

Book Offers Further Instruction On Advanced Methods Of  
The Fast Track to Determining Transfer Functions of Linear Circuits: The Student Guide, Christophe Basso, 267 numbered pages, 4 index pages, glossy soft cover, 8.5 × 11 inch, Faraday Press, ISBN 9781960405197, 2023, $54.95. Reviewed by Dennis Feucht, Innovatia Laboratories, Cayo, Belize uthor Christophe Basso has designed converter control ICs for ON Semiconductor in Toulouse, France and has written related books, such as Transfer Functions of Switching Converters: Fast Analytical Techniques at Work with SmallSignal Analysis,[1] which was previously reviewed in How2Power Today. This earlier work and the book under review here are compendiums of methods of passive and active circuit analysis that reduce the amount of mathematics that otherwise would be required when applying Kirchhoff's current and voltage laws (KCL, KVL) and Ohm's Law (ΩL). Somewhat higher level than those basic circuit laws are the nodevoltage and loopcurrent methods. Even higherlevel laws are presented in undergraduate passivecircuits classes such as the maximum powertransfer theorem but they are few. Whether you are fast or slow, the methods presented in this book are conceptually more abstract than basic circuit laws and are derived from them mathematically as theorems. They impose various conditions on the circuit that simplify the application of basic circuit laws and simplify analysis. The history of development of higher "designoriented" circuit theorems is shown in the figure (taken from reference[2]). Major advancements in this development tree are opencircuit timeconstant (OCTC) methods for finding poles, leading to the CochrunGrabel method and the ExtraElement Theorem (EET) of R. D. Middlebrook that includes shortcircuit timeconstants (SCTCs). From these follow related theorems, the impedance EET and tabular nEET.
Beyond the historical developments in circuit analysis depicted in the figure, there were other refinements and restatements of these theorems by Vatché Vorpérian.[3] And following his lead are Basso's books. This book is a sequel to reference [1] in that it works out in some detail in chapters 5 through 7 the analyses of commonlyencountered circuits with one to three reactive elements. Before presenting these analyses, the first four chapters explain the techniques and the concepts supporting them with simpler examples. The first chapter covers transfer functions, their poles and zeros from reactive elements connected across circuits as ports, their open and shortcircuit timeconstants, and the normalized form of transfer functions as providing more insight into circuit poles and zeros than the canonical form. Port resistances with reactive elements removed (open) or other ports shorted provide timeconstant resistances. Circuits are illustrated in color, sometimes with pictures of test equipment as sources and component pictures as comprising a network (circuit). Active circuits start as opamps, but on page 31, a simple commonemitter NPN BJT circuit is shown as an example, with a twoelement hybridπ model—a good place to start in incrementally modeling BJTs. Chapter 2 introduces designoriented methods. At frequency extremes of s = 0 Hz (or 0+ Hz for incremental circuits) and s → ∞, capacitance and inductance are either opencircuit or shortcircuit. Circuits like the RC integrator and differentiator demonstrate how to determine the pole from the OCTC and the zero (for the differentiator) from the SCTC. Expanding to secondorder (tworeactance) circuits, the timeconstants (TCs) are determined by the CochrunGrabel method (CG) for poles as a triangular table. The EET expands the method to include zeros. Basso has his own nomenclature for designating the TCs, and it is equivalent to CG, the EET, and the nomenclature used in reference [2]. Chapter 3 is about finding circuit zeros, the frequencies (or corresponding timeconstants) where the output is zero. Basso's method of finding zeros is that of the EET—of adjusting sources to null the output. At first this might seem obfuscating, but in the method, it is quite simple. The procedures follow what was originally introduced by Middlebrook in the ExtraElement Theorem (EET) which produces both the poles and zeros of the circuit transfer function. The latter part of chapter 3 works through the extended and rather complicated (though important) example of a BJT with external emitter resistance. Basso is careful to include numerous steps to not leave any reader behind. (This is also worked out in reference [2] under "General SingleStage CE Gain" by following a different path in the construction of the formidable transfer function, applying the same circuit theorems.) Chapter 4, "Generalized Transfer Functions," has an emphasis on SCTCs for finding zeros and higherorder coefficients in the denominator (poles) and numerator (zeros) polynomials. It completes the general procedure which is powerful in determining complicated yet exact transfer functions for even some of the most common circuits in designs, yet often is left without indepth analysis in the electronics literature because of the extensive amount of algebra required. Chapters 5 through 7 present many detailed circuit solutions beginning with firstorder (onereactance) circuits in chapter 5. These circuits have no resonance and are easier to derive. Basso also includes the timedomain step response that models what is seen while probing the circuit driven by a squarewave, and Bode plots are presented for frequencyresponse analysis. Everything is in living color. Chapter 6 is more complicated, with nonminimumphase circuits and resonances. Yet secondorder circuits have seconddegree (quadratic) equations and can be solved with the quadratic formula, thereby factoring the poles or zeros into the desired normalized form of transfer functions. The thirdorder circuits of the last chapter pose the polynomial factoring problem. Although there is a method for solving cubic equations, it is not a simple formula like the quadratic equation, and the book resorts to simulation. It is often possible for real circuits with widely separated poles or zeros to approximate them as lowerdegree polynomials, though approximations do not appear in the book; it is about exact derivations. Appendix A summarizes the method discussed throughout the book What does not appear in the book about transfer functions is a comparison of nodal versus OCTC timeconstants. They are not the same and this can be a confusing topic when learning circuit dynamics. Another omitted topic is analysis of a generalized amplifier, with general input, output, and feedback impedances and a quasistatic Gm gain. When solved, the three timeconstants have equivalent circuits that make analysis of the amplifier simpler. Another highlevel theorem is Miller's theorem, but less common is the frequencydependent version of it. Finally but not least important is the highfrequency modeling of BJT and feedback amplifiers that reveals why spurious oscillations occur in circuits. These topics go somewhat beyond the range of what is covered in this book, which remains focused on transferfunction derivations. This is another good book from Basso who patiently explains (in color) each procedure stepbystep, then applies it to various examples. It is somewhat like the old Schaum's Outline Series books which served the same role. I recommend this book for anyone who has not yet mastered dynamic circuit analysis at the component level. The topic will not go away. Basso uses simulations to check the equations for agreement, but simulations do not give insight into the effects of circuit parameters on the behavior of the circuit. Mathematical analysis does. References
About The Author
To read Dennis' reviews of other texts on power supply design, magnetics design and related topics, see How2Power's Power Electronics Book Reviews.


<<Contents  <Previous  Page 8  Next>  
If you or anyone in your company is interested in getting on the distribution list for future issues of PSMA UPDATE, please send email to: power@psma.com. Be sure to include your name and
