 100 Hz (from eq (3)), and the Q-value is 10 (from eq (4)).

We arrived at a Q-value which is considerably better than that of a quartz crystal oscillator!

5.6 Effects on the Atomic Resonator Frequency

Before we discuss effects which might cause changes in the output

frequency of an atomic standard, we should make a very important statement: The atomic resonance frequency itself is given to us by nature,

it will not drift or age. Hence, atomic resonators with Q-value s of 1 or higher may be expected to have accuracies of a part in 10 or better

because we will not be able to pull the resonance frequency further away

than the linewidth of the resonance.

In the following, we are not exhaustive but list only the major

perturbing effects:

43
(a) Noise : Random noise in the crystal oscillator, the detector, the

microwave cavity, and the frequency synthesizer will cause corresponding fluctuations of the output frequency.

(b) Cavity pulling : The microwave cavity is itself a resonator. Thus

we have an additional frequency-determining element besides the

atoms. It influences the output frequency by pulling the combined

resonance frequency to a value which usually lies between the resonances of the atom and cavity. This necessitates the tuning of

the cavity to the atomic resonance. The requirements for tuning

will be relaxed if the Q-value of the atomic resonance is as high as

possible and the cavity-Q as low as possible.

(c) Microwave spectrum; If the exciting microwave signal has not a symmetric but an asymmetric distribution of frequencies , a frequency pulling occurs which conceptually is related to the mechanism

of cavity pulling. By careful design in the electronics, this effect can be made negligible.

(d) Collisions : Collisions between the atoms, and between the atoms and

the walls of a vessel (gas cell) in which the atoms may be contained,

will not only shorten the duration of the oscillation but also cause a frequency shift. Obviously, these effects can be minimized by having

low atom densities and no walls, if possible.

(e) Popple r effect : The apparent change in frequency if the emitter moves

relative to an observer is called Doppler effect. Everybody knows

this for acoustic waves from the experience of an approaching,

whistling locomotive or from automobile racing. Here, the moving

objects are the oscillating atoms and the observer is the microwave

The microwave signal will never be just one single frequency but will

have a certain distribution of frequencies (spectrum).

44
cavity. The Doppler effect can be highly reduced by choosing a particular direction of the atomic beam with respect to the direction

of the oscillating magnetic microwave field in the cavity; in our

acoustic example, this corresponds to the passing of the whistle at some large distance instead of having the whistle move directly

towards the observer. An alternate way of reducing the Doppler

effect is the containment of atoms in a region small compared to

the wavelength of the microwave radiation, e.g., by placing a gas

cell inside of the cavity,

(f) Magnetic field : Of the effects which we discuss here, this is the

only one which directly affects the atomic resonance. We remember

that we used a small magnetic dipole antenna as the model for the

atomic resonance. If this antenna is placed in an external static

magnetic field (as that of a permanent magnet) the tuning of the

antenna changes, i.e., the atomic resonance frequency changes.

This necessitates magnetic shielding, which is a characteristic

design feature of all presently used atomic frequency standards.

The shielding is usually quite elaborate and reduces the external

magnetic fields, e.g., the earth's magnetic field, to 1% or less of

its external value. This residual magnetic field can then be measured

quite precisely by using the atomic resonance itself. In fact, the

associated measurement precision is so good that magnetic field

effects do not seriously impair the accuracy of atomic frequency

standards. However, fluctuations of the external magnetic field, or

the movement of the device through a varying field, e.g., as in a

relocation, may perturb the frequency of the atomic standard.

45
Generally speaking, one tries to minimize all of the effects listed

above, and to keep their influence as stable with time as possible.

Such an approach suffices for most applications . For laboratorystandards, however, where frequency accuracy is the primary purpose,

all effects must be evaluated in a series of experiments, and revaluations must be done occasionally in order to detect changes with time.

6. AVAILABLE ATOMIC FREQUENCY STANDARDS

We will now discuss the design and performance of the three types

of atomic frequency standards which are currently in operational use.

6. 1 Cesium Beam Frequency Standard

The atomic resonance is at 9192 631 770 Hz. The standard is based

on the atomic beam method using spatial state selection and atom

o detection. An oven contains the cesium metal. If heated to about 100 C,

enough cesium gas will be produced to form an atomic beam which leaves

the oven through one or many channels into a vacuum chamber. This

chamber is evacuated to a pressure of less than 10 of atmospheric

pressure. The beam traverses first the state selecting magnet, then

12 the microwave cavity where an external microwave signal acts on the

beam, and finally reaches the atom detector after passing another state selecting magnet. The atom detector is simply a wire (typically

The magnetic effect is an exception. The residual magnetic field inside

of the shields must be evaluated and possibly reset any time after changes

in the external field occur, e.g., after moving the device. The magnetic

shields may also have to be demagnetized.

12 Typically, a cavity with separated interrogation regions is used. This

design offers certain advantages over a simple cavity of a length

equivalent to the separation of the two regions.

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made from tungsten) whichis heated to about 900 C by passing an

electric current through it. Cesium atoms which impinge on this wire

(which is biased •with a few volts dc) become electrically charged (ionized)

and can be collected on an auxiliary electrode. The stream of electrically

charged atoms at this electrode represents an electric current which is amplified, detected, and fed into the feedback network.

The speed of the atoms and the length of the cavity determine the

Q-value of the atomic resonator. Typical atom speeds are 100 meters

per second. In commercial devices which have to be reasonably small,

the cavity is about 0.4 meter long; the corresponding interaction time

T is four thousandths of a second. From eqs (3) and (4), we calculate a linewidth of a few hundred hertz and a Q-value of a few 10 .

In laboratory devices one can go to very long cavities. Cavities of up

to 4 meters long are used, leading to Q-values of a few 10 . The

fractional frequency stability of both commercial and laboratory devices

reach 10 at sampling times of hours to days. The short-term frequency

stability is limited by fluctuations in the atomic beam intensity which are

basic and unavoidable ("shot noise"). These fluctuations affect the frequency stability less if more intense atomic beams are used. Such

devices, which are becoming available, improve the stability at sampling

11 12 times of 1 second from about 5 parts in 10 to about 6 parts in 10 . In contrast to commercial devices, the laboratory standards are designed

to allow a complete evaluation of all effects on the frequency. Cesium

standards are used extensively where its high reproducibility and unexcelled

long-term stability (sampling times of more than a day) are needed. For

most applications, cesium standards need not be calibrated. They are the

work horses in most of today's standard frequency and time services.

The laboratory standard serves to realize the definition of the second

(see sec. 1).

49
6.2 Rubidium Gas Cell Frequency Standard

The atomic resonance is at 6834 682 608 Hz. The standard is based on the gas cell method using optical state selection and optical

detection. The gas cell contains rubidium gas at a pressure of only

about 10 of atmospheric pressure. In order to reduce the effect of

collisions among the rubidium atoms, an inert buffer gas (e.g., argon)

is introduced into the cell at a pressure of 1/1000 of atmospheric

pressure. This allows lifetimes of the rubidium atom oscillations

(the oscillation lifetime T is still limited by atom collisions) of about

1/100 second. From eqs (3) and (4) we calculate a corresponding

linewidth of about 100 Hz and a Q-value of several 10 . Atomic collisions as well as the light and the microwave signal acting simultaneously on the

same atoms cause frequency shifts of the order of 10 . These frequency shifts depend strongly on the composition, temperature, and

pressure of the buffer gas and on the intensity of the light. As a result,

rubidium gas cells vary in their resonance frequency by as much as

10 depending on the particular setting of the frequency shifting parameters

during manufacturing. Since these influences cannot be expected to stay

unchanged as time goes on, rubidium standards need not only initial

calibration but also recalibrations because they exhibit a frequency

drift, i.e., an aging analogous to crystal oscillators. The stability

performance of rubidium standards is nevertheless quite spectacular.

At one second sampling time they display a stability of better than 10

and perform near the 10 level for sampling times of up to a day. For

longer times the frequency stability is spoiled by the frequency drift

which is typically 1X10 per month (much less than the drift of crystal

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oscillators). Rubidium standards are used where excellent mediumterm stability (minutes to a day) is needed, where its reduced costs,

size, and weight, as compared to cesium standards, are important,

and where a crystal oscillator with its more frequent needs for recalibrations and its greater environmental sensitivity does not suffice.

6. 3 Atomic Hydrogen Maser

The atomic resonance frequency is at 1420 405 752 Hz, The

standard is based on the atomic beam method using spatial state selection

and microwave detection. The beam source is a radio frequency gas

14 discharge in molecular hydrogen which produces atomic hydrogen with

high efficiency. The atomic hydrogen beam leaves the source through

one or many channels into a vacuum chamber. The beam then traverses

a state selecting magnet and enters a storage bulb in the microwave

cavity. The storage bulb is made from quartz glass which has low

electric losses and thus does not spoil significantly the cavity-Q.

The storage bulb is evacuated to a pressure of less than 10 of atmospheric pressure. Its inner walls are lined with a fluorocarbon

coating, a substance similar to the non-stick coating in cookware.

This coating allows many collisions of the hydrogen atoms with the

walls without significantly disturbing the oscillations of the atoms.

The underlying physical mechanisms are not yet fully understood. The

storage bulb is typically 0. 15 meters in diameter and dimensioned in

such a way as to keep hydrogen atoms for a time of about one second.

Maser is an acronym meaning microwave amplification by stimulated

emission of radiation.

All natural hydrogen gas is composed of hydrogen molecules; each

hydrogen molecule is formed by chemical bonding of two hydrogen atoms,

53
Then they leave the bulb and thus leave also the microwave cavity.

From eqs (3) and (4) we calculate a linewidth of about 1 Hz and

a Q-value of about 10 , the highest Q-value of all presently existing

atomic resonators. If the intensity of the hydrogen beam, which consists

only of upper state atoms (emitting atoms), is sufficiently large and if the

cavity losses are sufficiently low, self-oscillation will start in the cavity;

i.e., the maser itself will generate a microwave signal. We have a maser-oscillator with an output frequency directly derived from the

atomic resonance. A crystal oscillator can be locked to this frequency

by frequency comparison techniques. As compared to the cesium

standard, the hydrogen maser is not quite as accurate because of

experimental difficulties in the evaluation of the frequency shift due to

the collisions of the hydrogen atoms with the fluorocarbon surface of

the storage bulb. In order to obtain self-oscillation the cavity- Q must

be relatively high. Thus cavity pulling is relatively strong, and it limits

the long-term stability (over times longer than several days) to values

not quite as good as those possible with cesium standards. In the region

from a few seconds to a day the hydrogen maser has the best stability of

all existing standards. Its application is rather limited to uses where

these stabilities are critical and where a rather bulky device is no

handicap. Unlike cesium and rubidium standards, hydrogen masers

have not yet been evaluated under adverse environmental conditions.

The number of hydrogen masers in use is very small compared to the

numbers of cesium beam devices and of rubidium devices.

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8. TRENDS

All devices which were discussed in this report have improved

over the past years in one or more of the following aspects: reliability,

size, weight, stability performance, and environmental insensitivity.

A considerable amount of effort is still being expended to go further in

this direction; however, it would be inappropriate here to try to estimate

the improvement of performance specifications which might (or might

not) be achieved in the future.

There are several other devices, designs, and concepts which

have been studied or are being investigated with some potential for

future use in frequency standards. Most of these are summarized in

Table 2.

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62
9. LITERATURE

The following references are a limited selection. They are intended as a guide for those who wish to penetrate the subject in greater depth.

A. Introduction

(1) J. Kovalevsky , "Astronomical Time", Metrologia 1 (1965)169.

(2) H. M. Smith /'International Time and Frequency Coordination",

Proc. IEEE 60 (1972) (to be published).

(3) The American Ephemeris and Nautical Almanac , U. S. Government

Printing Office , Washington, D. C.

(4) P. P. Viezbicke, "NBS Frequency and Time Broadcast Services"

NBS Special Publication 236 (1971).

B. Basic Concepts

(1) D. W. Allan, "Statistics of Atomic Frequency Standards, " Proc. IEEE 54 (1966) 221.

(2) J. A. Barnes et al, "Characterization of Frequency Stability"

IEEE Trans, on Instr. and Meas, IM-20 (1971) 105.

(3) L. S. Cutler and C. L. Searles , "Some Aspects of the Theory and

Measurement of Frequency Fluctuations in Frequency Standards, " Proc. IEEE 54 (1966) 136,

C. Frequency Standards, General Aspects

(1) Most general physics textbooks.

(2) A. E. Siegmann, "An Introduction to Lasers and Masers'J

Chapter 2, McGraw-Hill 1971.

D. Quartz Crystal Devices

(1) E. A. Gerber and R. A. Sykes, "State of the Art - Quartz

Crystal Units and Oscillators," Proc. IEEE 54 (1966) 103.

(2) E. A. Gerber and R. A. Sykes, "A Quarter Century of Progress

in the Theory and Development of Crystals for Frequency Control

and Selection, " Proc. 2 5th Annual Symp. on Frequency Control,

Ft. Monmouth, N. J. (1971) 1 (available from Electronic Industries

Assoc. , Washington, D. C. ). (3) R. A. Heising, "Quartz Crystals for Electrical Circuits, " Van Nostrand, 1946.

63
Atomic Resonance Devices

(1) N. F. Ramsey, "History of Atomic and Molecular Control of

Frequency and Time, " Proc. 25th Annual Symp. on Frequency

Control, Ft. Monmouth, N. J. (1971) 46 (available from Electronic

Industries Assoc. , Washington, D. C. ). (2) N. F. Ramsey, "Molecular Beams, " Oxford, 1956.

(3) A. E. Siegmann , "An Introduction to Lasers and Masers",

McGraw-Hill, 1971.

Available Atomic Frequency Standards

(1) A. O. McCoubrey , "A Survey of Atomic Frequency Standards, " Proc. IEEE 54 (1966) 116.

(2) D. Kleppner, H. C. Berg, S. B. Crampton, N. F. Ramsey,

R. F. C. Vessot, H. E. Peters, and J. Vanier, "Hydrogen-Maser

Principles and Techniques, " Phys. Rev. 138 (1965) A97 2,

(3) R. E. Beehler, R„ C. Mockler, and J. M. Richardson, "Cesium

Beam Atomic Time and Frequency Standards, " Metrologia 1 (1965) 114.

(4) P. Davidovits and R. Norvick, "The Optically Pumped Rubidium

Maser',' Proc. IEEE 54 (1966) 155.

G. Trends

(1) H. Hellwig, "Areas of Promise for the Development of

Primary Frequency Standards, " Metrologia 6 (1970) 118.

(2) H„ S. Boyne, "Laser Frequency Stabilization Techniques and

Applications," IEEE Trans, on Instr. and Meas. IM-20 (1971) 19-

64
ACKNOWLEDGMENTS

The author wishes to thank Byron E. Blair for his assistance in

setting up the basic outline of this paper, and Donald Halford and David

W. Allan for their assistance in the preparation of this paper.

65

form NBS-114A (1-711 U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

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1. PUBLICATION OR REPORT NO. NBS Technical Note 61

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4. TITLE AND SUBTITLE Frequency Standards and Clocks: A Tutorial Introduction5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

Helmut Hellwig

8. Performing Organization

10. Project/Taslc/Work Unit No. 2730418

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS, Boulder Labs.

DEPARTMENT OF COMMERCE Boulder, Colorado ;80 302

11. Contract/Grant No. E111M-6

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Richards Gebaur Air Force Base

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16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) The topic of frequency standards and clocks is treated in a tutorial and non- mathematical way. The concepts of time, frequency, frequency stability, and

accuracy are introduced. The general physical principles and design features

of frequency standards and clocks are described. The design, performance,

and limitations of quartz crystal oscillators and atomic devices (cesium, hydrogen,

rubidium) are discussed in detail and critically compared for laboratory devices

as well as for devices intended for field usage.

17. key WORDS (Alphabetical order, separated by semicolons) Cesium beam; Clocks (atomic); Crystal

oscillator; Frequency accuracy; Frequency stability; Frequency standards; Hydrogen

maser; Quartz crystal; Rubidium gas cell; Timekeeping

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