This chapter deals with the operation and circuitry of transistor oscillators. In general, these fall into two categories: the feedback (or vacuum tube equivalent) types, and the negative-resistance (or current multiplying) type. Transistor oscillators are capable of sine-wave generation by every mode of operation now feasible in vacuum-tube circuits, plus some additional novel modes. This chapter covers the capabilities of the transistor as an oscillator in basic rather than specific designs. A number of numerical examples and specific values are included to illustrate the fundamental concepts involved. An analysis of relaxation, frequency multiplication, frequency division, and triggering in the transistor is also included.

**Feedback Oscillators**

* Transistor Hartley Oscillator. *

In the earlier chapters, it was shown that transistor properties, in every important respect, are equivalent to those of the vacuum tube. It is reasonable then to assume that any vacuum-tube oscillator configuration has an equivalent transistor circuit. For example, consider the vacuum-tube oscillator, illustrated in Fig. 6-1 (A) , which represents one form of Hartley oscillator. Positive feedback is accomplished by arranging the resonant tank E to be common to both the input grid and output plate circuits. The equivalent transistor circuit using a grounded emitter connection is illustrated in Fig. 6-1 (B) . Again, positive feedback is provided by placing the resonant tank so that it is common to both the input base and output collector circuits. If ground is removed from the emitter lead, and placed at the bottom of the tank circuit, the electrical operation of the oscillator is unchanged. Notice that when this circuit is rearranged as illustrated in Fig. 6-1 (C) , it is now in the grounded-base connection. While the grid bias of the vacuum-tube oscillator in Fig. 6-1 (A) is regulated by the grid leak resistor RG, the equivalent transistor base in Fig. 6-1 (C) is self-biased through resistor RB. In all three circuits, the battery supply is decoupled by an R-F choke.

**Fig. 6-1. Vacuum tube and transistor Hartley oscillator circuits.**

The major difference between the operation of the vacuum-tube Hartley oscillator and that employing a transistor lies in the loading effect of the emitter resistance on the tank coil. This resistance is reflected into the tank circuit and acts as an equivalent shunting resistance. The tank is also shunted by the collector resistance, and the equivalent shunt resistance of the resonant circuit becomes Oscilation starts when the equivalent shunt resistance of the tank is counterbalanced by the reflected negative-resistance of the emitter. The optimum tap point of the coil (as determined both mathematically and experimentally) is , where T is the ratio of the feedback turns included in the emitter circuit to the total number of tank coil turns, and a is the emitter-to-collector current gain. Notice that when a approaches unity, the transistor oscillates at highest efficiency with a center-tapped tank coil. Under this condition the minimum allowable parallel resistance of the tank circuit is which sets the Q of the circuit at resistance, f_{o} is the resonant frequency, and L is the inductance of the tank coil. The operating resonant frequency is always lower than the isolated resonant tank frequency, because of the change in effective value of inductance caused by the coil tap.

The disadvantages of tapping the coil can be avoided by using a direct feedback path from the resonant circuit to the input terminal. Figures 6-2 (A) and 6-2 (B) illustrate two such possible arrangements. In both examples, the feedback resistor R_{F} (a choke may be used) and the effective impedance of the resonant circuit form an a-c voltage divider. The value of R_{F} can be adjusted to obtain the required amount of feedback for sustained oscillation.

*Transistor Clapp Oscillator. *

The transistor equivalent of the Clapp oscillator is illustrated in Fig. 6-3 (A) . The operating frequency is set by the series resonant circuit in the collector circuit. Feedback is taken from the voltage divider consisting of capacitors C_{1} and C_{2}. The upper frequency limit depends largely on the transistor in use, and can be increased considerably by careful selection of the unit. Upper frequencies as high as 3 mc can be attained using typical junction types in this basic circuit. The numerical values shown are based on the average of a group of Raytheon CK720 transistors. If crystal control is used, the frequency stability is improved, and there is also a considerable increase in the upper frequency limit of the oscillator. One method of achieving crystal control in this circuit is to replace the collector resonant circuit by a crystal.

**Fig. 6-2. Direct feedback connections: (A) collector to base, (B) collector to emitter.**

*Transistor Colpitts Oscillator. *

The transistor Colpitts oscillator is similar to the Clapp type except that the resonant load is a parallel arrangement in the collector circuit. Thus the circuit becomes voltage, rather than current, controlled. The feedback is again taken from a point between the two series capacitors connecting the collector to ground. The upper frequency limit for this oscillator is in the same range as that of the current-controlled Clapp arrangement. The typical values illustrated in Figure 6-3 (B) are again based on the average of a small group of Raytheon CK720 transistors.

In both cases, the parallel combination C_{B}R_{B} provides the necessary emitter bias. This arrangement provides some degree of amplitude stability similar to the control provided by bypassed cathode or grid leak resistors in vacuum-tube oscillator circuits.

**Fig. 6-3. (A) Transistor Clapp oscillator. (B) Transistor Ca!pith oscillator.**

In servicing transistor oscillators, the emitter bias measured at the base end of the C_{B}R_{B} combination is a useful indication of the signal amplitude. In addition, the variation of the emitter bias over the frequency range indicates the relative uniformity of the signal output. Special care is necessary during these measurements to avoid affecting circuit operation. A vacuum-tube voltmeter may be used without causing additional loading. The use of a high resistance meter also minimizes that oscillator loading due to the stray reactance of the measuring probe. While direct current measurement is better, it requires disturbing the circuit wiring.

**Fig. 6-4). Transistor multivibrator.**

**Fig. 6-5. Bask resistance controlled negative resistance circuit.**

Transistor Multivibrator. Figure 6-4 illustrates the transistor equivalent of a basic multivibrator circuit. This configuration is generally useful in the frequency range of 5 to 15 kc. The parameter values shown are for an 8.33 kc oscillator which uses two Raytheon CK720 transistors. The frequency is determined by the R_{B}C_{B} time constant. The value of R_{B} is limited to a maximum of about 200k ohms. C_{B} is limited to a minimum of .002 µf. The frequency stability is poor compared to the types previously discussed. The output collector waveform is almost a perfect square wave. The advantages of the transistor multivibrator are its simplicity and the small number of components required.

**Negative-Resistance Oscillators**

* Conditions for Oscillation. *

The preceding paragraphs indicate that transistor oscillators can be designed as equivalents for all the known types of vacuum-tube oscillators that use an external feedback path. In addition, the unique property of a transistor that furnishes current gain can also be used to design many other novel types of oscillators. In the earlier chapters it was found that the point-contact transistor, by virtue of its ability to multiply the input current (r_{m} greater than r_{e}) , is characterized by negative input and output resistances over part of its operating range. It is feasible, therefore, to use the point-contact transistor in this region to design oscillator circuits that do not require external feedback paths. As one engineer put it, "An oscillator is a poorly designed amplifier." This observation is particularly applicable in the case of the negative-resistance oscillator. The conditional stability equation for a point contact transistor was specified in Chapter 4 as:

(r_{11} + R_{g}) (R_{g} - r_{22}) — r_{12}r_{21} must be greater than zero. Thus for the

transistor to be unstable, that is for it to exhibit negative resistance characteristics, requires:

In general, external resistance can be added to any of the three electrode leads, as illustrated in Fig. 6-5. Substituting the transistor parameter values into equation 6-1 results in:

Notice that when r_{m} is less than r_{c} (as in the case of the junction transistor) , the condition for oscillation cannot be satisfied. This re-emphasizes the fact that negative-resistance oscillators can only be designed using the point-contact transistor. Notice also in this equation that if both R_{L} and r_{g} are small compared to the value of (r_{m} — r_{e}) , the conditional equation is primarily controlled by the value of R_{B}. The higher the value of R_{B}, the more definite the instability. Furthermore, as the external collector and emitter resistances are increased in value, a higher resistance of R_{B} is required to assure circuit oscillation. The control of oscillation in negative-resistance transistor oscillators, then, is determined by the following three factors, either separately or in combination: the external resistance of the emitter lead (a low value favors oscillation) , the external resistance of the base lead (a high value favors oscillation) , and the external resistance of the collector lead (a low value favors oscillation) .

*Basic Operation. *

If the control of an oscillator can be maintained by simple high or low resistance values in the three transistor electrode arms, the substitution of series and parallel L-C resonant circuits in their place is a natural step. The insertion of a parallel resonant circuit in the base lead will cause the circuit to oscillate at the resonant frequency because of the tank's high impedance at resonance. On the other hand, placing a series L-C circuit in the emitter or collector arms will cause oscillation at the resonance frequency due to the tank's characteristic low impedance at that point. Fig. 6-6 illustrates the a-c equivalent circuit of a negative-resistance oscillator that includes all three methods of controlling oscillation. Since L-C resonant circuits produce sine waveforms, the oscillators using L-C resonant tanks are generally referred to as *sine-wave oscillators.*

The use of only the point-contact transistor for the negative-resistance oscillator is readily explained on an electronic basis. Assume that for the conventional grounded base connection, a disturbance or electrical charge of some sort causes an a-c emitter current to flow. This results in an amplified collector current Bic = aaie in the collector circuit. Since there is no phase inversion, the current flows through the base in phase with the emitter current. If the base resistance is large, the regenerative signal will be larger than the original signal. This increased current is again amplified, causing a greater collector current to flow, which again is fed back to the emitter, and so forth. In a short time, the current passes out of the linear dynamic operating range, and the circuit breaks into oscillation. The frequency of this oscillation is determined by the time constant of the circuit. In brief then, the point-contact transistor is capable of basic oscillation, without external feedback path, because of its ability to provide current gain and internal feedback path without phase reversal through the base lead.

**Fig. 6-6. Bask impedance controlled
negative resistance oscillator.**

**Fig. 6-7. (A) Voltage controlled negative resistance equivalent circuit. (B) Idealized
current-voltage characteristic.**

**Fig. 6-8. (A) Current-controlled negative resistance equivalent circuit. (B) Idealized current-voltage characteristic.**

**Fig. 6-9. (A) Base-controlled negative resistance oscillator and idealized characteristic. (B) Emitter-controlled negative resistance oscillator and idealized characteristic. (C) Collector-controlled negative resistance oscillator and idealized characteristic.**

*General Types. *

Negative-resistance oscillators may be divided into two general classes: voltage controlled; and current controlled. The voltage-controlled oscillator is characterized by a high resistance load, and a low resistance power supply (constant voltage) . The fundamental schematic of a typical oscillator of this type is illustrated in Fig. 6-7 (A). This oscillator is composed of three major parts: the resonant L-C circuit, the negative resistance of the oscillator, and the d-c supply voltage E_{bb}.

Figure 6-7 (B) represents the idealized current voltage characteristics of this oscillator. It is typical of the negative-resistance oscillator that the resistance remains negative only over a limited portion of its operating range. The bias is established somewhere in the middle of this useful section to guarantee oscillation. It is evident that a constant voltage bias is required. A remaining condition for sustained oscillation is that the resonant load have a higher absolute value than the negative resistance presented by the oscillator at the operating point. The parallel L-C circuit that approaches an infinite impedance at resonance, then, is ideal for this purpose.

The current-controlled type is shown in Fig. 6-8 (A) . This oscillator is characterized by a low a-c load and a high d-c power source (constant current) : Figure 6-8 (B) represents the idealized current-voltage characteristics for this negative-resistance oscillator. As in the voltage-controlled type, the negative-resistance region is limited to a section of the operating range, and the bias is established somewhere in the middle of this negative-resistance region using a constant current source. The last condition to be satisfied for sustained oscillation is that the a-c load of the resonant circuit must be less than the absolute value of negative resistance of the oscillator at the operating point. The series L-C circuit, the resonant impedance of which is close to zero, is the ideal load for this application.

*Sine-wave Oscillators. *

These principles can now be applied to the three basic methods of controlling oscillation in the point-contact transistor: the insertion of low impedance loads in the emitter or collector circuits (current control) , or the insertion of a high impedance load in the base lead (voltage control) . Figure 6-9 (A) illustrates the basic base-controlled oscillator and its idealized current-voltage characteristics. This circuit is the most often used because it offers the best possibilities of the three types. Its main advantages are that it employs a constant voltage source (the easiest type to design) , and that the regenerative feedback is through the resonant tank in the base lead. This latter feature assures frequency stability, because maximum feedback occurs at the resonant frequency of the tank circuit. The effect of the internal base resistance is negligible due to the extremely high value of the parallel circuit at resonance in comparison to r_{b}.

Figure 6-9 (B) represents the basic emitter controlled negative- resistance oscillator and its idealized current-voltage characteristics. Fig. 6-9 (C) is the basic collector controlled type. The fundamental operation of both is essentially the same. Oscillation occurs at the series resonant frequency of the L-C combination because at this point the effective resistance in either the emitter or collector arm is at minimum.

The base resistance must be large enough to furnish positive feedback in order to sustain oscillation. The base resistance r_{b} is generally large enough to cause instability when either the emitter or collector is shorted to ground, on the basis of equation 6-1. In practical circuits, however, r_{b} alone is rarely enough for dependable operation. An external resistor R_{B} equal to at least 2,000 ohms is generally added.

**Fig. 6-10. (A) Basic measuring circuit for obtaining negative resistance
characteristics. (B) Typical negative resistance characteristic.**

*Negative Characteristic Measurements. *

The characteristics of the three basic negative-resistance connections are not generally supplied by the manufacturer. These, however, may be obtained by a point plot. This is not too arduous a task since the curves are reasonably linear and the changeover points are well defined. For most purposes it is sufficiently accurate to insert a sweep signal into the controlled electrode and observe the response on an oscilloscope. Figure 6-10 (A) illustrates the basic measuring circuit for this application when the transistor is in the emitter controlled connection. A typical resulting E_{e} — I_{e} characteristic is shown in Fig. 6-10 (B).

The measuring circuit is easily modified for application to the base or collector controlled type. The plotted curve is similar to those illustrated in Figs. 6-9 (A) and 6-9 (C).

*Bias Selection. *

It can be shown mathematically that the condition for locating the operating point in the center of the negative-resistance region is: Ee (2αR_{c} + R_{E}) = E_{c}R_{E}. This relationship indicates that the extent of the negative-resistance range depends upon the bias batteries and the values of R_{E} and R_{c}. The emitter-to-collector current gain a is, of course, fixed for a given transistor. For the characteristic in Fig. 6-10 (B) , then, all the parameters are specified with the exception of E_{e} and R_{E}. Notice, however, that these quantities are related to the value of d-c emitter current bias I_{e} that is required to establish a d-c operating point in the center of the negative resistance region. This condition is: E_{e} = R_{E}I_{e}.

The two conditional equations can be combined to evaluate RE in terms of known quantities:

This value defines the maximum limit of the impedance of the L-C series emitter circuit at resonance.

*Oscillator Stabilization. *

The generated signal of the sine-wave oscillator becomes badly distorted when the dynamic operating range of the circuit exceeds the negative-resistance region; excessive and uncontrolled distortion causes frequency instability. Obviously, the reduction of the harmonic content to a minimum is particularly important in those applications that require a stable and pure sine wave. But even in those cases where a high harmonic content is desirable, steps are necessary to keep the harmonic content of the signal constant to insure frequency stability of the oscillator.

**Fig. 6-11. Effect of a-c load on harmonic content: (A) idealized a-c resonant load;
(B) A-c load slightly less than negative resistance of characteristic.**

The value of the a-c load impedance has a large effect on the amount of harmonic distortion in the signal. This effect is illustrated in Fig. 6-11 for the emitter controlled type. Figure 6-11 (A) illustrates the distortion in the voltage waveform when a sine wave of current is generated in an ideal series L-C load having zero impedance at resonance. Figure 6-11 (B) illustrates how the distortion is reduced to a satisfactory level by increasing the resonant impedance of the load. The increased a-c load effectively limits the dynamic range of the oscillator to the negative-resistance region. Thus, when a current-controlled oscillator is required to operate with a low harmonic content, the a-c load impedance should be chosen to be slightly less than the absolute value of the resistance determined by the slope of the negative-resistance characteristic. This same condition applies when the oscillator is collector controlled. A similar situation exists in the base-controlled negative-resistance oscillator except that, since this is a voltage-controlled oscillator, the distortion occurs in the current waveform. In this latter circuit, low distortion operation is attained by reducing the value of the resonant impedance so that it is slightly greater than the negative-resistance slope of the characteristic curve.

The operating point must be stabilized in the center of the negative-resistance region in order to avoid distortion from unequal positive and negative signal amplitudes. When the external resistances are fixed, the main causes of operating point shifts are changes in the bias sup.- plies. An effective method of stabilization is the use of one supply battery for both the emitter and collector bias. This assures that the

ratio will remain constant in spite of variation in the battery potential.

Increasing the resonant impedance of a series resonant arm is accomplished by selecting a higher resistance inductor, or by increasing the value of the series resistor in the emitter or collector lead. Decreasing the resonant impedance of the base controlled tank circuit is not as simple. A reduction of the tank Q will, of course, decrease the resonant impedance, but a low Q tank tends to promote frequency instability. A more satisfactory method of decreasing the impedance is to tap the base lead at some point in the tank coil. This permits the retention of a high Q tank, and, at the same time, reduces the effective impedance connected in the base lead. In addition, this connection helps to reduce the effects of internal transistor reactances on the operating frequency.

These internal reactances, primarily caused by junction capacitances, are particularly troublesome because their values do not remain constant with changes in temperature and changes in operating currents and voltages. However, loose coupling between the tank and the base circuit minimizes the effect of internal transistor reactance. While this reduces the available power of the oscillator, the sacrifice of power for stable operation is generally justified. The level of the signal can always be increased by a stage or two of amplification.

**Fig. 6-12. (A) Stabilized base-controlled high-frequency oscillator. (B) Alternate
method of providing common bias supply.**

Amplitude stability in negative-resistance oscillators is generally accomplished by incorporating some form of automatic bias control in the circuit. Sometimes the required amount of degenerative feedback is obtained through a non-linear resistor, placed in either the collector or emitter circuit. In this case, the main problem involves finding a non-linear element that is sensitive to the small current changes involved. Amplitude stability may also be obtained by a loosely coupled tank in the base-controlled oscillator, since it automatically decreases positive feedback at frequencies off resonance.

*Stabilizing Circuitry. *

Figure 6-12 (A) illustrates one arrangement of a high-frequency base-controlled oscillator that incorporates the various stabilizing features discussed in the preceding paragraphs. C_{1} and C_{2} are phase compensating condensers. The base lead is connected to a tapped tank coil as a means of reducing the resonant impedance while maintaining a high Q tank. Bias stability is accomplished by using one common battery source. Notice also that positive emitter bias is supplied by the bypassed resistor R_{B}. Figure 6-12 (B) illustrates an alternate method of providing a constant collector-to-emitter bias ratio by means of a common battery supply. The advantage of this circuit is its design simplicity, since it is basically a voltage divider network. The values of C_{1} and C_{2} are not critical; they complete the a-c circuit between the collector, base, and emitter leads, and bypass the battery and bias divider network.

Except for the inductance and capacitance elements of the resonant network, the values of the external components in negative-resistance oscillators are not critical. The values of R_{E} and R_{e} should be large enough to limit their respective currents to safe values, but not so large that they cause excessive degeneration. The value of the base resistance R_{B} must be large enough to provide sufficient regeneration for sustained oscillation. Typical values for these parameters are: R_{E} = 50 to 2,000 ohms; R_{e} = 2,000 to 10,000 ohms; R_{B} = 10,000 to 20,000 ohms.

**Transistor Phase Shift**

* Contributing Factors. *

In general, transistor oscillators make use of their non-linear characteristics. While there has been considerable progress made in the mathematical analysis of non-linear circuits, particularly in the past few years, oscillator design is invariably based on the static characteristic curves. This is true since even the simplest mathematical approximations of non-linear operation are too involved for the average experimenter or engineer to handle.

When the operating frequency becomes more than 100 kc, the internal transistor parameters can no longer be considered as simple resistances. At this frequency, the values of the transistor reactive components become appreciable. In addition to the fixed-resonant circuit parameters, there are also stray reactances due to lead inductance, and others that have a considerable effect on the transistor characteristics. Static curves, then, are extremely useful to set bias points, and to approximate the negative-resistance range, optimum load, and wave-shapes. However, circuit values based on the low-frequency transistor characteristics are not exact. The experimenter finds that every high-frequency transistor oscillator requires some readjustment for optimum operation.

Phase Shift and Feedback. One effect of the reactive Components is to cause a phase shift between the input and output terminals. Phase shift reduces the in-phase component of the positive feedback signal. This is illustrated in Fig. 6-13 (A) where E_{F} is the feedback signal and Ø is the phase angle between the input and output signals. E_{F1} represents the feedback amplitude at, low frequencies when the reactive effects are negligible. As the operating frequency is increased, E_{2} and the input signal are no longer in phase. Thus, only the in-phase component of E_{F} is useful for maintaining circuit oscillation. When the phase angle becomes so large that the in-phase component is less than the critical minimum required value, oscillation stops.

**Fig. 6-14. Phase-shift oscillator.**

*Phase Shift Compensation. *

The reduction of value of the in-phase feedback signal requires either an increase in feedback EF or a form of phase compensation to decrease the angle Ø. In the base-controlled oscillator, some phase shift compensation is provided by shunting either or both the emitter and collector electrodes to ground through a small capacitor (3 or 4 µµf) . This simple modification usually doubles the upper frequency limit of a transistor.

One method of increasing the available feedback is to connect a resistor from the emitter to a tap point on the base tank coil. This provides regenerative voltage feedback to supplement the inherent current feedback of the circuit. The value of the resistor R_{F} is critical. The upper limit of the oscillator frequency drops as R_{F} is either increased or decreased from its critical value. For this reason, the feedback resistance is best determined on an experimental basis. Figure 6-13 (B) illustrates a basic oscillator incorporating these two methods of phase shift control and compensation.

*Phase Shift Oscillator. *

One very stable negative-resistance oscillator is the phase-shift type illustrated in Fig. 6-14. This circuit is particularly useful in the audio range when a low distortion sine-wave signal is required. The resistances R_{C}, R_{B}, and R_{E} are determined by the condition for instability specified by equation 6-1. The phase shift network used is a band-elimination filter at the desired operating frequency. At this frequency, the filter offers maximum attenuation (theoretically an open circuit) . At any other frequency, the network attenuation decreases, thereby providing a degenerative feedback path into the base lead. This degeneration counteracts the positive feedback through the base resistor R_{B}. Thus, oscillation is favored only at the operating frequency, namely, the frequency eliminated by the phase shift network. If the network is designed for both phase reversal and minimum attenuation at the operating frequency, it will also be a useful oscillator. Under these conditions the network provides positive feedback into the base, which supplements the normal regenerative signal through the base resistor. The band-elimination filter oscillator is limited to the lower frequencies since proper operation depends on a zero phase shift through the network at the operating frequency.

**Fig. 6-15. Crystal oscillators:
(A) base controlled; (B) emitter
controlled; (C) collector controlled.**

**Negative-Resistance Crystal Oscillators**

*Basic Types. *

The negative-resistance oscillator is easily adapted to crystal control, since crystals can operate as either series or parallel tuned circuits. Figure 6-15 (A) illustrates the basic circuit of the base-controlled crystal oscillator. The R-F choke which bypasses the crystal provides a d-c path to the base. A choke coil is used rather than a resistor for two important reasons: first, a resistor lowers the Q of the crystal; second, a resistor provides a positive feedback path for frequencies off resonance, thereby eliminating the major advantage of the base controlled circuit, namely, maximum regeneration at resonance, minimum regeneration off resonance. Since, in this case, the crystal is operated as a parallel resonant circuit, this oscillator is electrically equivalent to the base-controlled circuit illustrated in Fig. 6-12 (A).

Figures 6-15 (B) and 6-15 (C) represent the basic circuits of the emitter and collector-controlled crystal oscillators. The circuit shown in Fig. 6-15 (B) will operate satisfactorily if the base tank is replaced by a resistor. The inclusion of the tuned circuit, however, provides increased frequency stability and decreased harmonic distortion in the output signal. The series resonant circuit in the emitter arm of the collector-controlled oscillator illustrated in Fig. 6-15 (C) is added as a means of increasing the frequency stability. It can be replaced by a resistor.

*Frequency Multiplication.*

Since the power handling capacity of the transistor is small, it can seldom provide enough energy to excite a crystal into oscillation at the higher frequencies. For this reason, high-frequency crystal-controlled oscillators usually incorporate some form of frequency multiplication. Figure 6-16 illustrates one basic circuit for a crystal-controlled frequency-multiplier oscillator. The emitter and base circuits in this base-controlled oscillator are conventional. The collector lead, however, contains a parallel resonant circuit tuned to the desired harmonic of the crystal fundamental frequency. At first glance it may appear that the inclusion of this network in the collector arm violates one of the fundamental requirements of negative-resistance oscillators, that is, the need for a low resistance collector circuit (equation 6-1). However, the collector tank is tuned to a harmonic of at least twice the fundamental frequency. Insofar as the fundamental crystal frequency is concerned, then, the collector tank is a low impedance. The tank offers a high impedance to the required harmonic, and consequently establishes a good feed point for this frequency into the output circuit.

Proper operation of the frequency-multiplier oscillator requires that the fundamental frequency be rich in harmonics, since low distortion contains little harmonic energy. The inherent non-linearity of negative-resistance oscillators [Figs. 6-9 (A) , (B) , and (C)], makes it easy to generate a distorted waveshape. This necessitates the use of a high impedance resonant circuit in the base-controlled oscillator, and the use of a low impedance circuit in the emitter or collector-controlled types. Tight coupling of the base tank also promotes increased harmonic generation, but this feature is generally unsatisfactory because of its adverse effect on frequency stability.

**Fig. 6-16. Crystal-controlled frequency
multiplier.**

**Relaxation Oscillators**

*Basic Characteristics and Operation. *

One of the most inviting applications of the negative-resistance oscillator is as a relaxation type, particularly since its power requirements are low. Transistor relaxation oscillators have almost limitless use where a complex waveform, pulse generation, triggered output or frequency division is required. Like the equivalent vacuum-tube types, the periodic operation of the transistor relaxation oscillator usually depends on a R-C or R-L combination for the storage and release of signal energy. For this reason, they are characterized by abrupt changes from one operating point to another. This makes relaxation oscillators particularly useful for generating sawtooth waveforms.

**Fig. 6-17. (A) Basic emitter-controlled relaxation oscillator**

**with (B) idealized characteristic, and (C) waveforms.**

Figure 6-17 represents the basic emitter-controlled relaxation oscillator and its idealized current-voltage characteristic. The location of the frequency-determining network in the emitter circuit provides the largest measure of control. This basic type, therefore, is the most useful The fundamental operation is involved, but not difficult to understand. For simplicity, assume the operation starts at point A (Figure 6-17B) . At this point the transistor is cut off, since the emitter is biased in the reverse direction (—E_{A}) . Because of this reverse bias, the input circuit offers a high resistance path. The charge on capacitor C_{E} (equals —E_{A}) has to leak off through R_{E}, and the rate of discharge is determined by the time constant R_{E}C_{E}.

When the voltage across the capacitor is reduced to —E_{E}, operation is at point B, which represents the point of transition from the cut-off to the negative-resistance region. The values of the emitter and collector resistances drop quickly to near zero, and the battery current is then limited only by the value of R_{e}. If the small effect of the saturation current l_{co} is neglected, both the emitter and collector current increase from zero to almost instantaneously. In this instant, the operating point moves rapidly from point B through point C to point D. At the same time, the voltage across the capacitor starts to increase to its original value of —E_{A}. The rate is fixed by the time constant of C_{E} and the parallel equivalent of R_{B} and R_{C}. In the meantime, the emitter current decreases at the same rate, thereby moving the operating point back toward point C.

When the current reaches point C, operation passes from the saturation region to the negative-resistance region. Instability in this area causes the current to drop instantaneously to its value at point B. Because of this rapid drop, the condenser voltage does not change. The operating point returns to point A, and the condenser discharge action starts the cycle again.

Note that there are two time constants during a complete cycle. The first one T_{1} R_{E}C_{E} controls the discharge rate of the condenser when operation moves from point A to point D. The second time constant controls the charging rate when operation moves from point D to point A. The sawtooth voltage generated by this circuit is illustrated in Fig. 6-17 (C) . The frequency of operation is approximately

The frequency of the current wave is the same, but the waveform ap proximates a pulse, since the current only flows during the period when the condenser is charging (T2) . This simple oscillator, then, is useful as a voltage sawtooth or a current pulse generator.

*Base- and Collector-Controlled Oscillators. *

Base-controlled and collector-controlled relaxation oscillators are illustrated in Figs. 6-18 (A) and 6-18 (B) . Both operate very much like the emitter-controlled type, and are analyzed on the basis of their respective operating characteristics, illustrated in Fig. 6-9 (A) and (C) . The main difference is that the base-controlled type uses an inductance for the storage and release of circuit energy.

The fundamental difference between the sine wave oscillator and the relaxation oscillator is determined by which of the circuit parameters control the repetition rate. This, in turn, is determined by which has the lowest period of oscillation. For example, if in Fig. 6-12 (A) the time constant of the emitter network C_{1}R_{E} or the collector network C_{2}R_{c} is greater than that of the base L-C tank, the circuit becomes a relaxation oscillator. If a properly designed base-controlled high frequency sinusoidal oscillator suddenly switches to a different frequency and produces a distorted waveform, the trouble is most likely in the base resonant circuit.

While the R-C time constant of the collector- and emitter-controlled relaxation oscillator is fixed by the required operating frequency, the C to R ratio should be as high as possible. This causes minimum degeneration in the circuit, and, at the same time, increases the surge current handling capacity of the condenser. As before, the value of the base resistor R_{B} is determined by the amount of positive feedback required for sustained operation.

**Fig. 6-18. (A) Base-controlled relaxation oscillator. (B)
Collector controlled relaxation oscillator.**

**Fig. 6-19. Basic self-quenching oscillator.**

* Self-Quenching Oscillator.*

The relaxation oscillator in combination with the regular base-controlled type can be used to form the self-quenching oscillator. Figure 6-12 (A) illustrates a self-quenching type if the value of either C_{1} or C_{2} is increased sufficiently to make the emitter or collector time constant appreciably greater than that of the L-C tank circuit. Figure 6-19 represents the basic self-quenching oscillator. Due to its time constant, the R-C emitter network has primary control of the circuit and produces the sawtooth voltage and pulsed current waveforms illustrated in Fig. 6-17 (C) . The operation of the relaxation section of the circuit is independent of the base tank. The base network, however, depends entirely on the relaxation operation. Assume the cycle is moving in the charging direction (B of Fig. 6-17) , operation from point C to point A. When the operation reaches the negative-resistance region where sufficient regenerative energy is supplied, the base tank oscillates at its resonant frequency. The amplitude of the resulting wave is small initially, but rises to a peak at the point when C_{E} starts its discharge cycle (B of Fig. 6-17) , operation from point A to point D. The duration of the oscillation in the base tank is a function of the Q of the network, the amount of stored energy and the loading effect on the tank by the rest of the circuit. The relaxation or quench frequency in this case is while the resonant frequency of the tank is Notice that fQ must be less than f_{Q} for proper operation. The basic circuit becomes collector controlled if capacitor CE is moved into the collector circuit. The circuit operation is exactly the same.

**Fig. 6-20. Synchronized controlled (A) waveform, (B) frequency multiplication wave
forms, (C) frequency divider waveforms.**

*Synchronized Relaxation Oscillator. *

The operation of a synchronized relaxation oscillator is easily understood in view of the fundamentals of operation covered in the preceding paragraphs. The basic circuit is the same, but the relaxation frequency is made slightly less than the synchronizing frequency. Referring to Fig. 6-17 (B) , assume that operation is moving from point A toward point B, and that a positive pulse, large enough to instantly move operation to point B, is applied to the emitter. The effect, as illustrated in Fig. 6-20 (A) , is the same as decreasing the time constant R_{E}C_{E}, and the relaxation frequency becomes the same as that of the applied synchronizing pulse. The actual point at which the synchronizing signal arrives is not critical as long as the pulse amplitude is large enough to carry the operation into the negative-resistance region. Notice, however, that the magnitude of the sawtooth voltage is reduced by an amount equal to that of the pulse. The dotted line represents the voltage waveform without synchronization.

The synchronized oscillator can be used as a frequency multiplier. Figure 6-20 (B) illustrates one application in which the input frequency is approximately half that of the relaxation frequency. Any sub-multiple of the normal rate will work. The chief disadvantage of this type of operation is the lack of control over the frequency in the interval during synchronizing pulses.

Figure 6-20 (C) illustrates the application of the synchronized relaxation oscillator as a frequency divider. In this example, the input frequency is three times that of the relaxation rate. As long as the synchronizing rate is an integral multiple of the basic frequency, the oscillator remains under control. Theoretically, any division ratio is possible, but in practical circuits the ratio is limited by the non-linearity of the sawtooth wave near the critical voltage E_{B}. Consistent operation for division ratios up to approximately 10 to 1 can be easily attained. Ratios higher than these require critical design for reliable operation.

Negative synchronizing pulses can be used to operate the base or collector-controlled oscillator types. The many ramifications of the basic relaxation oscillator are too numerous to cover, but the experimenter may find many useful applications for this circuit. If, for example, time constants are inserted in both the emitter and collector circuits, the relaxation oscilitor can be synchronized by a pulse applied to either electrode. The circuit may also be biased in either the saturation or cut-off region, so that it remains non-oscillatory until pushed into the regenerative region by an external pulse. The last type falls under the general category of trigger circuits.

*Trigger Circuits*

The transistor oscillators considered to this point have one feature in common: the controlling electrode is biased in the negative resistance region. These types, whether synchronized, sinusoidal, or non-sinusoidal, come under the general classification of *astable operated*.

Triggered circuits, on the other hand, are biased in one of the stable regions and are non-oscillatory until the trigger pulse is applied. These types are classified as either *monostable operated* or *bistable operated oscillators.*

*Monostable Operation. *

The basic monostable circuit is illustrated in Fig. 6-21 (A) . The only difference between this circuit and the emitter-controlled relaxation oscillator illustrated in Fig. 6-17 (A) is the elimination of the emitter resistor RE. Since this action removes the d-c emitter current bias (I_{E} = 0) , the operating point shifts from the negative-resistance region (P_{2}) to the point intersection of the voltage axes at I_{E} = 0 (P_{1}) . This change is illustrated in Fig. 6-21 (B) . The circuit is no longer capable of self-sustained oscillation since it is biased in the stable cut-off region. Now, if a pulse of sufficient magnitude (at least equal to I_{P}) is applied to the emitter, operation is forced into the regenerative region. The current jumps to its value at point D, and the negative charge on the emitter condenser starts to build up. When the charging current is reduced to its value at point C, operation again enters the regenerative region, and the current is quickly reduced to its value at A. The charge on the condenser gradually leaks off through the emitter base circuit (r_{e} + r_{b} + R_{B}) until the stable operating point P_{1} is reached. The circuit is now ready for another trigger pulse.

The emitter resistance is very high in the cut-off region due to the reverse bias. As a result, the same constant C_{E} (r_{e} + r_{b} + R_{B}) is large compared to that of the relaxation type illustrated in Fig. 6-17 (A) . This is the major factor limiting the repetition rate of the trigger pulse if sensitive operation is required.

**Fig. 6-21. (A) Basic monostable trigger circuit. (B) Idealized characteristic.**

**Fig. 6-22. (A) Basic bistable trigger circuit. (B) Idealized charaderistics.**

*Blistable Operation. *

Figure 6-22 (A) illustrates the basic bistable circuit. The fundamental requirement for this type of operation is that the load line intersects the characteristic curve once in each of the three operating regions. This automatically establishes three operation points: one in the unstable negative-resistance region; one in the saturation region; and one in the cut-off region. The last two points are stable, hence, circuit operation is properly defined as bistable. The operation shown in Figure (6-22 (B) is as follows: When operation is at point P_{1}, the circuit is stable, since the current is low; this is referred to as the o*ff-state*. If a positive pulse is now applied to the emitter, operation enters the regenerative region at point A. The operation swings rapidly to the saturation region where, at point P_{3}, the circuit is again stabilized. Since the current at this point has considerable magnitude, this is referred to as on-state. To move operation back into the off-state requires a negative trigger pulse whose magnitude is at least equal to E_{3}. This pulse moves operation back into the unstable negative-resistance region at point B, where it rapidly swings back to the stable off-state point P_{1}.

The value of R_{E} is selected to provide the three necessary operating points. It is not critical and may vary considerably but, in general, it should be fairly low. Notice that the potential of the emitter battery Ee fixes the location of P_{1}, which in turn determines the required value of the trigger pulse E_{1}. A low battery voltage, then, causes sensitive operation, since the triggering can be accomplished with a small pulse. A large value of E_{1} results in less sensitive but more reliable operation, since the circuit is less likely to be triggered by noise or other unwanted circuit disturbances. The final choice of both E_{e} and R_{E} should be based on the most sensitive combination providing reliability.