# Clock and Watch Movements

### From Pendulum Clocks to Atomic Clocks

This page describes some key technical developments in the measurement of time with accuracies improving from 15 minutes per day to 1 second in 300 years.

## Accuracy

Time is measured by counting events such as the Sun's motion across the sky, a pendulum's swing, the oscillations of a quartz crystal or the vibrations of an atom. For want of an accurate timekeeper, Galileo used his heart beat to determine time periods, while John Harrison of "Longitude" fame used the apparent movement of the stars to calibrate his clocks. The more frequent the event, the greater the potential accuracy of the clock.

## The Mechanical Timekeeper's Main Components

The energy source which drives a mechanical clock or watch is usually either a heavy weight suspended on a cord, or a chain, looped around the circumference of a drum causing it to rotate, or alternatively, a large spring serving the same purpose. In both cases the drum or the spring must be wound regularly to replenish the energy. The component which controls the timepiece's heartbeat is the escapement and its pulse rate, or timekeeping, is regulated by a harmonic oscillator consisting of a pendulum or a balance wheel incorporating a small balance spring.

The torque from the energy source is transmitted through the gear train to the escapement which only allows power to "escape" from the energy source in short impulses of fixed duration and frequency which are transmitted through the gear train to the counting mechanism or pointers. The oscillator is a resonant device with a fixed characteristic resonant frequency of oscillation, often called the "beat" frequency which depends on its construction, its materials, its degrees of freedom its restoring force and its operating conditions. It is the property of resonant devices that they resist oscillating at other rates and tend to return to their resonant rate if subject to a temporary disturbance and it is this property which controls the timekeeping. If the operating conditions change however, the device will run at a different resonant frequency unless some form of compensation is applied.

A timekeeping mechanism is said to be "isochronous" if it continues to run at the same rate regardless of changes in its operating conditions, such as the drive force, the amplitude of the motion or the ambient temperature, so that it keeps correct time as the mainspring unwinds or as the temperature affects the balance spring or the pendulum.

In the case of the pendulum, the resonant frequency is determined by its length. It does not depend on the weight of the pendulum bob and for low amplitudes it is independent of the amplitude of the swing.

Huygens determined that the period P of a pendulum is given by:

P = 2 π √(l/g)

Where l is the length of the pendulum and g is the acceleration due to gravity.

In the case of a balance wheel, the frequency is mainly determined by its mass and the elasticity of the balance spring.

## Escapement Mechanisms

Dozens of different escapement mechanisms have been developed by horologists over the years but most of them have in common, a toothed escape wheel, geared to, or mounted on the same shaft as the driving pinion gear, and two pallets, mounted on opposite ends of an oscillating shaft or bar. (Five examples are shown below.) The oscillator's rocking bar is connected to the pendulum, or to the spring of the balance wheel, which cause the bar to rock back and forth in unison with each swing of the pendulum or the balance wheel. The pallets are inserted and withdrawn alternately, one in while the other is out, between the teeth close to opposite sides of the escape wheel, in a rocking motion to lock or release the wheel which is held under constant torque by the clock's or the watch's mainspring and gears. With each swing of the rocking bar, as one pallet is withdrawn, there is a short delay before the second pallet engages with the opposite tooth in the escape wheel and this period, when neither pallet is engaged with the escape wheel, provides the time for the wheel to make a small, predetermined rotation which drives the pointers. This duration of this delay is most important since this is what controls the timekeeping. At the same time, as the pallet exits from the tooth during the release of the escape wheel, the releasing tooth gives the oscillating bar a slight push to replace the energy lost by friction during its cycle in order to keep the timekeeper oscillating. While the escapement provides the energy for the oscillator, it is designed to be as detached from it as possible to allow the oscillator to swing as freely as possible.

The sudden stopping of the escapement's pallet in the escape wheel is what generates the characteristic "ticking" sound in mechanical clocks and watches.

Wear and tear on the moving parts contribute to poor timekeeping. Applying lubricants to overcome this brought its own problems. A wide range of lubricants was used in early clocks, many of which deteriorated leaving deposits of variable thicknesses on the pallets and escape wheels and this uncontrolled geometry also affected the timekeeping.

## Compensating Devices

Various devices have been developed to overcome the non-linear performance of watch mainsprings and to compensate for the effects of temperature on timing devices. These include the fusee and the remontoire which are designed to maintain a constant torque on the main driving pinion, the gridiron pendulum which keeps the pendulum's length constant and bimetallic strip which adjusts the tension on the balance spring to maintain constant restoring force on the balance wheel. Examples and explanations are shown below.

## Verge Escapement and Foliot

### The Verge and Foliot Escapement, dating from 1285, is the earliest known mechanical clock movement.

Power is derived from a falling Weight suspended from a cord wrapped around a Drum geared to the Pinion Gear which also drives the clock's Pointers.

The tension due to the weight hanging on the cord causes the drum to rotate turning the pinion gear which is fixed to the cup shaped Crown Wheel or Escape Wheel.

The Escapement prevents the free rotation of the pinion gear and only allows intermittent rotation of the shaft in fixed intervals.

Two Pallets are mounted on the Verge shaft and engage with the Ratchet Teeth on opposite sides of the crown wheel. The pallets are not mounted in the same plane but offset from eachother, perpendicular to the verge shaft, but with an angular displacement around it so that only one pallet can be engaged with a tooth in the crown wheel at any one time. The crown wheel must have an odd number of teeth, otherwise the pallets would not be free to move as the crown wheel rotated.

The clock's Timing Cycle, its characteristic Tick, occurs as follows:

The rotation of the crown wheel is initially blocked temporarily by one of the pallets bearing on one of its teeth while the second pallet is not in contact with the crown wheel. The crown wheel rotates due to the force derived from the falling weight or spring and, as it does so, its blocked tooth pushes the pallet out of the way causing the verge shaft to rotate. This rotation of the verge pushes the second pallet into the path of the crown wheel teeth on the opposite side of the wheel, blocking its movement once again. Once more the crown wheel tooth pushes the pallet out of the way, but since the tooth is on the opposite side of the wheel, it pushes the pallet in the opposite direction, turning the verge shaft back to its initial position. Then the cycle repeats rotating the verge back and forth by about 100° in each direction.

The Foliot or balance bar, connected to the verge shaft, is the basic timekeeping device, oscillating back and forth with the rotation of the verge, it is used to provide the clock's Regulation. It is not however a true resonant oscillator with a characteristic resonant frequency, as defined above, so that it does not provide an external reference restoring force to change the verge direction. Instead the verge is driven back by the escape wheel itself. The foliot's period is determined only by the inertia of its crossbar and weights which determine the speed at which the verge shaft can rotate and hence the timing interval. Moving the weights outward from the shaft increases the inertia and slows the oscillations and the duration of the timing cycle.

Shortcomings of the verge escapement include:

• Because the verge system using the foliot balance does not have a characteristic resonant frequency which could be used as a reference, it is not a reliable timekeeper.
• Due to potential overshoot of the foliot bar at the end of each swing, the gear train is briefly driven backwards (recoils) as the balance oscillates, contributing to wear and inaccuracy.
• It is also sensitive to variations in the driving torque.

Timekeeping accuracy was no better than 15 minutes per day.

Later verge clocks kept the verge escapement but replaced the timekeeping foliot with a Balance Wheel or a Pendulum oscillator to improve accuracy and regulation.

In 1656, Christiaan Huygens was the first to apply a pendulum to timekeeping in mechanical clocks. He used it with a verge escapement with a vertical drive axis and a horizontal verge axis.

The incorporation of a pendulum improved the accuracy to around 15 seconds per day.

His design, though innovative, was not successful because of the very large amplitude angular swings of the pendulum needed by the verge escapement.

See more about the Verge Escapement.

## Anchor Escapement

The Anchor Escapement, a simpler, more accurate, improvement on the Verge pendulum escapement was invented by Robert Hooke around 1658. Also called the Recoil Escapement because of its distinctive recoil movement, it was a major breakthrough in timekeeping accuracy and became the standard escapement used in pendulum clocks until the late 1800s.

It was constructed from three essential components an escape wheel, driven by the clock's gear train, and a pendulum to which was connected to a pivoted bar with a pallet at each end, called an anchor because of its shape. As the anchor is tilted from side to side by the pendulum, its pallets alternately mesh with the teeth of the escape wheel temporarily locking and unlocking the wheel. The inertia and trajectory of the pallet hitting the tooth, as it enters the escape wheel, creates a short, undesirable recoil on the wheel, but as the pallet begins to exit from between the teeth, the wheel is released and continues its rotation and the recoil is followed by the tooth pushing on the anchor giving it an impulse which it transmits to the pendulum to replace the energy it lost by friction, thus keeping it swinging.

• The use of a separate reference pendulum oscillator provided a stable time base which was key to improving timekeeping accuracy.
• As discovered by Huygens, the linearity of the pendulum's swing is much better at low amplitudes than high amplitudes. The anchor escapement avoided the very high, awkward swings of around 100° needed with the verge escapement.
• All the components and their motions were in the same plane making the motion more stable, simplifying manufacturing and allowing thinner designs.
• The exact shapes of both the escape wheel teeth and the anchor pallets were not crucial.

Weaknesses were:

• The most serious issue was the recoil which propagates back down the drive gear train with each swing of the pendulum, increasing wear, backlash and inaccuracy.
• The friction of the pallets sliding on the teeth of the escape wheel was also a source of wear and poor long term timekeeping.

The Anchor Escapement was eventually superseded by the Deadbeat Escapement.

The Deadbeat Escapement was invented by Richard Towneley around 1675 and first widely used by clockmaker George Graham beginning in 1715 and often attributed to him as the Graham Escapement.

It is similar to the Anchor Escapement but was designed to avoid its recoil and its long sliding contacts between the pallets and the escapement teeth by changing the profile and positioning of the pallets and the profile of the teeth. The escape wheel has long deep teeth and the pallets make only a very short contact with them. The pallets are also arranged to that the forward pallet, the one which enters the approaching tooth, contacts it on its outside surface, while the lagging pallet contacts the leaving tooth with its rear surface. In this way the escape wheel does not suffer any recoil, hence the name "deadbeat".

Because of its reduced friction, its time between windings was also greatly extended.

The Deadbeat Escapement delivered superior accuracy and timekeeping and is still used in most pendulum clocks today.

## Balance Spring Escapement

The Balance Spring Escapement was invented in 1675 for use in watches and portable timepieces by Christiaan Huygens.

In 1657, Robert Hooke first proposed the idea of using a straight, flat balance spring as the basis of a clock's timing oscillator instead of the traditional pendulum. Instead of gravity providing the restoring force, it could be provided by a spring which, following to Hooke's Law, provides a restoring force proportional to its displacement.

Huygens, meanwhile, realised that a spiral torsion balance spring enabled the design of smaller, more practical and robust clocks. The example opposite shows an early balance spring oscillator used with a version of the verge escapement.

The oscillating balance wheel, fixed to the verge shaft, replaces the inertia of the foliot balance bar while the balance spring, often called a "hairspring", which winds and unwinds with each cycle converts it into a true harmonic oscillator with a characteristic resonant frequency.

The incorporation of the balance spring oscillator improved the timekeeping of portable timepieces previously measured in hours per day to less than 10 minutes per day but still much worse than the pendulum clock.

Remaining shortcomings included:

• Sensitivity of the balance spring's elasticity to changes in temperature.
• Reduction in the torque from the mainspring as the spring wound down.
• Increasing friction as the lubricating oil ages.

From its invention in the 17th century until tuning fork and quartz movements became available in the 1960s, virtually every portable timekeeping device used some form of balance wheel oscillator.

## Grasshopper Escapement

The Grasshopper Escapement was designed in 1722 for use with pendulum clocks by English clockmaker John Harrison who made the first successful marine chronometer.

Harrison was obsessed with eliminating friction and wear in order to improve timekeeping and his complicated, friction free, grasshopper escapement, like the Deadbeat Escapement, was an improvement on the Anchor Escapement. The pallets jump clear of the escape wheel and make no sliding contact with the escape wheel teeth. It also did not suffer from recoil. Being originally designed for use with a pendulum, it was also used in Harrison's first marine chronometer.

 Public Domain

## Fusee Regulator

The fusee - constant force mechanism is a beautifully simple device used in early spring-driven clocks and watches to overcome the problem that the force from the mainspring was not constant but gradually reduced as the spring wound down causing the clock to slow down and lose time.

The drive from the mainspring barrel was connected to the main timekeeping gear by a chain or cord running over a helical groove around a cone shaped pulley which acted as a variable ratio gear thus maintaining a constant driving force. The name fusee comes from the French fusée a 'spindle full of thread'.

The fusee mechanism dates from the early 15th century when it was used in pulley systems and is shown in contemporary sketches by Leonardo da Vinci, but the original inventor is not known. Early examples of its use in clocks were the Burgundy Clock, commissioned by the Duke of Burgundy, dating from around 1430 and held in the German National Museum in Nuremberg, and a clock, held by the Society of Antiquaries of London, made for the King of Poland in 1525 by Jacob Zech of Prague who is often incorrectly credited with inventing the first fusee clock mechanism.

## Remontoire Regulator

The remontoire - constant force escapement (French remonter "to wind") is a small secondary source of power, derived from the main power source, which is designed to give identical, controlled timing impulses to a watch or clock's timekeeping mechanism. It accumulates energy in a separate mechanism to a given trigger level then releases it independently to the escapement. By isolating the sensitive escapement from the main drive mechanism, variations in power due to the mainspring winding down or friction and unevenness in the gear train can thus be avoided. The escapement is driven by a separate low force spring or a weight which is automatically rewound by the main power source at intervals of around 15 seconds to an hour, triggered when the remontoire's weight or spring reaches the end of its power. Though there may be slight changes in the drive force during the remontoire cycle, they tend to be regular and are evened out by the frequent rewinding. Early remontoires did not provide power to the escapement during the winding periods but modern remontoire mechanisms are all designed to deliver power to the escapement during the reset cycle.

The remontoire is thus an alternative to the fusee.

The gravity remontoire was invented around 1595 by Swiss clockmaker Jost Burgi for German astronomer William IV of Hesse-Kassel and provided an improvement of between one and two orders of magnitude in timekeeping. Burgi's original clock is now held in the Kassel museum.

The spring remontoire was invented by John Harrison in 1739 and used in his H2 chronometer.The modern spring remontoire usually takes the form of a spiral spring attached to one of the train wheels, which is periodically wound up by the mainspring. As long as there is enough energy from the mainspring to wind it, the remontoire spring will provide almost unvarying energy to the escapement. Remontoire springs can be rewound as frequently as once per second, or as infrequently as every five minutes or even longer.

Robin Remontoire

Over the years, many different and complex remontoires have been invented. The example opposite, illustrating the principle is a very simple design made by Robert Robin of France in 1772

(The large spring or weight driving the main drive pinion is not shown.)

The sequence starts with the main drive pinion and consequently the intermediate drive wheel locked by the detent on lever A which latches on to a pin attached to the rim of the main drive wheel.

• Energy Release
• As the remontoire weight descends, the counterweight rises, and the escapement drive wheel turns. The main gear train remains locked until the remontoire weight reaches its rewind position at the bottom of its travel.

• Rewind
• When the weight depresses lever B it pulls down lever A, lifting the detent and releasing the main drive pinion. This unlocks and rewinds the remontoire by causing the intermediate wheel to turn, raising the remontoire weight and lowering the counterweight until, after one revolution of the main drive wheel, the detent latches on to the pin once more, locking the main drive wheel and causing the sequence to start again.

Note that the torque on the escapement wheel is very low depending on the difference in weight between the remontoire and the counterweight and not on the high torque from the main drive.

A remontoire should not be confused with a maintaining power mechanism, which is used only to keep the timepiece going while it is being wound.

## Temperature Compensation

Gridiron Pendulum

Automatic temperature compensation was invented by John Harrison in 1726 in order to maintain a fixed length of the pendulums used in his clocks. Huygens had shown in 1656 that the period of a pendulum is proportional to its length. Harrison was aware that increasing temperature would cause the length of a pendulum to increase and thus cause a clock lose time. He therefore devised the gridiron pendulum using two metals, with different coefficients of expansion, arranged in such a form that the metal with the greatest expansion would expand in the opposite direction compensating for the expansion in the other metal. In this case the shorter rods of brass with a coefficient of expansion 1.5 times that of steel, lifted the longer central steel rod carrying the pendulum bob maintaining an overall fixed length of the pendulum.

This was one of the world's first automatic control systems.

Bimetallic Strip

In 1759 Harrison also invented the bimetallic strip, whose shape is temperature dependent, which he used as a variable compensation component in his spring powered timekeepers.

When two metal strips with different coefficients of expansion are riveted together and heated, the bimetallic strip will tend to bend as the metal with the highest coefficient expands more than the other metal. bending in the opposite direction due to contraction when the temperature falls. He used the phenomenon to provide a temperature compensating device based on a bimetallic strip of brass and steel. It was held fixed at one end with the other end free to move and connected to the balance spring of the clock or watch. As the temperature increased, the elasticity of the balance spring would change affecting the timing, but at the same time, the bending of the strip was used to control the tension on the balance spring to counteract the temperature effect and thus maintain the timing.

Bimetallic strips are still used today as switching devices in components such as thermostats used in electrical appliances and heating systems.

See more about Harrison's Clocks and Watches

## Electrical and Electronic Timekeepers

Modern timekeepers are electrically powered and much more accurate but they still depend on some form of oscillator such as a quartz crystal or atomic resonator to provide the time keeping pulses and some method of counting them. The availability of inexpensive digital displays has eliminated the need for mechanical gears driving the pointers but analogue displays are still commonly used in response to user preferences.

## Lip Electric Watch Oscillator

How it Works

• Construction
• Two mu-metal magnetic alloy lugs are mounted on the rim of the balance wheel 180° apart. Two fixed solenoids, mounted on a steel base plate, also 180° apart, provide a uniform magnetic field across the balance wheel which rotates in the gap between the solenoids. Power to the solenoid coils is fed from the battery through a very fine wire which completes the circuit through a spring contact on the balance wheel shaft.

• Operation
• As the magnets approach the solenoids, the battery contact is closed and electric current flows in the solenoids setting up a magnetic field which attracts the magnets towards the solenoid poles giving them a mechanical impulse causing the balance wheel to rotate. As the wheel turns and the magnets enter the gap between the solenoids, the electrical contact of the wire on the balance shaft is opened, removing the power, and hence collapsing the solenoids' magnetic field allowing the magnets' inertia to carry them past the solenoid poles. The balance wheel continues to rotate, tensioning the balance spring, until its kinetic energy is expended, when the balance spring unwinds restoring the wheel back to its original position as in a conventional mechanical watch. The battery spring contact with the shaft is then closed once more and the sequence starts again.

The accuracy was aound ±10 seconds per day.

See more about the History and Performance of the Lip Watch.

## Hamilton Electric Watch Oscillator

How it Works

• Construction
• The solenoid which provides the magnetic impulse is a large, flat oval shaped, open "air cored" coil occupying a segment of the balance wheel and spanning about one sixth of its circumference with its longer diameter parallel to the rim of the wheel. It is balanced by timing screws on the opposite side of the wheel. Mounted on a steel plate below the balance wheel are two magnets, also the same distance apart as the widest diameter of the coil, one with its South pole pointing upwards and the other with its North pole pointing upwards. Current is fed to the coil by a fine wire, via a switched contact on the balance wheel shaft.

• Operation
• As the balance wheel rotates and the coil approaches the point where its outer diameter would begin to cover the two magnets simultaneously, the electrical contact closes, energising the coil. The flow of the current through the outer arc at one end of the coil is in a radial direction pointing inwards over the South pole of the first magnet. With the current flowing in a radial direction in a magnetic field pointing downwards, the electrical conductor will experience a tangential force in the clockwise direction. (Fleming's Left Hand Rule). The opposite end of the coil will at the same time be over the North pole of the second magnet and the current flowing in the coil will be pointing outwards in the radial direction while the magnetic field from the North pole is pointing upwards. The resultant force on the segment of the coil above the North pole will also be in the same clockwise tangential direction as the force from the first magnet so that the balance wheel will thus receive two simultaneous impulses in the clockwise direction. As the coil moves away from the magnets, the contact switch on the balance shaft is opened cutting off the current and the balance wheel continues winding up the balance spring. The spring's restoring force brings the balance wheel back and the sequence starts again, just as in the Lip watch.

See more about the History of the Hamilton watch and the performance of the Lip Watch with which it is similar.

## Bulova Accutron Tuning Fork Electronic Watch

### How it Works

Construction

• The Tuning Fork
• A soft iron cup the end of each of the vibrating tines of the tuning fork contains a small magnet which runs in the core of a fixed impulse coil which is attached to the frame of the watch. The iron cups serve to concentrate the magnetic field through which the coils move. Each of the impulse coils is made up from 8,100 turns of insulated copper wire of 0.015 mm diameter (1/2000th of an inch) and 80 meters (87 yards) long.

One of the impulse coils also has a secondary, phase sensing, feedback coil built into it.

• The Electric Circuit
• Apart from the coils, the electric circuit consists of just four components, a transistor, a resistor and a capacitor located in a cavity in the watch frame and a 1.35 Volt button cell also located in a separate cavity.

• The Indexing Mechanism
• The index mechanism consists of an index or ratchet wheel and two very fine flat springs, an index spring and a pawl spring. Cemented with epoxy at the end of each spring is a synthetic ruby jewel which engages with the teeth of the index wheel. The index spring is fixed to, and moves with, one of the tuning fork tines and the pawl spring is fixed to the watch frame.

Because the amplitude of the tuning fork vibrations is very small, the teeth of the index wheel must likewise be very small. The wheel was only 2.4 mm (a tenth of an inch) in diameter and 0.04 mm (0.016") thick with 320 teeth, each 1/100 mm (0.0004") high and 0.02mm (0.0008") apart. The ruby jewels are 0.18mm (0.007") square and 0.06mm (0.002') thick. The components are so small that they can only be observed with a microscope. Producing the index mechanism was an outstanding technical achievement.

Operation

• The Oscillator
• The resonant tuning fork, sustained by the electronic circuit, forms a simple oscillator vibrating at 360Hz (or 720 beats per second). This compares with 5 to 10 beats per second for a mechanical watch. The transistor acts as a switch. When the voltage on the base is high, current flows through the transistor energising the impulse coils in the primary circuit producing a magnetic field which acts on the magnets driving the tines together. At the same time the movement of the magnet in the sensing coil generates a negative voltage in the feedback path which drives the transistor base voltage negative cutting off the primary current so that the tines fly back. This change of direction of the magnets causes a positive voltage on the sensor coil switching the transistor on again and repeating the sequence.

• The Indexing Mechanism
• The indexing mechanism converts the vibrating motion of the tuning fork tines into a rotary motion to drive the watch's gear train and hands. The animation illustrates the functioning of the indexing system. (Not to scale)

The index jewel is shown in pink and the pawl jewel is shown in blue.

The index and pawl springs both apply pressure on the rim of the index wheel in a radial direction to keep the jewels in contact with the teeth. The index spring however, being connected to the vibrating tine of the tuning fork, also vibrates in a tangential direction on the teeth of the wheel. As the tine moves towards the index wheel, the index jewel pushes the wheel around by slightly more than one tooth, a distance equal to the amplitude of the tuning fork vibration. As it does so, the pawl jewel, which is fixed to the watch frame, drops into place between its corresponding teeth. Then as the tine moves away from the index wheel, the index jewel moves back towards its start position dropping over the next tooth back as it moves. The friction between the index jewel and the index wheel as it retracts causes the index wheel to move backwards, but it is blocked by the pawl jewel when it reaches the next tooth (the one it has just passed over). When the index jewel reaches its new start position (one tooth further back) the sequence repeats, rotating the index wheel and hence the gear train. Because of the pawl locking motion, the index wheel can only advance by precisely one tooth per cycle of the tuning fork vibration. This also makes the mechanism immune to voltage variations on the tuning fork impulse coils. Amazingly, the system proved to be incredibly reliable.

The Accutron was guaranteed to be accurate to within 2 seconds per day or 1 minute per month.

See more about the History of the Bulova Electronic Watch.

 Source: Federation of the Swiss Watch Industry FH 1 Battery 2 Integrated circuit 3 Quartz crystal 4 Trimmer capacitor   (frequency regulator) 5 Stepping motor 6 Gear-train 7 Analogue display

## The Quartz Watch

How it Works

• Construction
• The diagram opposite shows the functional parts of a typical quartz watch.

• Operation
• The Quartz Crystal is a piezoelectric material which has the property that it generates an electrical charge across its bulk when mechanical pressure is applied to it. Conversely it contracts or expands slightly when an electric potential is applied across it. When coupled to an electronic oscillator, the crystal will vibrate with a characteristic, natural resonant frequency which depends on its cut, shape and thickness. The smaller the piece, the faster the vibrations.

The quartz crystals used in timekeepers are usually cut into the form of a tuning fork because that shape is more responsive to maintaining resonance and its resonant frequency can be set during manufacturing by precision lapping and laser trimming the length of the tines. The resonant frequency specified for a quartz watch is normally 32,768 Hertz. This frequency allows the crystals to be made in a convenient size. Lower frequency crystals have a larger physical size, unsuitabale for watches, and higher frequency crystals have a higher current drain which reduces the battery life of the watch. The precise resonant frequency is however chosen to make it more convenient for a digital frequency counter to process the frequency count. The frequency of 32,768 Hertz is equal to 215 cycles per second and can be represented by a 15 bit binary number. A power of 2 is chosen so that a simple chain of digital divide-by-2 stages can derive the 1 Hz signal needed to drive the watch's second hand.

Quartz is a crystal of Silicon dioxide SiO2 and is ideal for use in timekeeping devices. It is inexpensive and abundant and is the major constituent of sand. It can also be produced synthetically in pure form and is used extensively in the semiconductor industry where advanced process technolgies have been developed in support of its applications. Apart from its piezoelectric properties, it is mechanically and chemically stable, it loses very little energy as it vibrates, it is very hard, corrosion free and relatively unaffected by temperature, humidity and pressure compared with brass and steel typically used in the manufacture of timekeepers.

The Trimmer is a variable capacitor which can fine tune the resonant frequency of the oscillator.

The integrated circuit has three circuit functions:

• The Oscillator: A feedback amplifier which provides the sustaining energy to the resonant quartz crystal keeping it oscillating at 32,768 Hertz. Similar in function to the Accutron oscillator above.
• The Frequency Divider: A digital circuit which divides the oscillator frequency by 2, 15 times. When the oscillator frequency is 32,768 Hertz, the counter gives an output pulse once every second precisely.
• The Driver Circuit: An output circuit which conditions the pulses from the counter to a level and duration sufficient to drive the stepping motor.

The Stepping Motor does not rotate at constant speed but steps one pulse at a time through a very precise angular rotation. Because it only moves the pointers once per second, its power consumption is very low.

The Gear Train is driven by the stepping motor and in turn drives the Pointers of the watch. In Digital Watches which were introduced later, there are no mechanical parts. The output from the frequency divider is fed to an integrated circuit which keeps a running count of the output pulses and converts the total to minutes and hours and feeds the data to LCD or LED digital displays. These displays however, particularly the LEDs, cause a much greater battery drain and hence shorter battery life.

The Battery supplies the energy for all of the above processes.

Standard quality quartz watches typically have a long-term accuracy of about 6 parts per million which is equivalent to ±15 seconds per month or ±0.5 seconds per day.

See more about the History of Quartz Watches.

## The Atomic Clock

The atomic clock is an application of quantum physics. Atomic theory describes how all atoms consist of a nucleus surrounded by orbiting electrons. Quantum theory describes how atoms can only exist in certain discrete ("quantised") energy states determined by which orbits or shells their electrons occupy and the nature of their spin. Changes to the electron's orbit or spin can only occur in discrete increments and these changes are associated with the absorption or emission discrete amounts, or quanta, of energy in the form of packets of electromagnetic radiation called photons. For example when the atoms certain gases or vapours are excited by heating, or some other stimulus such as an electromagnetic field, some of their electrons may absorb energy and move from their ground state to higher energy levels. As they return to their ground state, they emit photons with very specific energy content as defined by E=hν, - Planck's Law. The frequency of the radiation associated with this transition is typically in the optical spectrum and the colour of the radiated light is unique to the particular element used. (This property is often used to identify chemical elements).

There are however other possible lower energy transitions including what are known as hyperfine structure transitions such as reversing the spin of the atom's outer electron by directing it through an electromagnetic field oscillating at the atom's natural resonant frequency. Because this is a lower energy transition than changing orbits, the frequency of the emitted radiation will also be lower and in the case of Caesium-133 for example, it will be in the microwave spectrum. This last property is used as the basis for constructing an atomic clock, but several other important factors and conditions apply.

Atomic Clocks

Benefits and Conditions

• Clocks typically depend on counting the pulses or oscillations of a highly stable oscillating source to determine the elapsed time. There is no more stable source than the radiated emission resulting from transitions in the energy states of an atom or molecule. The frequency of the radiation is constant and impervious to changes in temperature, pressure, humidity and gravity, or to friction,and age.
• The potential accuracy of a clock depends on the frequency of its oscillator. The higher the frequency the shorter the time between pulses and the smaller the time increments which can be distinguished.
• To set up and sustain the natural resonant frequency emission from the atom, it must be coupled to an external oscillator, which provides the necessary electromagnetic field oscillating at the same frequency to stimulate the emission. A feedback circuit is necessary to synchronise and lock the externally generated field frequency with the frequency of the atom's radiated energy.
• It is desirable that the frequency of the emitted radiation should be in a range which can be easily managed and measured.
• The emitted radiation should come from a single type of transition and should not be mixed with other emissions emanating from the same source, such as transitioning between orbits, since this would complicate detection.

Caesium Clocks

Why use Caesium?

The stable isotope of Caesium, Cs-133, is an ideal choice for constructing a precise and stable frequency source.

• All of its 55 electrons except for the single electron in the outermost shell are confined to five stable electron orbital shells. The outermost electron in the sixth shell is less stable than the others and can be induced to transition between two energy states in a controlled and measurable process.
• The two possible energy states depend on whether the electron spin is in the same or opposite direction to the spin of the nucleus.
• The stable electrons in the innermost shells are less susceptible to change of state so that they do not disturb the operations on the outer electron which can thus take place independently without being contaminated by electrical "noise" from unwanted and uncontrolled transitions.
• State transitions employed in the atomic clock involve changing the spin direction of the outer electron from "spin up" to "spin down" and vice versa, absorbing a photon in one direction and emitting a photon in the reverse transition. For Caesium, the photon frequency of the radiation involved in these transitions is precisely 9,192,631,770 Hertz (9.19 GHz or 32.63 mm wavelength) which is in the microwave band for which ample support technology is available. This frequency is often called the atom's "natural" or "resonant" frequency for that particular type of state transition.
• The electrons can be induced to change their spin direction by resonating the Caesium atoms with a microwave source oscillating at the photon frequency.
• The energy required to sustain the state changes is very small.
• Caesium is near liquid at room temperatures with a melting point of 28.4 °C (83.1 °F) and a boiling point of 641 °C (1,186 °F), the lowest of all metals apart from Mercury, which makes it relatively easy to generate the necessary source of gaseous atomic particles.
• Electronic feedback control circuits enable an external quartz oscillator to be synchronised with the Caesium atom's resonant frequency.
• Free gaseous atoms with up or down spin direction can be separated by passing them through a magnetic field.
• The number of spin reversals can be measured using a simple particle detector.

Operation

1. The process takes place in an extremely high vacuum within a sealed chamber so that the stream of Caesium particles is not affected by other extraneous particles or radiation.
2. It starts with the heating of liquid Caesium to a gaseous state in an oven. The atoms escape at high velocity through an aperture in the side of the oven with a random distribution of spin energy states, either spin up or spin down.

3. For simplicity, let's call the two states "state A" (shown in red in the above diagram) and "state B" (blue).
4. The stream of atoms first passes through two electromagnets which separate the atoms according to their electron spin direction into two convergent beams, one beam containing only red particles is deflected to the left and and the other containing only blue particles is deflected to the right. These two beams continue in straight lines through a resonant microwave cavity where they cross over at a slit, in the middle of the cavity, which blocks off-course atoms and the beams emerge without further deflection in two divergent beams at the other side.

5. A microwave oscillator with a frequency of 9.19 GHz, corresponding to the photon frequency of the electron spin transition, feeds two microwave resonators which launch an oscillating electromagnetic field into the cavity. The effect causes the atoms to resonate at their natural frequency and this in turn causes the spin direction of the a proportion of the electrons to flip to the opposite direction with the maximum number of transitions occurring when field frequency is tuned precisely to the natural resonant frequency of the Caesium atom.
• The microwave oscillations are derived by multiplying up, the output from a lower frequency quartz controlled oscillator. The frequency output of the quartz oscillator can be adjusted over a small range by means of an integral trimming circuit.
6. Both the emerging beams now contain atoms which have flipped to the opposite spin direction, (indicated in the diagram by a changed colour) as well as those which have not (colour remains the same). They then pass through a second set of electromagnets, similar to the first set, and these magnets similarly separate the atoms from within each beam according to their electron spin direction with the red particles directed to the left and the blue particles directed to the right, just as before.
7. The atoms which have not changed state as they traverse the system undergo two deflections in the same direction by the two sets of magnets and are thus deflected away from the main beam. For the particles which have flipped their spin state as they pass through the resonator, the second set of magnets reverses the deflection of both the atom beams, since their spin states have reversed, causing them to converge on a detector. Thus the only particles to reach the detector are those which have changed state. The particles which have not changed state are deflected away and trapped.
8. The detector converts the particle flow to an electric current which is used in a feedback loop to synchronise the oscillator frequency with the atom's natural frequency.
9. The number of particles reaching the detector represents the number of particles which have changed state and is a measure of how close the oscillator frequency was to the atom's resonant frequency. The number of particles captured, and the detector current, will both be a maximum when the two frequencies are perfectly in synchronism, but if there was a slight frequency difference, the number of particles captured and the detector current would be reduced. The amplifier in the feedback loop is designed to sense this frequency error and provide a control signal to the oscillator to bring it into synchronism with the atom's resonant frequency.
10. Since the frequency of the quartz oscillator is locked in synchronism with the Caesium resonant frequency, its output can also be fed to a counting circuit to provide a display of the clock time or frequency.

The accuracy of the first Caesium atomic clock made by NPL in 1955 was ±1 second in 300 years. Newer atomic clocks achieve greater accuracy by using alternative source elements with greater energy state changes which emit correspondingly higher frequency radiation.

See more about the History of the Atomic Clock

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