Linear circuit transfer functions : an introduction to fast analytical techniques

463 Pages·2016·42.594 MB·English

by  Basso, Christophe P

LINEAR CIRCUIT
TRANSFER FUNCTIONS

LINEAR CIRCUIT
TRANSFER FUNCTIONS
AN INTRODUCTION TO FAST
ANALYTICAL TECHNIQUES
Christophe P. Basso
ONSemiconductor,Toulouse,France
Thiseditionfirstpublished2016
2016JohnWiley&Sons,Ltd
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LibraryofCongressCataloging-in-PublicationData
Names:Basso,ChristopheP.,author.
Title:Linearcircuittransferfunctions:anintroductiontofastanalytical
techniques/ChristopheBasso.
Description:Chichester,WestSussex;Hoboken,NJ:Wiley,2016.|Includes
index.
Identifiers:LCCN2015047967|ISBN9781119236375(cloth)|ISBN9781119236351
(epub)
Subjects:LCSH:Transferfunctions.|Electriccircuits,Linear.
Classification:LCCTA347.T7B372016|DDC621.3815–dc23LCrecordavailableathttp://lccn.loc.gov/2015047967
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:9781119236375
Setin9.5/11.5ptTimesLTStd-RomanbyThomsonDigital,Noida,India
1 2016
Contents
AbouttheAuthor ix
Preface xi
Acknowledgement xiii
1 ElectricalAnalysis–TerminologyandTheorems 1
1.1 TransferFunctions,anInformalApproach 1
1.1.1 InputandOutputPorts 3
1.1.2 DifferentTypesofTransferFunction 6
1.2 TheFewToolsandTheoremsYouDidNotForget . . . 11
1.2.1 TheVoltageDivider 11
1.2.2 TheCurrentDivider 12
1.2.3 Thévenin’sTheorematWork 14
1.2.4 Norton’sTheorematWork 19
1.3 WhatShouldIRetainfromthisChapter? 25
1.4 Appendix1A–FindingOutputImpedance/Resistance 26
1.5 Appendix1B–Problems 37
Answers 39
2 TransferFunctions 41
2.1 LinearSystems 41
2.1.1 ALinearTime-invariantSystem 43
2.1.2 TheNeedforLinearization 43
2.2 TimeConstants 44
2.2.1 TimeConstantInvolvinganInductor 47
2.3 TransferFunctions 49
2.3.1 Low-entropyExpressions 54
2.3.2 HigherOrderExpressions 59
2.3.3 Second-orderPolynomialForms 60
2.3.4 Low-QApproximationfora2nd-orderPolynomial 62
2.3.5 Approximationfora3rd-orderPolynomial 68
2.3.6 HowtoDeterminetheOrderoftheSystem? 69
2.3.7 ZerosintheNetwork 76
2.4 FirstStepTowardsaGeneralized1st-orderTransferFunction 78
2.4.1 Solving1st-orderCircuitswithEase,ThreeExamples 82
vi Contents
2.4.2 ObtainingtheZerowiththeNullDoubleInjection 89
2.4.3 CheckingZerosObtainedinNullDoubleInjectionwithSPICE 94
2.4.4 NetworkExcitation 95
2.5 WhatShouldIRetainfromthisChapter? 100
References 101
2.6 Appendix2A–Problems 102
Answers 105
3 SuperpositionandtheExtraElementTheorem 116
3.1 TheSuperpositionTheorem 116
3.1.1 ATwo-input/Two-outputSystem 120
3.2 TheExtraElementTheorem 126
3.2.1 TheEETatWorkonSimpleCircuits 130
3.2.2 TheEETatWork–Example2 132
3.2.3 TheEETatWork–Example3 137
3.2.4 TheEETatWork–Example4 138
3.2.5 TheEETatWork–Example5 140
3.2.6 TheEETatWork–Example6 146
3.2.7 InvertedPoleandZeroNotation 150
3.3 AGeneralizedTransferFunctionfor1st-orderSystems 153
3.3.1 GeneralizedTransferFunction–Example1 156
3.3.2 GeneralizedTransferFunction–Example2 159
3.3.3 GeneralizedTransferFunction–Example3 163
3.3.4 GeneralizedTransferFunction–Example4 170
3.3.5 GeneralizedTransferFunction–Example5 174
3.4 FurtherReading 180
3.5 WhatShouldIRetainfromthisChapter? 180
References 182
3.6 Appendix3A–Problems 183
Answers 185
References 218
4 Second-orderTransferFunctions 219
4.1 ApplyingtheExtraElementTheoremTwice 219
4.1.1 Low-entropy2nd-orderExpressions 227
4.1.2 DeterminingtheZeroPositions 231
4.1.3 RearrangingandPlottingExpressions 233
4.1.4 Example1–ALow-PassFilter 235
4.1.5 Example2–ATwo-capacitorFilter 241
4.1.6 Example3–ATwo-capacitorBand-stopFilter 245
4.1.7 Example4–AnLCNotchFilter 248
4.2 AGeneralizedTransferFunctionfor2nd-OrderSystems 255
4.2.1 InferringthePresenceofZerosintheCircuit 256
4.2.2 Generalized2nd–orderTransferFunction–Example1 257
4.2.3 Generalized2nd–orderTransferFunction–Example2 262
4.2.4 Generalized2nd–orderTransferFunction–Example3 266
4.2.5 Generalized2nd–orderTransferFunction–Example4 273
Contents vii
4.3 WhatShouldIRetainfromthisChapter? 277
References 279
4.4 Appendix4A–Problems 279
Answers 282
References 311
5 Nth-orderTransferFunctions 312
5.1 Fromthe2EETtotheNEET 312
5.1.1 3rd-orderTransferFunctionExample 317
5.1.2 TransferFunctionswithZeros 320
5.1.3 AGeneralizedNth-orderTransferFunction 327
5.2 FiveHigh-orderTransferFunctionsExamples 335
5.2.1 Example2:A3rd-orderActiveNotchCircuit 341
5.2.2 Example3:A4th-orderLCPassiveFilter 349
5.2.3 Example4:A4th-orderBand-passActiveFilter 355
5.2.4 Example5:A3rd-orderLow-passActiveGICFilter 368
5.3 WhatShouldIRetainfromthisChapter? 383
References 385
5.5 Appendix5A–Problems 385
Answers 388
References 431
Conclusion 433
GlossaryofTerms 435
Index 439