Frequency Control with Quartz Crystals
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Engineering Bulletin E-6: Frequency Control with Quartz Crystals |
In oscillator circuits, employed for the majority of radio transmitter installations, the crystal operates in the same manner as a parallel, or anti-resonant, electrical circuit. For this reason, quartz crystals employed for frequency control of vacuum tube oscillators usually are calibrated at their anti-resonant frequencies.
The effective value of the capacity, C1, changes when a crystal is placed in a vacuum tube oscillator circuit. In the theoretical analysis, C1 represents the capacity between the crystal electrodes with the crystal acting as the dielectric. When, however, the crystal is connected in an actual circuit, the value of C1 will vary with different crystal holders and will, in addition, be affected by the dynamic input impedance of the oscillator tube and the capacity added by connecting wires between the crystal and the tube. The impedance in the plate circuit of the tube will, naturally, also influence the dynamic impedance of the grid circuit to an extent dependent on individual operating conditions.
It is evident that the total capacity added to C1 by the oscillator will vary between different circuits and layouts, thereby causing the crystal frequency to assume different values in each particular oscillator setup. Because of the possible variations in frequency, Bliley Crystals normally are guaranteed to operate within a certain variation from the calibrated frequency (generally .02% .03%, including customary manufacturing frequency tolerance) when operated in the purchaser's equipment despite the fact that each crystal is accurately calibrated in the manufacturing laboratory. The crystals are, for the same reason, supplied complete with holders only. For details concerning crystal specifications to meet definite frequency accuracy requirements, reference should be made to Bliley Catalog G12. This publication contains pertinent information relative to the choice of crystals and mountings for all services other than amateur.
When a quartz crystal is required for a specific service or application where frequency accuracy is most important, the possible change in frequency between the manufacturer's calibrating oscillator and the final equipment must be considered. This is especially important where the allowable frequency tolerance is very small.
By taking advantage of the fact that the parallel capacity will influence the frequency of a crystal, it is possible to include a variable frequency feature. This is invaluable to radio broadcast services in the standard broadcast band where the carrier must be held within 20 cycles of the assigned value. It is an equally valuable feature in many other services where the frequency must be held within close limits and in amateur service where a simple method of shifting the station frequency often permits contacts under ordinarily impossible conditions of interference.
There are two methods of effecting the change in the oscillating frequency of a crystal operating at, or near, anti-resonance. The obvious arrangement is to connect a variable air-condenser in parallel with the crystal to bring about a variation in C1, (figure 2). As the capacity of the condenser is increased, the frequency will be lowered until the capacity becomes sufficiently large to effectively short out the crystal. In any event, the added capacity will "load up" the crystal thereby decreasing its oscillating ability. For small ranges of frequency adjustment the effect of the condenser will not be harmful, however, and the decrease in the oscillating properties of the crystal is readily offset by the variable frequency feature. This method of shifting the frequency is generally applied with crystals higher than 2000kc. but can be used at lower frequencies if desirable. At the very high frequencies it is not particularly satisfactory because the amount of capacity sufficient to stop oscillation is quite small. This, of course, greatly limits the amount by which the frequency can be varied.
A variable air-gap crystal holder offers the most convenient method for shifting frequency. In a typical holder of this type, one of the crystal electrodes is mounted on a micrometer screw such that the electrode may be raised or lowered over the crystal. This brings about a simultaneous change in the Values of C1 and C2 (figure 2). When the air-gap between the movable electrode and the crystal is increased, the frequency will be raised with an accompanying decrease in oscillating properties. For small ranges of frequency adjustment, the detrimental effect of the air-gap is not serious and the only essential consideration is that the crystal be used in a circuit where the driving voltage will not reach high values. Unless this precaution is taken, an arc will be developed across the air-gap causing erratic oscillation and, sometimes, damaging the crystal because of the concentrated heat of the arc.
The impedance of a quartz crystal, in the region near its natural frequency, is lowest at the resonant frequency and highest at anti-resonance. At frequencies remote from these values the crystal acts merely as a fixed condenser. This is illustrated by the representative reactance curve shown in Figure 3. The property of a crystal to act as a resonant circuit, with an extremely rapid increase in impedance on either side of resonance, is most useful in radio frequency filters and for frequency control of certain types of oscillator arrangements.
Relaxation oscillators, which rely on the time constant of resistance-capacity networks, have characteristics which are desirable in some applications. Such oscillators are mechanically simple and have a high harmonic output but are not very stable. They can, however, readily be stabilized by substituting a quartz crystal for one of the coupling condensers. The crystal, acting as a resonant circuit, determines and controls the frequency of oscillation. Because of practical limitations in obtaining resistance-capacity combinations with a very short time constant, circuits of this type are limited to frequencies below about 150kc.
Another arrangement, more widely used, employs an inductance-capacity tank with the crystal connected directly into the tank circuit. This is the modified Colpitt's Oscillator shown in figure 16 and discussed in the section LOW FREQUENCY OSCILLATORS. The crystal acts as a filter and controls the frequency of oscillation by virtue of its impedance-frequency characteristic. Circuits of this type are outstanding for high frequency stability and, for that reason, are used in precision frequency standards.
The frequency of a crystal oscillating purely at resonance cannot be varied by means of a parallel condenser. It can, however, be shifted by effecting a change in C2 (figure 2). This may be accomplished with a variable air-gap holder or by connecting either a variable air-condenser or an inductance in series with the crystal. Increasing the value of a series inductance will lower the frequency while an increase in frequency will result if the capacity of a series condenser is decreased. A series condenser, with its greater stability and ease of adjustment, provides more satisfactory control than a variable inductance. Whether a condenser or an inductance is used, it must be stable in itself or the frequency stability brought about by the use of a quartz crystal will be considerably lessened. The amount of possible frequency adjustment is limited by the fact that the impedance of the series element reduces the voltage across the crystal (excitation) and by the natural consequence that circuit frequency stability is lowered as the series impedance is increased.
The resonant properties of quartz
crystals are advantageously employed in modern communications
receivers to obtain a very high degree of selectivity. Since crystals
ground for filter purposes have an extremely high Q (9,000 to
16,000) the frequency discrimination, or selectivity, will be
many times better
than could be obtained with ordinary tuned circuits. As a matter
of fact the selection is so great that it is not difficult to
limit the pass band to 50 cycles.
Figure 4 shows the fundamental arrangement of a quartz-crystal-filter stage in a modern superheterodyne communications receiver. It will be noticed that the tapped transformer, the crystal, and the variable condenser, C1, form a bridge circuit. The use of a tapped transformer can be avoided by employing a dual condenser for C and grounding the common connection between the two; the final effect, however, is the same. At frequencies remote from the resonant frequency of the crystal, the bridge circuit is balanced and no voltage appears on the grid of the following amplifier tube. When, however, the transformer voltage is at the resonant frequency, the crystal impedance drops to a low value thereby upsetting the balance and permitting a signal voltage to appear on the grid of: he amplifier tube.
Despite the apparent simplicity of the filter circuit, an exact analysis of its operation is most difficult; practically all filters of this type are designed empirically on the basis of experimental data. For a basic understanding of the principles involved, however, it is convenient first to assume that the bridge is perfectly balanced. The lower portion of the bridge, including the balancing condenser C1, can then be ignored for practical purposes. It now can be seen that the induced voltage in the upper ha If of the secondary of transformer T1 is in series with the impedance of the transformer secondary, the crystal, and the output transformer T2 as shown in figure 5.
An inspection of figure 5 reveals that a voltage divider exists such that the output signal voltage is proportional to Zt2 ÷ Zt1 + Zc + Zt2.
The impedance of the crystal, Zc, is, of course, a variable highly dependent on frequency and, on this fact, is derived the circuit action. If Zt1 and Zt2 are chosen to have high values, the effect of the varying Zc is lessened and the selectivity is relatively broad. Likewise, if the impedances are low, the influence of Zc is pronounced and selectivity is high. As a matter of fact, it is an easy matter to realize high selectivity whereas it is difficult to reduce the selectivity to a point satisfactory for reception of radiotelephony.
In the foregoing discussion, it has been presumed that the induced voltage would be the same regardless of total circuit impedance and that the impedances Zt1, Zt2, possess constant values independent of frequency. This, of course, is not strictly true. A full consideration of the vectorial values of all impedances and the magnitude of input voltage would, however, greatly complicate an initial analysis without altering the generalized conclusions.
It is generally understood that transformer T1 should not be tuned to exact resonance if maximum selectivity is to be realized. This is due to the fact that the secondary impedance is highest at that point, thereby causing an actual decrease in selectivity because of the voltage divider action; sharpest selectivity occurs with the transformer slightly detuned such that the developed voltage is still high but the secondary impedance is lowered. Advantage of this influence on filter sharpness can be taken to establish a degree of control over selectivity. The procedure is to provide a panel control for the secondary tuning condenser of T1 so that the secondary impedance can be varied by tuning.
The impedance and impedance-frequency characteristic presented to the filter circuit by T2 will, naturally, also influence selectivity. This is advantageously employed for controlling selectivity by the insertion of a variable resistance in series with the primary winding of T2. (Footnote 1) The variable resistance alters the Q, or impedance-frequency characteristic, resulting in variable selectivity. By means of the voltage divider theory, and taking into account the variation of Zc and Zt2 with frequency, it can be shown that maximum selectivity occurs at lowest Q while minimum selectivity results when the resistance is entirely out of the circuit.
Condenser, C1, usually termed
the phasing control, is primarily for the purpose of balancing
the bridge circuit. It does, however, have some influence on selectivity
when set away from the balance position. It will be noted from
figure 4 that the phasing condenser, in series with the crystal
holder capacity,
is in parallel with the secondary of T1. This means that C1 has
an influence on the tuning of T1. Such influence is, as a matter
of fact, undesirable for best filter performance and is normally
minimized by keeping the crystal holder capacity at a low value.
A further divorcing of the effect can be accomplished through
the use of a so called constant-capacity variable condenser. (Footnote
2) Such a condenser has two rotor sections ganged oppositely;
that is, when one condenser section is approaching maximum capacity
the other is nearing minimum capacity. The net series capacity
of such an arrangement can be made to remain substantially constant
with rotation, and, if the common rotor terminal is connected
to the crystal, one stator to the lower end of T1 and the other
stator to ground or to the upper end of T1, little detuning by
the phasing control will occur. Of course, without detuning present,
the phasing control will have little or no influence on overall
selectivity.
When the phasing control is set for bridge balance, signals on either side of the crystal resonant frequency will be almost equally attenuated.
If, however, the control is set somewhat away from balance position, the attenuation at some side frequency will be considerably increased. This is a useful feature in communications because it enables the operator to emphasize attenuation on a particular interfering signal whose frequency is close to the one desired.
The action of the phasing control in rejecting signals is simply a matter of circuit balance. For any particular setting of the phasing control, other than for perfect balancing of the crystal holder capacity, there will be one frequency which will be passed in nearly equal magnitude, but in opposite phase, through the crystal arm and through the phasing control arm of the filter circuit. Because the voltage in each arm is out of phase at the common terminal, cancellation occurs. Whether the rejection point exists above or below the resonant frequency of the crystal depends, of course, on the actual capacity of the phasing condenser with respect to the capacity required for perfect bridge balance.
Footnotes:
1. See QST, December 1938, page 33
2. See QST, September 1937, page 24
