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CIRCUIT ANALYSISand FEEDBACKAMPLIFIER THEORY© 2006 by Taylor & Francis Group, LLCCIRCUIT ANALYSISand FEEDBACKAMPLIFIER THEORYEdited byWai-Kai ChenA CRC title, part of the Taylor & Francis imprint, a member of theTaylor & Francis Group, the academic division of T&F Informa plc.Boca Raton London New YorkUniversity of IllinoisChicago, U.S.A.© 2006 by Taylor & Francis Group, LLCThe material was previously published in The Circuit and Filters Handbook, Second Edition. © CRC Press LLC 2002.Published in 2006 byCRC PressTaylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742© 2006 by Taylor & Francis Group, LLCCRC Press is an imprint of Taylor & Francis GroupNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10987654321International Standard Book Number-10: 0-8493-5699-7 (Hardcover) International Standard Book Number-13: 978-0-8493-5699-5 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted withpermission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publishreliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materialsor for the consequences of their use.No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, orother means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any informationstorage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. Fororganizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only foridentification and explanation without intent to infringe.Library of Congress Cataloging-in-Publication DataCatalog record is available from the Library of Congress Visit the Taylor & Francis Web site at http://www.taylorandfrancis.comand the CRC Press Web site at http://www.crcpress.comTaylor & Francis Group is the Academic Division of T&F Informa plc.© 2006 by Taylor & Francis Group, LLCvPrefaceThe purpose of Circuit Analysis and Feedback Amplifier Theory is to provide in a single volume acomprehensive reference work covering the broad spectrum of linear circuit analysis and feedbackamplifier design. It also includes the design of multiple-loop feedback amplifiers. The book is writtenand developed for the practicing electrical engineers in industry, government, and academia. The goalis to provide the most up-to-date information in the field. Over the years, the fundamentals of the field have evolved to include a wide range of topics and abroad range of practice. To encompass such a wide range of knowledge, the book focuses on the keyconcepts, models, and equations that enable the design engineer to analyze, design and predict thebehavior of large-scale circuits and feedback amplifiers. While design formulas and tables are listed,emphasis is placed on the key concepts and theories underlying the processes.The book stresses fundamental theory behind professional applications. In order to do so, it is rein-forced with frequent examples. Extensive development of theory and details of proofs have been omitted.The reader is assumed to have a certain degree of sophistication and experience. However, brief reviewsof theories, principles and mathematics of some subject areas are given. These reviews have been doneconcisely with perception.The compilation of this book would not have been possible without the dedication and efforts ofProfessor Larry P. Huelsman, and most of all the contributing authors. I wish to thank them all.Wai-Kai ChenEditor-in-Chief© 2006 by Taylor & Francis Group, LLCviiEditor-in-ChiefWai-Kai Chen, Professor and Head Emeritus of the Depart-ment of Electrical Engineering and Computer Science at theUniversity of Illinois at Chicago, is now serving as AcademicVice President at International Technological University. Hereceived his B.S. and M.S. degrees in electrical engineering atOhio University, where he was later recognized as a Distin-guished Professor. He earned his Ph.D. in electrical engineeringat the University of Illinois at Urbana/Champaign.Professor Chen has extensive experience in education andindustry and is very active professionally in the fields of circuitsand systems. He has served as visiting professor at Purdue Uni-versity, University of Hawaii at Manoa, and Chuo University inTo kyo, Japan. He was Editor of the IEEE Transactions on Circuitsand Systems, Series I and II, President of the IEEE Circuits andSystems Society, and is the Founding Editor and Editor-in-Chief of the Journal of Circuits, Systems and Computers. Hereceived the Lester R. Ford Award from the Mathematical Asso-ciation of America, the Alexander von Humboldt Award from Germany, the JSPS Fellowship Award fromJapan Society for the Promotion of Science, the Ohio University Alumni Medal of Merit for DistinguishedAchievement in Engineering Education, the Senior University Scholar Award and the 2000 FacultyResearch Award from the University of Illinois at Chicago, and the Distinguished Alumnus Award fromthe University of Illinois at Urbana/Champaign. He is the recipient of the Golden Jubilee Medal, theEducation Award, the Meritorious Service Award from IEEE Circuits and Systems Society, and the ThirdMillennium Medal from the IEEE. He has also received more than a dozen honorary professorship awardsfrom major institutions in China.A fellow of the Institute of Electrical and Electronics Engineers and the American Association for theAdvancement of Science, Professor Chen is widely known in the profession for his Applied Graph Theory(North-Holland), Theory and Design of Broadband Matching Networks (Pergamon Press), Active Networkand Feedback Amplifier Theory (McGraw-Hill), Linear Networks and Systems (Brooks/Cole), Passive andActive Filters: Theory and Implements (John Wiley), Theory of Nets: Flows in Networks (Wiley-Interscience),and The VLSI Handbook (CRC Press).© 2006 by Taylor & Francis Group, LLCixAdvisory BoardLeon O. ChuaUniversity of CaliforniaBerkeley, CaliforniaJohn Choma, Jr.University of Southern CaliforniaLos Angeles, CaliforniaLawrence P. HuelsmanUniversity of ArizonaTucson, Arizona© 2006 by Taylor & Francis Group, LLCxiContributorsPeter AronhimeUniversity of LouisvilleLouisville, KentuckyK.S. ChaoTe xas Tech UniversityLubbock, Te xasRay R. ChenSan Jose State UniversitySan Jose, CaliforniaWai-Kai ChenUniversity of IllinoisChicago, IllinoisJohn Choma, Jr.University of Southern CaliforniaLos Angeles, CaliforniaArtice M. DavisSan Jose State UniversitySan Jose, CaliforniaMarwan M. HassounIowa State UniversityAmes, IowaPen-Min LinPurdue UniversityWest Lafayette, IndianaRobert W. NewcombUniversity of MarylandCollege Park, MarylandBenedykt S. RodanskiUniversity of Technology, SydneyBroadway, New South Wales, AustraliaMarwan A. SimaanUniversity of PittsburghPittsburgh, PennsylvaniaJames A. SvobodaClarkson UniversityPotsdam, New YorkJiri VlachUniversity of WaterlooWaterloo, Ontario, Canada© 2006 by Taylor & Francis Group, LLCxiiiTable of Contents1 Fundamental Circuit Concepts John Choma, Jr 1-12 Network Laws and Theorems 2-12.1 Kirchhoff's Voltage and Current Laws Ray R. Chen and Artice M. Davis 2-12.2 Network Theorems Marwan A. Simaan 2-393 Terminal and Port Representations James A. Svoboda 3-1 4 Signal Flow Graphs in Filter Analysis and Synthesis Pen-Min Lin 4-1 5 Analysis in the Frequency Domain 5-15.1 Network Functions Jiri Vlach 5-15.2 Advanced Network Analysis Concepts John Chroma, Jr. 5-106 Tableau and Modified Nodal Formulations Jiri Vlach 6-1 7 Frequency Domain Methods Peter Aronhime 7-18 Symbolic Analysis1 Benedykt S. Rodanski and Marwan M. Hassoun 8-19 Analysis in the Time Domain Robert W. Newcomb 9-110 State-Variable Techniques K. S. Chao 10-111 Feedback Amplifier Theory John Choma, Jr. 11-112 Feedback Amplifier Configurations John Choma, Jr. 12-113 General Feedback Theory Wai-Kai Chen 13-1© 2006 by Taylor & Francis Group, LLCxiv14 The Network Functions and Feedback Wai-Kai Chen 14-115 Measurement of Return Difference Wai-Kai Chen 15-116 Multiple-Loop Feedback Amplifiers Wai-Kai Chen 16-1© 2006 by Taylor & Francis Group, LLC1-11FundamentalCircuit Concepts1.1 The Electrical Circuit 1-1Current and Current Polarity • Energy and Voltage • Power1.2 Circuit Classifications 1-10Linear vs. Nonlinear • Active vs. Passive • Time Varying vs. Time Invariant • Lumped vs. Distributed1.1 The Electrical CircuitAn electrical circuit or electrical network is an array of interconnected elements wired so as to be capableof conducting current. As discussed earlier, the fundamental two-terminal elements of an electricalcircuit are the resistor, the capacitor, the inductor, the voltage source, and the current source. Thecircuit schematic symbols of these elements, together with the algebraic symbols used to denote theirrespective general values, appear in Figure 1.1.As suggested in Figure 1.1, the value of a resistor is known as its resistance, R, and its dimensionalunits are ohms. The case of a wire used to interconnect the terminals of two electrical elements correspondsto the special case of a resistor whose resistance is ideally zero ohms; that is, R = 0. For the capacitor inFigure 1.1(b), the capacitance, C, has units of farads, and from Figure 1.1(c), the value of an inductor isits inductance, L, the dimensions of which are henries. In the case of the voltage sources depicted inFigure 1.1(d), a constant, time invariant source of voltage, or battery, is distinguished from a voltagesource that varies with time. The latter type of voltage source is often referred to as a time varying signalor simply, a signal. In either case, the value of the battery voltage, E, and the time varying signal, v(t),is in units of volts. Finally, the current source of Figure 1.1(e) has a value, I, in units of amperes, whichis typically abbreviated as amps.Elements having three, four, or more than four terminals can also appear in practical electricalnetworks. The discrete component bipolar junction transistor (BJT), which is schematically portrayedin Figure 1.2(a), is an example of a three-terminal element, in which the three terminals are the collector,the base, and the emitter. On the other hand, the monolithic metal-oxide-semiconductor field-effecttransistor (MOSFET) depicted in Figure 1.2(b) has four terminals: the drain, the gate, the source, andthe bulk substrate.Multiterminal elements appearing in circuits identified for systematic mathematical analyses are rou-tinely represented, or modeled, by equivalent subcircuits formed of only interconnected two-terminalelements. Such a representation is always possible, provided that the list of two-terminal elements itemizedin Figure 1.1 is appended by an additional type of two-terminal element known as the controlled source,or dependent generator. Two of the four types of controlled sources are voltage sources and two arecurrent sources. In Figure 1.3(a), the dependent generator is a voltage-controlled voltage source (VCVS)in that the voltage, v0(t), developed from terminal 3 to terminal 4 is a function of, and is thereforeJohn Choma, Jr.University of Southern California© 2006 by Taylor & Francis Group, LLC[...]... Such ideas were discussed more fully in Chapter 1 Circuit analysis merely provides the tools for analyzing the end result The radiation of electromagnetic energy is, on the other hand, a quite different aspect of circuit theory As will be seen, circuit analysis falls within a regime in which such behavior can be neglected Thus, the theory of circuit analysis we will expound has a limited range of application:... element bodies and replace them with open space The result is given in Figure 2.7 We refer to each of the interconnected “islands” of a conductor as a node This example circuit has six nodes, and we labeled them with the numbers one through six for identification purposes b c g a f © 2006 by Taylor & Francis Group, LLC d e FIGURE 2.6 An example circuit 2-4 Circuit Analysis and Feedback Amplifier Theory 3... and 2.19 Redrawing a circuit using ground reference symbols does not alter the circuit topology, the circuit graph Suppose the red probe were moved to node 5 As described previously, no element is directly connected between nodes 5 and 1; hence, node voltage v5 is not an element voltage However, the element voltages © 2006 by Taylor & Francis Group, LLC 2-10 Circuit Analysis and Feedback Amplifier Theory. .. the initial node and node 4 is the final node Thus, a direction is associated with a path, and we can indicate it diagram- 1We assume that no element has its two leads connected together and that more than two elements are in the path in this definition © 2006 by Taylor & Francis Group, LLC 2-6 Circuit Analysis and Feedback Amplifier Theory b 3 i3 P1 a 2 4 f 1 c 5 P2 g iz d 6 e FIGURE 2.11 Circuit paths... in the circuit from terminal 1 to terminal 2 As is the case with the two controlled voltage sources studied earlier, the preceding two equations collapse to the linear relationships i0 (t ) = g mv i (t ) (1.7) i0 (t ) = aαii (t ) (1.8) and when g(⋅) and a(⋅), respectively, are linear functions of their arguments © 2006 by Taylor & Francis Group, LLC 1-4 Circuit Analysis and Feedback Amplifier Theory. .. conceivably large numbers of charges are transported back and forth across the junction © 2006 by Taylor & Francis Group, LLC 1-6 Circuit Analysis and Feedback Amplifier Theory Arbitrary Cross Section i(t) q(t) − + + qo (a) i(t) q(t) − + − q o (b) i(t) − q1(t) + q2(t) (c) FIGURE 1.5 (a) Transport of a positive charge from the left-hand side to the right-hand side of an arbitrary crosssection of a conductive... delivered to the signal source is ps (t ) = −v s (t )is (t ) (1.16) Because, as stated previously, vs(t) = v(t) and is(t) = i(t), for the circuit at hand, (1.16) can be written as ps (t ) = −v (t )i(t ) © 2006 by Taylor & Francis Group, LLC (1.17) 1-10 Circuit Analysis and Feedback Amplifier Theory The last result implies that the power delivered by the signal source = +v (t )i(t ) ≡ pe (t ) (1.18) that... terminal voltage is a constant and in which energy is stored and therefore available for use behaves as a battery If the preceding analysis is repeated for the inductor of Figure 1.8(c), it can be shown that the energy, wl (t), stored in the inductive element form time t = 0 to time t is © 2006 by Taylor & Francis Group, LLC 1-12 Circuit Analysis and Feedback Amplifier Theory w l (t ) = 1 2 Li (t ) 2... them, and the element leads At this point, we loosely consider a circuit to be any collection of elements and conductors, although we will sharpen our definition a bit later Axiom 1 means that we can run tests on an element in the laboratory, then wire it into a circuit and have the assurance that it will not exhibit any new and different behavior Axiom 2 means that it is only the topology of a circuit. .. large currents approaches zero in ideal conductors The electrical properties of semiconductors such as germanium, silicon, and gallium arsenide © 2006 by Taylor & Francis Group, LLC 1-8 Circuit Analysis and Feedback Amplifier Theory lie between the extremes of those for an insulator and a conductor In particular, semiconductor elements behave as insulators when their terminals are subjected to small voltages, . CIRCUIT ANALYSIS and FEEDBACK AMPLIFIER THEORY © 2006 by Taylor & Francis Group, LLC CIRCUIT ANALYSIS and FEEDBACK AMPLIFIER THEORY Edited. Applied Graph Theory (North-Holland), Theory and Design of Broadband Matching Networks (Pergamon Press), Active Network and Feedback Amplifier Theory (McGraw-Hill),
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