`
`
`
`Design of Analog CMOS
`Integrated Circuits
`
`Behzad Razavi
`Professor of Electrical Engineering
`University of California, Los Angeles
`
`
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`ay
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`Boston Burr Ridge, IL Dubuque, [A Madison, WI
`New York San Francisco St. Louis
`Bangkok Bogoté Caracas Lisbon London Madrid Mexico City
`Milan New Delhi Seoul Singapore Sydney Taipei Toronto
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`INTEL 1224
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`INTEL 1224
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`McGraw-Hill Higher Education 39
`
`A Division of TheMcGraw-Hill Companies
`
`DESIGN OF ANALOG CMOSINTEGRATED CIRCUITS
`Published by McGraw-Hill, an imprint of The McGraw-Hill Companies, Inc, 1221 Avenue of the Americas,
`New York, NY, 10020. Copyright © 2001, by The McGraw-Hill Companies, Inc. All rights reserved. no part of
`this publication may be reproducedordistributed in any form or by any means, or stored in a databaseorretrieval
`system, without the prior written consent of The McGraw-Hill Companies,Inc., including, but notlimited to, in
`any networkor otherelectronic storage or transmission, or broadcast for distance learning.
`Someancillaries, including electronic and print components, maynotbe available to customers outside the United
`States.
`
`This bookis printed on acid-free paper.
`
`34567890 FGRFGR 0987654321
`
`ISBN O0-07-234035e-e2
`
`Vice president/Editor-in-chief: Kevin T. Kane
`Publisher: Thomas Casson
`Sponsoring editor: Catherine Fields
`Developmentaleditor: Michelle L. Flomenhoft
`Senior marketing manager: John 7. Wannemacher
`Project manager: Jim Labeots
`Production supervisor: Gina Hangos
`Senior designer: Kiera Cunningham
`New media: Phillip Meek
`Compositor: Interactive Composition Corporation
`Typeface: 10/12 Times Roman
`Printer: Quebecor World Fairfield
`
`Library of Congress Cataloging-in-Publication Data
`
`Razavi, Behzad.
`Design of analog CMOSintegratedcircuits / Behzad Razavi.
`p. cm.
`ISBN 0-07-238032-2 (alk. paper)
`1, Linear integrated circuits—Design and construction. 2. Metal oxide semiconductors,
`Complementary. I. Title.
`
`TK7874,654. R39 2001
`621.39'732-de21
`
`00-044789
`
`ii
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`MOSIV Characteristics
`
`21
`
`
`Sec, 2.2 $1
`
`— . oe|c> lo
`
`
`
`wl c> b,
`°
`ly
`l
`
`Figure 2.17 Saturated MOSFETs operating as current sources,
`
`With the approximation L ~ L/, a Saturated MOSFETcan be used as a current source
`connected between the drain and the source (Fig. 2.17), an important componentin analog
`design. Note that the current sources inject current into ground ordraw current from Vpp.
`In other words, only one terminal of each current sourceis “floating.”
`Since a MOSFEToperating in saturation produces a current in response to its gate-
`source overdrive voltage, we maydefine a figure of merit that indicates how well a device
`converts a voltage to a current, More specifically, since in processing signals we deal with
`the changes in voltages and currents, we definethe figure ofmerit as the change in the drain
`current divided by the change in the gate-source voltage. Called the “transconductance”
`and denoted byg,,, this quantity is expressed as:
`
`&m =
`
`(2.16)
`
` aIp
`aVes VDS,const.
`Ww
`i LnCox 7Ves =! Vig).
`(2.17)
`Ina sense, &m represents the sensitivity of the device: fora high gm, a small change in
`Vas results in a large change in Jp. Interestingly, 8min the saturation region is equalto the
`inverse of R,, in deep triode region.
`The reader can provethat g,, can also be expressed as
`
`é
`
`8m = y2a Cox = Ip
`
`2Ip
`= :
`Ves — Vru
`
`.
`
`i,
`
`(2.18)
`
`2.19
`el)
`
`Plotted in Fig. 2,18, each of the above expressions provesuseful in studying the behavior
`of g», as a function of one parameter while other parameters remain constant. For example,
`(2.17) suggests that g,, increases with the overdrive if W/L is constant whereas (2,19) im-
`
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`plies that g,,, decreases with the overdrive if Ip is constant. The conceptoftransconductance
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`Chap.2
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`Basic MOSDevice Physics
`
`Ves—VrH
`W/L Constant
`
`Ip
`
`W/L Constant
`
`Vas~ “ru
`Ip Constant
`
`Figure 2.18 MOStransconductanceas a function of overdrive and drain current.
`can also be applied to a device operating in the triode region,as illustrated in the following
`example.
`
`
`
`
`Example 2.2 eR
`For the arrangement shownin Fig. 2.19, plot the transconductanceas a function of Vps.
`
`'
`
`Im
`
`
`Vo- Vou
`Vos
`
`Figure 2.19
`
`Solution
`It is simpler to study gy, as Vos decreases from infinity. So long as Vps = Vp — Vru, My is in
`saturation, Ip is relatively constant, and, from (2.18), so is gm. For Vps < Vp — Vero, Myis in the
`triode region and:
`
` a
`
`fi
`
`Ww
`
`4
`
`(2.20)
`8m = a0; {FenCorr [2Ves ~ Vru)Vps — vs]
`Ww
`(2.21)
`= Un Cox Vos.
`Thus, as plotted in Fig. 2.19, the transconductance drops if the device enters the triode region. For
`amplification, therefore, we usually employ MOSFETsin saturation.
`ser
`sei
`——— EE ae
`cis
`
`The distinction between saturation and triode regions can be confusing,especially for
`PMOSdevices.Intuitively, we note that the channel is pinched off if the difference between
`the gate and drain voltagesis not sufficient to create an inversion layer. As depicted concep-
`tually in Fig. 2.20, as Vg — Vp of an NFET drops below Vru, pinch-off occurs. Similarly,
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`:
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`We now re-examine Eq. (2.18) for the transconductance of a MOSdevice operating in
`the subthreshold region.Is it possible to achieve an arbitrarily high transconductance by
`increasing W while maintaining Ip constant?Is it possible to obtain a higher transconduc-
`tance than thatof a bipolar transistor (Ic/ Vr) biased at the same current? Equation (2.18)
`was derived from the square-law characteristics Ip = (1 /2)Un Cox(W/L)Ves — Vruy.
`
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`However, if W increases while Jp remains constant, then Ves —> Vry and the device enters
`
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`the subthreshold region. As a result, the transconductanceis calculated from (2.30) to be
`
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`8m = Ip/(¢ Vr), revealing that MOSFETsareinferior to bipolar transistors in this respect.
`
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`The exponential dependence of Ip upon Vgs in subthreshold operation may suggest
`
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`the use of MOSdevices in this regime so as to achieve a higher gain. However, since
`such conditions are met by only a large device width or low drain current, the speed of
`
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`subthreshold circuits is severely limited,
`,
`
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`Voltage Limitations MOSFETsexperience various breakdowneffects if their terminal
`
`
`voltage differences exceedcertainlimits. At high gate-source voltages,the gate oxide breaks
`
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`downirreversibly, damaging thetransistor. In short-channel devices, an excessively large
`
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`drain-source voltage widensthe depletion region aroundthe drain so muchthatit touchesthat ,
`
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`around the source,creating a very large drain current. (This effectis called “punchthrough.”)
`
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`Otherlimitations relate to “hot electron effects” and are described in Chapter 16.
`
`
`2.4 MOS Device Models
`
`
`2.4.1 MOS Device Layout
`
`
`Forthe developments in subsequentsections,it is beneficial to have some understanding of
`the layout of a MOSFET. We describe only a simple view here, deferring the fabrication
`
`
`details and structural subtleties to Chapters 17 and18.
`
`
`The layout of a MOSFETis determined by both the electrical properties required ofthe
`
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`device in the circuit and the “design rules” imposed by the technology. For example, W/L
`
`
`is chosen to set the transconductanceor other circuit parameters, while the minimum L is
`
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`dictated by the process. In addition to the gate, the source and drain areas must be defined
`
`
`properly as well.
`
`
`Shown in Fig. 2.28 are the “bird eye’s view” and the top view of a MOSFET.The gate
`
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`polysilicon and the source and drain terminals are typically tied to metal (aluminum) wires
`
`
`that serve as interconnects with low resistance and capacitance. To accomplish this, one or
`more “contact windows” must be opened in each region,filled with metal, and connected
`
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`to the upper metal wires. Note that the gate poly extends beyondthe channel area by some
`
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`amountto ensure reliable definition of the “edge”of the transistor.
`The source and drain junctions play an importantrole in the performance. To minimize
`
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`the capacitance of S and D,thetotal area of each junction must be minimized. We see from
`
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`Fig. 2.28 that one dimension of the junctions is equal to W. The other dimension must
`
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`be large enough to accommodate the contact windowsandis specified by the technology
`
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`design rules.’
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`TThis dimensionis typically three to four times the minimum allowable channellength.
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`Chap.2
`
`Basic MOS Device Physics
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`

`Chapter 3
`
`Single-Stage Amplifiers
`
`eee
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`47
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`Amplificationis an essential functionin most analog (and manydigital) circuits. We amplify
`an analogor digital signal becauseit may be too small to drive a load, overcomethe noise
`of a subsequentstage, or provide logicallevels to a digital circuit. Amplification also plays
`a critical role in feedback systems (Chapter8).
`In this chapter, we study the low-frequency behavior of single-stage CMOSamplifiers.
`Analyzing both the large-signal and the small-signal characteristics of each circuit, we
`developintuitive techniques and models that prove useful in understanding more complex
`systems. An important part of a designer’s job is to use proper approximations so as to
`create a simple mental picture of a complicated circuit. The intuition thus gained makes
`it possible to formulate the behavior of mostcircuits by inspection rather than by lengthy
`calculations.
`Following a brief review of basic concepts, we describe in this chapter four types of
`amplifiers: common-source and common-gate topologies, source followers, and cascode
`configurations. In each case, we begin with a simple model and gradually add second-order
`phenomenasuchas channel-length modulation and body effect.
`
`3.1 Basic Concepts
`The input-output characteristic of an amplifier is generally a nonlinear function (Fig. 3.1)
`that can be approximated by a polynomial over some signal range:
`(3.1)
`Y(E)
`Oi + OyX(t) + Orx7(E) + bax") x1 <x S x2,
`The input and output may be current or voltage quantities, For a sufficiently narrow range
`of x,
`
`(3.2)
`y(t) © a + ax(t),
`where ao can be considered the operating (bias) point and a, the small-signal gain. So
`long as ax(t) < ai, the bias point is disturbed negligibly, (3.2) provides a reasonable
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`

`

`Chap. 3
`
`Single-Stage Amplifiers
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`x4
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`Xg
`
`x
`
`Input-output characteristic
`Figure 3.1
`of a nonlinear system.
`
`Noise <>Linearity
`
`approximation, and higher order terms are insignificant. In other words, Ay = oAx,
`indicating a linear relationship between the increments at the input and output. As x(t)
`increases in magnitude, higher order terms manifest themselves, leading to nonlinearity
`and necessitating large-signal analysis. From another point of view, if the slope of the
`characteristic (the incremental gain) varies with the signallevel, then the system is nonlinear.
`These concepts are described in detail in Chapter 13.
`Whataspects of the performanceof an amplifier are important? In addition to gain and
`speed, such parameters as power dissipation, supply voltage,linearity, noise, or maximum
`voltage swings may be important. Furthermore, the input and output impedancesdetermine
`how the circuit interacts with preceding and subsequentstages. In practice, most of these
`parameters trade with each other, making the design a multi-dimensional optimization
`problem.Illustrated in the “analog design octagon”ofFig. 3.2, such trade-offs present many
`challenges in the design ofhigh-performance amplifiers, requiring intuition and experience
`to arrive at an acceptable compromise.
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`Input/Output 7". |
`Impedance
`oss
`
`Voltage
`
`Voltage
`Speed<i——6,
`wings
`
`i
`.
`Figure 3.2 Analog design octagon.
`
`3.2 Common-Source Stage
`
`3.2.1 Common-Source Stage with Resistive Load
`Byvirtue ofits transconductance, a MOSFET converts variations in its gate-source voltage
`to a small-signal drain current, which can pass through a resistor to generate an output
`voltage. Shownin Fig. 3.3(a), the common-source (CS) stage performs such an operation.
`
`

`

`Vout = Vpp _- RozMa Cox [2(Vin - Vri)Vout _ Vout| .
`
`1
`Ww
`(3.3)
`Vout = Vpp _~ Ro 5bn Cox >Vin _ Vern)’,
`where channel-length modulationis neglected. With furtherincreasein V;,,, Vout drops more
`and the transistor continues to operate in saturation until Viz exceeds Voy1 by Vry [point A
`in Fig. 3.3(b)]. At this point,
`
`Sec. 3.2|Common-Source Stage
`
`
`
`Figure 3.3 (a) Common-sourcestage, (b) input-output characteristic, (c) equivalent
`circuit in deep triode region, (d) small-signal modelforthe saturation region.
`
`Westudy both the large-signal and the small-signal behavior of the circuit. Note that the
`input impedanceofthecircuit is very high at low frequencies,
`If the input voltage increases from zero, M;is off and Voy, = Vpp [Fig. 3.3(b)]. As Vin
`approaches Vr, M, beginsto turn on, drawing current from Rp and lowering Vou. If Vop
`is not excessively low, M, turns on in saturation, and we have
`
`(3.4)
`
`Vint ~ Vru = Vop ~— Rp anCox =(Vint - Vrn)’,
`from which V;,; — Vry and hence Vou can be calculated.
`For Vin > Vinj, M;, is in the triode region:
`
`1
`
`Ww
`
`1
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`Ww
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`i
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`254
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`Chap. 8
`
`Feedback
`
`Sec. €
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`Now suppose we apply feedback to the amplifier such that the gain and bandwidth are
`modified to 10 and 100 MHz,respectively. Placing two of these amplifiers in a cascade
`[Fig. 8.10(b)], we obtain a much faster response with an overall gain of 100. Ofcourse,
`the cascade consumes twice as much power, but it would be quite difficult to achieve this
`performancebythe original amplifier evenif its power dissipation were doubled,
`Nonlinearity Reduction A very important property of negative feedback is the sup-
`pression of nonlinearity in analog circuits. We defer the study ofthis effect to Chapter 13,
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`8.1.2 Types of Amplifiers
`Most ofthe circuits studied thus far can be considered “voltage amplifiers” because they
`sense a voltage at the input and produceavoltage at the output. However, three other
`types of amplifiers can also be constructed suchthat they sense or produce currents. Shown
`in Fig. 8.11, the four configurations have quite different properties: (1) circuits sensing
`
`Transimpedance Amp.
`fin
`
`Transconductance Amp.
`out
`
`Current Amp.
`fin
`Tout
`
`+
`Vout
`
`+
`+
`A Vout
`
`! in
`
`+
`Vin
`
`+
`Vin
`
`! out
`
`!in
`
`I out
`
`Voltage Amp.
`
` .
`
`+
`Vout
`
`+
`Vin
`
`(a)
`
`(b)
`
`(c)
`
`(d)
`
`Figure 8.11 Types of amplifiers along with their idealized models,
`
`a voltage must exhibit a high input impedance (as a voltmeter) whereas those sensing a
`current must provide a low input impedance(as a current meter); (2) circuits generating a
`voltage must exhibit a low output impedance(as a voltage source) while those generating
`a current must provide a high output impedance(as a current source), Note that the gains
`of transimpedance and transconductance‘ amplifiers have a dimension of resistance and
`conductance, respectively, For example, a transimpedance amplifier may have a gain of
`2 kQ, which meansit produces a 2-V output in response to a 1-mA input. Also, we use the
`sign conventions depicted in Fig. 8.11, for example, the transimpedance Ro = Voy;/Tin if
`Tin flows into the amplifier.
`
`“This terminologyis standard but not consistent. One shoulduse either transimpedance and transadmittance
`or transresistance and transconductance.
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`

`

`General Considerations
`
`255
`
`Vop
`
`R
`
`8 V
`
`out
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`V;
`
`ino—Th My
`
`=
`
`(a)
`
`Vop
`
`R
`
`out
`
`e V
`<|K-° Vp
`
`M,
`
`I in
`
`(b)
`
`lout
`ino My
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`2
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`V;
`
`(c)
`
`lout
`M }- Vb
`1
`
`:
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`in
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`(d)
`
` Sec. 8.1
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`
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`(c)
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`(d)
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`Figure 8.13 Fourtypes of amplifiers with improved performance.
`
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`Figure 8.12 Simple implementations offour types of amplifiers.
`
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`In Fig. 8.12(a), a
`Figure 8,12 illustrates simple implementations of each amplifier.
`common-source stage senses and produces voltages and in Fig. 8.12(b), a common-gate
`circuit serves as a transimpedance amplifier, converting the source current to a voltage
`at the drain. In Fig. 8.12(c), a common-source transistor operates as a transconductance
`amplifier, generating an output current in response to an input voltage, and in Fig. 8.12(d),
`a common-gate device senses and producescurrents,
`Thecircuits ofFig. 8.12 maynotprovide adequate performancein manyapplications. For
`example,the circuits of Figs. 8.12(a) and (b) sufferfromarelatively high output impedance.
`Fig. 8.13 depicts modifications that alter the output impedance orincrease the gain,
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`256
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`Chap.8
`
`Feedback
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`Sec. 8.1
`
`G
`
`OC)CS
`Calculate the gain of the transconductance amplifier shown in Fig. 8.13(c).
`
`Solution
`
`The gainin this case is defined as Gy, = Inu: / Vin. Thatis,
`
`(8.22)
` SRE
`
`_ Vx Tout
`Vin
`Vx
`= —gmi(roillRp) « 8m.
`
`Gm
`
`While most familiar amplifiers are of voltage-voltage type, the other three configura-
`tions do find usage. For example, transimpedance amplifiers are an integral part of optical
`fiber receivers because they mustsense the current produced by a photodiode, eventually
`generating a voltage that can be processed by subsequentcircuits.
`
`8.1.3 Sense and Return Mechanisms
`
`Placing a circuit in a feedback loop requires sensing the output signal and returning (a
`fraction) of the result to the summing nodeat the input. With voltage or current quantities
`as input and outputsignals, we can identify four types of feedback: voltage-voltage, voltage-
`current, current-current, and current-voltage, where the first entry in each case denotes the
`quantity sensed at the output and the second the type of signal returned to the input.>
`It is instructive to review methods of sensing and summingvoltagesor currents. To sense
`a voltage, we place a voltmeterin parallel with the corresponding port [Fig. 8.14(a)], ideally
`introducing no loading. When usedin a feedback system,this type of sensing is also called
`“shunt feedback.”
`
`Coos
`
`Vino
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`
`
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`
`
`
`
`
`
`i out
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`! out
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`a@Voltmeter Ry, Ry
`
`
`
`(a)
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`(b)
`
`Current Meter
`
`~ Vs +
`
`(c)
`
`Figure 8.14 Sensing(a) a voltage by a voltmeter, (b) a current by a current meter, (c) a current by
`a small resistor.
`
`To sense a current, a current meter is inserted in series with the signal [Fig. 8.14(b)],
`ideally exhibiting zero series resistance. Thus, this type of sensing is also called “series
`feedback.” In practice, a small resistor replaces the current meter [Fig. 8.14(c)], with the
`voltage drop across the resistor serving as a measure of the output current.
`The addition of the feedback signal and the input signal can be performed in the voltage
`domain or current domain. To add two quantities, we place them in series if they are
`
`5Different authors use different orders or terminologies for the four types of feedback.
`
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`Sec. 8.4
`
`General Considerations
`
`257
`
`i
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`Figure 8.15 Addition of (a) voltages
`and (b) currents,
`(b)
`{a)
`voltages and in parallelifthey are currents (Fig, 8,15
`the operation of the open-loop amplifier itself, the feedback networkin reality introduces
`
`out
`(c)
`
`(a)
`
`(b)
`
`(h)
`(g)
`Figure 8.16 Practical means ofsensing and adding voltages and currents,
`
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`