Design of Analog CMOS
`Integrated Circuits
`
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`
`
`Behzad Razavi
`
`Professor of Electrical Engineering
`University of California, Los Angeles
`
`
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`fifw
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`Boston Burr Ridge, IL Dubuque, IA Madison, WI
`New York San Francisco St. Louis
`Bangkok Bogota 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 fig
`A Division of TheMcGraw-Hill Companies
`
`DESIGN OF ANALOG CMOS INTEGRATED 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 reproduced or distributed in any form or by any means, or stored in a database or retrieval
`system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in
`any network or other electronic storage or transmission, or broadcast for distance learning.
`Some ancillaries, including electronic and print components, may not be available to customers outside the United
`States.
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`This book is printed on acid-free paper.
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`34567890 FGR/FGR 0987654321
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`ISBN 0-07-236038-2
`
`Vice president/Editor-in-chief: Kevin T Kane
`Publisher: Thomas Carson
`
`Sponsoring editor: Catherine Fields
`Developmental editor: Michelle L. Flomenhoft
`Senior marketing manager: John T Wannemacher
`Project manager: Jim Labeots
`Production supervisor: Gina Hangar
`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 CMOS integrated circuits IBehzad Razavi.
`p. cm.
`ISBN 0-07—238032-2 (alk. paper)
`1. Linear integrated circuits—Design and construction. 2. Metal oxide semiconductors,
`Complementary. I. Title.
`
`TK’7874.654. R39 2001
`621.39'732~dc21
`
`00-044789
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`ii
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` Sec. 2.2 M08 IN Characteristics
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`21
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`51
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`p
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`V013
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`V013
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`1
`Vb H E>
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`I 1
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`I 2
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`Figure 2.17 Saturated MOSFETs operating as current sources.
`
`
`
`
`-
`
`(2.16)
`
`(2.17)
`
`
`
`
`8 ID
`
`gm =
`
`‘
`
`.)
`2
`e’
`:8
`al
`to
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`n
`I]
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`0
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`t
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`f'
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`f
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`~
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`With the approximation L W L’, a saturated MOSFET can be used as a current source
`connected between the drain and the source (Fig. 2.17), an important component in analog
`design. Note thatthe current sources inject current into ground or draw current from VDD.
`In other words, only one terminal of each current source is “floating.”
`Since a MOSFET operating in saturation produces a current in response to its gate—
`source overdrive voltage, we may define 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 by gm, this quantity is expressed as:
`
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`_
`aVGS VDS,const.
`W
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`= Meal—(Va —— VTH).
`
`In a sense, gm represents the sensitivity of the device: for a high g,,,, a small change in
`VGs results in a large change in ID. Interestingly, gm in the saturation region is equal to the
`inverse of R0,, in deep triode region.
`The reader can prove that g,,, can also be expressed as
`
`.
`
`,
`
`W
`.
`gm : VZMMCaxZ'ID
`
`21
`'
`,
`D
`VGs ‘* VTH '
`
`=
`
`.
`
`,
`
`(2.18)
`
`.
`(2.19)
`
`
`
`
`
`Plotted in Fig. 2.18, each of the above expressions proves useful in studying the behavior
`of g,,, as a function of one parameter while other parameters remain constant. For example,
`(2.17) suggests that gm increases with the overdrive if W/L is constant whereas (2.19) im—
`plies that g,,, decreases with the overdrive if ID is constant. The concept of transconductance
`
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`Chap. 2
`
`Basic MOS Device Physics
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`gm
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`Vcs — VTH
`W/L Constant
`
`ID
`
`WIL Constant
`
`Ves ‘ VTH
`I D Constant
`
`Figure 2.18 MOS transconductance as 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 W a
`L L m m
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`
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`For the arrangement shown in Fig. 2.19, plot the transconductance as a function of VDS.
`
`
`Vb " VTH
`Vos
`
`Figure 2.19
`
`SolutiOn
`It is simpler to study gm as VDS decreases from infinity. So long as VDS Z V}, — VTH, M1 is in
`saturation, ID is relatively constant, and, from (2.18), so is gm. For VDS < Vb - VTH, M1 is in the
`triode region and:
`
` a
`gm = 6sz {Ewan-f [was — Vrvas — V33”
`
`W
`
`i
`
`W
`: MnCox’L‘ VDS-
`
`(2.20)
`
`(2.21)
`
`Thus, as plotted in Fig. 2.19, the transconductance drops if the device enters the triode region. For
`amplification, therefore, we usually employ MOSFETs in saturation.
`w
`w
`- ML Lam-
`t
`,__.
`1‘! W
`
`M
`
`The distinction between saturation and triode regions can be confusing, especially for
`PMOS devices. Intuitively, we note that the channel is pinched off if the difference between
`the gate and drain voltages is not sufficient to create an inversion layer. As depicted concep—
`tually in Fig. 2.20, as VG — VD of an NFET drops below VTH, pinch-off occurs. Similarly,
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`i
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`ii1s
`!g
`li1,
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`i111i
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`Chap. 2
`
`Basic MOS Device Physics
`
`We now re—~examine Eq. (2.18) for the transconductance of a MOS device operating in
`the subthreshold region. Is it possible to achieve an arbitrarily high transconductance by
`increasing W while maintaining ID constant? Is it possible to obtain a higher transconduc—
`tance than that of a bipolar transistor (Ic/ VT) biased at the same current? Equation (2. 18)
`was derived from the square—-law characteristics ID ———(1/2)u,, Cox(W/L)(VGS — VTH)?
`However, if W1ncreases while ID remains constant, then VGS ——> VTH and the device enters
`the subthreshold region. As a result, the transconductance is calculated from (2.30) to be
`gm = ID /(C VT), revealing that MOSFETs are inferior to bipolar transistors in this respect.
`The exponential dependence of ID upon VGS in subthreshold operation may suggest
`the use of MOS devices in this regime so as to achieve a higher gain. However, since
`such cenditions are met by only a large device width or low drain current, the speed of
`subthreshold Circuits is severely limited.
`'
`
`Voltage Limitations MOSFETS experience various breakdown effects if their terminal
`voltage differences exceed certain limits. At high gate~source voltages, the gate oxide breaks
`down irreversibly, damaging the transistor. In short~channel devices, an excessively large
`drain—source voltage widens the depletion region around the drain so much that it touches that '
`around the source, creating a very large drain current. (This effect is called “punchthrough.”)
`Other limitations relate to “hot electron effects” and are described in Chapter 16.
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`2.4 MOS Device Models
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`
`2.4.1 MOS Device Layout
`
`
`For the developments in subsequent sections, 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 and 18.
`‘
`
`
`The layout of a MOSFETis determined by both the electrical properties required of the
`
`
`device1n the circuit and the “design rules” imposed by the technology. For example, W/L
`
`
`is chosen to set the transconductance or othe1 circuit parameters, while the minimum L1s
`
`
`dictated by the process. In addition to the gate, the source and drain areas must be defined
`
`
`properly as well.
`
`
`Shown'1n Fig. 2.28 are the “bird eye’s View” and the top view of a MOSFET. The gate
`
`
`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 opened1n each region, filled with metal, and connected
`
`
`to the upper metal wires. Note that the gate poly extends beyond the channel area by some
`
`
`amount to ensure reliable definition of the “edge” of the transistor.
`The source and drain junctions play an important rolein the performance To minimize
`
`
`the capacitance of S and D, the total area of each junction must be minimized. We see from
`
`
`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 windows and is specified by the technology
`
`design rules.7
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`
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`7This dimension is typically three to four times the minimum allowable channel length.
`
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`

`

`WWwemWW
`
`Amplification is an essential function in most analog (and many digital) circuits. We amplify
`an analog or digital signal because it may be too small to drive a load, overcome the noise
`of a subsequent stage, or provide logical levels to a digital circuit. Amplification also plays
`a critical role in feedback systems (Chapter 8).
`In this chapter, we study the low~frequency behavior of single-stage CMOS amplifiers.
`Analyzing both the large—signal and the small—signal characteristics of each circuit, we
`develop intuitive techniques and models that prove useful in nude
`systems. An important part of a designer’s job is to use proper
`create a simple mental picture of a complicated circuit. The intuition thus gained makes
`it possible to formulate the behavior of most circuits 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
`phenomena such as channel-length modulation and body effect.
`
`Single-Sz‘age Amplifiers
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`“N
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`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:
`
`y(t) *5 a0 + 051260) + 0122620) + -
`
`'
`
`- + a,.X"(t)
`
`x1 5 x 5 x2.
`
`(31)
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`The input and output may be current or voltage quantities. For a sufficiently narrow range
`of x,
`
`W) % Olo + a1x(t),
`
`(3.2)
`
`where 010 can be considered the operating (bias) point and 011 the small-signal gain. So
`long as w1x(t) << 050, the bias point is disturbed negligibly, (3.2) provides a reasonable
`47
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`

`

`Chap. 3
`
`Single-Stage Amplifiers
`
`Input—output characteristic
`Figure 3.1
`of a nonlinear system.
`
`Noise <——~—>Linearity
`
`\ .
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`Dissipation
`‘\ ~
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`‘\ NN s
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`‘~
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`Input/Output ,,,,,"mg ‘
`Impedance
`' “ ~
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`approximation, and higher order terms are insignificant. In other words, Ay = ale,
`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 signal level, then the system is nonlinear.
`These concepts are described in detail in Chapter 13.
`What aspects of the performance of 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 impedances determine
`how the circuit interacts with preceding and subsequent stages. 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 of high—performance amplifiers, requiring intuition and experience
`to arrive at an acceptable compromise.
`
`
`
`Voltage
`SpeedHSwings
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`Figure 3.2 Analog design octagon.
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`3.2 Common-Source Stage
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`3.2.1 Common-Source Stage with Resistive Load
`By virtue of its 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. Shown in Fig. 3.3(a), the common-source (CS) stage performs such an operation.
`
`

`

`Sec. 3.2
`
`Common-Source Stage
`
`
`
`Van! = VDD * RD‘Z‘MnCox'Z [2(Vin “ VTH)Vout " Vozur] -
`
`We study both the large—signal and the small—signal behavior of the circuit. Note that the
`input impedance of the circuit is very high at low frequencies.
`If the input voltage increases from zero, M1 is off and V0“, = VDD [Fig 3.3(b)]. As Vin
`approaches VTH, M1 begins to turn on, drawing current from RD and lowering Vow. If VDD
`is not excessively low, M1 turns on in saturation, and we have
`
`Figure 3.3 (a) Common-source stage, (b) input—output characteristic, (0) equivalent
`circuit in deep triode region, ((1) small-signal model for the saturation region.
`
`(d)
`
`1
`W
`Vaur = VDD _ RD'Z‘IJIMCon‘U/in "‘ VTH)2:
`
`(3-3)
`
`where channel-length modulation is neglected. With further increase in Vin, Va”, drops more
`and the transistor continues to operate in saturation until Vi" exceeds Va", by VTH [point A
`in Fig. 3.3(b)]. At this point,
`
`1
`W
`Vinl " VTH = VDD “ RD'Z‘MnCax‘fU/inl “ VTH)2,
`
`(3-4)
`
`from which Vim —— VTH and hence Va“, can be calculated.
`For Vin > Vin 1, M1 is in the tn'ode region:
`
`1
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`W
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`

`

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`;
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`254
`
`Chap. 8
`
`Feedback
`
`Sec. E
`
`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. Of course,
`the cascade consumes twice as much power, but it would be quite difficult to achieve this
`performance by the original amplifier even if 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 of this effect to Chapter 13.
`
`8.1.2 Types of Amplifiers
`
`Most of the circuits studied thus far can be considered “voltage amplifiers” because they
`sense a voltage at the input and produce a voltage at the output. However, three other
`types of amplifiers can also be constructed such that they sense or produce c'urrents. Shown
`in Fig. 8.11, the four configurations have quite different properties: (1) circuits sensing
`
`Voltage Amp.
`
`Transimpedance Amp.
`
`Transconductance Amp.
`
`Current Amp.
`
`
`
`[in
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`[out
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`[In
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`[out
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`+
`
`Vout
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`+
`
`Vin
`
`”—1—;
`
`_—“T‘—‘
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`—T‘—“—
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`I in
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`I out
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`[in
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`I out
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`+
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`+
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`_ Vout
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`+
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`Vm
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`(b)
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`(C)
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`(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 transconductance4 amplifiers have a dimension of resistance and
`conductance, respectively. For example, a transimpedance amplifier may have a gain of
`2 k9, which means it produces a 2—V output in response to a l-mA input. Also, we use the
`sign conventions depicted in Fig. 8.11, for example, the transimpedance R0 = Vow/Ii" if
`[in flews into the amplifier.
`
`4This terminology is standard but not consistent. One should use either transimpedance and transadmittance
`or transresistance and transconductance.
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`

`General Considerations
`
`255
`
`V00
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`V00
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`V-
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`"1H M1
`
`R
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`F!
`
`D V
`out
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`[.4vb
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`D V
`out
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`M1
`
`I in
`
`(b)
`
`=
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`(a)
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`"‘°"‘| M1
`
`IOU!
`
`:'
`
`V
`
`[out
`|-—-G Vb
`
`1, I
`
`M
`
`1
`
`in
`
`(C)
`
`(d)
`
`
`
`
`Figure 8.12 Simple implementations of four types of amplifiers.
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`
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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(0), 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 produces currents.
`The circuits of Fig. 8.12 may not provide adequate performance in many applications. For
`example, the circuits of Figs. 8.12(a) and (b) suffer from a relatively high output impedance.
`Fig. 8.13 depicts modifications that alter the output impedance or increase the gain.
`
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` Sec. 8.1
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`(C)
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`(d)
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`Figure 8.13 Four types of amplifiers with improved performance.
`
`

`

`
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` iiiiiiat
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`256
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`
`
`Chap. 8
`
`Feedback
`
`Sec. 8.1
`
`G
`
`Example 8.1
`
`.
`
`
`Calculate the gain of the transconductance amplifier shown in Fig. 8.13(c).
`
`Solution
`
`The gain in this case is defined as G,n = ID,“ / Vin. That is,
`
`
`Ian!
`__ Xi
`G _
`VX
`Vin
`m
`[I
`
`“81221(r01i|RD)'gInZ-
`
`
`(822)
`
`_
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`_
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`Vlno—w
`
`
`
`
`
`.awareness,1,a
`
`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 must sense the current produced by a photodiode, eventually
`generating a voltage that can be processed by subsequent circuits.
`
`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 node at the input. With voltage or current quantities
`as input and output signals, 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.5
`It is instructive to review methods of sensing and summing voltages or currents. To sense
`a voltage, we place a voltmeter in parallel with the corresponding port [Fig. 8. l4(a)], ideally
`introducing no loading. When used in a feedback system, this type of sensing is also called
`“shunt feedbac .”
`
`I out
`
`I out
`
`E0 Voltmeter
`
`RL
`
`Current Meter
`
`HL
`
`(a)
`
`(b)
`
`(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.
`
`
`
`

`

`
`
`k
`
`Sec. 8.1
`
`General Considerations
`
`257
`
`
`
`Figure 8.15 Addition of
`and (b) cun‘ents.
`
`(a) voltages
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