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# Practical Oscillator Handbook 1997-Irving M Gottlieb

(Parte **1** de 6)

Preface

The subject of oscillators has been somewhat of a dilemma; on the one hand, we have never lacked for mathematically oriented treatises~the topic appears to be a fertile field for the 'long-haired' approach. These may serve the needs of the narrow specialist, but tend to be foreboding to the working engineer and also to the intelligent electronics practitioner. On the other hand, one also observes the tendency to trivialize oscillator circuits as nothing more than a quick association of logic devices and resonant circuits. Neither of these approaches readily provides the required insights to devise oscillators with optimized performance features, to service systems highly dependent upon oscillator behaviour, or to understand the many trade-offs involved in tailoring practical oscillators to specific demands. Whereas it would be unrealistic to infer that these two approaches do not have their place, it appears obvious that a third approach could be useful in bringing theory and hardware together with minimal head-scratching.

This third approach to the topic of oscillators leans heavily on the concept of the universal amplifier. It stems from the fact that most oscillators can be successfully implemented with more than a single type of active device. Although it may not be feasible to directly substitute one active device for another, a little experimentation with the d.c. supply, bias networks, and feedback circuits does indeed enable a wide variety of oscillators to operate in essentially the same manner with npn or pnp transistors, N-channel of P-channel JFETs, MOSFETs, op amps or ICs, or with electron tubes. Accordingly, this book chooses to deal with basic operating principles predicated upon the use of the universal active-device or amplifier. This makes more sense than concentrating on a specific device, for most oscillator circuits owe no dependency to any single type of amplifying device.

Once grasped, the theory of the general oscillator is easily put to practical use in actual oscillators where concern must be given to the specific active device, to hardware and performance specifications, and to component values. To this end, the final section of the book presents numerous viii Preface solid-state oscillators from which the capable hobbyist and practical engin- eer can obtain useful guidance for many kinds of projects.

It is felt that the reader will encounter little difficulty acclimatizing to the concept of the universal amplifier, for it is none other than the triangular symbol commonly seen in system block diagrams. Although it hasn't been widely used in conjunction with other circuit symbols, the combination works very well with oscillators. It is respectfully submitted that this book will thereby serve as a unique format for useful information about oscillators.

The symbol used for a.c. generator is usually assumed to be a constant voltage generator, i.e., with zero internal resistance. However, in many instances in this book, it must be assumed to be a constant current generator, or at least to have a high internal resistance. For example, this is the case in Fig. 1.41, where if the generator shown is an ideal voltage generator, it will short out L~. This will a}ter circuit operation and make the quoted formula for3~ wrong. It is recommended therefore that the reader bear this in mind when presented with an a.c. generator in this book. Irving M. Gottlieb PE

Frequency-determining elements of oscillators

A good way to understand oscillators is to view them as made up three essential sections. These are:

* the frequency-determining section o the active device * a source of d.c. power

The validity of this viewpoint does not require that the three sections be physically separate entities. This chapter will treat the characteristics of the elements involved in the frequency-determining section.

Parallel-tuned LC circuit

Academically and practically, the parallel LC arrangement known as a 'tank' circuit is the most important element for us to become familiar with. In its simplest and most frequently encountered form, it is made up of a single inductor and a single capacitor. Whether or not we desire it, the inevitable 'uninvited guests', a number of dissipative losses, are always present. (See Fig. 1.1.) In the circuit, these losses behave as resistances. Their presence can, indeed, be closely simulated by simple insertions of resistance into the tank circuit. In Fig. 1.2 we see a possible way in which this can be done. This is the most convenient method and will be used frequently in the equations for computing the various tank circuit quantities.

Losses in a tank circuit

Different losses predominate under different situations. In general, the higher the frequency, the greater the radiation loss. Magnetic hysteresis is

2 Practical Oscillator Handbook

Skin effect and

Hysteresis in ohmic losses core material inwinding

in coil wire | |.. / |

Eddy currents j /

AC "" ~ hysteresis !~'1" generator ~ ~ i~' /:-'r~ qL .-.~'.:~ J, Leakage I\ resistance I \

/~~, ::\[ ~:~ J in dielectric J \

Insulation / ~" 1 Plate~ losses .:; i, '.:'. J and lead :..i :i | resistance

~< |

""~ "Eddy currents in adjacent metal

Fig. 1.1 Some possible losses in an L C tank circuit only of consequence when a ferromagnetic core is used, such as powdered iron. The losses due to eddy currents are, in reality, brought about by transformer action in which the offending material constitutes a short- circuited 'secondary'. This being true, we must expect eddy-current losses in the cross-section of the coil winding itself. Skin effect is an a.c. phenom- enon that causes the current to concentrate near the surface of the conduc- tor. This is because the more central regions of the conductor are encircled by more magnetic lines than are the regions closer to the surface (see Fig. 1.3). The more lines of magnetic force encircling a conductor, the greater the inductance of the conductor. Hence, the central regions of a conductor carrying alternating current offer higher inductive reactance to the flow of current.

The higher the frequency, the more pronounced is this effect; that is, the greater the tendency of current to concentrate at or near the surface, thereby reducing the effective cross-section of the conductor. Because ofskin effect, the resistance offered to the passage of high-frequency current is much higher than the d.c. resistance. (Inductance does not affect the flow or distribution of d.c.) We are not surprised that skin-effect losses are reduced by using hollow conductors of copper content equal to small gauge wire, but which possess a much greater surface area. Also, stranded wire offers more surface for high-frequency conduction than does its 'd.c. equivalent'

Frequency-determining elements of oscillators 3

A.C. generator

Rc I ". RL

Fig. 1.2 Representation of losses in an L C tank circuit by series resistances RL and Rc

Fig. 1.3 Flux-density from A.C. in a conductor and the high frequency skin-effect. At low frequencies most of the current flows throughout the cross-section of the conductor. At high frequencies, almost all current is in the outer 'skin' of the conductor in solid wire. Stranded wire with each individual wire insulated (Litz wire) is particularly well suited for the flow of high-frequency current.

Dielectric hysteresis in insulating materials is the electrostatic counterpart of magnetic hysteresis in magnetic materials. A frictional effect is displayed by the polarized molecules when they are urged to reverse their charge orientation under the influence of an alternating electric field. There are other losses. Those described and those shown in Fig. 1.1 are, however, the most important. Significantly, in many applications, only the losses in the inductor are of practical consequence, for capacitors often have negligible losses from the standpoint of many practical oscillator circuits.

Characteristics of 'ideal' LC resonant circuit

We find ourselves in a much better position to understand the proprieties of an actual 'lossy' tank circuit by first investigating the interesting characteris-

4 Practical Oscillator Handbook " owatts '

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Fig. 1.4 Voltage and current in an ideal inductor and capacitor tics displayed by an 'ideal' tank circuit in which it is postulated that no losses of any kind exist. It is obvious that such an ideal tank circuit must be made up of an inductor and a capacitor that, likewise, have no losses. In Fig. 1.4, we see the important feature of such ideal elements, i.e., when an a.c. voltage is impressed across an ideal inductor or an ideal capacitor, current is consumed, but no power is dissipated. Although there is current through these elements, and voltage exists across them, the wattmeters show a zero reading. This may seem strange at first; such a situation is the consequence of the 90 ~ difference in phase between voltage and current. This phase condi- tion is shown in Fig. 1.5 for the ideal conductor, and in Fig. 1.6 for the ideal capacitor.

In both instances, power is drawn from the source for a quarter cycle, but is returned to the source during the ensuing quarter cycle. This makes the power frequency twice that of the voltage or current waves. This need not be cause for surprise, since the same situation prevails for a resistance energized from an a.c. source. It turns out that the double-frequency power curve is of little practical consequence as such. Of great importance is the fact that the negative portions of the power curves in Figs 1.5 and 1.6 represent power returned to the source; conversely, in the resistance circuit of Fig. 1.7 we note there are no negative portions of the power curve. (All the power drawn by the resistance is dissipated as heat and/or light; no power is returned to the source at any time.)

Negative power

We observe in Figs 1.5 and 1.6 that sometimes the voltage is positive when the current is negative and vice versa. By the algebraic law of signs (the product of quantities having unlike signs yields a negative number) it is just such occurrences that produce the negative excursions of the power wave- form. Also, every time either voltage or currently crosses the zero axis, the power wave must also cross the zero axis. (Zero times any number is zero.) Inasmuch as the power curve results from multiplying instantaneous voltage

Frequency-determining elements of oscillators 5 Fig. 1.5 Voltage, current and power curves for an ideal inductance

Fig. 1.6 Voltage, current and power curves for an ideal capacitance by instantaneous current valves, we see why the power curve is twice the frequency of the voltage or current waves. Although negative voltage is every bit as good as positive voltage and despite the fact that the same is true for negative and positive current, this reasoning cannot be extended to

Power Voltage

6 Practical Oscillator Handbook

Fig. 1.7 Voltage, current and power curves for an ideal resistance. The two loops of the power curve (the largest of the three curves) should be the same size and shape explain the physical significance of negative power. Positive power is the power taken from the a.c. source by the load; negative power is returned to the source from the load.

Although the ideal inductor and the ideal capacitor do not themselves consume or dissipate power, the current that they cause to flow in the line can and does cause power loss in the resistance of the line or connecting conductors and in the internal resistance of the source. We see that it still holds true that current flowing through a resistance causes power loss. Thus, although our ideal elements would produce no power loss within themselves, their insertion in a circuit must, nevertheless, cause power loss within other portions of the circuit. These matters are fundamental and should be the subject of considerable contemplation before going on. (We reflect that a flywheel, a rotating mass behaving in an analogous way to inductance, consumes no power from the engine. Also, an ideal, that is, frictionless, spring returns all of the mechanical power used to deflect it.)

Performance of ideal tank circuit

We are now better prepared to consider the performance of the ideal tank circuit formed by connecting the ideal inductor and ideal capacitor in parallel. Such a tank circuit is shown in Fig. 1.8. Let us suppose that the generator delivers a frequency equal to the resonant frequency of the LC combination. Resonance in such a circuit corresponds to that frequency at which the reactance of the inductor and the reactance of the capacitor are equal, but of opposite sign. From the individual properties of ideal inductors and ideal capacitors, we should anticipate that no power would be con- sumed from the source. This is indeed true. However, we would also find

Frequency-determining elements of oscillators 7 f 1 2=VLC

ILine c

.! C sw

Fig. 1.8 A resonant tank composed of ideal elements that, at resonance, no current is drawn from the line either. Can we correctly infer from such a situation that the source is not actually needed to sustain oscillations in the ideal tank circuit?

From a theoretical viewpoint such a conclusion is entirely valid. The switch in Fig. 1.8 could be opened and large currents would circulate in oscillatory fashion between the ideal inductor and the ideal capacitor. Our ideal tank circuit would now be self-oscillatory at its resonant frequency. We would have a sort of perpetual motion, but still not the variety attem- pted by inventors unversed in physical law. That is, the ideal tank circuit, though self-oscillatory, could not long supply power to a load; as soon as we extracted power from such a tank circuit, we would effectively introduce resistance, thereby destroying its ideal nature. An 'ideal' pendulum involv- ing no frictional losses whatsoever would swing back and forth through eternity; however, if we attempted to harness the motion of the rod to perform mechanical work of some sort, we would dissipate its stored energy, thereby damping the amplitude of successive swings until oscillation ceased entirely.

Resonance in the parallel-tuned LC circuit

We saw in Fig. 1.5 that the current in an ideal inductor lags the applied voltage by a quarter cycle or 90 ~ We saw in Fig. 1.6 that the current in an ideal capacitor leads the applied voltage by a quarter cycle or 90 ~ Sig- nificantly, at some frequency, the current in the line feeding a parallel combination of ideal inductor and ideal capacitor will neither lead nor lag the applied voltage, but will be in phase with it. The frequency must be such that inductive reactance and capacitive reactance are equal numerically, for only then can exact cancellation of phase displacement between current and applied voltage occur. At other frequencies, the phase displacement be- tween current and applied voltage will be less than 90 ~ lead or lag, but cannot be zero.

8 Practical Oscillator Handbook

We may think of inductance and capacitance as tending to cancel each other's power to cause phase shift between current and applied voltage. Inductive reactance, XL, increases as frequency is increased (XL = 2nfL). Capacitive reactance Xc decreases as frequency is increased: \[Xc = 1/ (2nfC)\]. Therefore, at the one frequency known as the resonant frequency, and at this frequency only, the two reactances are numerically equal. (see Fig. 1.9). Inasmuch as the phase leading and lagging effects of the two reactances then cancel, the tank circuit no longer behaves as a reactance, but rather as a pure resistance. In the ideal tank circuit, this resistance would be infinite in value; in practical tank circuits, we shall find that this resistance, R0, has a finite value dependent upon the inductance, capacitance, and resistance in the tank circuit.

(Parte **1** de 6)