Frequency Control with Quartz Crystals
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Engineering Bulletin E-6: Frequency Control with Quartz Crystals |
Crystal controlled oscillators have their origin in some basic self-excited oscillator arrangement frequency control is brought about by connecting a quartz crystal into the circuit in such a manner that the crystal becomes the frequency determining element. The conventional triode or pentode crystal oscillator, as shown in figures 8 and 13, is merely the well-known tuned-plate tuned-grid circuit with a quartz crystal substituted for the grid tank. For purposes of discussion, such circuits are sometimes called tuned-plate crystal-grid oscillators.
Oscillator circuits are remarkably self-regulating; the circuit values can be varied over wide ranges and the oscillator will continue to function. With any set of component values which do not prohibit oscillation entirely, the various currents and generated voltages will distribute themselves for best performance under those conditions. Of course, there are circuit values which will give optimum performance and efficiency, but, for practical applications, these require no great consideration. Representative components are generally chosen and then, by cut-and-try methods, the most satisfactory values determined.
The crystal controlled oscillator is equally self-regulating, and, for that Particular reason, it requires more care in design and operation. A quartz crystal, as previously explained, has mechanical limitations in that an excessive vibration amplitude will cause the crystal to be shattered. It is necessary to design a crystal controlled oscillator such that the circuit, in attempting to correct for varying operating conditions, will not cause the crystal excitation to become excessive. This consideration necessitates a reasonably careful choice of circuit values and, in addition, limits crystal control to comparatively low powered oscillators.
The crystal excitation in the usual type of oscillator circuit depends on the amplification factor of the tube, the bias, the d.c. operating potentials, the circuit feedback, and the activity of the crystal. For a given power output, the tube with the highest amplification factor will generally require the least excitation (lowest crystal current). This is immediately apparent in the performance of pentode crystal oscillators as compared to triode oscillators; screen-grid tubes, having the highest amplification factor, require much less crystal excitation for a given power output.
Beam-power tubes are excellent crystal oscillators due to the very small amount of excitation required for full output. In the conventional tetrode crystal oscillator circuit, good output and performance are easily obtained. Where the tube performs as a combination crystal oscillator and frequency multiplier, however, Beam-power tubes such as the 6L6 have a strong tendency toward the development of parasitics, especially at the higher frequencies. This is due to the power sensitivity and to the fact that the screen grid in such tubes is not fully effective at radio frequencies.
The crystal excitation in a particular oscillator setup is determined by the r.f. voltage across the oscillator tank. Because this voltage is applied to the crystal circuit, the excitation naturally will increase as the r.f. tank voltage is raised. The L to C ratio of the oscillator tank determines its impedance and, as the ratio is increased, the r.f. voltage will also increase. A reasonably high L to C ratio is desirable with conventional pentode or tetrode oscillators, while a lower ratio is better with triode tubes. The greater internal plate-to-grid capacity and the low amplification factor of most triodes, requires that the tank voltages be limited such that the crystal excitation will not become excessive. This applies also to the cathode tank of the Tri-tet circuit because the oscillating portion is a triode.
The feedback in conventional tuned-plate crystal-grid oscillators is brought about by the internal plate-to-grid capacity of the tube. The excitation requirements of active quartz crystals are so small that, even with screen-grid tubes, this internal capacity is usually sufficient to bring about ample excitation of all but low frequency crystals. Some tubes, such as the 802 and RK23, have very low internal capacities and a small amount of external feedback capacity is recommended by the manufacturer. Most active crystals above 1500kc. will oscillate without the addition of the external capacity; every effort should be made to operate the circuit without the added capacity before any attempt is made to increase the feedback. Excessive feedback, whether through the intentional use of a condenser or through the presence of stray circuit capacities, will bring about high excitation and endanger the crystal. With screen-grid tubes, proper bypassing of the screen grid is essential. If the bypassing is inadequate, the grid will assume an r.f. potential greatly increasing the feedback to the crystal.
The bias on the tube is an important consideration. In general, the higher the bias the greater will be the crystal current and the power output. Beyond certain limits, however, an increase in bias will cause a considerable increase in crystal current with only a small gain in power output. Too much bias can bring about excessive excitation.
Bias is most generally obtained by the use of a grid-leak resistor, a cathode resistor, or a combination of both. With grid-leak bias, an increase of resistance will be accompanied by an increase in the crystal current. Also, the crystal starts oscillating under conditions of zero bias with a continually increasing bias as the crystal excitation becomes greater. This means that the crystal current will be greatest when the oscillator is not loaded because the plate tank voltage, and the bias, will be highest under that condition. As a result of the zero bias in a non-oscillating condition, the crystal may be hard starting and may not key well, especially when a low value resistor is employed. By resorting to cathode bias, the crystal will start oscillating under more favorable conditions. The initial bias provided has a tendency to increase the effective plate-to-grid feedback and also brings about a grid condition more conducive to the starting Of oscillation. Too much bias of this type, however, will produce the opposite effect; the crystal will be hard starting and the current will be high. The correct value of cathode resistor generally lies between 200 and 500 ohms, 350 ohms being a good all-around value.
With pentode or tetrode type tubes, best performance usually is obtained by combining grid-leak and cathode bias. In general, the grid-leak resistor should not be higher than 20,000 ohms while the cathode resistor will lie between the values already given. It is customary practice to insert an r.f. choke in series with the grid-leak resistor so as to offset the low impedance otherwise presented to the crystal. This procedure is recommended where the grid resistor has a value of less than 50,000 ohms. Standard quality multiple-pie 2 mh. to 3 mh. chokes are excellent for frequencies above 1500kc.
When using triode tubes in the tuned-plate crystal-grid circuit with high frequency crystals, it is best to connect an r.f. choke directly across the crystal to provide a path to ground for the d.c. grid current, and then employ cathode bias exclusively. The addition of a grid resistor usually will greatly increase the crystal current without effecting a corresponding increase in power output.
The d.c. plate voltage on an oscillator will, naturally, influence the crystal excitation. As the potential is raised, the developed r.f. voltage will increase bringing about additional excitation. With pentode and tetrode type tubes the screen-grid voltage becomes an important factor; the higher this voltage the greater will be the crystal current and the power output.
Crystal activity it an equally important factor in the design of crystal oscillator circuits. This subject has been fully discussed in the section entitled CRYSTAL ACTIVITY and need not be repeated.
Circuit losses must be properly considered in the design of a crystal oscillator. The circuit should be carefully arranged so that there will be a minimum of stray feedback capacities which may increase the crystal excitation. It is readily possible, with improper layout, to fracture a crystal because of additional feedback brought about by stray circuit capacities. If any appreciable coupling exists between the oscillator and other stages of the transmitter working at the same frequency, the crystal excitation may easily be increased to an excessive amount; thorough inter-stage shielding in high power transmitters is imperative. At the higher frequencies, especially above 6000 kc., the tank circuit should be well constructed and preferably made self-supporting. If coil forms are used, these should be of the best quality. The copper wire in the tank inductance should be sufficiently large to carry the circulating tank current, for, if the wire is too small, the resultant losses will effect a considerable decrease in power output. When the cathode of the oscillator tube is operated at an r.f. potential, the heater leads should be bypassed to ground at the tube socket.
While it is often desirable to obtain relatively high power outputs from crystal oscillators, it should be remembered that a crystal oscillator is fundamentally a frequency controlling stage; the "heart" of a transmitter. With the present low cost of tubes, it is much better to work the crystal easily by using a low powered oscillator and adding an additional tube to obtain sufficient driving power for the following stages. This assures good frequency stability and removes the danger of crystal failure through excessive excitation in an attempt to obtain sufficient power output.
TRIODE OSCILLATORS: The conventional triode crystal oscillator is shown in figure 13. It is a universal circuit because it performs well with crystals at all frequencies. Cathode bias, as indicated, is best for crystals above 1500kc. while grid-leak bias is preferable at lower frequencies. The proper cathode resistor varies with different type tubes but normally will be between 200 and 500 ohms. grid-leak bias, in addition to cathode bias, is recommended only for low frequencies.
A relatively low L to C ratio tank should be employed for best stability and reduced crystal current. The d.c. plate potential directly influences the crystal current and the voltage, therefore, should not be too high. Some tubes may be operated at potentials up to 350 volts while with others, the potential must be limited to 250 volts or less. In any event, maximum safe potential for any individual triode oscillator will depend on the amplification factor of the tube, the bias and the tank L to C ratio.
The dual-triode crystal oscillator frequency multiplier is an excellent arrangement for frequency multiplying. This circuit is shown in figure 14. Although the tank circuit values are given for 10 and 5-meter operation, the circuit can be adapted for any crystal frequency by choosing the correct tank constants. If it is desired to use the second section as a buffer at the crystal frequency, neutralization must be incorporated. This is necessary to prevent feedback into the oscillator. The maximum oscillator plate voltage for tubes such as the 6E6 and RK34, is 325 volts while tubes such as the 53 and 6A6 may be operated with a maximum of 350 volts. It is best practice, however, to limit the plate voltage of the oscillator section of all dual-triode circuits to a maximum of 300 volts; the multiplier section can be operated cat a higher voltage if greater harmonic output is desired.
Because the excitation requirements of most triode tubes are quite high, their power output as crystal oscillators is relatively low under conditions or safe crystal current. Power outputs of up to 5 watts are normal with the usual type of triode tube at frequencies above 1000 kc. In the dual-triode circuit the power output, when frequency doubling, is in the neighborhood of 3-1/2 watts.
PENTODE AND TETRODE OSCILLATORS: The conventional pentode or tetrode crystal
oscillator is the most practical and commonly employed circuit.
A representative pentode oscillator is diagrammed in figure 8.
The general characteristics of pentode and tet
rode oscillators are identical inasmuch as the essential difference
between the tubes lies in the method of suppressing secondary
emission from the plate.
A combination of grid-leak and cathode bias gives the most satisfactory results with all crystals above 1500kc. The correct value for the grid resistor usually will be between 5000 and 20,000 ohms, while the cathode resistor will be from 200 to 500 ohms. A representative combination for most pentode and tetrode tubes is a 20,000 ohm grid resistor and a 350 ohm cathode resistor. At low frequencies, best performance is generally obtained with simple grid-leak bias.
The screen-grid voltage has a considerably greater influence on the crystal current than the plate voltage. A potential of 250 volts is generally maximum for normal plate potentials while a lower value is preferable when the plate potential is greater than 400 volts. Proper bypassing of the screen grid is important, especially so with Beam-power tubes. The bypass condenser, preferably of the mica type, should be placed directly at the tube socket. With pentode tubes, where the suppressor grid is connected to one of the base terminals, an increase in power output can be accomplished by operating the suppressor grid at a low positive voltage.
Pentode and tetrode tubes, having a high amplification factor, will provide the greatest power output for a given crystal current. Furthermore, the frequency stability with such tubes is much better than obtainable in the conventional triode oscillator due to the action of the screen grid. This grid reduces the internal plate-to-grid feedback and also has a compensating action on the tube impedance under conditions of changing power supply voltages. With tubes such as the RK23, 802 and 807, which are designed specifically for use at radio frequencies, power outputs of 10 to 15 watts can be obtained at frequencies above 1000kc. with a reasonably low crystal current.
PUSH-PULL OSCILLATORS: A push-pull pentode crystal oscillator is diagrammed in figure 9. Oscillators of this type are only advantageous in that the output circuit is balanced and even harmonics are cancelled out.
Only with tubes which require very low grid drive is it possible to obtain a substantial increase in power output with the push-pull arrangement. The two tubes will require approximately twice as much driving power as a single tube of the same type and it follows, therefore, that the crystal must vibrate more intensely to drive both tubes to full output. As a result, it is necessary, with most tubes, to reduce the operating voltages so that the crystal current will be within safe limits under all conditions of performance. The final effect is only a small power output increase over the use of a single tube oscillator.
TRI-TET OSCILLATORS: Developed by James Lamb, the Tri-tet is an excellent frequency multiplying arrangement. It is, as shown in figure 15, a combination triode crystal oscillator and pentode (or tetrode) frequency multiplier--the oscillating portion is a triode with the screen grid serving as the plate. By inserting the tuning tank in series with the cathode, the screen grid is grounded to r.f. At the same time, some regeneration results at harmonic frequencies by reason of the fact that the common tank circuit carries currents at both the crystal and the harmonic frequencies.
Since the oscillating portion of the Tri-tet is a triode, the usual consideration of employing a low L to C ratio applies to the cathode tank. For lowest crystal current and highest output at harmonics, the tank should be tuned to a frequency considerably higher than that of the crystal. As a matter of fact, the circuit should not be operated with the cathode tuned close to the crystal frequency for the result will be high crystal current and decreased output. For proper results, the tank should be tuned for greatest power output at the particular harmonic without serious regard to the relation between cathode tuning and d.c. plate current.
For each particular type of tube there will be an optimum cathode tank L to C ratio. This is discussed by James Lamb in the April, 1937 issue of QST magazine. In general, the higher the multiplying factor employed, the higher should be the cathode L to C ratio. If the capacity is too high, the voltage drop at the harmonic frequency will be low and regeneration will, therefore, be small. Likewise, if high stray circuit capacity is allowed across the crystal, regeneration will be lowered. When a Tri-tet is to be used both for multiplying and working straight through, it should be noted that the best cathode tank L to C ratio for multiplying is too high when working straight through; the low C can bring about high crystal current and, possibly, cause fracturing of the crystal. When the plate tank is operated at the crystal frequency, the use of a high-C cathode tank is essential.
It will be seen that, as far as r.f. is concerned, the cathode and plate tanks are in series. For this reason, when the plate tank is tuned to the crystal frequency, the crystal current will be lowest at no load and will increase with loading. The crystal current, when frequency multiplying, remains substantially constant with loading because the oscillator portion then functions nearly independently of the remainder of the circuit.
A condition of decreased power output at the second, harmonic can exist if the cathode tank should happen to be tuned to that frequency. This condition is obviously corrected by slightly retuning the cathode tank.
Since the screen grid serves as the Plate of the crystal oscillator, the screen-grid d.c. potential will influence the crystal current to a large extent. A potential of 250 volts is considered maximum, while a lower Value is preferable. The proper bias conditions are somewhat different from a simple triode oscillator due to the fact that the bias also influences the power output on harmonics. In general, bias recommendations given for the pentode and tetrode crystal oscillators should be followed with the Tri-tet.
The effectiveness of the screen grid in tubes employed as Tri-tet oscillators requires consideration. If the shielding is poor at radio frequencies, the circuit should be used only for frequency multiplying--this is most important with crystal frequencies much above 3000kc. When poor internal shielding does exist, the crystal excitation can become excessive as a result of additional feedback when the plate tank is tuned to the crystal frequency. Tubes such as the 802 and RK23 have excellent radio frequency characteristics while others, such as the 6L6, 6F6, 2A5, 42, 59 and 89, are poorly shielded since they were designed primarily for use at audio frequencies. When operating at the crystal frequency, especially with poorly shielded tubes, it is best practice to convert the circuit to a conventional pentode or tetrode oscillator by shorting out the cathode tank. This is easily accomplished by bending the tips of the cathode condenser rotor plates such that the condenser can be shorted out simply by rotating it to full capacity position.
The Tri-tet has excellent frequency stability inasmuch as the coupling between the oscillator and the output circuit is brought about electronically within the tube. The power output, when operating straight through with a suitable tube such as the 802 or RK23 and at a crystal frequency above 1000 kc., is in the neighborhood of 12 watts. When frequency doubling, it is about 8 watts.
PIERCE OSCILLATORS: In the Pierce circuit, as shown in figure 10, the crystal is connected between the plate and control grid of the tube. This arrangement is essentially a Colpitt's Oscillator with the crystal displacing the usual tank inductance.
It can be seen that the crystal is connected, in series with the feedback condenser C1, directly across the plate circuit. The crystal excitation, therefore, will be largely influenced by the value of C1. Increasing the feedback capacity decreases the circuit reactance and brings about higher crystal current while a decrease in capacity will have the opposite effect. Accompanying the change in crystal current, there will be a shift in the oscillating frequency which may amount to about 2kc. at 4000kc. If C1 is made too large, excessive excitation can result, even though the plate voltage May be low. At 500kc., C1 should be about 250 mmf. while 20 mmf. to 30 mmf. is ample at 7000kc.
In addition to properly determining the feedback capacity C1, it is necessary to operate the oscillator at low voltages to limit the r.f. voltage developed in the plate circuit. The d.c. potentials indicated in the circuit diagrams should be considered maximum values.
The plate circuit must have a capacitive reactance to satisfy conditions for oscillation. A capacitive reactance can be obtained with a detuned tank, an r.f. choke having a resonant frequency lower than the crystal frequency, or a resistance. A pure resistance, of course, has no reactance, and, by itself, would not satisfy the conditions for oscillation. The internal plate-to-grid capacity of the tube is in parallel with the resistance, however, and this provides the necessary capacitive reactance. For the amateur frequencies, a 2.1 mh. or 2.5 mh. r.f. choke is generally employed while a considerably larger inductance is required at lower frequencies.
The crystal current, as in other circuits, will be influenced by the amount of grid bias. Bias, when using pentode or tetrode tubes, can be obtained with a grid-leak resistor alone or in combination with a cathode resistor. Best performance, however, is generally obtained with the combination of grid-leak and cathode bias. In the triode circuit, grid-leak bias is best. The grid resistor, in either Case, should be limited to a maximum of 50,000 ohms for crystals above 1500kc. while 100,000 ohms is better at the lower frequencies. When using cathode bids, the resistor must be considerably smaller than would be employed with other circuits; about 250 ohms is sufficient for pentode or tetrode tubes and 125 ohms for triodes. It is possible to reduce the crystal current by employing a low value grid resistor in series with an r.f. choke but this is not always satisfactory because the circuit may oscillate as a tuned-plate tuned-grid oscillator with the grid and plate chokes determining the frequency.
Tuned tanks are not required in the simple Pierce circuit and, therefore, a rather wide range of crystal frequencies can be used without any serious change in circuit values. This is advantageous in some types of transmitters but limits the choice of crystal frequencies to fundamental crystals. Harmonic-type crystals will not perform properly because such crystals will oscillate at the true fundamental rather than at the intended harmonic frequency. This is due to the fact that a frequency discriminating tank is not present and, therefore, the crystal automatically will work at its most active resonant frequency.
The outstanding advantage of the Pierce circuit is simplicity of circuit components. It is limited, however, to low power output and requires careful circuit adjustment to prevent excessive excitation. Also, because the circuit frequency is influenced to an appreciable extent by the values of the circuit components, the overall frequency stability is somewhat dependent upon the oscillator construction and upon the electrical stability of the component parts.
PIERCE OSCILLATOR-MULTIPLIERS: Pentode or tetrode tubes can be used in a crystal oscillator frequency-multiplier circuit with a Pierce oscillator rather than the conventional triode oscillator as employed in the Tri-tet. A circuit of this type is illustrated in figure 11. in the Reinartz arrangement of this circuit the tank, L2 C2, is tuned to approximately 11/22 the crystal frequency. With the Jones' arrangement, a small r.f. choke is tuned, by an associated condenser, to a frequency in the neighborhood of 300 kc.
Both arrangements have the same essential characteristics and provide power outputs comparable to the Tri-tet. At frequencies below 4000kc., the cathode capacity C2 may have any suitable value from 100 mmf. to 250 mmf. The circuits are quite critical at higher frequencies, however, and the value of C2 becomes an important factor. For each type of tube, tank L to C ratio, degree of loading, and crystal, there is an optimum value of C2 which will give greatest power output consistent with good circuit stability. If C2 is smaller than the critical capacity, there will be a strong tendency to develop parasitics, especially with Beam-power tubes, and the crystal current will be high. In fact, it is possible for the parasitics to become sufficiently intense to fracture a crystal. Capacities greater than the critical value will result in lowered crystal current and decreased power output.
C2 should preferably be a variable condenser with a maximum capacity of about .00025 mf. In any event, the actual amount of capacity in use should be no less than .0001 mf. and, even then such a low value should be employed only when frequency multiplying. Representative values are .00015 mf. when multiplying and .00025 mf. when working straight through. In some instances, it may be necessary to increase the capacity to as much as .0005 mf. for proper performance.
In addition to influencing the crystal current and circuit stability, C2 affects the power output at harmonics. At the higher harmonics, greatest power output is obtained with low values of C2. It must be remembered, however, when operating the circuit at a harmonic with a very low value of C2, that the capacity must be increased when changing to fundamental operation--the conditions for best harmonic output care not generally satisfactory for fundamental operation and excessive excitation may result. The importance of carefully determining the proper operating value of C2 for crystal frequencies above 4000kc. cannot be too strongly emphasized.
The oscillator portion of this circuit, like the simple Pierce circuit, has no positive choice of crystal frequency. Harmonic type crystals, therefore, normally will oscillate at the fundamental rather than the calibrated frequency. With the proper value for C2, however, a harmonic crystal can be caused to work at its intended frequency by tuning the plate tank to that frequency; at all other settings, the crystal will oscillate at its fundamental frequency.
When the output tank is tuned to the fundamental crystal frequency, the operating characteristics are similar to the Tri-tet; that is, the crystal current rises with load and excessive feedback can result when tubes with insufficient internal shielding are employed for working straight through.
The bias considerations for the Pierce circuit in general, apply to the oscillator portion of these arrangements. For frequency multiplying, a combination of grid-leak and cathode bias generally results in best performance.
An improvement in circuit performance can be realized by adding a small amount of external capacity directly between the oscillator control-grid and cathode. This capacity is equivalent to C1 in figure 10 and stabilizes the crystal feedback. The amount of capacity added, however, should be much smaller in order to prevent excessive crystal excitation and to avoid a reduction of harmonic output. About 10 mmf. to 15 mmf. is sufficient at 7000kc. in general, the value of C2 (figure 11) should be raised somewhat when the additional feedback is applied to an existing oscillator.
Grid-cathode feedback is particularly advantageous when variable frequency crystals, such as the Bliley VF1, are to be used in the oscillator. The presence of the feedback helps to offset the falling off of effective crystal activity as the crystal frequency is raised. The result is decreased power output variation over the full adjustable frequency range and better keying at high frequency settings.
MODIFIED PIERCE OSCILLATORS: A unique modification of the Pierce oscillator is shown in figure 12a. It will be noticed that the circuit has the same components as the Pierce oscillator multiplier (figure 11) but the screen grid is tied to the control grid. As a matter of fact, any triode tube can be used but, by using a pentode tube in this manner, a high-mu triode is formed such that the plate current is nearly zero with the circuit non-oscillating. When the crystal goes into oscillation, the plate current will rise to normal operating value.
Excitation of the crystal is brought about by the r.f. drop across L2C2. This tank is, in the same manner as in the Pierce oscillator-multiplier (figure 11), tuned to a frequency considerably lower than that of the crystal. The crystal will tend to oscillate almost independently of the tuning of L1C1 (by shorting out L1C1, the circuit becomes a simple Pierce oscillator). Output will be developed when L1C1 is tuned to the crystal frequency or, with a Harmonic-type crystal, to the intended harmonic oscillating frequency. With fundamental oscillating crystals, frequency multiplying can be accomplished by tuning to any harmonic of the crystal frequency.
An increase in power output can be brought about by bypassing the screen grid and applying a small positive voltage. Along with the increase in output, there may be an actual decrease in crystal current. If the screen-grid voltage is raised appreciably, however, the circuit performance reverts to the original Pierce oscillator-multiplier arrangement previously discussed.
With a 1 megohm screen dropping resistor, good output can be obtained with low crystal current.
At high frequencies, this modified Pierce circuit is prone to develop self-oscillation. In fact, when a 10-meter crystal is used, the circuit tends to perform in the same manner as a locked oscillator; that is, the circuit may self-oscillate at a frequency largely determined by the plate tank, but, when the circuit tuning is brought to the crystal frequency, the crystal will assume control.
Figure 12b shows a circuit arrangement developed by Jones. It is electrically equivalent to the modified Pierce circuit just discussed and the operating characteristics are the same; the capacity, C2, functions in the same manner as the cathode tank, L2C2. The crystal is excited by the r.f. voltage drop across C2 and, therefore, the value of C2 directly influences the crystal current. If C2 is made too small, excessive excitation easily can result. The condenser, C3, is merely a blocking condenser to prevent the d.c. plate voltage from being applied to the crystal.
The optimum value for C2 varies with individual circuit arrangements, depending upon actual circuit conditions encountered. As a general rule, the correct capacity will lie between 150 mmf. and 500 mmf. As should be expected, a relatively low capacity is desirable for bringing about harmonic regeneration when frequency multiplying. At the same time, however, the crystal excitation will undoubtedly be excessive should the plate tank be tuned for output at the fundamental frequency.
By using a pentode or tetrode tube rather than the triode, and operating the screen grid at a normal potential, there will be a considerable increase in power output. Either the triode or the pentode arrangement can be used as a frequency multiplying circuit with fundamental crystals or for operating harmonic-type crystals at their intended harmonic frequencies.
Both of these arrangements will also develop self-oscillation at high frequencies. Circuits of this general type, therefore, are best limited to crystal frequencies below approximately 4000kc.
