The principle of oscillator circuits using vacuum tubes is well known, and a number of the techniques which apply to vacuum-tube circuits are applicable to transistor circuits. This chapter reviews some of the fundamentals of oscillator circuit design and theory, and shows how these are applicable to designs using transistors.
The term harmonic oscillators may be applied to those oscillators which are op-erated in such a way as to produce a reasonably sinusoidal output voltage. In these circuits, a resonator is usually employed to fix the frequency of operation.
The resonator acts to make the output sinusoidal, even though the current or voltage applied to the circuits may be highly distorted.
12.1. CRITERIA FOR OSCILLATION
It will be helpful to examine some of the basic concepts of a sine-wave oscilla-tor. Figure 12.1 shows that such an oscillator is composed of an amplifier to pro-vide power gain, a resonator to fix the frequency of oscillation, and a feedback network to provide oscillation. If this arrangement is to operate as a stable oscil-lator, the gain around the closed loop should be unity. If a gain greater than this exists, the output will increase until the loop gain is reduced to unity, because of the limiting which will occur at high levels.
It can also be shown that the phase shift around the closed loop of Fig. 12.1 should be zero. If the phase shift is not zero, the frequency of oscillation will
Pi
.1
AmplifierI
~----~--~ GPi1
Resonator1
~-.--~--~ Po1 gain =
G i l
loss P~ 1 Power toload
1
Feedback networkl
Pi +pr'---11 loss PL' 1
Fig. 12.1. Elements of an oscillator circuit.
180
Low-frequency Harmonic Oscillators 181
change in such a way as to make it zero. These two conditions of unity power gain and zero phase shift around the loop are known as Barkhausen criteria for oscillations.
12.2. FEEDBACK PATHS
The feedback path class of oscillators embraces those that require an external path to couple the energy from the output to the input. Only a general discussion of these circuits will be given here, to show some of the various configurations which may be used to obtain oscillations.
Figure 12.2 shows several circuits which employ LC circuits as resonators to fix the frequency of oscillation. These circuits are shown using PNP transistors; how-ever, NPN transistors are equally suitable if the biasing potentials are reversed.
In Fig. 12.2a, the resonant circuit is in the collector, and the feedback is obtained by transformer coupling from the collector to the base. In Fig. 12.2b, the resonant circuit is placed again in the collector; however, this time the feedback is taken to the emitter. In this case, it is necessary to use a somewhat larger turns ratio than that in Fig. 12.2a, since the input impedance of the emitter is lower than that of the base.
The circuit of Fig. 12.2c is the same as Fig. 12.2a except that the tank circuit is a-c coupled to the collector with a coupling capacitor.
The circuit of Fig. 12.2d is similar to that of Fig. 12.2b except that the coupling from the tank is accomplished by using the tank inductor as an autotransformer.
The capacitor is needed only to block the d-c potential which exists between the collector and emitter.
Fig. 12.2. Some basic transistor oscillators using external feedback.
-E
Fig. 12.3. Bridge-type oscillator.
The circuit of Fig. 12.2e is similar to those of 12.2a and 12.2d except that the coupling in this case is obtained through tapped capacitors instead of a tapped inductor. This technique results in a voltage and impedance transformation similar to that resulting from a tapped coil.
The circuits shown here are only a representation of a few of the many circuits which have evolved. Other types of external feedback oscillators, which produce a sinusoidal output but do not employ an LC resonant circuit, are the bridge and phase-shift oscillators.
A bridge oscillator in one of its simplest forms is shown in Fig. 12.3. Ql is operated as a grounded-base amplifier with a very high collector load so as to give a large voltage gain. Q2 is used as a grounded-collector amplifier (emitter-follower) to couple this high-impedance collector to two feedback paths. One feedback path to the emitter is broad-tuned and is regenerative, and the other path is to the base and is made up of a bridged-T network. The feedback through this network is all degenerative; however, the bridged-T has a sharp null at one frequency which reduces the degenerative feedback and causes oscillation to occur at this frequency.
Fig. 12.4. Phase-shiff-type oscillator.
Low-frequency Harmonic Oscillators 183
The nonlinear element shown in the positive-feedback path provides a limiting action, so that the transistor can operate in a class A condition.
A phase-shift oscillator can be built using a similar circuit. In Fig. 12.4, two transistors are used again, one (Ql) to obtain high voltage gain and one (Q2) to obtain an impedance match. In this circuit the feedback is applied to the base of Ql. A phase shift of 1800 is obtained in three RC networks, and the additional 1800 required for oscillation is obtained through the grounded-emitter amplifier Ql.
12.3. DESIGN DATA
In order to illustrate the design of a transistor oscillator, a procedure for the design of a typical circuit is given:
As stated before, the Barkhausen criteria require that the power gain around the loop be unity and the phase shift around the loop be zero. These two factors are easily separated in oscillators having only external feedback loops. A block diagram of a feedback oscillator is given in Fig. 12.5. The amplifier has been converted to an equivalent Th6venin voltage generator with a voltage e1Kmin series with a resistance, ro, the output impedance of the amplifier which is considered to be part of the feedback network. The input impedance of the amplifier is con-sidered infinite, since any reactive component may be canceled at anyone frequency, and the resistive component may be considered as a part of R. The phase angle, B, is assumed to be a function of all external parameters, such as temperature and voltage. The primary factors affecting the stability of the frequency of operation now become cp(j), the resonator phase-shift characteristics as a function of fre-quency and B(s), the variation of phase shift of the amplifier due to external effects.
For stable frequency operation, it is desirable to make dBjds as small as possible and dcpj df as large as possible.
The factors influencing cp(f) are the geometry and element values of the frequency-controlling network. The choice of the network geometry is limited only by practical values of K and roo For most transistors, ro is too large unless a trans-former is used, in which case the ratio K2 jro remains constant for any transformer.
This is true because the reflected impedance of a transformer varies as the square of the voltage ratio. Thus, the amplifier and transformer may be characterized in terms of Band K2jro = A.
L ____________ ~ L ________________ ~
Fig. 12.5. Block diagram of feedback-type oscillator.
r - - - l
. Fig. 12.6. Simplified schematic of feedback oscillator.
To illustrate this method for designing a practical oscillator, the network shown in Fig. 12.6 is analyzed as follows: Let oscillator and A as determined for the amplifier, ro can be determined from Eq. (4).
When ro is known, then the correct turns ratio of the transformer can be determined.
If ro and R could both be made zero and still maintain oscillations, the change in frequency produced by a small change in amplifier phase shift, M, would be
tJ.j=
M/o
2Q for M small (5)
where
and 1
!o =
yLCLow-frequency Harmonic Oscillators 185
for the resonant element
For values of (ro
+
R) other than zero, Eq. (5) must be modified by makingQ= Xl
Rl