Engineering Bulletin E-6:
Frequency Control with Quartz Crystals


Quartz crystals in the frequency range from 16kc. to approximately 500kc. are classed as low frequency crystals. They are placed in this definite classification due to the fact that their oscillating characteristics are somewhat different from crystals in the most commonly used range from 500kc. to 10,000kc.

Low frequency crystals have, in comparison, a low activity. The activity rapidly decreases with frequency and is lowest at 16kc. This decrease is the natural result of the increased mass of the crystals since the ability of any body to follow rapid changes in motion is directly connected with the mass of that body. The lower activity does not, however, infer a low Q (Q = 2 FL ÷ R) for the inductance of a crystal is directly related to its mass, i.e., the greater the mass the higher the inductance.

Because of their greater mass, low frequency crystals cannot vibrate as vigorously as crystals at higher frequencies without danger of being shattered. This means that the crystals must be used in low powered oscillators to keep the vibration amplitude at low values. Tubes such as the 27, 56, 6C5, 57, 1852 (6AC7) or 6J7 with rated voltages are generally employed although other types Can be used with reduced voltages. Low grid-drive tubes such as the 837, 802 and RK23 are often used in transmitting equipment (150kc. and higher) to obtain a reasonable amount of power without endangering the crystal.

Any of the oscillator circuits previously discussed can be used with low frequency crystals providing proper circuit values are chosen. To insure sufficient excitation, the tuning tank circuit must have a high L to C ratio. This is often accomplished by employing an untuned inductance coil which has a suitable self-resonant frequency. No direct formula can be given for such inductances as the distributed capacity of various types of coils is dependent on the method of winding; the proper size is best determined by cut-and-try methods. Bias is best obtained by means of a grid-leak resistor but this resistor must be considerably larger than would be required for higher frequency crystals. At 500kc., 100,000 ohms is satisfactory while values up to 5 megohms are necessary at the lowest frequencies. An improvement in circuit performance sometimes can be obtained through the addition of a small amount of cathode bias. Too much cathode bias, however, will be detrimental rather than helpful.

Triode tubes have sufficient internal plate-to-grid capacity that additional feedback is seldom necessary. With pentode or tetrode tubes, however, this capacity is too small to provide sufficient excitation for low frequency crystals. The additional feedback required can be obtained by connecting a coil in series with the crystal and inductively coupling it to the tank, by neutralization circuits, or merely by adding an external plate-to-grid capacity. The latter method is the simplest and is most generally employed. The correct capacity usually will be between 2 mmf. and 10 mmf. depending on the crystal activity and individual circuit conditions.

The Tri-tet circuit is useful due to its high harmonic output and inherently good stability. The cathode tank does not require a very high L to C ratio and, therefore, can be a conventional tuned circuit. If the plate tank is a choke coil with small distributed capacity, the output will be rich in harmonics which can be used for frequency calibrating purposes. The apparent crystal activity can be increased, wherever necessary, by connecting a coil in series with the crystal and inductively coupling it to the cathode circuit.

Good harmonic output can be obtained with triode and pentode oscillators by using an untuned tank. The higher the L to C ratio, the greater will be the harmonic output. Also, the higher the grid-leak resistance, the more distorted will be the output and, thereby, the greater the harmonic strength.

In conventional triode, tetrode or pentode oscillator circuits with grid-leak bias, maximum output occurs when the circuit is tuned for minimum plate current. This point is, however, unstable and operation must be below it on the low C side (tank tuned towards a higher frequency). For best performance, the circuit should be operated, whether the tank is tuned or untuned, at the lowest plate current consistent with positive starting of the crystal. With low frequency crystals, this generally will occur at 50% to 60% of the maximum drop in plate current which can occur by tuning.

A circuit often used in frequency standards, and particularly recommended for use with Bliley low temperature-coefficient crystals from 85kc. to 150 kc., is the modified Colpitt's Oscillator shown in figure 16. This arrangement has a relatively low power output but is exceptional for frequency stability. The crystal is connected directly into the frequency determining tank where it serves as a filter element. When the tank is tuned to a frequency at, or close to, the resonant frequency of the crystal, the crystal will assume control by reason of the fact that its impedance is lowest at its resonant frequency and rises very rapidly for other nearby frequencies. The crystal will maintain control over a comparatively large tuning range of the tank but, beyond that range, it no longer controls the oscillations, serving only as a series condenser in the tank circuit.

Figure 16

Figure 16--Standard Frequency Oscillator

The oscillating frequency of the circuit, with the crystal assuming control, can be varied over a limited range by the tuning condenser. At 100kc. this amounts to about ±8 cycles which is sufficient to correct for any frequency changes which might result from aging of the circuit components or from moderate variations in operating temperature. Any receiver-type pentode tube, such as the 6J7, is satisfactory for use in this circuit but the 1852 (6AC7) is particularly recommended because of its high transconductance.

The circuit values shown in the diagram are suitable for frequencies from 20kc. to 300kc. L and C should be of such values that, with the crystal shorted out, the circuit can be made to oscillate at a frequency slightly below the resonant frequency of the crystal at the approximate mid-position of the tuning condenser. The exact L to C ratio is not extremely critical but it does affect the frequency stability. Greatest frequency stability will occur with a fairly low L to C ratio because the crystal impedance Can then rapidly become large in proportion to the reactance of L if there is any tendency of the circuit frequency to deviate appreciably from the resonant frequency of the crystal. Of course, as the L to C ratio is lowered, the range over which the circuit frequency can be adjusted is also decreased. A net operating tank capacity of about 85 mmf. (working value, 170 mmf. per section) is best for crystals at 100kc. and gives a total frequency range of about 16 cycles. if the frequency range appears to be too large with any crystal, reduce the L to C ratio; and, conversely, if a greater frequency range is desired (at the expense of frequency stability), the L to C ratio can be increased.

The modified Colpitt's Oscillator is not particularly suitable for frequencies much above 300kc. As the frequency is increased, it becomes more difficult to keep the circuit 'locked-in' with the crystal the circuit will have a strong tendency to self-oscillate at other frequencies and the tuning range of the condenser over which the crystal assumes control becomes increasingly narrowed. Also, since the crystal is required to carry the circulating tank current, the circuit power must, of a necessity, be kept at a low level.

The modified Pierce circuit, shown in figure 12b, is excellent for low frequencies because of the positive feedback afforded. This arrangement is recommended particularly for use with low drift crystals from 150kc. to 400kc. A self-resonant inductance can be used for purposes of circuit simplicity but, where design permits, it is preferable to employ a conventional tuned tank.

It is characteristic of the bar-type crystals employed for low frequencies to possess two definite modes of vibration: the intended length oscillation and a thickness vibration. When the bars are mounted without mechanical restriction, such as in fixed or variable air-gap holders, either mode of oscillation can be excited by tuning the oscillator circuit to either frequency. This property is utilized in dual frequency calibrator crystal units (Bliley SMC100, 100kc.­1000kc.). If the bar is clamped, say between knife edges, the thickness mode often can be completely discouraged such that, in effect, it becomes nonexistent.

The two possible oscillating frequencies of freely mounted bar-type crystals are generally so well separated that the correct frequency, in a 'single' frequency crystal, is easily identified and no confusion results. In some circuit arrangements, however, where self-resonant tanks are employed, conditions can be encountered whereby the thickness rather than the length frequency will be excited. Particularly troublesome is the situation where the crystal frequency will start at one value and then hop to the other during operation. In any case of this nature, the performance can be corrected by increasing the size of the self-resonant coil or by placing fixed capacity in parallel with it. The effect of either alternative is, of course, to tune the oscillator toward the desired frequency and, simultaneously, detune it away from the thickness frequency of the crystal. Representative values of the plate coil and condenser for a simple Pierce circuit to operate at frequencies from 150kc. to 400kc. are 10 mh. to 16 mh. (single pi r.f. choke) and 400 mmf. In the same circuit, the grid-to-cathode feedback capacity should be in the order of 150 mmf.