There are all sorts of resonances around us, in the world, in our culture, and in our technology. A tidal resonance causes the 55 foot tides in the Bay of Fundy. Mechanical and acoustical resonances and their control are at the center of practically every musical instrument that ever existed. Even our voices and speech are based on controlling the resonances in our throat and mouth. Technology is also a heavy user of resonance. All clocks, radios, televisions, and gps navigating systems use electronic resonators at their very core. Doctors use magnetic resonance imaging or MRI to sense the resonances in atomic nuclei to map the insides of their patients. In spite of the great diversity of resonators, they all share many common properties. In this blog, we will delve into their various aspects. It is hoped that this will serve both the students and professionals who would like to understand more about resonators. I hope all will enjoy the animations.

Origins of Newton's laws of motion

History of mechanical clocks with animations
Understanding a mechanical clock with animations
includes pendulum, balance wheel, and quartz clocks

## Sunday, March 20, 2011

### Understanding a quartz analog mechanical clock

 previous:part 2 up: home

## Understanding a mechanical clock - with animations - Part 3

### 5. Modern quartz "analog" clocks and watches

 Fig. 10. Typical quartz tuning fork resonator for modern quartz clocks and watches. One image is of the naked tiny tuning fork and the other (the insert) is of the vacuum canister that surrounds the tuning fork.

### A tiny quartz tuning fork

A modern quartz clock is built around a tiny tuning fork (see Fig. 10) made of extremely pure single crystal quartz and packaged in a very small vacuum canister. Because of the vacuum and very low internal dissipation (of the vibrations of the tuning fork) of the pure quartz, this quartz resonator has an extremely high Q [see my related work and wikipedia] and therefore a very narrow resonance curve. Q's of 106 are typical, 1000 to 100,000 times the Q's of regular tuning forks and bells. Furthermore, the tuning fork is made of quartz with just the right orientation of its crystal axis relative to the tuning fork so that its resonant frequency changes very little with temperature. This means it can be counted on to resonate at one exact frequency (to at least a part in 106), that frequency being 32,768Hz which is equal to 215. It is a miracle of modern technology and mass production that these super resonators can be made in tremendous quantities for pennies apiece.

### The whole quartz clock (or watch)

An animated diagram of a whole quartz clock is shown in Fig. 11. There are five major parts to the clock:

• The quartz tuning fork resonator as discussed above.
• The resonator driver circuit which amplifies electrical signals from the tuning fork and also keeps the tuning fork oscillating. The piezo-electric property of quartz provides a coupling between its mechanical motion and electric charge on electrodes printed on the tuning fork's surface. This property means that oscillations of the tuning fork will create small electrical signals in the "sense" electrode on the tuning fork. It also means that more powerful drive oscillating signals applied to the "drive" electrode can sustain the oscillations.
• The divide-by 32,768 circuit takes the 32,768Hz oscillations from the above resonator driver circuit and produces a pulse for each 32,768 oscillations. Such a divide by N circuit consists of a series of 15 D-type flip-flops, each dividing the frequency by a factor of two. A final stage converts these to alternating positive and negative pulses of 30ms duration occurring every second.
This circuit serves a similar function as a gear train, precisely reducing the frequency of the resonator to a usable frequency. In a digital watch, additional circuits of this type would reduce the frequency further and also drive the digital displays. In the clock as shown, the gear train reduces the frequency further and drives the analog clock hands.
• The motor-drive amplifier that amplifies these pulses so that they are sufficiently strong to drive a small electric motor.
• The electric motor. For more details on this, see Fig. 13 below and its caption.
• A gear train with hands as discussed earlier.
• The clock case, dial face, and battery holder (none shown) that constitute the body and appearance of the clock.

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 Fig. 11. Workings of a typical modern quartz electric clock, animated. An example of such a clock is seen in Figure 6b above. Mouse over the illustration to set it in motion. The motion is a little faster than in a real clock to make the motion a little more visible. The motion of the tuning fork vibrations is also exaggerated. The "waves" traveling down the wire from the quartz tuning fork are shown to illustrate the idea that the signals on that wire are produced by the tuning fork (when vibrating) and are used by the amplifier. In reality, there are not really waves present on the wire: the signals traveling at the speed of light are transmitted instantaneously through this short length of wire. This is also true of the two other propagating sin waves: the waves are shown only to illustrate the time dependence of the signals, where they are generated, and where they are received. It is noted that clocks and watches usually have coaxial shafts as discussed above but these were not shown here in order to make the gear train's action easier to understand. The Britannica website has a nice illustration of a similar quartz watch with a coaxial shaft.
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### The circuit board of quartz clock

 Fig. 12. Small circuit board from a modern quartz clock (other parts of which are shown in Fig. 6 above). In the left photo, we see a black alarm buzzer, the shiny magnetic flux guide, and the solenoid (with its many turns of copper wire). The right photo shows the back side of the same circuit board. There we see the black circular integrated circuit and the tuning fork canister, along with "printed on" copper traces (pathways) to take electrical power and signals from one location to the next. The circuit includes other features, not illustrated in Fig. 11, such as the alarm. The motor armature (shown in Figs. 11 and 13) is not shown here.

### The electric motor in quartz watches and clocks

 Fig. 13. An electric motor typical of that found in modern "quartz" clocks. The motor typically receives a positive electrical pulse for about 30ms (30 thousandths of a second), then is non-energized for 970ms, then receives a negative electrical pulse for another 30ms and has another resting period of 970ms. The cycle then repeats. The complete cycle time is 30ms+970ms+30ms+970ms = 2000ms = 2seconds. The permanent magnet armature (the rotating part of the motor) is forced to make a full rotation in this time (every 2 seconds). A very simplistic view of the magnetic structure (solenoid plus iron flux guide) would indicate that magnetic fields are purely horizontal in the region of the armature. You can see this by clicking on "simplified fields" and clicking repeatedly on "step". The magnetic fields are shown in green. As is indicated, the direction of rotation of the armature in response to this field is uncertain. Motors of this type were used in old electric clocks which needed to be manually started in the correct direction. This uncertainty in direction is unacceptable in modern electric clocks. A more realistic assessment of the actual structure of a typical clock motor indicates that the flux guide is quite minimalistic and badly leaks magnetic flux. The result is that while the solenoid is operating, much of the magnetic field at the armature comes directly from the closest end of the solenoid and only part of the magnetic field is channeled through the flux guide. Click on "realistic fields" and step through the cycle to see the effect of this magnetic field pattern. During the time that the solenoid is energized, the effective pole of the solenoid induced field around the armature is shifted to a one o'clock position (shown in red). The other pole representing the magnetic field coming through the flux guide is more diffuse and weaker and might be considered to be at the 9 o'clock position (also shown). The strong one o'clock pole repels the armature so that it rotates 135 degrees as shown. When the solenoid is in the non-energized state, the only magnetic field is that due to the armature itself, and this causes the armature to further rotate 45 more degrees (also shown) so that its N and S poles are oriented horizontally. Step through the animation to see the complete cycle. We see that there is no ambiguity in the direction of rotation.