Frequency Control with Quartz Crystals
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Engineering Bulletin E-6: Frequency Control with Quartz Crystals |
Fundamentally, a primary standard of frequency consists of a temperature controlled crystal oscillator, a series of multivibrators for subdividing the oscillator frequency, and a synchronous motor-driven clock. The oscillator frequency may be 20kc., 30kc., 50kc. or 100kc., but 50kc. is more common. The crystal temperature is held to within a maximum variation of 0.01 degree Centigrade in a heated chamber while the oscillator circuit components are temperature controlled to a lesser degree. No provisions are made in commercial instruments to eliminate the effects of varying atmospheric pressure but, in the high precision instruments maintained by the U. S. Bureau of Standards, the crystals are operated at a substantially constant pressure in glass enclosed chambers.
The oscillator frequency is subdivided by multivibrators to provide a series of standard frequencies and to obtain a suitable low frequency for driving the synchronous motor clock. Since the time as indicated by the clock is entirely dependent on the frequency of the exciting current, and since the driving frequency is derived from the crystal oscillator, the clock actually serves as a counter for the number of oscillator cycles which occur in a given passage of time. By comparing the clock time with true time, the average frequency of the oscillator can be determined. The time comparison can be made to within a very small fraction of a second and the oscillator frequency, therefore, can be known within close limits of absolute.
The frequency of commercial primary standards can be held to within 2 parts in 10 million (0.00002%) if carefully checked, while better stabilities can be obtained with more elaborate equipment such as employed by the U. S. Bureau of Standards. This figure refers to the fundamental accuracy of the crystal oscillator but does not directly indicate the accuracy to which frequencies can be measured. As a result of accumulative errors in associated measuring equipment, the overall accuracy may be reduced to 1 part in 1 million (.0001%) depending on the manner in which the measurement is made.
A primary standard is merely a generator of standard frequencies; to perform actual measurements, additional equipment is required. A calibrated receiver is, of course, a necessity. For general frequency measurements the receiver should preferably be the simple regenerative type but superheterodyne receivers can be used when desired. If a superheterodyne receiver is used, extreme care must be taken to make certain that the signal being measured is properly tuned in as erroneous measurements can easily result from false reception through images, harmonics, or odd beats between the signal and the receiver oscillator. This is most troublesome when the intensity of the signal being measured is quite high.
The process of measuring a certain radio frequency against a primary standard is, briefly, to locate that frequency with respect to two adjacent harmonics of the standard frequency generator. This is illustrated in figure 19. Measurements can be made with a fair degree of accuracy by using only the receiver and the frequency standard. The signal to be measured (fx) is tuned in and the receiver dial setting carefully noted. The output from the standard is then connected to the receiver and the dial setting noted for the two harmonics of the standard which are immediately adjacent to the frequency, fx. If a regenerative receiver is employed, the detector should be in an oscillating condition and tuned to zero beat with each signal. The frequency of the two standard harmonics is known from the approximate receiver calibration and, by interpolation, fx can be determined. A graphical picture, and correct formula, is given in figure 19.
The same general process can be followed by beating a calibrated oscillator against fx, and the two adjacent standard frequencies, in the receiver. The interpolation is then carried out from dial settings of the oscillator corresponding to f1, f2 and fx. This latter method is advantageous where the signal strength of fx is very low or where it is varying widely due to such effects as fading. The accuracy of the measurements will depend on the linearity of the receiver or oscillator calibration, the frequency stability during the measurements, and the precision to which the dial settings can be determined.
It is generally necessary, with the direct interpolation method, to use harmonics of the standard frequency oscillator rather than of a 10kc. multivibrator. The harmonic spacing of 10kc. is usually covered by such a small rotation of the tuning dial that the position of the various frequencies cannot be precisely determined. If greater accuracy is desired, fx afterwards can be mixed in a receiver with harmonics of the 10kc. multivibrator. Fx, beating with each of the adjacent 10kc. harmonics, will produce two audio-frequency notes in the output of the receiver and either of these notes can be measured by zero-beating with a calibrated audio oscillator or by the use of an audio-frequency measuring instrument. The frequency of either one of these notes will, of course, be the frequency difference between fx and the corresponding 10kc. harmonic. A knowledge of the approximate frequency can serve to show which beat is being measured, but the preferable and more accurate method is to employ a calibrated oscillator as described and raise its frequency slightly above fx. If the audio note increases in frequency, the beat is against the lower 10kc. harmonic, and vice versa.
When mixing frequencies, it is preferable to use a regenerative receiver in a non-oscillating condition. If a superheterodyne receiver is used, adjust for minimum selectivity and tune to either one of the 10kc. harmonics or to fx, whichever is weakest.
If fx is below the fundamental frequency of the standard, or if it is higher than the usable harmonics of the standard and the multivibrator, a calibrated oscillator, termed a frequency meter or heterodyne frequency meter, must be employed. The frequency of this instrument is set such that it is equal to some harmonic of fx, or such that fx is some harmonic or the frequency meter. Then the procedure is to measure the frequency of the frequency meter and determine the value of fx by multiplying or dividing that value by the harmonic number. It is, of course, necessary to know the approximate frequency or fx so that the harmonic order can be determined. This can be done with a wavemeter or by determining several successive frequencies which will give harmonics or sub-harmonics at fx. If fx is lower than the frequency meter, fx will be equal to the difference between any two successive frequency meter settings. Should fx be higher, its frequency will be nf, where n is a harmonic number and f the reading of the frequency meter. It also follows that fx will be equal to (n+1)f1, (n+2)f2, (n+3)f3, etc. where f1, f2 and f3 are successive frequencies of decreasing values whose harmonics are equal to fx. Therefore, nf = (n+1)f1 or, n = f1/ff1 where n is the harmonic order for frequency f (the higher of the two successive frequency meter frequencies).
The frequency meter, the receiver (heterodyne detector) and the audio oscillator (interpolation oscillator) are regular equipment for a complete primary standard frequency measuring assembly. In practically all cases the measurements are made as described and herewith summarized for a complete accurate measurement: (1) determine the approximate value of fx by interpolation with the frequency meter, (2) set the frequency meter such that its fundamental, harmonic or subharmonic frequency is at zero beat with fx, (3) mix the output of the frequency meter and of the 10kc. multivibrator in a receiver, (4) measure one of the audio frequencies produced in the output of the receiver by means of the interpolation oscillator and, (5) calculate fx from all known values. To determine whether the measured audio beat is produced against the upper or lower 10kc. harmonic, it is necessary only to slightly raise the frequency of the frequency meter. The audio note will increase if the beat is with the lower harmonic or it will decrease if the beat is against the upper harmonic.
