Linear Circuit Transfer Functions: An Introduction to Fast Analytical TechniquesISBN: 9781119236375
460 pages
May 2016, WileyIEEE Press

Description
Linear Circuit Transfer Functions: An introduction to Fast Analytical Techniques teaches readers how to determine transfer functions of linear passive and active circuits by applying Fast Analytical Circuits Techniques. Building on their existing knowledge of classical loop/nodal analysis, the book improves and expands their skills to unveil transfer functions in a swift and efficient manner.
Starting with simple examples, the author explains stepbystep how expressing circuits time constants in different configurations leads to writing transfer functions in a compact and insightful way. By learning how to organize numerators and denominators in the fastest possible way, readers will speedup analysis and predict the frequency response of simple to complex circuits. In some cases, they will be able to derive the final expression by inspection, without writing a line of algebra.
Key features:
* Emphasizes analysis through employing time constantbased methods discussed in other text books but not widely used or explained.
* Develops current techniques on transfer functions, to fast analytical techniques leading to lowentropy transfer functions immediately exploitable for analysis purposes.
* Covers calculation techniques pertinent to different fields, electrical, electronics, signal processing etc.
* Describes how a technique is applied and demonstrates this through real design examples.
* All Mathcad^{®} files used in examples and problems are freely available for download.
Table of Contents
Preface xi
Acknowledgement xiii
1 Electrical Analysis – Terminology and Theorems 1
1.1 Transfer Functions, an Informal Approach 1
1.1.1 Input and Output Ports 3
1.1.2 Different Types of Transfer Function 6
1.2 The Few Tools and Theorems You Did Not Forget . . . 11
1.2.1 The Voltage Divider 11
1.2.2 The Current Divider 12
1.2.3 Thévenin’s Theorem at Work 14
1.2.4 Norton’s Theorem at Work 19
1.3 What Should I Retain from this Chapter? 25
1.4 Appendix 1A – Finding Output Impedance/Resistance 26
1.5 Appendix 1B – Problems 37
Answers 39
2 Transfer Functions 41
2.1 Linear Systems 41
2.1.1 A Linear Timeinvariant System 43
2.1.2 The Need for Linearization 43
2.2 Time Constants 44
2.2.1 Time Constant Involving an Inductor 47
2.3 Transfer Functions 49
2.3.1 Lowentropy Expressions 54
2.3.2 Higher Order Expressions 59
2.3.3 Secondorder Polynomial Forms 60
2.3.4 LowQ Approximation for a 2ndorder Polynomial 62
2.3.5 Approximation for a 3rdorder Polynomial 68
2.3.6 How to Determine the Order of the System? 69
2.3.7 Zeros in the Network 76
2.4 First Step Towards a Generalized 1storder Transfer Function 78
2.4.1 Solving 1storder Circuits with Ease, Three Examples 82
2.4.2 Obtaining the Zero with the Null Double Injection 89
2.4.3 Checking Zeros Obtained in Null Double Injection with SPICE 94
2.4.4 Network Excitation 95
2.5 What Should I Retain from this Chapter? 100
References 101
2.6 Appendix 2A – Problems 102
Answers 105
3 Superposition and the Extra Element Theorem 116
3.1 The Superposition Theorem 116
3.1.1 A Twoinput/Twooutput System 120
3.2 The Extra Element Theorem 126
3.2.1 The EET at Work on Simple Circuits 130
3.2.2 The EET at Work – Example 2 132
3.2.3 The EET at Work – Example 3 137
3.2.4 The EET at Work – Example 4 138
3.2.5 The EET at Work – Example 5 140
3.2.6 The EET at Work – Example 6 146
3.2.7 Inverted Pole and Zero Notation 150
3.3 A Generalized Transfer Function for 1storder Systems 153
3.3.1 Generalized Transfer Function – Example 1 156
3.3.2 Generalized Transfer Function – Example 2 159
3.3.3 Generalized Transfer Function – Example 3 163
3.3.4 Generalized Transfer Function – Example 4 170
3.3.5 Generalized Transfer Function – Example 5 174
3.4 Further Reading 180
3.5 What Should I Retain from this Chapter? 180
References 182
3.6 Appendix 3A – Problems 183
Answers 185
References 218
4 Secondorder Transfer Functions 219
4.1 Applying the Extra Element Theorem Twice 219
4.1.1 Lowentropy 2ndorder Expressions 227
4.1.2 Determining the Zero Positions 231
4.1.3 Rearranging and Plotting Expressions 233
4.1.4 Example 1 – A LowPass Filter 235
4.1.5 Example 2 – A Twocapacitor Filter 241
4.1.6 Example 3 – A Twocapacitor Bandstop Filter 245
4.1.7 Example 4 – An LC Notch Filter 248
4.2 A Generalized Transfer Function for 2ndOrder Systems 255
4.2.1 Inferring the Presence of Zeros in the Circuit 256
4.2.2 Generalized 2nd–order Transfer Function – Example 1 257
4.2.3 Generalized 2nd–order Transfer Function – Example 2 262
4.2.4 Generalized 2nd–order Transfer Function – Example 3 266
4.2.5 Generalized 2nd–order Transfer Function – Example 4 273
4.3 What Should I Retain from this Chapter ? 277
References 279
4.4 Appendix 4A – Problems 279
Answers 282
References 311
5 Nthorder Transfer Functions 312
5.1 From the 2EET to the NEET 312
5.1.1 3rdorder Transfer Function Example 317
5.1.2 Transfer Functions with Zeros 320
5.1.3 A Generalized Nthorder Transfer Function 327
5.2 Five Highorder Transfer Functions Examples 335
5.2.1 Example 2: A 3rdorder Active Notch Circuit 341
5.2.2 Example 3: A 4thorder LC Passive Filter 349
5.2.3 Example 4: A 4thorder Bandpass Active Filter 355
5.2.4 Example 5: A 3rdorder Lowpass Active GIC Filter 368
5.3 What Should I Retain from this Chapter ? 383
References 385
5.5 Appendix 5A – Problems 385
Answers 388
References 431
Conclusion 433
Glossary of Terms 435
Index 439
Author Information
Christophe Basso, Engineering Director, ON Semiconductor, Toulouse, France
Christophe Basso holds a BSEE equivalent from Montpellier University (France) and an MSEE from the Institut National Polytechnique of Toulouse. He has over 20 years of power supply industry experience. His recent research interests focus on developing new offline PWM controller specifications. On top of his 3 published books on Switch mode power supplies, Basso also has 30 patents on power conversion and has authored numerous conference papers and trade magazines.
Reviews
Electronics engineers begin to acquire this skill in the undergraduate engineering course on passive circuits, and it becomes more complicated in the activecircuits course. In circuits with n independent inductances and capacitances, basic sdomain circuit analysis (which, by the way, requires little more than preuniversity algebra, so that technicians having only introductory calculus can do it) results in nthdegree transfer function polynomials. When the polynomials are factored into real and complex pairs, the poles and zeros of the circuit are determined, and they determine the dynamic circuit behavior. Yet factoring a polynomial higher that a quadratic (that is, having s2 as the largest power in the polynomial) is difficult enough to drive most engineers to computer circuit simulation instead. So why this book?
Circuits can often be compartmentalized into stages with only one or two reactances in each stage. These circuits can be formidable to analyze for engineers unaccustomed to using much math, yet Basso’s book presents higherlevel circuit theorems or methods that reduce their apparent complexity. Chapter one starts easy, explaining basic concepts such as a port, the four possible transfer functions (inputoutput combinations of voltage and current), voltage dividers, Thevenin’s and Norton’s theorems, and how by shorting and opening circuits at the reactances, time constants can be found. These concepts form the “building blocks” for finding the three parameters of greatest interest: the transfer functions and input and output impedances.
Chapter 2 shows, using simple examples, how the structure of circuits relates to the coefficients in the transfer function polynomials. It begins what is continued in Chapter 3 that was a forte of Robert David Middlebrook of Cal Tech, that of simplified methods for analyzing circuits. Middlebrook developed the Extra Element Theorem (EET), a refinement of previous methods that include those of Blackman, Mulligan, Cochrun and Grabel, and Paul E. Gray and Campbell Searle at MIT. (I published a tenpart article on EDN starting January 2013 called “DesignOriented Circuit Dynamics” that gives more of the history and detailed development of these methods.) Chapter 3 includes, along with the EET, the important and basic superposition theorem.
The EET is explained stepbystep by Basso and should eventually make its way into undergraduate circuits courses. This book is suitable as a textbook for an advanced activecircuits course; it has an extensive set of problems at the end of each chapter, with a chapter summary and references. The EET is a clever way of finding the effect on a circuit with an existing transfer function of adding an additional circuit element, usually a reactance. It is a way of starting with a simplified circuit, such as a transistor amplifier stage with an infinitely fast transistor (no Ce or Cc), and incrementally developing its transfer function by adding one capacitance for each invocation of the EET. Beware however, that these successive increments of transfer function development can become as algebraicallyintensive as straightforward circuit analysis using the nodevoltage and loopcurrent methods. Yet the EET is an improvement because it offers greater insight into how circuit elements affect the overall circuit behavior.
In chapter 3, Basso does not leave the reader wondering how to apply the methods he is explaining because he gives detailed, stepbystep examples to illustrate them. Chapters 4 and 5 continue this trend with transfer functions which have seconddegree (quadratic) polynomials. The EET procedure is the same only the examples become more complicated. Finally, in chapter 5, the EET is expanded to circuits with n independent reactances, and the nEET, a further development of the EET (mainly by Ali Hajimiri) and aided by the CochrunGrabel method (which I also cover in Transistor Amplifiers, at Innovatia, but to a far lesser extent than in Basso’s book).
Besides Middlebrook, who is known for his emphasis on conceptual simplification and clarification of circuit analysis, Basso also credits Vatché Vorpérian who also has a book on methods of simplified circuit analysis. Basso’s book continues the tradition of finding ways of simplifying both an understanding of and analytical procedures for circuits. The book includes a glossary of key expressions and an index.
Planet Analog (http://www.planetanalog.com) Article by Dennis Feucht, Electronics Engineer, 6/21/2016