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`IPR2021-00985
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`McGraw-Hill
`~
`A Division ofTheMcGraw-HiUCompanies
`
`MICROELECTRONIC CIRCUIT DESIGN
`
`Copyright© 1997 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in
`the United States of America. Except as permitted under the United States Copyright
`Act of 1976, no part of this publication may be reproduced or distributed in any form or
`by any means, or stored in a data base or retrieval system, without the prior written
`permission of the Publisher.
`
`This book is printed on acid-free paper.
`
`I 2 3 4 5 6 7 8 9 DOW DOW 9 0 3 2 I O 9 8 7
`
`ISBN 0-07-032482-4
`
`This book was set in Tunes Roman by Publication Services.
`The editor was Lynn B. Cox; the editing supervisor was Eva Marie Strock;
`the interior designer was Mel Haber;
`the cover designer was Francis Owens;
`the production supervisor was Natalie Durbin.
`R. R. Donnelley & Sons, Wtlard, was the printer and binder.
`
`Library of Congress Cataloging-in-Publication Data
`
`Jaeger, Richard C.
`Microelectronic circuit design / Richard C. Jaeger.
`p.
`cm. -
`(McGraw-Hill series in electrical and computer
`engineering)
`Includes bibliographical references and index.
`ISBN 0-07-032482-4
`I. Integrated circuits-Design and construction.
`2. Semiconductors-Design and construction. 3. Electronic circuit
`design.
`I. Title.
`II. Series.
`TK7874.J333 1996
`621.3815--dc20
`
`96-26208
`CIP
`
`INTERNATIONALEDffiON
`Copyright 1997. Exclusive rights by The McGraw-Hill Companies, Inc. for manufacture
`and export. This book cannot be re-exported from the country to which it is consigned
`by McGraw-Hill. The International Edition is not available in North America.
`
`When ordering this title, use ISBN 0-07-114386-6
`
`http://www.mhcoDege.com
`
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`12.1 THE DIFFERENTIAL AMPLIFIER
`
`489
`
`12 .1 THE DIFFERENTIAL AMPLIFIER
`The basic differential amplifier is shown in schematic form in Fig. 12.1. The amplifier has
`two inputs, to which the input signals V+ and V- are connected, and a single output v0 , all
`referenced to the common (ground) terminal between the two power supplies V cc and VEE.
`In most applications, V cc ~ 0 and - VEE ::5 0, and the voltages are often symmetric-that
`is, ±5 V, ± 12 V, ± 15 V, ± 18 V, ±22 V, and so on. These power supply voltages limit the
`output voltage range: - VEE ::5 Vo ::5 V cc.
`For simplicity, the amplifier is most often drawn without explicitly showing the power
`supplies, as in Fig. 12.2(a), or the ground connection, as in Fig. 12.2(b)-but we must
`remember that the power and ground terminals are always present in the implementation
`of a real circuit.
`For purposes of signal analysis, the differential amplifier can be represented by
`its input resistance Rw, output resistance Ro, and controlled voltage source Av;d, as in
`Fig. 12.3. This is the simplified g-parameter two-port representation from Chap. 11 with
`C12 = 0.
`
`A = voltage gain (open-circuit voltage gain)
`V;J = (v+ - v-) = differential input signal voltage
`Rw = amplifier input resistance
`Ro = amplifier output resistance
`
`+V c r o - - - - - - - - - ,
`
`(12.1)
`
`Figure 12.1 The differential
`amplifier,
`including power
`supplies.
`
`V_
`
`Figure 12.2 (a) Amplifier
`without power supplies ex-
`plicitly included. (b) Differ-
`ential amplifier with implied
`ground connection.
`
`+
`vid
`
`(a)
`
`+
`Vo
`
`1_-
`-
`
`+
`vid
`
`(b)
`
`-
`
`+
`Vo
`
`1_-
`-
`
`Rgure 12.3 Differential am(cid:173)
`w,llfier.
`
`v_o------+---'
`
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`490
`
`CHAPTER 12 OPERATIONAL AMPLIFIERS
`
`The signal voltage developed at the output of the amplifier is in phase with the voltage
`applied to the + input terminal and 180° out of phase with the signal applied to the -
`input
`terminal. The V+ and V- terminals are therefore referred to as the noninverting input and
`inverting input, respectively.
`In a typical application, the amplifier is driven by a signal source having a Thevenin
`equivalent voltage Vs and resistance Rs and is connected to a load represented by the resistor
`RL, as in Fig. 12.4. For this simple circuit, the output voltage can be written in terms of the
`dependent source as
`
`*
`A
`RL
`Vo = ViciR
`R
`0 + L
`
`(12.2)
`
`and the voltage Vici is
`
`Rm
`Vici = Vs R
`R
`ID+ S
`Combining Eqs. (12.2) and {12.3) yields an expression for the overall voltage gain of the
`amplifier circuit in Fig. 12.4 for arbitrary values of Rs and RL:
`
`(12.3)
`
`{12.4)
`
`Operational-amplifier circuits are most often de-coupled amplifiers, and the signals
`v0 and Vs may in fact have a de component that represents a de shift of the input away from
`the Q-point. The op amp amplifies not only the ac components of the signal but also this de
`component. We must remember that the ratio needed to find Av, as indicated in Eq. (12.4),
`is determined by the amplitude and phase of the individual signal components and is not a
`time-varying quantity, but w = 0 is a valid signal frequency!
`
`+
`
`v,
`
`Figure 12.4 Amplifier with
`source and load attached.
`
`EXAMPLE 12.1: Calculate the voltage gain for an amplifier with the following pa(cid:173)
`rameters: A = 100, Rm = 100 kO., and Ro = 100 0., with Rs = 10 kO. and
`RL = 1000 0.. Express the result in dB.
`
`SOLUTION: Using Eq. {12.4)
`
`Av = 100 ( 10 k~~ ~~ kO. )( lOO ~°':\~ o,) = 82.6
`AvdB = 20 log IA vi = 20 log 182.61 = 38.3 dB
`
`*Author's note: Recall from Chapters 1 and 11 that v,, v0 , i2 and so on represent our signal voltages
`and currents and are generally functions of time: v,(t), v0 (t), i2(t). But whenever we do algebraic
`calculations of voltage gain, current gain, input resistance, output resistance, and so on, we must use
`pbasor representations of the individual signal components in our calculations: Vs, v0 , i2. Note that
`the signals v,(t), v0 (t), i2(t) may be composed of many individual signal components, one of which
`may be a de shift away from the Q-point value.
`
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`12.2 THE IDEAL OPERATIONAL AMPLIFIER
`
`491
`
`DiscussION: The amplifier's internal voltage gain capability is A = 100, but an over(cid:173)
`all gain of only 82.6 is being realized because a portion of the signal source voltage
`( = 9 percent) is being dropped across Rs and part of the internal amplifier voltage
`(Avid) (also= 9 percent) is being lost across R0 .
`♦
`
`The Ideal Differential Amplifier
`An ideal differential amplifier would produce an output that depends only on the volt(cid:173)
`age difference Did between its two input terminals, and this voltage would be independent
`of source and load resistances. Referring to Eq. (12.4), we see that this behavior can be
`achieved if the input resistance of the amplifier is infinite and the output resistance is zero
`(as pointed out previously in Sec. 11.5). For this case, Eq. (12.4) reduces to
`
`or
`
`Vo
`Av= -
`VicJ
`
`= A
`
`(12.5)
`
`and the full amplifier gain is realized. A is referred to as either the open-circuit voltage
`gain or open-loop gain of the amplifier and represents the maximum voltage gain available
`from the device.
`As also mentioned in Chapter 11, we often want to achieve the fully mismatched
`resistance condition in voltage amplifier applications (Rm >> Rs and Ro << RL), so that
`maximum voltage gain in Eq. (12.5) can be achieved. For the mismatched case, the overall
`amplifier gain is independent of the source and load resistances, and multiple amplifier
`stages can be cascaded without concern for interaction between stages.
`
`12.2 THE IDEAL OPERATIONAL AMPLIFIER
`As noted earlier, the term "operational amplifier" grew from use of these high-performance
`amplifiers to perform specific electronic circuit functions or operations, such as scaling,
`summation, and integration, in analog computers. The operational amplifier used in these
`applications is an ideal differential amplifier with an additional property: infinite voltage
`gain. Although it is impossible to realize the ideal operational amplifier, its conceptual use
`allows us to understand the basic performance to be expected from a given analog circuit
`and serves as a model to help in circuit design. Once the properties of the ideal amplifier
`and its use in basic circuits are understood, then various ideal assumptions can be removed
`in order to understand their effect on circuit performance.
`The ideal operational amplifier is a special case of the ideal difference amplifier in
`Fig. 12.3, in which Rm = oo, Ro = 0, and, most importantly, voltage gain A = oo. Infinite
`gain leads to the first of two assumptions used to analyze circuits containing ideal op amps.
`Solving for Yid in Eq. (12.5),
`
`Vo
`VicJ = -
`A
`
`and
`
`lim Yid= 0
`A---->oo
`
`(12.6)
`
`HA is infinite, then the input voltage Did will be zero for any finite output voltage. We will
`refer to this condition as Assumption 1 for ideal op-amp circuit analysis.
`An infinite value for the input resistance Rm forces the two input currents i+ and L
`to be zero, which will be Assumption 2 for analysis of ideal op-amp circuits. These two
`results, combined with Kirchhoff's voltage and current laws, form the basis for analysis of
`all ideal op-amp circuits.
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`14.3
`
`fuLLOWER ORCLITS---C.oMM0!'-1-CoLLECTOR AND CoMMO, -DRAIN AMPLIFIERS
`
`673
`
`The numeric results for the two specific amplifier cases are collected together in
`Table 14.2. The common-emitter and common-source amplifiers have similar voltage
`gains. The C-E amplifier approaches the Rd Rs limit (-6) more closely because gm Rs =
`29.4 for the BIT case, but only 0.982 for the MOSFET. The C-S amplifier provides ex(cid:173)
`tremely high input resistance, but that of the BIT amplifier is also substantial due to the
`µ, f Rs term. The output resistance of the C-E amplifier is also much higher than the C-S
`amplifier because µ, f is much larger for the BIT than for the FET. The input signal levels
`have been increased above the Rs = 0 case-again by a substantial amount in the BJT
`case. The current gains are identical to those of the individual transistors.
`
`,,,,,..
`
`T a b I e 14.2
`Common-Emitter/Common-Source Amplifier Comparison
`
`Voltage Gain
`Input Resistance
`Output Resistance
`Input Signal Range
`Current Gain
`
`C-E Amplifier
`
`C-S Amplifier
`
`-5.71
`313 k!l
`4.55 Mfi
`159 mV
`-100
`
`-4.46
`
`00
`
`442 k!l
`297 mV
`
`00
`
`14.3 FOLLOWER CIRCUITS-COMMON-COLLECTOR
`AND COMMON-DRAIN AMPLIFIERS
`We now consider a second class of amplifiers, the common-collector (C-C) and common(cid:173)
`drain (C-D) amplifiers, as represented by the ac equivalent circuits in Fig. 14.14. As in
`Sec. 14.2, the BIT circuit in Fig. 14.14(a) is analyzed first, and then the MOSFET circuit
`in Fig. 14.14(b) is treated as a special case with r7T -
`oo.
`
`1.96 kQ r
`
`0.981 u,
`
`7
`
`11.5 kQ
`
`(a)
`
`u"'
`
`-
`--
`
`(b)
`
`Rlh
`
`2kQ r
`
`0.998 u,
`
`R1N
`
`7
`
`Ro!IT
`
`10.7 kQ
`
`Figure 14.14 (a) ac Equivalent circuit for the C-C amplifier. (b) ac Equivalent circuit for the C-D
`amplifier.
`
`Voltage Gain
`The bipolar transistor in Fig. 14.14(a) is replaced by its small-signal model in Fig. 14.15
`(r O is again neglected). The output voltage v0 now appears across load resistor RL connected
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`67 4
`
`0-iAJ>TER 14 S INGLE-TRANSISTOR A\fPLIFIERS
`
`r,,
`
`+
`
`14.15 Small-signal
`Figure
`model for the C-C amplifier.
`
`to the emitter of the transistor and is equal to
`Vo = +(/3 o + l)iRL
`Current i is found from an expression similar to Eq. (14.7):
`Vtb = iRth + irr, + (/3 o + l )iRL = i[Rth + rr, + (/3 o + l)Ri]
`
`(14.38)
`
`(14.39)
`
`Combining Eqs. (14.38) and (14.39) yields an expression for the voltage gain of the C-C
`amplifier:
`
`(14.40)
`
`where the last approximation holds for large /3 0 • For gmRL >> 1, which is usually the case,
`AS~ = + 1
`1) in Eq. (14.40) yields the corresponding gain for the
`
`(14.41)
`
`co (and a 0 -
`Letting /3 0 -
`single FET amplifier:
`
`which again reduces to
`
`A CD _ 1
`Vth -
`
`(14.42)
`
`(14.43)
`
`for gmRL >> 1.
`The C-C and C-D amplifiers both have a gain that approaches 1. That is, the output
`voltage follows the input voltage, and the C-C and C-D amplifiers are often called emitter
`followers and source followers, respectively. In most cases, the BJT does a better job of
`achieving gmRL » 1 than does the FET, and the BJT gain is closer to unity than that of
`the FET. However, in both cases the value of voltage gain typically falls in the range of
`
`0.75:::; A vth:::; 1
`
`(14.44)
`
`Obviously, the gain in Eq. (14.43) is much less than the amplification factor µ, f , so ne(cid:173)
`glecting r0 in the model of Fig. 14.15 is valid, unless the FET is operating at very high
`currents.
`
`EXAMPLE 14.3: Calculate the gain of the C-C and C-D amplifiers using Eqs. (14.40)
`and (14.42) and the parameter values from Example 14.1.
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