The heart of the instrument is a thin wafer cut from a natural crystal of quartz. Two basic properties of the wafers account for their attractiveness as timekeepers. First, they are so elastic that when they are struck a sharp blow they vibrate as much as five million times before the amplitude of vibration falls to half its initial value. In contrast, the swing of a good pendulum in a vacuum falls to half its initial value after 100,000 oscillations. Since the rate of oscillation of any resonant system is disturbed by the application of an external force, this characteristic of the quartz wafer gives it a clear advantage over the pendulum: the vibration of the quartz can be sustained with less energy. Second, quartz crystals can be driven electrically, without mechanical linkage, and can also be used as generators of alternating current. An electric field distorts the crystal physically: it becomes longer in one dimension and shorter in the transverse dimension. Conversely, when the crystal is distorted by a mechanical force applied to either of these dimensions, electric charges of opposite sign appear on the facets at right angles to the plane of the applied force.

As a vibrating element for measuring time the crystal has still other inherent advantages. Its performance is independent of gravity; accordingly its rate of oscillation is not altered by changes in altitude and latitude or by tidal effects. It can be supported at the node of its vibration and is therefore free from the class of errors introduced by the suspension of a pendulum. The rate at which the crystal vibrates is virtually independent of the amplitude of vibration. Finally, the crystal is small, durable and self-contained.

Like the swing of a pendulum, the rate of vibration of a quartz wafer is influenced by changes in temperature and atmospheric pressure. The rate is also disturbed by certain effects associated with the aging of the crystal. These can be minimized, however, by appropriate expedients. It turns out that wafers cut from a larger crystal in a certain direction (called the X axis) have a negative temperature coefficient of frequency: the rate of vibration falls with increased temperature. Wafers cut at right angles to the X axis (the Y axis) exhibit the opposite effect: the frequency increases with temperature. It is possible to cut wafers at an intermediate (G-T) angle between the X and Y axes so that the rate of vibration remains constant through a limited range of temperatures. Even these wafers show some variation in rate during intervals when the temperature is changing, but the vibration returns to its former rate when all parts of the wafer have reached the same temperature. The frequency of X-cut crystals falls 30 parts per million per degree centigrade of temperature change; the frequency of Y cuts increases about 100 parts per million per degree. In contrast, the rate of intermediate cuts remains constant within one part per million per degree, depending on the operating temperature. A G-T wafer designed for operation at 30 degrees C. will vibrate precisely at the frequency for which it is ground at any temperature between about 20 and 40 degrees, after all parts of the wafer reach that temperature

Like a swinging pendulum, a vibrating crystal gives up energy to the surrounding air at a rate depending on the atmospheric pressure. Changes in air pressure are therefore reflected by the rate of vibration. This source of error is minimized by mounting the wafer in a housing from which air can be evacuated. The frequency is also affected by surface contamination. A film of oil from the fingers, for example, can increase the effective mass of the wafer enough to reduce its frequency one part per million. The best crystals are equipped with supporting lead-in wires, are scrupulously cleaned and are immediately enclosed in glass or metal envelopes from which the air is pumped.

Certain other factors, not all of them well understood, affect the rate. One appears to arise from stresses set up in the surfaces of the wafer during the grinding operation. Such stresses are relieved spontaneously during the life of the wafer and therefore induce long-term changes in rate. The defect can be minimized by grinding the wafer slowly, giving the wafer a final etch with hydrofluoric acid and aging it artificially by heating.

Anyone who has figured and ground a telescope mirror should be able to make a satisfactory crystal. Radio amateurs used to cut their own to control the frequency of short-wave transmitters. Today, however, homemade crystals are rare. Excellent crystals ground to specified frequencies can be bought new from $5 to $25, depending on the cu and the method of mounting. Temperature-compensated G-T cuts are generally priced higher than X cuts.

For maximum performance crystals should be enclosed in a constant-temperature oven and operated in an oscillator circuit of the bridge type. An adequate oven can be made of wood or plastic lined with glass wool and controlled by a heater and thermostat of the kind used in home aquariums. A variety of suitable oscillator circuits will be found in reference texts prepared for radio amateurs. If one wishes, the crystal, oscillator and oven can be bought as a unit from a crystal manufacturer.

Crystals operate at frequencies ranging from about 16 kilocycles per second to a few megacycles. Clock motors operate from sources of low frequency, ordinarily a 60-cycle power line. This means that the crystal frequency must be divided to a value appropriate for the clock motor. Several electronic devices can perform this division, but the so-called free-running multivibrator seems best for amateur purposes. This device utilizes a pair of triode vacuum tubes so connected that the output of each tube feeds energy to the input of the other. The circuit is violently unstable. In effect each tube functions as a sequential trigger for its companion, so that the tubes conduct current alternately. The rate at which conduction alternates is largely determined by the rate at which the capacitors linking the grids of the tubes to the plates of their opposite numbers can charge and discharge through resistors included in the circuits. By choosing appropriate values for the grid capacitors and companion resistors, multivibrators can be designed to operate at any frequency from a small fraction of a cycle per second to many megacycles.

Normally multivibrators oscillate at a reasonably constant rate. But their action can be momentarily speeded up by introducing a voltage pulse from an external source into the grid circuit of either tube. The external pulse causes the tubes to switch conduction early. Thus if a multivibrator is designed to oscillate at the rate of 55 cycles per second, and if a source of voltage that alternates at 240 cycles is connected to the grid of either tube, the multivibrator will lock into step with the submultiple of 240 cycles that is nearest to 55 cycles, i.e., 60 cycles. The multivibrator performs reliably up to 10-fold divisions. Divisions greater than 10 are accomplished by interconnecting two or more multivibrators in cascade. A quartz crystal of any frequency can therefore be used to drive a clock motor if the selected crystal frequency is a multiple of the frequency at which the motor is designed to operate. Most electric clocks run on 60-cycle current. Crystals ground to vibrate at 120 kilocycles, the 2,000th harmonic of 60 cycles, are commercially available and have been used by amateur clockmakers.

Jim Phillips of Phoenix, Ariz., recently joined the ranks of these enthusiasts. "For years," he writes, "I have been consumed with the desire to know what time it is down to the smallest fraction of a second that can be read on a dial. This led me to buy several pocket watches of the type used by railway employees. Good as they were, the best of these watches gained or lost several seconds per month. Last year, while casting about for a project required for completing a course in electrical engineering, I ran across a reference to an article in Scientific American that explained how to build a quartz crystal clock [see "The Amateur Scientist"; September, 1957]. This struck me as the ideal project-one that should satisfy my desire for a really accurate timepiece as well as meet the course requirement.

"The clock had been developed by W. W. Withrow, Jr., of Teague, Tex. Withrow is to be congratulated on a fine design. Anyone considering the construction of a similar clock should make a point of reading his description. I decided to modify the design in some respects, chiefly to facilitate duplication of the circuit, allow the interchange of components such as vacuum tubes and simplify the required adjustments and synchronization of the clock with time signals broadcast by WWV, the radio station maintained by the National Bureau of Standards.

"The crystal oscillator of my clock was made by the International Crystal Manufacturing Company of Oklahoma City. It comes complete in the form of a printed circuit, with provision for plugging in a 6BH6 oscillator tube and the 120 kilocycle F-13 crystal shown at upper left in the accompanying diagram [Figure 6]. I modified the unit to the extent of adding a 50-microfarad trimmer capacitor between one terminal of the crystal and ground. This serves as vernier adjustment for varying the crystal frequency through a narrow range.

"A major difference between my circuit and that of Withrow is the design and arrangement of the multivibrators. His units reduced the frequency of the 120-kilocycle crystal to 60 cycles by successive divisions of 20, 5, 5 and 4 that respectively give frequency steps of 6,000, 1,200, 240 and 60 cycles. He had difficulty adjusting the first multivibrator, mainly because the unit was required to divide by a larger number than multivibrators can handle reliably. I distributed the successive divisions in steps of 10, 10, 5 and 4. This also enabled me to eliminate the preamplifier that Withrow inserted between the output of the crystal oscillator and the first multivibrator. In addition, I used asymmetrical multivibrators in all but the 60-cycle stage. The grid capacitor and associated resistor of one tube in each pair was made substantially smaller than the value required for establishing the free-running frequency of the stage. This tube would therefore react more quickly than its companion. The rate of oscillation was fixed by the other tube of the pair. This tube was in the conducting state most of the time, whereas the quick-acting tube conducted just long enough to initiate a new cycle. The asymmetry increases the time available for injecting the incoming signal into the tube of shortest conduction time and simplifies the adjustment of the stage in addition to increasing its reliability.

"The 60-cycle multivibrator must operate symmetrically because the clock is designed to run from alternating current in the form of a sine wave. The frequency division of this stage is low, but it is not loaded heavily and symmetrical operation was easily achieved by feeding the input signal to the grids of both tubes simultaneously. As an operating convenience the grid circuits of all tubes concerned with frequency control were equipped with adjustable resistors.

"I must acknowledge that the power amplifier for supplying the clock is a strange-looking duck, the result of 'cut and try' design. But it works well in the several clocks I have made and does not overload the 60-cycle multivibrator. It was possible, therefore, to eliminate the voltage amplifier that Withrow used between the final multivibrator and power amplifier of his clock. The value given for the inductor in the plate circuit of the power amplifier is approximate. (It was a gift and bore no value markings.) Any inductor in the range of 4 to 10 henrys should work if the parallel capacitor is selected to produce both satisfactory voltage and a reasonable wave form at the clock terminals when the clock is plugged in. As a first approximation the size of the capacitor in microfarads can be taken as approximately equal to four divided by the inductance in henrys. Fortunately clock motors are easy to please both in respect to voltage and wave form.

"The power supply is conventional except that oversize components were used, as shown in the accompanying diagram [Figure 2]. The fact that the unit is intended for continuous operation should be kept in mind when substitutions are made for the parts recommended.

"A feature of the circuit that may be novel, and which certainly is a convenience, is the three-point switch that connects the output of the 240-cycle multivibrator to the input of the 60-cycle one. It is used for synchronizing the clock with the time signals broadcast by WWV. The switch is spring-loaded so that it centers automatically and closes the circuit between the cathode of the second tube of the 240-cycle multivibrator and the input of the 60cycle multivibrator. Holding the switch to the right opens the circuit and allows the 60-cycle multivibrator to run free at about 55 cycles. This slows the clock. Holding the switch to the left short-circuits the 110 K resistor in the grid circuit of both tubes, which allows the unit to run free at approximately 65 cycles per second and so speeds up the clock.

"These are the circuits. Gather up the parts and assemble them on a chassis that measures approximately 17 inches long, 12 inches wide and 3 inches deep. Routine care should be exercised in layout and construction. Anyone who does not know what that means should call on a radio amateur for advice. When all the connections have been inspected for workmanship, plug new tubes into the sockets, set the voltage-regulator rheostat of the power supply at about 2,800 ohms, the multivibrator potentiometers to midrange, turn the 600 K potentiometer that feeds input to the power amplifier all the way down, plug in a clock that draws no more than three watts, turn on the juice-and stand back! The voltage-regulator tube should fire within a few seconds. When it does, advance the 600 K potentiometer that feeds the power amplifier until the clock motor starts. Then adjust the 60-cycle multivibrator so that the clock runs at a reasonable rate.

"The multivibrators are next adjusted for correct frequency division. This procedure requires a cathode-ray oscilloscope. If the builder does not own one, doubtless a radio amateur or television serviceman can be induced to co-operate in the venture. Two types of display are possible. The one suggested by Withrow produces a Lissajous figure on the scope that resembles a crown viewed sideways. The number of spikes that appear on the crown represents the division ratio. In other words, if the crown displays 10 spikes and does not rotate when the scope is connected between the crystal oscillator and the first multivibrator stage, the division is 10-fold and the multivibrator is locked to the frequency of 12,000 cycles.

"To make scope connections twist one lead of a 1-megohm resistor to each probe of the scope. Half-watt resistors are adequate. Thereafter use the free leads of the resistors as test probes. Starting with the 12-kilocycle multivibrator, connect the probe for the horizontal amplifier of the scope to test point A and the vertical probe to point O, the output of the oscillator. After the amplifiers of the scope have been adjusted for a figure of reasonable proportions, the crown described above should appear. If it fails to appear, adjust the multivibrator until the 10 spikes are counted. Next, shift the vertical probe to test point 00 (the output of the 12-kilocycle multivibrator) and the horizontal probe to test point B. Adjust the 1.2-kilocycle multivibrator for another 10-spiked crown. The 240-cycle and 60-cycle multivibrators are easiest to adjust with the horizontal input probe connected to the ungrounded side of the filament supply. The vertical probe is connected to test points C and D respectively, and each of the multivibrators is adjusted until the scope displays a crown with four spikes and one spike respectively. The clock motor is now locked to the 2,000th submultiple of the crystal frequency.

"An alternate scope display, and the one that I prefer, permits you to observe what is really going on. In this scheme the vertical probe of the scope is connected to the grid test points of the first tube of each multivibrator pair. Horizontal deflection is provided by the internal sweep oscillator of the scope. The scope is adjusted for a pattern similar to the one shown in the accompanying illustration [Figure 3]. The base pips in the illustration represent the signal that is being divided. The remainder of the pattern reflects the irregular rise and fall of grid voltage of the first multivibrator tube. The ratio of the input to output frequencies is determined by counting the pips. Counting is facilitated by equipping the scope with a conventional screen of crossed lines. The scan frequency and horizontal gain of the scope should be set so that pips appearing on the exponential rise of the voltage display coincide with any convenient vertical lines on the screen. The number of pips per cycle can be determined by counting the number of vertical lines from base pip to base pip.

"One final adjustment remains to be made before the oscillator is tuned. The operating range of the OD3 voltage-regulator tube of the power supply extends from about 5 to 45 milliamperes. The 8K rheostat should be set to limit the current through the OD3 to about 25 milliamperes. Connect an appropriate milliammeter in the circuit temporarily and make the adjustment. The same result can be had by connecting a 100-ohm resistor in the circuit and adjusting the rheostat until 2.5 volts appear across the resistor.

"To tune the oscillator, set the vernier capacitor (.5 to 8 picofarads, or micro microfarads) to midrange. Synchronize the second hand of the clock as closely as possible with the seconds signals broadcast by WWV by operating the spring-centered rate switch in the input of the 60-cycle multivibrator. Then adjust the rough frequency control (the 7-49 variable capacitor of the oscillator) by observing deviations from WWV. Finally, bring the crystal into step with WWV by adjusting the vernier."

Herbert Harris of Mount Wilson, Calif., proposes a somewhat less ambitious project in electronics for those interested in electric thermometers. "A number of the solid-state diodes now available on both the regular and the surplus market have excellent negative temperature coefficients of resistivity," he writes. "They appear to be more plentiful than thermistors and much less costly. I decided to build one into a circuit for indicating the outdoor temperature at our local hotel and am gratified by the results. The relative performance of several diodes, together with the circuit used during this series of experiments, is shown by the accompanying graph [below]. With this circuit the scale of my meter reads backward and about a third of it is unused. Other circuits, including bridges and semibridges, can be improvised for meters of other types. The experimenter should not overlook the fact that losses occur in diodes; the current should be kept low if accuracy is desired. The leads between the diode and meter can be extended to any reasonable length but must be included in the circuit when the instrument is calibrated. A comparison thermometer is used for calibration. Three calibration points can be established by successively placing the sensing elements in a refrigerator, in boiling water and exposing them to room temperature."

Bibliography

THE AMATEUR SCIENTIST. C. L. Stong. Simon and Schuster, 1960.

ELECTRONICS: EXPERIMENTAL TECHNIQUES. William c. Elmore and Matthew L. Sands. McGraw-Hill Book Company, Inc., 1949.

THE EVOLUTION OF THE QUARTZ CRYSTAL CLOCK. W. A. Marrison in The Bell System Technical Journal, Vol. , 27, No. 3, pages 510-588; July, 1948.

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