Baixe Practical Oscillator Handbook 1997-Irving M Gottlieb e outras Manuais, Projetos, Pesquisas em PDF para Eletrônica, somente na Docsity! PRACTICAL OSCILLATOR HANDBOOK o o o o o o o. IRVING M.GOTTLIEB P E. Copyrighted Material Newnes An imprint of Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP A division of Reed Educational and Professional Publishing Ltd (GA member of the Recá Elevier ple group OXFORD BOSTON JOHANNESBURG MELBOURNE NEW DELHI SINGAPORE First published 1997 Transferred to digital printing 2004 O Irving M. Gotileib 1997 All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patients Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Rd, London, England W1P 9HE. Applications for the copyright holder's written permission to reproduce any part of this publication should be addressed to the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN O 7506 6312 3 Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress Typeser by Vision Typesetting, Manchester Copyrighted Material Copyrighted Material Contents v Loading of oscillators 136 The electron-coupled oscillator 140 Some practical aspects of various oscillators 143 Three types of Hartley oscillators 143 The Lampkin oscillator 147 The tuned-plate/tuned-grid oscillator 149 The Miller oscillator 150 The Colpitts oscillator 151 The ultra-audion oscillator 152 The Pierce oscillator 153 The Clapp oscillator 154 The tri-tet oscillator 155 The Meissner oscillator 157 The Meacham bridge oscillator 158 Line oscillators 160 The magnetostriction oscillator 162 The Franklin oscillator 163 The Butler oscillator 164 Bipolar transistor oscillators 165 The unijunction transistor oscillator 167 Optimizing the performance of the Miller crystal oscillator 169 Optimizing the performance of the Colpitts crystal oscillator 171 Universal oscillator circuits 174 The universal amplifier: the three-terminal device 174 100 kHz transistor Butler oscillator 175 An example of a dual-gate MOSFET oscillator 176 Single transistor parallel-T oscillator 178 Several special-interest feedback circuits 179 A harmonie oscillator using a fundamental-frequency crystal 184 A bipolar transistor overtone crystal oscillator 186 An overtone crystal oscillator circuit using a FET 187 The use of diodes to select crystals electronically 188 Electronic tuning with a reverse-biased silicon diode 188 Wien bridge oscillator 191 The op amp square-wave oscillator 192 Oscillator using an IC timer 194 A simple function generator 195 Square-wave oscillator using logic circuits 197 A few words about the SN7400 NAND gate IC 198 Logic circuit square-wave oscillator with crystal stabilization 200 A clock oscillator formed from cross-coupled tt NAND pates 200 Voltage-controlled oscillators 203 Copyrighted Material Copyrighted Material vi Contents The Schmitt-trigger oscillator 207 6 Special oscillator topics 209 Guidelines for optimizing VFO performance 210 Some notes on VXOs 216 The ceramic filter oscillator 218 The regenerative modulator—is it an oscillator? 219 The phase-locked loop and synthesized oscillators 220 À second way of synthesizing frequencies from a reference oscillator 225 Quelling undesired oscillations 227 Fancy oscillator functions for the 555 IC timer 234 Wide tuning range via the difference oscillator 237 Microwave oscillators 240 The Gunn Diode 242 Gated oscillators for clean tum-on and tum-off 245 Index 247 Copyrighted Material 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 2 Practical Oscillator Handbook Skin effect and Hysteresis in ohmic losses core material inwinding Eddy currents j / in coil wire . ..|.. / AC " " ~ hysteresis ! ~ ' 1 " generator ~ ~ i ~ ' / : - ' r ~ qL .-.~'.:~ J, Leakage I \ resistance I \ / ~ ~ , ::[ ~:~ J in dielectric J \ Insulation / ~ " 1 P l a t e~ 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 ,q 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 " o w a t t s ' :, v; W A.C. L @' _ 9 0 W a t t s v 9 E 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; n o power is returned to the source at any time.) N e g a t i v e p o w e r 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 7 f - ~ 1 2=VLC ILine c .! C sw IL : QL 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. Inductance~capacitance relationships for resonance At resonance, XL and Xc are equal. Therefore we may equate their equival- ents thus, 2nfoL-1/(2nj~C). If we next make the algebraic transpositions necessary to solve this identity for the resonant frequency, j~, we obtain j~= 1 / ( 2 n x ~ . We see from this equation that for a given resonant frequency,j~, many different combinations of L and C are possible; we may resonate with large inductance and small capacitance, or with the converse arrangement (see Fig. 1.10). Above and below the frequency of resonance, XL and Xc no longer cancel and the tank circuit behaves as a reactance. Specifically, at higher than resonant frequencies, the tank 'looks' capacitive; at lower than resonant frequencies the tank displays the characteristics of an inductor. If for the moment we disregard the nature of the tank circuit impedance, paying no attention to whether it is inductive, resistive, or capacitive, we can more easily pinpoint one of the most important of all properties possessed by the parallel tank circuit. We refer here to the fact that the impedance is maximum at resonance and decreases as the applied frequency departs on either side of resonance. This means that the tank circuit will develop maximum voltage at the resonant frequency; voltages at other frequencies will be suppressed or rejected by the 'shorting' action of the relatively low impedance they experience across the tank circuit terminals. In the ideal tank circuit, the resonant frequency is supported freely across a resistive impedance infinitely high; frequencies only slightly higher or lower than the resonant frequency experience a short circuit and are thereby rejected. Practical tank circuits gradually discriminate against off-resonant frequencies (see Fig. 1.11). The better they do this, that is, the greater the rejection for a given percentage of departure from true resonance, the greater we saw is the selectivity of the tank circuit. In Fig. 1.11, the resistance R is not part of the tank circuit, but is used to isolate the tank circuit from the source. Otherwise, a low impedance source could mask the impedance variations of the tank circuit. E e.- o c ~ t - t3 13 : Frequency-determining elements of oscillators 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , Inductive and capacitive reactances are numerically equal here Reactan ~ R e ~ a ~ a n ~ o f capacitor, Xc ~ inductor, X L Xc_ 1 . ~ I " ~ , X L=2~ fk I I I '1 f I " I ' l ' i i I i u i i ~r i ! fo Frequency Fig. 1.9 Variation of inductive and capacitive reactance with frequency 1 lo--2~/LC = 2~ ~/(50 ~ 106 x 500 X 10 -~2) 50 pH -- 1.0 MHz = 2~/(500 .~, 10 ~x 50 x 10i2i =i" 50 pF 500 I~H = 1.0 MHz = 2~ ~/(500"X 106;~ 5 ~ 10q2) 5000 I~H =5mH = 1.0 MHz Fig. 1.10 Different combinations of L and C for obtaining the same resonant frequency The following conditions at resonance of a parallel LC tank circuit (RL and Rc are small) apply in Fig. 1.12: 9 the applied voltage, V, and the line current, IL~.,~, are in phase 9 inductor current, IL, and capacitor current, Ic are of equal value because inductive reactance and capacitive reactance are equal 9 the voltage, V, applied across the tank circuit rises to its maximum value because the impedance of the tank circuit attains its highest value 9 the tank circuit behaves as a pure resistance 9 the line current, lu,,~, attains its minimum value 12 PracticalOscillatorHandbook . . . . Ro 1. Qo = - - - ~ - - (2~fo)(L) 2. Qo = (Ro)(2~fo)(C) 1 3. Qo= (2= fo)(C)(Rs) 1 4. Thus, Qo = (2=fo)(C)(R0 (2~fo)(L) 5. Q o = ~ Rt (0.5)($) fo-fx ~ Q 0 - ~ - ~ Where Ro is the impedance across the tank terminals at resonant frequency fo. Where Rs is the sum of the losses in the inductor and capacitor expressed as equivalent series resistances. That is, Rs = RL + Rs in Fig 1.12. In many practical cases, we may reasonably say that Rs = RL, Rc being negligible. Where Rc is negligible. (2=f)(L) It is aso true that Q= ~ , that is, the R, Q of the inductor at any frequency, f, is obtained by substituting f for fo. (Inas- much as losses vary with frequency, RL is likely to be a different value if f differs appreciably from fo.) Where f• is the frequency below or above resonance which causes the impedance (or voltage) across the tank terminals to be 70% of the impedance (or voltage) at resonance. 7. Qo (2~)(energy stored per cycle) = or, for practical purposes, (energy dissipated per cycle) volt-amperes (V)(/Line) Qo = which is obtained from watts W I, Ic 8. Also, Qo = luo~ ILine when the tank is at resonance. 9. In Qo/= cycles the oscillating voltage across a shock-excited tank circuit falls to 37% of its maximum value if additional disturbances are not applied to the tank circuit. 10. In Qo/2= cycles, the stored energy in a tank circuit falls to 37% of its maximum value unless replenished before elapse of that time. We imply here, the time interval following a pulse or disturbance, or after diconnection of the a.c. source. When sufficient resistance is introduced 11. Significance of Qo = or less to make Qo =89 a resonant circuit is criti- cally damped; no oscillation can be pro- voked by transients or shock excitation. This condition prevails when the tank cir- cuit is overdamped by making Qo less than 89 Chart 1.1 Relationships of the Resonant Q Factor (Qo) in the Parallel L C Tank Frequency-determining elements of oscillators 13 Fig. 1.14 ILi le I " ~ 1 .... .. ~ ,,/- Parallel L C tank circuit for use with Charts 1.1, 1.2 and 1.3 high. When the sum of Rc and RL is high, the Q is low. It fortunately happens that the vast majority of LC networks intended to function as tank circuits have Qs that exceed ten. Qs of 20 to 100 are commonly found in receivers. Qs of several hundred may be found in transmitters. Quartz crystals and microwave cavities commonly have Qs of several tens of thousands and the Q of special quartz crystals may be on the order of a half million. Figure of merit, 'Q' We will concern ourselves primarily with the value of Q that exists at (or very close to) resonance. It will be convenient to designate Q for this condition as (20. A great deal ofinsight into the parallel LC tank circuit can be gained by a serious study of the Q0 relationships shown in Chart 1.1 (also see Fig. 1.14). The fact that Q0 can be expressed in so many ways is, in itself, indicative of the importance of this tank-circuit parameter. We see that a knowledge of Q and one quantity other thanj~ is sufficient to enable us to start a chain of calculations from which we can determine all of the many parameters associated with the parallel LC tank circuit. Physical interpretation of R0 R0 is the impedance seen across the tank terminals at resonance. Significant- ly, R0 appears as a pure resistance. It is interesting to contemplate that, although R0 is purely resistive, its value is largely governed by reactances. This is revealed by the two relationships: = Qo (2rtJa)(L) and 14 PracticalOscillatorHandbook 1. no= (Qo)(2=fo)(L) (2=fo)(L) 2. no= Qo 6. Rs= Qo (2=fo)(C) Qo(Rs) - - . . . _ . . . _ _ . _ . 3. L= Ro 7. L= 2=fo (Qo)(2~fo) (2=fo)(L)* 1 8. RE= 4. C= Qo (Qo)(Rs)(2~fo) (Qo)(RL)* 1 9. L = ~ 5. C= 2=fo (Qo)(RL)(2=fo) 10. IL = It = (Qo)(/u,.) *When capacitor losses are negligible. Chart 1.2 Calculation of Parallel L C Tank Circuit Parameters with the Aid of the Resonant Q Factor, Qo 1. XL=Xc=~--Lc 1 2. BW= (2=)(Ro)(C) Rs 3. B W = ~ (2=)(L) 4. XL = (2=f)(L) 1 5. Xc= (2~f)(C) 1 6. fo=2~ ~ 7. R o = ~ (Rs)(C) This relationship holds true only at resonance. These formulas enabled us to calculate the bandwidth of a parallel LC tank circuit. BW is the bandwidth in hertz where the impedance, or voltage, is 71% of the value at resonance. Where XL is the reactance of the inductor at any frequency, f. Where Xc is the reactance of the capacitor at any frequency, f. Chart 1.3 Additional Relationships Existing in the Parallel L C Tank Circuit R O ' - - ~ Qo In these relationships, we note that (219~)(L) is inductive reactance and 1/(2g~)(C) is capacitive reactance, both reactances being designated for the resonant frequency3~. Chart 1.2 is included to depict the numerous parallel LC tank calculations that involve the resonant value of Q, that is, Q0. Chart 1.3 is a list of other * Q 0 " " ~ (2nfo)(L) Rs (2nfo)(L) & Frequency-determining elements of oscillators 17 Where capacitor losses Rc are much less than inductor losses RL 3. At resonance VL = Vo = (2)o Vuoo 4 Rr =v~ 9 Io 5. R,= Rs= R, + Rc L 6 . 0 0 = (2nfo)(C)(Rs) L -(2nfo)(C)(R0 Vo 7. /o=~s Where R~ is the effective resistance of the circuit seen by the a.c. source when resonance exists. It, in the series tank corresponds to Ro in the parallel tank. Where Vo is the terminal voltage at reson- ance. Where/o is the line current at resonance. When Rc is negligible. Chart 1.4 Parameters of the Series Tank Circuit associated with the parallel tank circuit shown in Fig. 1.15. Whereas the parallel tank circuit is inductive at frequencies below resonance, we find the series circuit is capacitive in this frequency region. Similarly, at frequencies above resonance, the series circuit is inductive rather than capacitive as we found to be the case in the parallel tank circuit. It is interesting to note that the voltages existing across the inductor and capacitor of the series circuit can be many times the value of the line voltage impressed across the circuit terminals (see Fig. 1.18). We recall the counterpart of this phenomenon in the parallel tank circuit wherein the circulating current, i.e.,/L and Ic, can be many times the value of the line current, /Line. L/C ratio in tank circuits Of considerable practical importance is the effect of the inductance-to- capacitance ratio on Q0 in tank circuits. In both parallel and series tank circuits, a given resonant frequency,j~, can be attained by numerous combi- nations of inductance and capacity (see Fig. 1.10). In the parallel tank circuit, for a given value of R0 and f0, we increase Q0 as we make the capacitance larger and the inductance smaller. However, in the series tank circuit, Q0 is increased, for a given value of Rs and f0, by making the capacitance smaller and the inductance larger. Both the parallel tank circuit and the series tank circuit 18 PracficalOscillatorHandbook Variable frequency source Line current , , G) 0 r E i ~ #. 0 0 ! \ / ~ ~ tL""lmpedance / ' j,,~, ~current l 0 Frequency Fig. 1.16 Typical frequency response of a series LC tank circuit are prevented from having an infinite Q0 by the presence of Rs. Whereas high capacitance is necessary to make Q0 high in the parallel tank circuit, high inductance is necessary to make Q0 high in the series tank circuit. These statements are mathematically true, but in practice we cannot increase either the capacitance in the parallel tank, or the inductance in the series tank indefinitely without incurring losses, which ultimately bring us to a point of diminishing returns, where in Q0 begins to decrease rather than increase. For example, any resonant frequency,j~, can be attained in a parallel tank by means of a one-turn coil and an appropriate capacitor. However, as we make J~ lower in frequency, the capacitor required to achieve resonance becomes larger. The dielectric losses in a physically large capacitor would mount up until further expansion of its physical size would add sufficient losses to cause subsequent decrease of Q0 with any further pursuit of this trend. A similar argument can be presented for the inductor in the series tank. Thus, in practical tank circuits of both varieties, we find that we are restricted to a Q0 value, which cannot be exceeded by further change in the ratio of inductance to capacitance. Furthermore, in the parallel tank circuit, the change in the value of R0 with the LC ratio introduces other difficulties. Often, the parallel tank is required to have an R0 value within a certain range. This may conflict with the Q0 requirement and a compromise must Frequency-determining elements of oscillators 19 c~ co o o = "6 t~ r D. +900 +700 +500 R c +30 o +10 o . oo .30 o +50o +70 o +90o , , Frequency ~ fo Fig. 1.17 Typical phase response of a series-tuned LC circuit At resonance: V L -- V C --. (QO) (VLINE) v A Line ~ Fig. 1 .18 Voltage step-up in a resonant series tank circuit be made. Also, we should appreciate the fact that an extremely high Q0 is not always desirable. The selectivity of a high Q0 tank circuit can be sufficient to discriminate against the frequency spectrum required in voice modulation. In other instances, the sharp tuning of the high Q tank may result in critical adjustments that are not mechanically stable. In transmitters, dia- thermy, and induction and dielectric heating equipment, too high a Q produces excessive circulating current in parallel tank circuits, thereby dissipating power and generating heat where least desired. Finally, we note that in both types of tank circuits, it is possible to have losses and a high Q0 simultaneously. For example, series-mode resonance in a quartz crystal is accompanied by a relatively high value of R,. However, Q0 is nevertheless very high due to the high ratio of effective L to R,. 22 Practical Oscillator Handbook 1 Cut-off frequency, fo = - - - - I~ # L C Characteristic impedance, R o = ~/L/C Propagation time per section, t = .,/LC is in Hertz ~is in Hen,s C is in Farads t is in seconds (c) Artificial line F ig . 1 .21 Delay lines lators are used quite extensively in radar and in digital techniques. The delay line is essentially a transmission line. Nevertheless, its operating mode, and generally its physical appearance also, differ from the lines employed as high-Q resonating elements in sinusoidal oscillators. The simplest delay line comprises a length of open wire or coaxial transmission line. Pulses introduced at one end require a precise time interval to reach the opposite end. If the far end of the line is terminated in a resistance equal to the characteristic impedance of the line, the pulse dissipates its energy in the resistance. If the far end of the line is either open circuited or short circuited, the pulse undergoes reflection and is thereby returned to the source end of the line. Under such conditions, a more efficient use is made of the lines because the pulse is forced to traverse its length twice. Thus, the obtainable time delay is twice what it would be if the pulse energy was absorbed in a resistor at the far end of the line (see Fig. 1.21). Ifa line is open circuited at its far end, the returned voltage pulse will have the same polarity as the initiating pulse. If the line is short circuited at its far end, thereturned voltage pulse will have opposite polarity with respect to the initiating pulse voltage. The latter case is particularly useful, for the arrival of the reflected pulse is readily utilized to terminate the conduction state of the oscillator responsible for the generation of the leading edge of the pulse. In this way a precise pulse duration is established, being determined by the Frequency-determining elements of oscillators 23 electrical length of the line rather than by time constants of resistances and capacitances associated with the oscillator. Variations in power supply volt- age and tube or transistor temperature cannot exert appreciable effect upon pulse duration when an oscillator is stabilized by a delay line. An electrical disturbance propagates along typical transmission lines at speeds between 60% and and 98% the speed of light in free space, depending upon the dielectric employed for line spacing. A delay of one microsecond would require a line length on the order of a city block! Thus, except when delays of a small fraction of a microsecond suffice, the ordinary transmission line would assume impractical physical proportions. Fortunately, it is feas- ible to construct compact networks which simulate transmission line oper- ation, but at relatively slow speeds of pulse propagation (long delay times). The artificial transmission line From electric wave filter theory, it is known that the low-pass filter con- figuration behaves in many respects as a transmission line. A few inductances and capacitances can be connected in such a network to provide a physically compact artificial transmission line from which relatively long delay times can be attained. Three important operating parameters are associated with the artificial transmission line. These are: t, the delay time per section (such a network generally consists of a number of cascaded elementary filter sec- tions), the cut-off frequency, j~, and the characteristic impedance, Z0. All three of these parameters are governed, although in different ways, by the values of inductances and capacitances. Other things being equal, pulse fidelity tends to be better as the cut-off frequency is made higher, and also as more elementary, or 'prototype' sections are cascaded. For proper oper- ation, the characteristic impedance should be nearly the same as the internal generator resistance of the oscillator during pulse production. These re- quirements impose contradictory design approaches and the construction of delay lines has become a competitive art for specialists. One of the criterions of performance of these devices is the ratio of pulse delay time to pulse rise time. The 'goodness' of a delay line increases as this ratio becomes higher. Delay-line stabilized blocking oscillator The repetition rate of the blocking oscillator shown in Fig. 1.22a is primarily governed by the resistance-capacitance combination, R~R~. The pulse dur- ation, however, is precisely determined by the delay line. The electrical length of the delay line corresponds to a shorter period of time than the pulse would endure in the absence of the delay line. When the blocking oscillator commences its 'on' state, the emitter of the pnp transistor becomes positive with respect to its base (and ground). This initiates propagation of a positive- going wavefront down the line. Reflection occurs at the shorted (grounded) 24 Practical Oscillator Handbook R 1 _ _ = / 1 _ i~ [ - ' : l ~ " ..L_ T1 I I I / ' , \ Pulse termination Possible duration from 'echo' of of pulse in a b s e n c e d e l a y line of delay line (a) Transistor blocking oscillator v, v, R rgm, [ fg'~ T , Delay line ,. I l l v, v2 ,,Vv,.,__. v, j - - . V - ' - - - - - - . ~ (b) Tunnel-diode relaxation oscillator Fig. 1.22 Stabilization of wave duration by use of delay fines end of the line and an inverted voltage pulse is propagated back toward the emitter end of the line. When the wavefront of this reflected pulse arrives at the emitter, the transistor is deprived of forward conduction bias. This causes the blocking oscillator to abuptly switch to its 'off' state, thereby terminating the duration of its generated pulse. Delay-line stabilized tunnel-diode oscillator In Fig. 1.22b, a simple but very useful oscillator is shown. Relaxation oscillations occur, but with the pulse duration controlled by the shorted delay line. It will be noted that the delay line is used in place of the inductor Frequency-determining elements of oscillators 27 i i i Any frequency ,C, Any length Q' Qv' ' V i All current meters read the same regardless of frequency. All voltmeters read the same regardless of frequency (a) Terminated line =,,, , ,~ c.i L C .c ' ( ) v [ / - / Current is the same Voltage is the same at all frequencies at all frequencies R L = R c = V L/C (b) Analogous situation for lumped-element tar~circuit Fig. 1 .24 Termination of line by resistance equal to its characteristic impedance destroys resonance completely characteristic impedance of the line. The characteristic impedance of the line is determined by wire diameter, wire spacing and the dielectric constant ofthe insulating material. Coaxial lines operate in the same way as open lines but have the advantage that the external surface of the outer conductor may be operated at ground potential. This produces effective shielding that prevents radiation. The Q is thereby increased, and interferences and feed- back troubles are virtually eliminated. The highest Q in coaxial lines is attainable when the ratio of conductor diameters is 3.6 to 1. This results in a characteristic impedance of 77 ~. Concept of field propagation in waveguides The evolution of 'lumped' circuitry into spatially distributed reactance, as illustrated in Fig. 1.23b, aids our visualization of the transmission line. However, the transmission line is not the ultimate configuration; we can carry the process a step further. This is best approached by considering the coaxial transmission line. Suppose we make the central conductor smaller and smaller in diameter. What must ultimately happen? We can expect an increase in characteristic impedance and perhaps a change in the losses. However, we have nothing to correlate with our experiences with 'wired' circuits to help us ascertain the result of eliminating the central conductor altogether. We might intuitively conclude that this would end the usefulness of the cable as a means of conveying high-frequency energy. Such a deduction would indict us as victims of the commonly believed concept that physical conductors are necessary to provide a means of 'go' and 'return' for high-frequency currents. Such is not actually the case. 28 Practical Oscillator Handbook The physicist and mathematician view the phenomenon in a somewhat differing light. They do not refute the notion that a varying magnetic and electric field accompany the flow of current in conductors; however, they do subscribe to the notion that the flow of alternating current in such a 'circuit' as a transmission line, is the result of an alternating magnetic and electric field propagated down the line, that is, between the two conductors. If this is true, why not eliminate the need for supplying the energy by ohmic contact? Rather, let us deliver energy to the line by means of a small antenna or loop so that the energy is initially supplied in the form of fields. If we can accomplish this, why bother with a 'return' conductor? Such indeed is the logic which permits us to evolve transmission lines into waveguides and cavities. Some important features of lines and guides In the association of guided-wave elements with oscillators, it is not necess- ary in many practical situations to deal directly with the rather formidable mathematics of the electromagnetic propagation of energy in these ele- ments. A number of physical configurations of such waveguides exist; these include two-wire transmission line, coaxial cable, hollow pipes and single wires or plane surfaces. And all of these may be associated with various dielectric material other than air. Even a rod of a dielectric material may serve as a waveguide obedient to the same relationships pertaining to 'more natural' guides. Indeed, all of these are premised on the same fundamental principles~the constraint and guidance of various patterns or 'modes' of electric and magnetic fields. Although electronic practitioners are not con- ditioned to thinking of transmission-line voltages and currents as the effects of propagating fields, rather than the other way around. The truly basic way of dealing with such phenomena needs no 'go and return' conductor. From the viewpoints of physicists and mathematicians, we have been putting the cart before the horse. This turns out to be a voluminous topic. We will limit our discussions to quarter-wave lines and guides because of their useful property as simulated parallel-resonant 'tanks'. We shall find, however, that the practical insights attained will shed light on other configurations and functions of lines and guides. One of our main objectives will be to demystify the disparity between the physical length of a section of waveguide or line and the true electrical length. Although these can be identical, they often are quite different. For example, in the technical literature, it is commonplace to depict the length of coaxial cable serving as a quarter-wave section by the dimension, ,~/4, where the Greek symbol 2 represents wavelength. How- ever, were we to make the physical length of this coaxial line a quarter wavelength as 'naturally' suggested by the free-space wavelength of the Frequency-determining elements of oscillators 29 involved frequency, we would be heading for trouble. In resolving this discrepancy, we must deal with two important para- meters. One is the guide wavelength. This, we must recognize as the 'true' electrical wavelength and the value we must use in sizing the physical length of the line or guide. We shall see that the guide wavelength can be either shorter than, the same as, or longer than the free-space wavelength. It depends upon the nature of the insulating (dielectric) material used, and upon the cross-sectional shape of the guide when in the form of pipes. The other important parameter is the low-frequency cut-offofthe line or guide. This implies that only frequencies above the cut-off value can be propagated within the guide. This, as we shall see, has some interesting ramifications. For the moment, it will suffice to think of hollow pipes as high-pass filters. From the mathematical point of view, the coaxial cable and the two-wire transmission lines also have low-frequency cut-offs, the value being zero frequency or d.c. That is, such lines will propagate energy at d.c. Of course, we could infer this without resort to the logic of the mathema- tician because of the ohmic connections to the two 'go and return' conduc- tors. Figure 1.25 should help clarify the comparison between transmission lines and hollow waveguides. In the ordinary way of utilizing coaxial and two-wire transmission lines, we say that they operate in their principal mode. This is defined as the field patterns within these lines that allow transport of the very lowest frequency, which as we have seen, is d.c. It is not common knowledge by otherwise knowledgeable practitioners that higher modes can also exist. And each of these higher modes, or field patterns, will be characterized by its own low-frequency cut-off, now no longer d.c. In ordinary usage these higher modes may transport no energy because of the way the generator and load are normally connected to the line. If, however, we were to inject and extract radio frequency energy by some non-ohmic means, the higher modes could be excited and utilized to propagate electromagnetic energy down the line. So-called non-ohmic techniques could make use of loops, probes or antennas, apertures or irises. Due consideration would have to be given to the geometric orientation of such injection and extraction devices, but the salient fact is that the central conductor of the coaxial cable could then be entirely dispensed with. We have thus sacrificed the capability to carry d.c., but we have made the thought transition from coaxial cable to hollow waveguide! We now are in a position to consider a sort of 'Ohm's law' that has practical use for all types of electromagnetic waveguides. This interesting relationship enables us to easily calculate the true physical length of lines and guides that internally act as desired sections (as quarter-wave lines, for example). The form of this relationship, shown below, is particularly well adapted to many practical situations: 32 Practical Oscillator Handbook Table 1.1 List of commonly-used coaxial cables Characteristic Velocity factor Cable impedance (fl) (%) Dielectric* RG-8/M 52 75 Foam-PE RG-8/U 52 66 PE RG-8/U Foam 50 80 Foam-PE RG-9A/U 51 66 PE R.G-11A/U 75 66 PE RG-58/U 53.5 66 PE RG-59/U 73 66 PE RG-141/U 50 70 PTFE i ,, i i | i , | i , , i i , , t pE is solid polyethylene, Foam-PE is foamed polyethylene, PTFE is polytetra- fluoroethylene, commonly known as Teflon. Note: When the insulating material is foamed, or partially displaced by air, the dielectric constant of the material is 'diluted'. This results in a lower dielectric constant. (The dielectric constant of air is close to 1.0 and this would be accom- panied by a 100% velocity factor, as is approximated in two-wire open transmission lines.) impractical, but a convenient remedy is at hand by coiling the line. This is permissible with coax, but not generally with two-wire transmission line. Three-plus turns with a diameter of about six inches could prove suitable.) What we have done here is to calculate the internal wavelength, or 2g, the guide wavelength. A little contemplation will show the logic to then making the external physical length equal to 2g. (Because of inevitable stray par- ameters, we probably would trim the line just a bit to optimize its quarter- wave behaviour at 25 MHz.) Interestingly, we can arrive at the same result without a velocity factor table if we know the dielectric constant of the insulation used in the R G - 8 / U coaxial cable. This cable utilizes polyethylene to separate the inner and outer conductors. The delectric constant of this ~naterial is close to 2.3. With this information, we can determine the velocity factor. To do this, we 20 substitute 2.3 for e under the square root symbol. Next, the fraction ~ is scrutinized; it is noted that 2r is infinite, corresponding to zero frequency cut-off. This effectively makes the entire fraction zero, so we are left with just the reciprocal of the square-root of 2.3. We accordingly have 1/1.517 yielding 0.659 for the velocity factor, substantially in agreement with the value previously found in Table 1.1. As before, the product of velocity factor and free-space wavelength gives us 1.98 m, the physical length of the quarter-wave line. It should be appreciated that this second calculation reveals that coaxial Frequency-determining elements of oscillators 33 line is just a special member of the family of guided-wave structures described by the mathematical equations. Note that for two-wire trans- mission line with air dielectric, the equation would have shown the velocity factor to be the reciprocal of square root of 1.0. Thus, such a quarter-wave line would be the length of the free-space wavelength. Suppose now, we are dealing with a microwave system in which the oscillator is a magnetron which generates radio frequency at a wavelength of 10 cm. The microwave energy is to be piped among several function blocks and ultimately delivered to an antenna load. We wish to determine the wavelength inside of the rectangular waveguide. Such information will enable fabrication of quarter-wave sections, resonant cavities, directional couplers, slotted lines, and will be required for impedance-matching tech- niques. This problem is premised on the fact that, as we shall see, the guide wavelength, in contrast to the situation with the coaxial line, is destined to be longer than the free-space wavelength. First, it can be found in handbooks on microwave technology that certain standardized rectangular waveguides are available. Assume that from con- siderations of power, cost and hardware parameters, we choose a guide in which the wide dimension is 7cm. This alone determines the cut-off frequency fl~, which is twice this value or 14 cm. (The smaller rectangular dimension only affects power-handling capability and suppression of unde- sired higher propagation modes. In practice, the smallest dimension would be selected consistant with power-handling capability.) We now have sufficient information to compute the velocity factor. Because of the air dielectric, e is 1, and the fraction under the radical sign is 10/14. Performing the indicated arithmetic operations then yields 1.43 for the velocity factor. Thus, the guide wavelength is 14.3 cm. This is tanta- mount to stating that the physical length of such a guide needed to transport the frequency corresponding to the magnetron's free-space wavelength of 10 cm is 14.3 cm. And, it follows that a quarter-wave section of the guide will be sized at 14.3/4 or 3.75cm. (For practical reasons, a microwave designer is likely to make such a section several or more odd quarter- wavelengths in physical length. For example, a section 3 x 3.75 or 11.25 cm could function electrically in a similar fashion to the diminutive line of just one-quarter wavelength. The information we have derived could, of course, be used to make half-wavelength sections. Keep in mind that the foregoing discussion assumes the use of the dominant mode. This will be the situation in most practical applications. In an experimental set-up with a variable frequency oscillator, the dominant mode would be found to be the lowest frequency that could be propagated through the waveguide. In rectangular guide, the dominant mode is defined as the TE~0 mode. In order to avoid excessive attenuation, the wide dimen- sion of rectangular guide is usually on the order of 0.7 flo. 34 Practical Oscillator Handbook Resonant cavities The simplest resonant cavities are essentially entirely closed sections of coaxial cable or more often, rectangular or cylindrical waveguide. At least one dimension, often the length, must accommodate a half-wavelength in order to allow a standing-wave pattern to exist. Such a standing-wave pattern allows an appropriately placed probe or loop to sample either a very low or a very high impedance over a narrow band around the resonant frequency. The very low impedance, corresponding to series resonance, can be of the order of tens of m~. More useful in practice is the very high impedance which also centres around a very narrow bandwidth. This behaviour simulates parallel resonance and can manifest impedance levels of hundreds of thousand of ohms. Another way of relating these facts is to describe the cavity resonator as developing exceedingly high Q levels. If the cavity is made from a metal which retains its physical dimensions despite temperature change and which is otherwise mechanically rugged, a frequency-governing element for oscillators is obtained which is compar- able to the frequency stabilization provided at low frequencies by quartz crystals. However, the resonant cavity does not function as simply as an LC tank circuit where one can usually feel secure that there will be just one unique and predictable resonance. A whole series of alternate parallel and series- type resonances can be expected from resonant cavities in much the same way that a length of transmission line will display resonant behaviours corresponding to odd and even quarter-wavelengths as the frequency is increased. And, complicating the matter further, there can be resonances involving different propagation modes. A cavity shape and size which will favour a desired resonant frequency can invoke a blend of art and science. The general idea is to design for operation at the lowest frequency possible for the geometry of the cavity. This is the same as designing waveguide for propagation in the dominant mode. In our favour is the fact that microwave oscillators themselves tend to favour operation at the lowest possible fre- quency. That is where the active device usually develops greatest gain. Also, if our luck holds out, the Q of cavity resonances usually tends to diminish at the successively higher frequencies. Quartz crystals Quartz is one of the crystalline substances that is known to exhibit the piezoelectric property. Such crystals undergo a change in physical dimen- sions when subjected to an electric field; conversely, they generate a voltage when subjected to physical deformation such as might result from applica- tion of a pressure or impact (see Fig. 1.26). Slabs or wafers cut from the body Frequency-determining elements of oscillators 37 Fig. 1.28 The two resonances, f~ and f2, of a quartz element greatly exceeds that attainable from tank circuits composed of physical inductors and capacitors. It is not possible to construct a coil with the high-Q inductance as respresented by the crystal, for either series or parallel resonance. When the quartz crystal oscillating element is series-resonated, it appears as a very large inductance in series with a tiny capacitor and a resistance, this series network then being shunted by the relatively large holder capacitance. The holder capacitance is not part of the equivalent series-resonant circuit and cannot exert a direct tuning influence. The capacitance of the holder, and also other capacitances that might appear in this circuit position, cannot exert a pronounced tuning effect. (Series-connected capacitors produce a resultant capacitance given by the relationship, (Ct • C2)/(Ct + C2). If (22 is, say, ten times larger than Ct, a little mathematical experimentation will show us that C2 can be doubled with only a slight effect upon the resultant capacitance.) Although the frictional losses of the vibrating crystals are relatively high, the very high mass enables attainment of high Q. Conditions for optimum stability Crystal oscillating elements are capable of maintaining frequencies stable from within one part in a million to better than one part in a hundred million, depending very much upon the precautions taken to reduce or compensate the effects of temperature variations. Initially, this precaution is met by detailed attention to the angle at which the wafer is sliced from the body of the crystal. Different cuts have different coefficients of frequency change with respect to temperature. It is possible to cut the wafer in such a way as to have a positive, negative or zero temperature coefficient. A 38 Practical Oscillator Handbook positive coefficient denotes increase in frequency as the temperature is increased. More generally, the zero temperature coefficient is considered most desirable. The second method of securing maximum frequency stabil- ity from the quartz oscillating element is to operate it at near-constant temperature inside a thermostatically controlled oven. Crystals are com- monly associated with low-power oscillators wherein their salient contribu- tion is stabilization of the generated frequency with respect to circuit conditions, temperature and mechanical shock or vibration. The crystal wafer cannot be excited too vigorously or it will shatter from excessive mechanical forces or be burned by excessive current that flows through it in the same manner as high-frequency a.c. flows 'through' any capacitor. A closer look at crystal operating conditions The resonance diagram (Fig. 1.29) is commonly encountered and suffices to convey a qualitative understanding of the two operating modes ofosciUating crystals. However, in practical crystal oscillator circuits, parallel mode oper- ation does not correspond to the anti-resonant frequency of the crystal in which its effective impedance would be at its maximum and would be purely resistive. Instead, the 'parallel resonant' crystal operates somewhere in its inductive reactive region. This is why parallel mode crystals are specified to work into a standardized capacitive 'load' of 32 pF. On the other hand, crystals intended to operate in the series mode of resonance can be expected to produce their stamped frequency regardless of the reactance placed across the terminals of the crystal. It is the oscillator circuit that primarily determines whether a crystal will oscillate in its series or parallel resonant mode. However, the manufacturer can process the crystal and its mounting technique so that one or the other mode occurs with optimum results. The important thing to note is that there may be considerable departure from the stamped frequency if a crystal is operated in other than its intended mode. For some applications, this will be of no consequence; for others, the ultimate frequency, especially if derived by multiplying, will be 'out of the band'. Afin Fig. 1.29 has a special significance. It is the difference between the series resonant frequency and the anti-resonant frequency due to holder capacitance alone. The bandwidth of the crystal is known asfand represents the maximum frequency 'pulling' theoretically attainable by associating variable series or parallel reactance with the crystal. Other things being equal, high-Q crystals are less amenable to frequency pulling than their lower Q-counterparts. This statement may have to be somewhat tempered in practice because the lower activity of a low-Q crystal may not allow reliable oscillation over the anticipated bandwidth. Also, it must be kept in mind that lower Q means lower frequency stability. Frequency-determining elements of oscillators 39 + | I. "0 c Q, I Practical 'parallel / ~ resonant' region// ; g/', / / , para, el / j / 0 Frequency y Fig. 1.29 A closer look at the operating conditions of crystals in practical oscillators. Crystals which are spoken of as operating in the 'parallel resonance' mode actually oscillate in a frequency region in which they appear as an inductive reactance In order to be able to conveniently take advantage of the crystal's bandwidth in applications where it is desirable to vary the frequency, the ratio C2/C~ should be as low as possible. (From Fig. 1.27, C2 is the holder capacitance and C~ is the equivalent series capacitance of the oscillating crystal.) The best the user can do is specify a low holder capacitance and to minimize circuit and stray capacitances that essentially increase the effective holder capacitance. If these matters are not implemented, an inordinately large tuning capacitor will be needed to change the frequency across the crystal's bandwidth. Frequency pulling in crystal oscillators An important use of crystals is found in the VXO, the variable frequency crystal oscillator. Indeed, many 'fixed frequency' crystal oscillators are provided with a frequency trimmer. The fact that a crystal oscillator can be made tunable seems a contradiction to the widely-held notion that crystal- stabilized frequencies are 'rock-bound'. The resolution of this dilemma is in the relatively small amount the frequency of an oscillating crystal can be 'pulled'. Although small, useful results stem from this phenomenon. For example, such controllable variations of frequency are directly beneficial in amateur communications where even a slight increase or decrease in cartier frequency can lessen the interference of other stations. In receivers, the ability to fine-tune beat-frequency oscillators and 'fixed' local oscillators 42 Practical Oscillator Handbook The above information is a miniscule condensation of a voluminous subject. Fortunately, one does not have to be versed in crystallography to design and use crystal oscillators. At the outset, however, it should be known whether the oscillator circuit makes use of series or parallel resonance in the crystal. Although most crystals, regardless of cut or vibrational mode, canbe operated in either the series or the parallel resonant condition, the best use of a crystal stems from operation in the resonant mode prescribed by the manufacturer. Such intended operation usually produces the highest Q, the best stability, the easiest starting, the most favourable temperature coeffi- cient, and the closest operation to a stipulated frequency. Some circuits obviously require a certain type of resonance. For example, the Butler and Pierce oscillators need crystals optimized for their series- resonance mode. The Miller oscillator (otherwise known as tuned-plate, tuned grid; or tuned collector, tuned base; or tuned drain, tuned gate) has to have parallel-resonant crystals. In these instances, it is customary for the manufacturer to stipulate a frequency corresponding to parallel resonance with a crystal 'load' of 32 pF. In other circuits, the mode of resonance may not be obvious. Nor can one infer series resonance just because a small capacitor is connected in series with the crystal. For example, the ordinary Colpitts oscillator will cause its crystal to resonate in its parallel mode providing the crystral is made to develop its highest activity in this mode. If, however, the crystal has been optimized to perform in the series resonant mode, the Colpitts oscillator will become a Clapp oscillator (a Colpitts with a series-resonant tank) even though this was not the designer's intent and even though it is not apparent from the topography of the circuit. Controlling and optimizing the temperature dependency of quartz crystals The effective Q of an oscillating quartz crystal may be made very high by appropriate processing and manufacturing techniques and its activity can be made great enough so that reliable start-up is attainable without inordinate emphasis on the active device or on loading. But this is not enough. The temperature dependency of the crystal must be given due consideration during the processing stage and also during circuit design. For best stability, both factors are important. Crystallography is a voluminous subject and will not be dealt with in this book, but the temperature behaviour of the popular AT-cut crystal provides a good insight into the situation. This is especially true when it is recognized that other crystal cuts generally have worse temperature behaviour than the AT-cut. Figure 1.30 shows several of the numerous cuts which may be processed from the quartz crystal. The cut greatly affects temperature coefficient, vibrational mode, Q, activity, spurious responses, harmonic behaviour and Frequency-determining elements of oscillators 43 . . . . . . . . . . . . . . . . . . . . . . . . . . AT-cut Z A a 350 A \ L X-cut X.q- ~ -'- -J. ,= - l - q ~ X-axis "-J'. Y-axis Y-cut Z-axis Fig. 1.30 Temperature coefficient and other characteristics depend upon the angle of cut. The A T-cut is processed approximately at 35 ~ with respect to the Z-axis. Minor angular deviations of this cut enables 'fine-tuning' of the temperature coefficient. The X-cut is made perpendicular to the X-axis. The Y-cut is made perpendicular to the Y-axis. Many other cuts have been used, each with its unique parameters and performance trade-offs frequency capability. Aside from the use of different angular cuts, oscillating crystals can assume other formats. One popular one for the approximately 32 kHz oscillator in electronic watches makes use of a quartz element in the shape of a tuning fork. The AT-cut is at a nominal 35 ~ with respect to the Z-axis of the quartz crystal. However, slight angular deviations of the cut enables the manufacturer to 'fine-tune' the all-important temperature co- efficient. Figure 1.31 shows how this comes about. Not only can a substantially-zero temperature coefficient be achieved over a useful temperature range, but it is possible to design in a temperature coefficient that will then cancel the temperature coefficient ofthe rest of the oscillator circuit. In this way, the overall temperature coefficient of a crystal oscillator can be made very small. Two other ways are useful in combating the temperature dependency of crystals. Circuit components, usually capacitors, are useful for this purpose because such capacitors are available with specified temperature behaviour. The idea, of course, is to cancel the temperature coefficient of the crystal, or better still, of the crystal oscillator circuit. Another long-used technique is to enclose the crystal in a temperature-stabilized oven. To be useful, the oven temperature must be above the ambient temperature. Ovens that cycle on and off have been used, but proportional types give more refined results. Sometimes it is expedient to include other oscillator components within the oven and in certain cases, the entire crystal oscillator circuit may be oven stabilized. After any or all of the alluded safeguards against temperature dependency are incorporated, several design considerations are still needed for attain- ment of best frequency stability. The crystal should not be driven too hard and should be 'decoupled' as much as possible from the active device. 44 Procticol Oscillotor Hondbook &f/f in parts per million +20 +10 + 6 o ~ ~ ! , +.6 ,~ "4 9 \ i / i +50 / ) : . . . . ! I \ i / i \ - ~ +, / q \ _ ' /i I \ +30 ,~ - +8' _..I--~ _'. . " I ~ ~ f f / LRiii, mii~ ' ,[ miNmiimw - 1 0 -20 - 3 0 - 4 0 - 5 0 / / / / - 6 0 / /ira m l r ~ / r~m / / i/" /(! / / i l l | I i / i / / I ~mmmim) mm=mmmi~~~imm mlmm am mmmm g i g B i m l m ) i i i l inmlnimimlml mnmimmmn=m/m lliimmiiminll /immmmmmmmemm mmmmiimimiinm . m m m m m m m m m m ~ m / / k I I I . . . . . I ,_. I I I ,I I i i i i I i ~ i _ - 7 0 - 6 0 - 4 0 - 2 0 0 +20 +40 +60 +80 +100 Temperature (oc) Fig. 1.31 Temperature characteristics of AT-cut crystals versus slight changes in cut-angle. By appropriate selection of the angle of cut relative to the Z-axis, crystals optimally suited for room temperature or oven operation can be produced. Also, crystals with temperature coefficients which cancel the known temperature behaviour of the oscillator circuity can be made Frequency-determining elements of oscillators 47 +20 +15 ~ ~ - 30% Nickel 70% Iron .~_ +10 "F= + 5 0 . . . . . . ~ - 5 ca. - 1 0 1"- - 1 5 ~ - 2 0 Iron ..,--, .c m -25 -30 c - O -35 -40 i ' , I , I . . . . . . . I I 500 1000 1500 2000 Magnetization in gausses Fig. 1.34 Fractional change in length caused by magnetostriction effect in several materials for each cycle of the exciting force. (This did not happen with the piezoelec- tric crystal because the crystal becomes thicker for one half-cycle of applied potential, then thinner for the second half-cycle. In other words, the vibrations of the crystal 'follow' the electrical oscillations.) It will be shown that the magnetostrictive element is suggestive of a transformer with very loose coupling at off-resonant frequencies, but with tight coupling at resonance. Need for bias The frequency-doubling property of the vibrating magnetostrictive rod is generally not desirable. In order to make the rod maintain pace with the applied magnetic oscillation, it is necessary to superimpose a constant magnetic force. This is readily obtained from the effect of a direct current that is either applied to a separate bias winding or allowed to circulate in a signal winding. This magnetic bias prevents reversal of the sense of magnet- ization, thereby causing the rod to vibrate at the same frequency as the signal (see Fig. 1.35). An analogous situation is found in the ear-phone, which must be provided with a small permanent magnet so that the magnetic force acting on the diaphragm does not reverse its sense. Without such provision, severe distortion would occur because the diaphragm would tend to vibrate at a frequency twice that of the electromagnetic signal representing the speech or music. 48 Practical Oscillator Handbook Vibration node is in centre of rod A~176 volts Nickel alloy I I Output / coil Clamp o ~ (i)::3 I=requency Variable frequency rator Input I I co,, Bias source Fig. 1.35 The magnetostrictive oscillating element Frequency/length relationships in magnetostrictive element A nickel alloy rod about four inches in length vibrates at a frequency of 25 kHz. The frequency of resonant vibration is inversely proportional to length so that practical limitations are encountered at both low and high frequen- cies. We see that a 100 kHz magnetostrictive element is on the order of an inch in length, whereas a 20-inch rod is required for 5-kHz oscillation. The magnetostriction oscillator When connected in conjunction with a suitable oscillation-provoking de- vice, such as a vacuum tube, an a.c. signal applied to an exciting coil subjects the biased rod to a magnetic force of cyclically varying strength. This causes the rod to change its length accordingly. The changes in rod length are accompanied by changes in its magnetization that in turn induce a signal in another coil. The induced signal is of maximum amplitude at the frequency corresponding to vibrational resonance of the rod, for it is then that the changes in length and magnetization are greatest. The signal undergoes amplification in the vacuum tube, or other device, then is reapplied to the exciting coil of the magnetostrictive oscillating element. In this way, oscilla- tion is maintained at the mechanical frequency of resonance in the rod. When the magnetostriction element is associated with an amplifier, phasing of the windings is made opposite to that necessary for conventional 'tickler' Frequency-determining elements of oscillators 49 or Hartley feedback oscillators. This is true because induced voltage from magnetostriction is, at any instant, of opposite polarity to voltage generated by ordinary transformer action. This is fortunate, for otherwise it would be very difficult to prevent oscillation at an undesired frequency due to elec- tromagnetic feedback. The tuning fork Besides the quartz crystal and the magnetostrictive rod, a third elec- tromechanical oscillating element is of considerable importance. This is the electrically driven tuning fork. A steel bar bent into a U shape can be excited into vibration by means of a solenoid placed near one of the fork ends. As we nfight expect, the maximum intensity of the vibration occurs when the frequency of the solenoid current is the natural resonance frequency of the fork. The region near the U junction is a nodal region where vibrational amplitude is at a minimum. On the other hand, the ends of the fork prongs execute transverse vibrations of relatively great amplitude. Suppose we place a second solenoid at a corresponding position near the opposite prong. If, then, we monitored the induced voltage in this winding, we would find that it peaked up sharply at the resonant frequency of the fork (see Fig. 1.36). The flux linking the pick-up winding undergoes its most intense variation at resonance due to the mechanical motion of the fork. This, in turn, produces the greatest change in flux in the pick-up winding thereby causing the observed rise in a.c. voltage developed in the pick-up winding. When the fork is connected to an amplifier to form an oscillating circuit, the pick-up winding delivers a signal to the input of the amplifier. The amplified signal appearing at the output of the amplifier energizes the exciting solenoid. The resultant magnetic impetus then serves to regenerate this oscillation cycle and sustained oscillation ensues. Applications Over the frequency range of about 100 Hz to several tens of kilohertz, such a fork behaves as a high-Q energy storage system capable of providing excellent frequency stability. Other types of tuning forks have been used. In one type, the fork carries contacts and the device becomes essentially a buzzer. In another version, the pick-up signal is obtained through the use of a carbon microphone. RC networks as oscillating elements Numbered among oscillating elements are certain combinations of resis- tance and capacity. Such networks are not 'natural' supporters of oscilla- 52 Practical Oscillator Handbook Variable frequency ~ generator C 1 C1 R2 R2 C2 R1 ~, A.C. output voltage (l) 0 Frequency ,,-| o m ~ 3600 .=_ ~.c_ r- ~-~o~ 18oo Q. '~ a. o ~ O0 r Frequency Fig. 1.38 The paralleI-T network R I ~ " , ~ ~ A,~ o A.C. . / " n. ~ 1"~/~'-'1 n output oltage Variable frequency generator (a) Circuit Provided R3 is twice the value of R 2 1 fo = 2~ R1 C1 where f.o is frequency for maximum rejection 0 Frequency (b) Output curve Fig. 1.39 The Wien bridge Frequency-determining elements of oscillators 53 (a) Circuit 0 o4 o> t:lO e " >~ g: P V ....... ~ Parallel branch 2 1 . -90 o , r - > -450 oo +450 g. +900 fo/10 fo lOfo Frequency applied to total network (b) Characteristic curves Fig. 1.40 Characteristics of reactive arms of Wien bridge In this case, the phase inversion is accompanied by maximum attenuation of the signal traversing the network. This is not the desirable response characteristic because it tends to defeat our purpose if we are to invert the output signal of an amplifier, but at the same time drastically reduce its amplitude. However, it is comparatively easy to compensate for the high attenuation by providing sufficient voltage amplification in the amplifier associated with the network. When this is done, oscillation takes place at the frequency 'null' of the network. Another bridge with phase and amplitude response similar to that of the parallel-T network is the Wien bridge depicted in Fig. 1.39. The Wien bridge is not always readily recognizable as such in schematics. This is because the draughtsman looks at the world differently from the electronics practitioner. Thus, it often happens that the arms of the bridge, instead ofbeing lumped together in a neat diamond configuration, are more or less randomly scattered about. (Incidentally the Q of this RC network is one third.) In any event, the characteristics of the bridge are shown in Fig. 1.40. See the section on oscillator theory for more details. A modified type of this oscillator is also described in Chapter 5. LC networks as phase shifters Of utmost importance are the phase properties of certain LC networks. These LC networks produce phase inversion at a discrete frequency, thereby enabling a portion of the output signal of an oscillator tube to be returned to 54 Practical Oscillator Handbook L~ e2 ): C A (a) Circuit fo= .,A 21r ~/(L1 + L2) C L2 e2 = - ~'1 el (at resonance) (b) Voltage waveform and formulas Fig. 1.41 An L C network that produces phase inversion (Hartley type) e2 C 2 r L (a) Colpitts type 01 1 f High Z Low Z (~ ~f A L , , . w (b) Pierce type el e2 Fig. 1.42 Additional L C networks that produce phase inversion the input circuit in proper phase relationship to reinforce the signal already there. The IC networks illustrated in Figs 1.41 and 1.42 are basic to the operation of the majority of LC feedback oscillators. However, they are not always immediately recognizable as being equivalent to these simple circuits. For example, what we have shown as an inductor may actually be a parallel-tuned tank operated slightly below its resonant frequency, under which condition such a tank appears inductive. Conversely, the inductor may be a series-tuned tank operated slightly above its resonant frequency. Active devices used in oscillators 57 these three modes. The three modes are, as one would expect, mathemat- ically equivalent, but it is not easy to show this for practical purposes. Practical oscillator applications are best served by discussing the salient characteristics of the most frequently encountered active devices. That is what we shall do in this chapter. Although the vacuum tube was once the dominant device, we have progressed into an era in which a number of solid-state devices offer advantages of cost, reliability, efficiency, longevity and physical compactness. Tubes continue to merit consideration in certain applications, however. Thus, some form of electron tube is often found in microwave ovens, radar, lasers and in induction-heating. The bipolar junction transistor The bipolar transistor is probably the simplest and the most versatile active device for oscillators. It is conveniently thought of as a current-activated three-electrode amplifier. Inasmuch as its control electrode, the base, con- sumes current even at direct-current operation, its input impedance is necessarily lower than voltage-actuated devices, such as the erstwhile elec- tron tube or the MOSFET. This low impedance can seriously degrade the Q of an LC resonant circuit, so design procedure must deal with this. If the LC tank is too drastically loaded down by this low input impedance, the oscillator will exhibit problems in stability, power transference to the load and in self-starting. One commonly alleviates this effect by choosing a high-grain transistor and 'tapping down' the connection to the inductor and by isolating the LC circuit as much as possible from the 'current-hungry' base of the transitor. This can be done with a small coupling capacitor, selected so that reliable oscillation just takes place. Most bipolar transistors are now silicon types, but some germanium transistors are still made and can be advantageously used in specialized applications. The threshold voltage for silicon transistors is about 0.6 V, but is only approximately 0.3 V for the germanium types. This defines the base-emitter voltage wherein collector current conduction just commences. Prior to attaining the required bias voltage, the input impedance to the transitor is exceedingly high, the transistor is effectively 'dead' as an active device. Once the bias voltage reaches the threshold level, input current is consumed, the input impedance becomes relatively low and collector cur- rent flows in the output of the device. Most circuits use the common-enfitter configuration, but the common- base circuit is actually more natural for the transistor. Its main shortcoming for oscillators is that the input impedance is much lower than for the common-emitter configuration. With modern high current-gain transis- tors, this low input impedance ordinarily doesn't prove troublesome until one deals with UHF and microwave oscillators. At these very high frequen- 58 Practical Oscillator Handbook 6 < E v 5 G) L_ o 4 o 13 -6 3 o 2 ~ v / ! I r j ~ / I .! 1 p . . _ . ~ . _ v 0 0 . . I ~ _ ~ .L.-.---- 100 I~A I ~ _ _ . . . . . ~ - 75 ~A ,.,.,.,.=..,~ | __..,._._~......__y.._.~...~ 50 BA i I I I,o -0 10 20 30 40 V o collector voltage (V) Fig. 2.1 Common-emitter output characteristics of a typical npn transis- tor. This is probably the most often used format in oscillator circuits. It tends to provide a reasonable balance of such features as power gain, input impedance, temperature stability and d.c. feed convenience. A small un- bypassed resistance connected in the emitter lead will often improve the waveshape of the oscillation cies, however, input impedance is just one of many non-ideal characteristics that must be traded off, such as lead inductance, low power gain, package capacitances, thermal limitations and device fragility. Here, the common- base circuit is likely to merit design consideration because it is much less vulnerable to 'parasitic' oscillation at unintended low frequencies than the common emitter configuration. Common-emitter and common-base out- put characteristics for a typical npn small-signal bipolar transistor are respect- ively shown in Figs 2.1 and 2.2. Transistor polarity and Darlington pairs Both bipolar and MOS devices are available in the two 'genders'. Thus, npn bipolar transistors operate with their collectors polarized positive with respect to their emitters or bases. In the npn transistor, 'on' bias is established by making the base positive with respect to the emitter. The converse situation pertains to pnp bipolar transistors wherein the collector is operated with negative polarity with respect to emitter or base. 'On' bias with these devices is brought about by making their base negative with respect to the emitter. Otherwise, very nearly identical operation can be obtained from Active devices used in oscillators 59 7 i 6 t " " " - A .-. /,,... r =o4 P --=3 I _o / 2 /,,,v / iy o f 0 I0 - 6 mA m n I I - 5 mA " ' I . . . . . . . . m I : '-4 mA I I - 3 mA ,, , ] , , , ' , - 2 mA I . _limA I ,c ot 20 30 40 V c collector voltage (V) Fig. 2.2 Common-base curves of the same transitor shown in Fig. 2. 1. In this family of curves involving different emitter currents, note the negative polarity indications. This is OK for such an npn device because the base remains pos i t i ve with respect to the emitter just as in the common-emitter connection. This graph depicts the nearly ideal behaviour of the common- base arrangement. Observe, however, that we are dealing with milliampere inputs contrasted to microampere inputs for the common- emitter circuit npn and pnp oscillators~it's largely a matter of serving the convenience of the d.c. power source at hand. However, there are probably a lot more npn types readily available. Not all npn types are made with a pnp matching type. Note the common-emitter output characteristics of the pnp transistor shown in Fig. 2.3. For many practical uses, manufacturers provide npn and pnp transistors which are very similar to one another. However, a study of semiconductor physics reveals that it is inherently difficult to make true 'mirror images'. This stems from the fact that electrons and holes, which have their roles transposed in the two types, have different mobilities. Despite this, there are interesting applications of complementary symmetry making use of an npn and a pnp transistor sharing operation as the active devices. This usually results in an easily implemented push-pull circuit without need for a centre-tapped tank. Another situation in which a pair of bipolar transistors comprise the active device is the use of one of the four Darlington configurations shown in Fig. 2.4. The Darlington connections feature high input-impedance, and very high-current and power gain. Oscillators configured around such Darling- 62 Practical Oscillator Handbook Io (A) 8 / f / / r r 4.5 V ~DS = 4.0 V ,, 3.5!V 3.0 V 2.5 V 2.0 v 0 2 4 6 8 VDs(V) Fig. 2.5 Output characteristics of a typical n-channel power MOSFET. Because positive gate-to-source bias is required for active operation, such devices are said to operate in the enhancement mode. Note the two operating regions: the sloping portion of the curves represents the linear region where on-resistance is approximately constant. (This is also known as the ohmic region.) The horizontal portion of the curves represents the saturation region where drain current is nearly constant. A point such as Vos,,, which divides these two operating-regions is established as: Vos =VGs -Vr where Vr is the threshold voltage given in the manufacturer's specifica- tions. (VT above is 1.5 V) because MOSFET power gain is nearly uniform over extremely wide frequency ranges. However, MOSFET oscillators often simulate electron tubes in their willingness to generate very high-frequency parasitic oscilla- tions. To guard against this undesirable performance, a non-inductive resistor of ten to a hundred ohms should be inserted directly at the gate terminal. Instead of the resistor, or in combination with it, a 'lossy' ferrite bead is often found useful in suppression of such parasitics. Although simultaneous parasitic oscillation may be benign, it can also be the agent of mysterious malperformances of the oscillator, as well as damage to the MOSFET. Small signal MOS devices are available in dual-gate types in which control can be independently (over a large range) extended by the individual gates. This is very useful for various mixing and modulating techniques. Also, isolation is readily provided between biasing and signal circuitry in these devices. The experimenter is reminded of multi-grid electron tubes. One often finds oscillator circuits in the technical literature with the two gates of such devices tied together. Active devices used in oscillators 63 Operating modes of MO$FETs and JFETs MOS devices are considered to be voltage actuated. In this respect, they simulate the ordinary operation of the electron tube. Their exceedingly high input impedance makes them attractive for oscillators because negligible loading is imposed on the resonant tank circuit. However, this statement, while essentially tree at low and moderate frequencies, must be further qualified at VHF and higher frequencies. For one thing, the input to these devices looks like a near-perfect capacitor at low frequencies. At very high frequencies, the current consumption of this input capacitance causes losses in the input circuit. Also, the capacitance itself is no longer as 'pure' as it appears to the lower frequencies. Although still a willing oscillator as we approach the microwave region, the MOS device no longer operates as if it develops near infinite current gain as at low and moderate frequencies. Indeed, it begins to simulate the 'current-hungry' operation of bipolar transistors. Most MOS devices are enhancement-mode types. That is, they are normally turned off when their gates are not provided with forward con- duction bias. When so provided, they 'become alive' in a similar manner to that of bipolar transistors. Unlike bipolar transistors, they consume no input at d.c. Depletion-mode types are also available; these are normally conduc- tive and the conduction can be both increased and decreased by varying the bias or by the impressed signal voltage. This is reminiscent of most of the electron tubes used in radio circuits. The control electrode of MOS devices can be a reverse-biased diode such as we have in the JFET, or the actual conductive plate of a capacitor such as is used in both small-signal and power MOSFETS. In both cases, the input impedance is essentially capacitive. In both cases, the conductance of a 'channel' is modulated by the electric field caused by the input voltage. The output characteristics of a typical JFET are shown in Fig. 2.6. Generally speaking, MOS devices tend to be immune to thermal runaway and to failure from secondary breakdown. This does not mean that abusive overloading will not damage or destroy them. All electrical devices can be 'burned out' from excessive temperature rise, current, or voltage. Take particular care in handling M OS devices; their thin silicon dioxide dielec- trics are easily punctured by gate voltages ranging from several-tens to several-hundreds of volts. Static electricity accumulated by the body, or generated by frictional contact between various insulating materials can easily manifest itself in thousands of volts. That is why these devices are packed with their leads inserted in conductive foam. During experimenta- tion and construction, grounding techniques should be used to ensure that no difference of potential can exist between the MOS device and one's body or tools. Once protected against such gate damage, MOS devices prove to be electrically rugged when properly operated in oscillator circuits. 64 Practical Oscillator Handbook 50 ID 25 (mA) Output characteristics (VD%~= - 3 V) I I VGS= 0 V , ~ ~ " - ' " " " ~ i / - 0 .4 V . . . . / i r ~ ' , / -0 .8 V - - - I . . . . -1.2v // i / / , I / - , 6v - 0v _-. - - - - " i ~ ,~"- i,, ..---" ~ - - - -2 .4 V 00 5 10 Vos(V) Fig. 2.6 Output characteristics of a junction field-effect transistor (JFET). These popular small-signal devices, unlike most other sofid-state ampfifiers, operate in the depletion mode. This infers that there is strong drain current when the gate-source voltage is zero, L e., the JFET is normally on. This JFET is an n-channel type inasmuch as the drain is made positive with respect to the source. All of the indicated polarities would be reversed for a p-channel JFET The voltage-follower format of active devices The common-collector circuit or voltage follower, otherwise known as the emitter, source or cathode follower, is also useful in oscillators. Inasmuch as these configurations exhibit less than unity voltage gain in practical applica- tions, a knee-jerk reaction might be that there could be no oscillation. However, when we have an LC resonant tank and a feedback path, oscilla- tion is always possible notwithstanding less than unity voltage or current gain of an associated active device. This follows from the criterion of oscillation with regard to powergain, which must equal or exceed unity. It so happens that the common collector circuit can provide respectable power gain. It does this by developing close-to-unity voltage gain, but very high current gain. One should contemplate how this situation differs from that of a trans- former. The transformer can produce either voltage or current gain, but it never can develop power gain. Indeed, practical transformers always show less than unity power gain. There is no way that ordinary linear transformers can be associated with an LC circuit to provoke oscillation. Even the saturable-core transformer, which somewhat resembles an active device, must be associated with switching elements in order to participate in the oscillatory process. Active devices used in oscillators 67 ;o. jv. 3 Q1 , Z "= J 0') }. ?i, ! j o,,, .......... . _ _ l I f ' ~ f ' ~ _ O F F S E T NULL Fig. 2.7 Schematic diagram of the LM741 op amp. A wide variety of such ICs are available. In addition to low-cost and compact physical dimensions, their salient features are that they can simulate the performance of the discrete devices, and they closely represent the concept of the 'universal amplifier'. Op amps tend to have high input impedance, high gain and low output impedance. This makes them very suitable for numerous oscillator circuits. Frequency capability, power level and temperature behaviour are readily available in manufacturers' literature shows the schematic circuit of the long-popular general-purpose LM741 op amp. Op amps often exhibit more gain than we might wish to use. Excessive gain causes hard-saturating switching action and the resultant square wave can prove difficult to 'tame' with the resonant tank circuit. Also, an op amp operating 'wide open' tends to be vulnerable to latch-up. The simple remedy is to deploy negative feedback. This is implemented by a two- resistor network with the shunt element connected to the output and inverting input terminals and the series element connected to the inverting terminal, as shown in Fig. 2.8. The voltage gain is then very nearly R2/R~. Modes of operation for op amps and logic circuits Somewhat different considerations prevail for op amps than for discrete devices with regard to oscillator operating mode. An op amp is a composite 68 Practical Oscillator Handbook R2 Input .. Output R2_~_ = R2/R I Input Z = R I if the two lower resistances -=- are not used Fig. 2.8 Negative feedback network for controlling voltage gain of an op amp. The balanced situation shown pertains to an idealized class A amplifier. In most oscillator circuits, the lower two resistances are not needed. Also, many practical oscillators can be implemented with R2 = 100 k~ and R ~ = 1 I~, yielding a voltage gain of 100. The LM741 'workhorse' op-amp provides an open-loop voltage gain of about 100 dB at ten 10 Hz. This gain falls at the rate of 20 dB per decade of frequency until it is O db at 1 MHz device and the amplifier stages are manufactured with their own fixed-bias sources. The reason for this is that the op amp's chief mission is to perform in the linear Class-A mode. So the notion of operation in Class B or Class C is not a practical one for oscillators designed around op amps. Indeed, the op amp merits consideration when, in the interest of oscillator stability and wave purity, exceedingly linear Class-A operation is desired. Inasmuch as most op amps work at relatively low power levels, efficiency and thermal problems have low priority. Paradoxically, the op amp can also function in oscillators as a switching device. As such, it behaves as a more ideal switch than discrete devices operating in their Class B or Class C modes. Such switching action in op amps is termed Class D operation. To a first approximation, it is brought about as the result of overdrive--a situation easily attainable because of the very-high gain in op amps. Indeed, steps are often taken to prevent this mode of operation. On the other hand, other op amp oscillators deliberately makes use of the switching mode; the multivibrator is one familiar example. However, an op amp crystal oscillator may also exploit Class-D behaviour, the idea being that the crystal provides the requisite frequency stability. Such circuits are vigorous oscillators and one is not likely to encounter start-up problems or to find that oscillation is readily killed by loading. The reliability of such over-driven op amp oscillators appeals to many designers. Often a sine wave is not needed. But even when it is, a simple low-pass or band-pass fdter or other resonant circuit can convert the square wave to a satisfactory sine wave. In a practical op amp oscillator using, say, a Active devices used in oscillators 69 Hartley circuit, a distorted output wave would probably signify the over- driven mode. In order to obtain a good sine wave, it would be necessary to decrease the amount of positive feedback. Logic devices operate like overdriven op amps, only 'more so '~ they are deliberately designed to operate in the switching mode. This is fine for R C and relaxation oscillators of the general multivibrator family. Resonant circuits and crystals are often inserted in the feedback loop to stabilize the frequency, or used as filters to produce a sine wave output. The concepts of Class -A, -B, -C operation have no relevancy here. Neon bulb as a switching device The simple two-element neon bulb constitutes a novel switching device. It is but one member of a large family of gaseous diodes, most of which contain an inert gas such as neon, argon, krypton or xenon. When low voltages are applied across the elements of such a device, the gas behaves as a fairly good insulator, permitting passage of virtually no current. As the voltage is raised, the electric force applied to the gas atoms ultimately becomes sufficient to tear outer-orbital electrons from the constraining force of the atomic nu- cleus. Such disrupted electrons collide with su~cient force with bound electrons to impact these from their respective orbits. The process quickly becomes a cumulative one in which an avalanche of electrons becomes available for collection at the positive element; this migration of electrons constitutes an electric current. Additionally, atoms from which electrons have been torn have thereby acquired a net positive charge and proceed to the negative element. There they restore, temporarily at least, their lost orbital electrons. This, too, constitutes current and is additive to the total current. The total process, whereby the gas is abruptly changed from an insulator to a conductor is known as ionization. Obviously, this phenomenon can be utilized as a switching mechanism. The important feature of gaseous diodes so far as concerns studies in this chapter, is their voltage hysteresis. This denotes a difference in the voltage causing ionization and the voltage at which the diode deionizes. Specifically we should appreciate that the ionization volt- age is higher than the deionization voltage. A gas-diode relaxation oscillator based on voltage hysteresis is shown in Fig. 2.9. Thyratrons The gas diode is not a practical switching device for shock-exciting oscilla- tions in a resonant tank circuit because there is no suitable way of syn- chronizing the pulsing rate with the resonant frequency of the tank. How- 72 Practical Oscillator Handbook (a) Grid voltage less than ionization value (b) Grid voltage sufficient for Ionization (d) Reduction of grid voltage does not extinguish tube (c) Deionization by removing plate supply voltage Fig. 2.11 Control of gas tubes oscillation. The output waveform tends to be an approximate square wave. A rough approach to a sine wave may sometimes be attained by inserting a choke in series with one of the power supply leads. This slows the rise and decay of the switching cycles. Contrary to the appearance of the circuit, there is virtually no filtering action due to the 'tank' circuit formed by the commutating capacitor in conjunction with the primary winding of the transformer. The resonant frequency of this LC combination is generally much higher Active devices used in oscillators 73 Ao "q_FLr outp~ C1 R1 Cx ~ V2 - - i $2 R2 Fig. 2.12 Basic thyratron inverter than the switching rate of the thyratrons. Even if the inverter pulsed at the natural resonant frequency of this LC combination, the effective Q of the tank would be too low to provide much frequency selectivity. This is due to the fact that one half of the transformer primary is always short-circuited. At the power levels generally used in electronics, thyratron inverters are not as efficient as, nor do they possess other desirable performance characteristics readily obtainable from, transitor saturable-core oscillators. However, thy- ratron inverters have potential application in power systems where it is desired to transform sizeable amounts of d.c. power to a.c. power. The tubes used for high power conversion resemble ignitrons or mercury-arc tubes with starter electrodes. These tubes do not have thermionic emitters in the ordinary sense, but can, for practical purposes, be considered as big brothers to the thyratron. S p a r k - g a p o s c i l l a t o r If we connect a high-voltage source ofa.c, across a gap formed by two metal electrodes separated a small fraction of an inch, a noisy display of sparks is produced in the gap. Although the flashing display of the dielectric break- down of the air in the gap appears to the eye as a continuous process, such is not actually the case. Rather, the arc is extinguished each time the voltage impressed across the gap passes through zero (or a relatively low value). For the a.c. sine wave, this occurs at double the rate of the frequency (Fig. 2.13). Thus, an arc energized by 60 Hz high voltage goes out 120 times per second. We see that such a spark gap is effectively a switch that interrupts a high voltage source 120 times/sec. If properly associated with a resonant LC circuit, these disturbances can provoke oscillations at the resonant frequency 74 Practical Oscillator Handbook Brass blocks for heat absorption 115 V V ~ ~ 60 Hz 3000 step-up transformer Tungsten electrode tips Spark gap acts as open switch ~ k Voltage impressed across spark gap / / Voltage too low to / ionize air in gap Spark gap acts as closed switch Fig. 2.13 The spark gap as a switching device 115V , Spark gap 3000 V ~ L o High frequency o output . . . . S 120 Pulse repetition rate = 120 wavetrains per second 1 Main frequency component in wavetrains = 2~ ~/(LC) Fig. 2.14 A spark-gap oscillator of the LC circuit (Fig. 2.14). The step-up transformers are special high leakage-reactance types. The LC circuit must produce many oscillation cycles for each switching pulse. Therefore, the oscillatory wavetrain is highly damped and generally decays to zero long before excitation by the forthcoming switching pulse. A considerable amount of the conversion of low-frequency to high-frequency power in the spark-gap oscillator is invested in harmonics and spurious frequencies that are not readily attenuated by practical LC tuned circuits. For this reason, the spark-gap oscillator is of historical interest only so far as concerns its use in radio communications. However, spark-gap oscillators remain useful for medical and industrial applications. For example, the spark-gap oscillator is often employed in conjunction with welding machin- es for initiating the arc between the welding rod and the work material. (Once the air between the welding rod and the work material is ionized by the high-voltage, high-frequency energy from the spark-gap oscillator, the Active devices used in oscillators 77 Screen grid Screen grid tube Screen grid Type 24 potential Plate Control ~ ! .... I ~ - ~ m i l l i a m p s Control / V grid , _ ~ , , I .... L ,-- b ias Plate volts (a) Test setup Type 24 +75 V K '~ - - -o Output ":" __ " - 1.5 V fo = 2~ ,/L-""~ - Dynatronoscillator (b) Schematic This region is used in normal class A amplification +5- "~ +4 + 2 q o = 01 - 2 t - 3 - Control grid bias = - 1 . 5 V Screen grid potential = +75 V (c) Characteristic curve F i g . 2 . 1 5 Negative resistance in the dynatron circuit electrons. If the plate voltage is high enough, the attracted electrons have sufficient kinetic energy to impact orbital electrons from the surface atoms of the plate metal. Electrons thus freed from their atomic bonds are called secondary electrons to distinguish them from the primary electron emission from the heated cathode. (No appreciable elevation of plate temperature is required for secondary emission.) Significantly, a single primary electron can liberate two or more secondary electrons. In the diode, or Class-A triode, secondary emission from the surface of the plate is not of any great conse- quence because such electrons are simply attracted back to the positive plate. Let us investigate what can happen in certain tetrodes. 78 Pracfical Oscillator Handbook Reason for dynatron property of negative resistance Suppose that considerable secondary emission is being produced at the surface of the plate in a tetrode or screen-grid tube, and that the screen-grid voltage is higher than the plate voltage. We see that it is only natural that the secondary electrons accelerate to the screen grid rather than return to the plate. This being the case, screen-grid current must increase at the expense of plate current. (Secondary electrons which leave the plate constitute a flow of current away from the plate.) The higher the plate voltage, to an extent, the more pronounced is the generation of secondary electrons. We have the condition wherein increased plate voltage produces a decrease in plate current. This condition manifests itself as negative resistance when the tube is properly associated with an LC tank circuit. At low plate voltages, insufficient secondary emission occurs to produce the negative-resistance characteristic. At plate voltages approaching and exceeding the value of the positive screen-grid voltage, the secondary electrons return in very greater numbers to the plate. These two conditions establish the limits of the negative-resistance region. We see that only a small portion of the plate-current versus plate-voltage relationship is suited for dynatron operation. Unfortunately, modern ver- sions of the Types 22 and 24 tubes are manufactured under a process designed to inhibit generation of secondary electrons. Pentode type tubes have a so-called suppressor grid located between the screen grid and the plate. This added element is operated at cathode potential. Electrons liber- ated from the plate bear a negative charge as to the primary electrons emitted from the cathode. Therefore, the negative suppressor grid repels the second- ary electrons, causing them to return to the plate, rather than accelerate to the screen grid. This results in the pentode tube having a more extensive region over which linear amplification can be obtained, but it is obvious that in the pentode we have eliminated the very mechanism required for dynatron negative resistance. Transitron oscillator Paradoxically, although the pentode will not perform as a dynatron oscil- lator, it has more or less replaced the tetrode dynatron tube as a negative- resistance device for provoking oscillation in an LC tank circuit. One of the disadvantages of the dynatron is the dependency upon secondary emission. This varies from tube to tube and with ageing. Indeed, it is quite difficult to obtain satisfactory dynatron action with present day tetrodes, for these are processed during manufacture to make secondary emission less copious than in tubes of earlier production. The pentode can be connected as a transitron oscillator to provide a negative-resistance region which, insofar as concerns Active devices used in oscillators 79 the resonant tank, behaves very similarly to the dynatron. The essential difference between the two circuits is that negative resistance in the dynat- ron involves the relationship between plate voltage and plate current, whereas negative resistance in the transitron involves the relationship be- tween screen-grid voltage and screen-grid current. Reason for transitron property of negative resistance In Fig. 2.16a we see that the suppressor grid of a pentode connected to exhibit transitron characteristics is biased negative with respect to the cathode. However, the actual value of the negative suppressor voltage is determined by the screen-grid voltage. This is so simply because the screen- grid voltage supply and the suppressor bias supply are connected in series. If we increase the screen-grid voltage, the suppressor grid bias becomes relatively less negative. This being the case, electrons passing through the screen-grid apertures are less likely to be repelled back to the screen grid; rather, such electrons are more likely to reach the plate where they add to plate current, but at the expense of screen-grid current. The converse situation likewise operates to establish the negative-resistance region. That is, if screen-grid voltage is decreased, suppressor-grid bias becomes relatively more negative, and electrons passing through the screen grid are deflected back to the screen grid, thereby adding to screen-grid current at the expense of plate current. Thus, we see that screen-grid current changes are opposite in direction to screen-grid voltage changes. Such a negative resistance does not exist over the entire range of screen-grid current versus screen-grid voltage character- istics, but only over a small portion of the total characteristics. We see this must be so because suppressor voltage cannot become positive, for then it would draw current as the result of attracting electrons that otherwise would be collected by the plate. At the other extreme, suppressor voltage cannot become too negative, for then it would cut off plate current by deflecting electrons back to the screen grid. For the transitron action to exist, the plate must be allowed to participate in apportioning the total space current. This it can do only when suppressor voltage is neither too low nor too high. Function of capacitor in transitron oscillator The capacitor, C2, in the transitron oscillator circuit of Fig. 2.16b, com- municates the instantaneous voltage developed across the tank circuit to the suppressor, where it is superimposed upon the fixed negative bias voltage. It is educative to observe that the suppressor grid exerts stronger control within the negative-resistance region than does the screen grid. Thus, when the voltage impressed at these two elements increases, we expect screen grid current to increase, for such would be the case at an anode, which the screen 82 Practical Oscillator Handbook applied polarity changes conduction from a high to low value in the ordinary junction diode. In the unijunction transistor, which is essentially a double-base junction diode, reversal of polarity between the centrally located p, or emitter element, and the n-type bar occurs abruptly, giving rise to a switching process in the external circuit. Consider the situation depicted in Fig. 2.17b. When the switch is initially closed, the p element will assume a potential relative to base No. 1, B~, equal to approximately half of the voltage applied by the battery connected to the two bases. This is true because the resistivity of the semiconductor bar is uniform along its length. At first, the major portion of the p element will be substantially in the nonconducting state because of insufficient voltage gradient between it and the n material of the semiconductor bar. However, the lower tip of the p element will be slightly in its forward-conduction region, that is, the lower tip will act as an emitter of positive charges (holes). (This is because the lower tip is off-centre.) The initial conductive state following closure of switch S is not stable. The positive charges injected from the lower tip of the p element rapidly 'poison' the lower half of the semiconductor bar. These charges are col- lected by negatively polarized base No. 1. The movement of these charges through the lower half of the bar constitutes current, In essence, the conductivity of the lower half of the bar is increased. This, in turn, shifts the distribution of potential drop within the bar so that the entire p element finds itself relatively positive with respect to adjoining n material of the bar. As a consequence, the entire p element becomes an injector of positive charges, thereby increasing conductivity of the lower half of the bar to a high degree. This occurs with extreme rapidity. This is the stable end result of the circuit as shown in Fig. 2.17d. The p element, that is, the emitter, in conjunction with the n material of the lower half of the bar and the ohmic base connection (No. 1), behaves as an ordinary pn junction diode passing heavy current under the operation condition of forward conduction. Instead of the battery, V/2, let us substitute a capacitor and a charging resistor (see Fig. 2.18). For a time, the capacitor will charge much as it would if the p element and base No. 1 acted as a very high resistance. When the capacitor voltage attains the value F (approximately one half the base-to- base voltage), depicted in the curve of Fig. 2.19, the cumulative process of increased charge injection and spread of charge-emitting surface will be initiated. The capacitor will then 'see' a relatively low resistance and its stored voltage will be rapidly depleted. During this discharge, the avalanch- ing of charge carriers continues within the lower half of the bar until the capacitor voltage is quite low-in the vicinity of 2 V. In other words, insofar as concerns the external circuit connected between the p element and base No. 1, there is a voltage-hysteresis effect analogous to that of the neon-bulb relaxation oscillator wherein ionizing voltage is higher than extinction Active devices used in oscillators 83 Approximately = ~ . . . . . . . . . . . . . V/2 " ~ E B2 V 1. ,, , Approximately 2V Pulse repetition rate = approximately 1 R is expressed in Ma 0:8 (RC) C is expressed in llF Fig. 2.18 Basic unijunction relaxation oscillator < E r - t,.) L - .:E_ E 6 z { / ) 0 3 ~ lf voltage is reduced below this value current abruptly drops 30 to a minute value. This is analogous to deionization in a gas tube 20 ~k X Firing point F- analogous to ionization in a 10 5- 0 I " I I I ' 1 I 0 2 4 6 8 10 Base No. 1: emitter voltage with emitter positive relative to base No. 1 (V) Fig. 2.19 Current-voltage relation in Base No. 1-to-emitter diode voltage. In any event, when the capacitor discharges to a sufficiently low voltage, injection of positive charges into the bar ceases, and the lower half of the bar reverts to its initial state of high resistivity. The capacitor charge- discharge cycle then repeats. In some cases the capacitor-charging resistor may be dispensed with. The capacitor then receives its charging current through the reverse-conducting upper half of the bar, which acts as a constant-current generator. This causes the capacitor to charge linearly with 84 Practical Oscillator Handbook Rin is a negative resistance P Fig. 2.20 Under certain conditions the input circuit of a triode may appear as a negative resistance respect to time and the resultant sawtooth has a suitable shape for many sweep circuit applications. This mode of operation imposes the practical limitation that the pulse repetition rate cannot be made as high as when a charging resistor is used. Triode input as negative resistance There is an important circuitry family of triode-tube oscillators, the oper- ation of which is generally ascribed as being due to feedback via the internal plate-grid capacitance ofthe tube. Actually, such oscillators are more closely related to those of the negative-resistance family than to the feedback group. This is so despite the fact that it can be shown mathematically than even 'true' feedback oscillators present negative resistance to their resonant tanks. In those oscillators we classify as of the feedback variety, the negative- resistance property is intimately associated with the presence of the resonant tank. However, in the so-called negative-resistance oscillator, the negative- resistance property is displayed by the tube or other device with or without the resonant tank. These considerations bring us to the interesting fact that the grid-cathode ~circuit of a 'grounded-cathode' triode amplifier can be made to appear as a negative resistance. This is brought about by making the plate load inductive (see Fig. 2.20). For a certain range of plate-circuit inductance, the grid circuit is capable of supplying power to a resonant tank. The action involved here is not easy to visualize without considerable mathematical analysis. Nevertheless, the effect is an important one and is a basic principle in the operation of the tuned-plate tuned-grid oscillator, certain variations of the Hartley oscillator, and the Miller crystal oscillator. These oscillators will be considered in detail in our discussion of practical devices. Although useful Active devices used in oscillators 87 increasingly heavy conduction. The other voltage appears across the portion of the winding between emitter and base of Q2 and is of such polarity as to clamp Q2 in its nonconducting state. The rapidly increasing current through the portion of the winding which feeds the emitter of transistor Q~ ultimately causes abrupt magnetic saturation of the core. When this occurs, electromag- netic induction of the voltages controlling the bases of the two transistors ceases. However, these voltages cannot instantaneously return to zero due to the energy stored in the magnetization of the core. Accordingly, the conduction states of the two transistors remain for a time as they were immediately preceding the onset of core saturation. However, once the collapse of the magnetic field gets well under way, sufficient reverse-polarity voltages are electromagnetically induced in the base-emitter portions of the winding. This reverses the conduction states of the transistors, turning Q~ off and Q2 on. The conduction of the emitter-collector diode of Q2 now repeats the cycle of events, but with core saturation ultimately being produced in the opposite magnetic sense. After an interval following this second saturation process, the transistors again exchange conduction roles, and the core is on the way to saturation in the same magnetic sense as originally considered. Thus, the transistors alternate states: when Q~ is on, Q2 is offand vice versa. Two additional saturable core oscillators are shown in Fig. 2.22. Saturation flux density, B,, for various core materials is given in Table 2.1. The following design data applies to Fig. 2.22 and to Fig. 2.21 as well: E x 108 N ' - ~ 4fB A where; N is the number of turns from CT, E is the battery voltage, f i s the frequency of oscillation in hertz, B~ is the flux density at saturation lines per sq. cm, A is the cross-sectional area of core in sq. cm. The number of turns in the windings indicated by 'n' in Figs 2.22a and b generally is equal to N/8 to N/3. The frequency of oscillation is determined by the battery voltage, the number of turns in the portion of the winding that feeds the emitters of the transistors, the flux density at which saturation occurs, and the cross-sec- tional area of the core. However, once the oscillator has been constructed, battery voltage is the only frequency-governing parameter that requires consideration, the others being fixed by the number of turns placed on the core, and the nature and geometry of the core material. This type of oscillator is very efficient, efliciencies exceeding 90% being readily obtainable. We note that there is no need for high power dissipation in the transistors. When a transistor is off, its collector voltage is high, but its collector current is 8 8 Practical Oscillator Handbook E" B Rb ' t ~ = ~ ~ , , ~ , n " o E _ - " N vvvv " ' . . . . . . . . . . c I . r ' 0 0 (a) Common-emitter circuit (b) Common-base circuit F i g . 2 . 2 2 Saturable-core oscillator circuits Table 2.1 Saturation flux densities, B,, for various core materials* , , , , , , , , 1 ,,, , , , , , , Saturation flux density in kilogauss Core material (thousands of lines/sq, cm) 60 Hz power transformer steel 16-20 Hipersil, Siletcron, Corosil, Tranco 19.6 Deltamax, Orthonol, Permenorm 15.5 Permalloy 13.7 Mollypermalloy 8.7 Mumetal 6.6 , i i * When using these B, values, make certain that the core area, A, is expressed in sq. cm. virtually zero. Conversely, when a transistor is fully on, its collector current is high, but its collector voltage is very low. In either conduction state, the product of collector voltage and collector current yields low wattage dissi- pation in the collector-emitter section. We see that one of the advantages of rectangular hysteresis loop material is that a core of such material permits rapid transition between off and on. This is desirable, because when a transistor is neither fully on nor fully off, the product of collector voltage and current can be high. If the transition is not rapid, efficiency will be lowered and the transistors will be in danger of being destroyed by generation of excessive internal heat. Silicon steel such as is used in 60 Hz transformers is often employed to save costs. However, less power output and lower efficiency are the result. We often see these saturating-core oscillator circuits with a capacitor connected across the load winding, or even across the primary winding. Active devices used in oscillators 89 However, no LC tank is formed by the addition of such capacitors and the frequency is not changed thereby. The capacitor is added in order to absorb voltage transients that can destroy the transistors. These transients, or 'spikes', are due to the abrupt saturation of the core. The frequency of these oscillators is generally limited, at least in units designed for high power, by the frequency capability of the power transistors. However, frequencies on the order of several hundred hertz to around 100 kHz are readily attainable and are well suited for high efficiency and small, light-weight cores. The electron beam in a vacuum In most of the electrical oscillating elements and oscillation-provoking devices we have considered, the described action resulted from the control- led or guided flow of electrons in metallic conductors of various geometric configurations. In waveguides and resonant cavities, we found that the electron was somewhat freed from the restrictions ordinarily prevailing in low-frequency ohmic circuits. In these nficrowave elements, much of the energy associated with the electron manifested itself as electric and magnetic fields external tjo metallic conducting surfaces. Thus, the electron move- ment, that is, the electric current in the walls of the waveguide, is at once influenced if we insert an obstruction within the aperture of the guide. Such an obstruction disturbs the pattern of the electric and magnetic force fields. We can go a step further than this. We can free the electron from confine- ment in matter completely, in which case it becomes highly susceptible to manipulation by various force fields. This is most directly accomplished by some arrangement involving a thermionic cathode and a positively biased anode, the basic objective being to create a beam of electrons in a vacuum. Historically, the X-ray tube has considerable relevance. In this tube, the electrons are imparted tremendous acceleration by the extremely high potential difference anode and cathode. The energy thereby acquired by the electrons is sufficient to produce dislocations in the orbital electrons of the atoms in the anode metal. Inasmuch as mass and compliance are associated with these orbital electrons, a wave motion in the form of an oscillating electromagnetic field is propagated into space. Although the frequencies of these waves are far beyond those generated by the oscillators dealt with in this book, we should realize that the X-ray tube utilizes the basic principle of all modern microwave tubes. This principle is the conversion of the energy in an electron beam to oscillatory power at a desired frequency. The magnetron The magnetron, like the X-ray tube, is a vacuum diode in which thermioni- cally freed electrons are imparted high kinetic energy by an intense electric