11111111111111111111 by Rufus TURNER 11111111111 LCRufus P.Circuits Turner,by Ph. D. Howard4300 WEST 62ND W. ST. INDIANAPOLIS, Sams & INDIANA Co., 46268 Inc. USA Copyright © 1980 by Howard W. Sams & Co., Inc. Technologically and historically,Preface the familiar combination FIRSTIndianapolis, PRINTINGEDITION Indiana -1980 46268 faringselectiveof This inductance afieldof radio book unitin manyapparatus, describes of and electronics. areas capacitance, aofthe number electronics. LC Originally circuit theof practical LC has delegated circuit, found LC iscircuitsapplication to the the basic tun- and writtenphotocopying,transmittedreproduced,All rights permission reserved. bystored recording,any inmeans,from No a retrievalpart theor electronic, otherwise,ofpublisher. this system, book mechanical,without No orshall patent be torsofresistance,offers them. and enough capacitors.A sufficientsince background that amount property theory of isspace to inherent promote has been in the practical devoted understanding induc-also to assumedforthisprecautioninformationliability errorsbook, is for ortheassumed has contained omissions.damages publisher been with taken herein.resulting assumesNeither respect in theWhile fromisnoto preparation any theresponsibility every the useliability use of ofthe mayplanationsposes.dent,Although find technician, A minimumcertain being the material parts andpreferred of experimenter, mathematicsof isit useful, addressedwhere iffeasible-andis more onlyemployed-physical to the foradvanced electronics reference frequent readers pur- stu-ex- il- LibraryInternationalthe information of Congress Standard contained Catalog Book herein. Number:Card Number: 0-672-21694-9 79-57616 virtuoso.lustrativeI hope examplesthat this bookdemonstrate will serve the necessaryboth the novicecalculations. and the Printed in the United States of America. RUFUS P. TURNER 2.102.92.72.8 SymmetricalSelfRangeBroadband -Resonance Coverage Tuning Circuits 53515053 2.132.122.112.14 DCWavemetersWaveVaractor -Tuned Traps Frequency Circuits Multiplier 57545956 FILTERS CHAPTER 3 60 Contents 3.43.33.23.1PowerWaveFilterBasic Sections FiltersFiltering-Supply Filters Properties of L and C 72646260 FUNDAMENTAL1.1 The AC THEORY Cycle -RateCHAPTER of Change 1 7 7 CHAPTER 4 1.51.41.31.2Nature ofof CapacitanceInductiveInductanceResistance Reactance 20191511 BRIDGES4.24.34.1 ANDHayAnderson BridgeOTHER Bridge MEASURING DEVICES 787776. 76 1.91.81.71.6FigureResonanceCombinedNature of Merit,CapacitiveReactance Q inReactance LC Circuits 27262624 4.74.64.54.4ResonantBridgedResonanceOwenMaxwell Bridge -T BridgeCircuit BridgesNull Network as Measuring Device 84828079 1.141.131.121.111.10 TimeInductivePracticalPureNature LConstant andof LCoupling Practical andC in C Combination in InductorCombination 313028 APPENDIX A 1.151.16 OscillationsRange of Application in LC CHAPTERCircuit of LC Circuits 2 363532 ANGULAR VELOCITY (w)APPENDIX B 86 TUNED2.42.32.22.1 CIRCUITSResonantParallelSeries -Resonant -Resonant -Circuit Circuit Constants Circuit 424037 37 REACTANCE OF INDUCTORSAPPENDIX AT 1000 Hz C . 87 2.62.5CoupledCircuitSelectivity Q Resonant Circuits 464543 REACTANCE OF CAPACITORS . 88 APPENDIX D RC TIME CONSTANTS APPENDIX E 90 CHAPTER 1 RL TIME CONSTANTS APPENDIX F 91 RESONANT FREQUENCY OFAPPENDIX LC COMBINATIONS G . 93 Fundamental Theory CONVERSION FACTORS . 95 readertheunderstandingare(LC)This essentialmathematics circuits. has chapter that to aThesebackground. digestsangeneral of understanding electronics, are thosefamiliarity specific parts and items of withof itinductancebasic electricalisrequiring assumed electronics -capacitance theoryfor that their that andthe Asvector1.1Fig. theTHE isvector1-lArotating ACE., CYCLE-RATEdepictsthe moves atmaximum constant ain sinusoidal a counterclockwise OFvaluevelocity. CHANGE attainedac voltageThe magnitudeby direction thein terms ac voltage.from of ofthis its a completestartingextendingtaneouswhich(Although increases pointvoltage, rotation. fromthe at vector from thee, Ifis tiphorizontal the initialdepictedis ofrotating figure the zero byvector isaxis, atto thedrawn constant360° itlengthto generates (27rtheto scale, angularof horizontalradians) the anthe half velocity, angle ininstan- chord eachaxis. 0 theatvoltagerate;Fromall, length see and is Fig.Table zeroisof maximum 1-1A,this 1-1.)at 0°,half it since ischord at easily 90°, here does since seenthe not half herethat change chord the halfinstantaneous hasat a chordno constant length has zero,its(7r/2 maximum increasesradians), length. returnsto the maximum Thus,to zero instantaneous at positive180° (7r valueradians), voltage (+Emax) increases e starts at 90° atto7 90° instantaneousunit radius (i.e., voltage E. = at 1), eany = it Emaxsin point,is equal therefore 0 to sin 0.is :The value(1-1) of 180° 360°0° (A) Rotating vector. sinusoidal).functionversusFig. 1-1B angle. from shows Thistrigonometry, the curve familiar is identical hence plot of the instantaneouswith term that sine of wave the voltage sine (or IllustrativeSinA(90°) close 60° value = 0.866.examination Example: of 162.6 From Thevolts. Equation 115-Vof Calculate Fig. 1-1,power 1-1 e the = shows-line 162.6(0.866) instantaneous voltage that hasnot = 140.8value a only maximum V.at is 60°. the 180 270 36027, RADIANSDEGREES (B) Voltage curve. thebutinstantaneous1-1.) thecurve This rate at canof points voltagechange be shown of also continuouslyinterest graphicallyis changing. and observingchanging by (See drawing Column during the slopetangents 3the in ofcycle,Table the to theandthe vectormaximumreturns has to negativezerotracedFig. at1-1. out360° valueDevelopment a (27rcomplete (-Erna.) radians). of sine atcycle, 270°wave. At thisand(37r/2 lattera new radians), point,cycle thepassingrateisattangent.(45°) noPoint cycleof changereveals change throughP2Thus, is (90°)passing ata thus in moderateall its Fig.has atmaximumis through this zerono1-1B, tiltratepoint. at the whatever 90° ofitspoints, tiltInchange, zeroand the of 270°and pointstangentsineand whereas is whenshows-wave maximum (0°, ab the attangent 180°,cycle,that Point cycle therewhen andthe cdP1 is age,ofbegins line is e,proportionalwithTable and the accordingly 1-1. continued Voltage to the the sinerotationChange value of angle andof the Rate0, vector. instantaneousandChange for The a circlelengthvolt- of slope360°).ofvoltage Thisthe = angularcan aroundAE/00. be shown rotation theFrom point mathematically Fig. at of that1-1B, interest point it isdivided equals: easily(1) The by theseen the incrementslope that increment ;atthus, 90° of (degrees)Rotation Voltage(V) Change* Voltage(V/degree)Rate Change of valueisingly(Point great. ofare P2), AO,(2) zero, AEFrom so whereas =the 0,calculus, slopeand atthe is 180° thesteepslope rate AE atand ofthisis ratechangevery point of large change andof a forthe sine accord- achange smallwave 40-5030-4020-3010-200-10 0.643-0.7660.5-0.6430.0342-0.50.174-0.3420-0.174 0.01430.01580.01680.0174 isofat 1,athatchange point so point. the ofis rate zerointerest The of at cosine change those is proportional ofpoints. is 90° maximum or The of to cosine270° the at those cosineis of zero, 0° points ofand so the ofthe where angle360° rate =80-9070-8060-7050-60 1 V 0.985-10.940-0.9850.866-0.9400.766-0.866 0.00150.00450.00740.010.0123 expressionradianssinetheAt cycle function a givenper crosses 27rf second isfrequency is1). oftenthe (where zero represented f, line fthe is in (thevoltage hertz, by maximum lowercase andvector 7T value describes=Greek 3.1416). of omega the 27rf Theco- : 8 betweenw. (Appendix 1 Hz Aand gives 100 values MHz.) of The co at maximum a number rateof frequencies of change9 themustfollowsin voltagerate occur offrom change atis thezero equal previous may-voltage to be 2711E. found discussionpoints by (also in multiplying the that written cycle. this At rate thecoE.), every maximumof change andpoint, it ifgrees, desired but : these time units0 = are 2irft easily = wt converted into an angle,(1-3) Forinterest:rate example, of changeRate inof a Changeby 500 the -Hz = cosine 2irfEmaxcos cycle havingof the 0 =aangle coEmaxcosmaximum at the voltage0 point(1-2) of where,tf isisisis the the3.1416,the time frequencyangle in in seconds, radians, in hertz, 15 V, the rate of change at 65°125 Hz (where cos 0 = 0.42262) is w is an -f. 0.004 directly,To convert change 0 to degrees,Equation multiply 1-30 = to 360 : by ft 57.296. To obtain degrees(1-4) OV) 0.001 0.002 0.003 0.005 0.0060.0070.008t (Seconds) ratetime1-2,NoteFig. of 1-2Bthe instants,the change rate rate shows ofof hereand changechange the gives(271-fErna0 relationship atexhibited sines0.004 and issecond betweenin 1570.8 thiscosines (180°,cycle. V/s.selected of From The 7Tthese radians)anglesmaximum Equation angles. and is t (A)0 Typical cycle. 0.7071of2 (3.1416) change = 1110.7 at125 0.001 (2) V/s ( s -1) ; (45°,and = 1570.8 the 7r/4 rate radians) ( -1)of change= -1570.8 is 2 (3.1416)125at 0.002V/s; the s (90°, rate(2) (seconds)0 (degrees)0 (radians)0 sin0 0 cos1 0 7r/2It shouldradians) be is clear 2(3.1416)125 by now that (2)0 the = 1570.8rate of changex 0 = 0. in voltage 0.0020.0030.001 9045135 2.35621.57080.7854 0.70711 -0.707100.7071 precedingmagnitudeat a selected fromexample, point the ininstantaneous for the instance, ac cycle voltage itis is markedly seen at that that point.different the instan- In the in 0.0060.0070.0050.004 270225315180 5.49784.71243.92703.1416 -1-0.7071-0.70710 -0.7071-10.70710 graph)oftaneousEquation change is voltage 1110.71-1) of voltage