**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

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**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),