i |
`
`| Design of Analog CMOS
`it
`3
`;
`hI
`Integrated Circuits
`
`
`
`
`
`it
`i |
`Wt
`
`Behzad Razavi
`
`|
`
`|
`
`|—
`
`Intel 1441
`TTA
`Intel v. Qualcomm
`Intel v. Qualcomm
`NaePL
`IPR2019-00129
`
`
`
`| Design of Analog CMOS
`it
`3
`;
`hI
`Integrated Circuits
`
`
`
`
`
`it
`i |
`Wt
`
`Behzad Razavi
`
`|
`
`|
`
`|—
`
`Intel 1441
`TTA
`Intel v. Qualcomm
`Intel v. Qualcomm
`NaePL
`IPR2019-00129
`
`
`
`
`
`McGraw-Hill Higher Education 5g
`A Division ofTheMcGrawHill 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 orretrieval
`
`
`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 broadcastfor distance learning.
`
`Some Ancillaries, including electronic and print components, maynotbe available to customersoutside the United
`States.
`
`This book is printed on acid-free paper.
`
`1234567890 FGR/FGR 909876543210
`
`
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`
`
`Razavi, Behzad.
`Design of analog CMOS integrated circuits / 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.
`
`
`00-044789
`
`ISBN 0-07-238032-2
`
`Vice president/Editor-in-chief: Kevin T. Kane
`Publisher: Thomas Casson
`Sponsoring editor: Catherine Fields
`Developmentaleditor: Michelle L. Flomenhoft
`Senior marketing manager: John T. Wannemacher
`Project manager: Jim Labeots
`Production supervisor: Gina Hangos
`Senior designer: Kierd Cunningham
`New media: Phillip Meek
`Compositor: Interactive Composition Corporation
`Typeface: [0/12 Times Roman
`Printer: Quebecor Printing Book Company/Fairfield
`
`Library of Congress Cataloging-in-Publication Data
`
`TK7874.654. R39 2001
`621.39'732-de21
`
`
`
`tage Amplifiers
`
`sec. 3.5
`
`Cascode Stage
`
`88
`
` Figure 3.49
`
`t re- Figure 3.50 Cascodestage.a
`
`The output impedanceis simply equalto
`
`Rout = {L1 + (gm + 8mbrolRp + ro}llRo.
`
`(3.116)
`
`(3.114)
`
`3.5 Cascode Stage
`As mentioned in Example 3.10 the input signal of a common-gate stage may bea current.
`Wealso knowthata transistor in a common-source arrangement converts a voltage signal to
`a current signal. The cascadeof a CS stage and a CGstageis called a “cascode”! topology,
`providing many useful properties. Fig. 3.50 shows the basic configuration: M; generates
`a small-signal drain current proportional to V;, and M2 simply routes the current to Rp.
`
`rent rather than a
`put impedance of
`
`4) to write
`
`(3.115)
`
`Wecall M, the input device and M2 the cascode device. Notethat in this example, M, and
`Mpcarry equal currents. As we describe the attributes of the circuit in this section, many
`advantages of the cascode topology over a simple common-source stage becomeevident.
`First, let us study the bias conditions of the cascode. For M, to operate in saturation,
`Vy > Vin — Vrii- If M; and M;areboth in saturation, then Vy is determined primarily by
`
`The term cascode is believed to be the acronym for“cascaded triodes,” possibly invented in vacuum tube
`days.
`
`
`
`
`
`Chap. 3
`
`Single-Stage Amplifiers
`
`Vp: Vx = Vp — Vosp. Thus, Vp — Ves2 = Vin — Vr and hence V, > Vin + Vas2 — Vrii
`(Fig. 3.51). For Mz to be saturated, Vous = Vp —Vrxo, that is, Vou = Vin — Vera + Ves2 —
`
`of the transconductance and body effect of M2.
`
`as well, causing Vy to fall. As V;,, assumes sufficiently large values, two effects occur: (1)
`Vx drops below Vi, by Vri1, forcing M, into the triode region; (2) Vou, drops below V;,
`by Vryo, driving M2 into the triode region. Depending on the device dimensions and the
`values of Rp andV;, one effect may occur before the other. For example, if V, is relatively
`low, M, mayenterthe triode regionfirst. Note that if Mz goes into deep triode region, Vx
`and V,,; become nearly equal.
`Let us now consider the small-signal characteristics of a cascode stage, assuming both
`transistors operate in saturation. If 4 = 0, the voltage gain is equal to that of a common-
`source stage because the drain current producedby the input device must flow through the
`cascodedevice.Illustrated in the equivalentcircuit of Fig. 3.53, this result is independent
`
`Figure 3.51 Allowable voltages in
`cascodestage.
`
`Vra2 if Vp is chosen to place M, at the edge of saturation. Consequently, the minimum
`output level for which both transistors operate in saturation is equalto the overdrive voltage
`of M, plus that of M2. In other words, addition of Mz to the circuit reduces the output
`voltage swing by atleast the overdrive voltage of M2. Wealso say M>is “stacked” on top
`of M, .
`We now analyze the large-signal behavior of the cascodestage shown in Fig. 3.50 as
`V;, goes from zero to Vpp. For Vi, = Vroy, M, and M, are off, Vou = Von, and
`Vy & V, — Vru (Gif subthreshold conduction is neglected) (Fig. 3.52). As Vj, exceeds
`Vr, M, begins to draw current, and V,,, drops. Since I> increases, Vgs2 must increase
`
`Vent
`
`Figure 3.52 Input-output characteris-
`tic of a cascodestage.
`
`
`
`
`
`ye Amplifiers
`
`’gs2 — Vrin
`ni + Ves2-
`
`the minimum
`‘drive voltage
`es the output
`icked” on top
`
`1 Fig. 3.50 as
`= Vop> and
`s Vj, exceeds
`must increase
`
`Cascode Stage
`
`85
`
`
`
`Figure 3.53 Small-signal equivalent circuit of cascode
`stage.
`
`Example 3.14
`
`
`
`Calculate the voltage gain of the circuit shown in Fig. 3.54 if A = 0.
`
`Vop
`
`Ap
`
`Vout
`
`Vb oe Ms
`
`Vin o—] M 1
`
`R
`
`P
`
`=
`
`Figure 3.54
`
`Solution
`The small-signal drain current of Mj, gm1 Vin, is divided between Rp and the impedanceseen looking
`into the source of M2, 1/(@m2 + 8mb2)- Thus, the current flowing through Mp is
`
`icteris-
`(2ni2 + 8mb2) Rp
`
`Ip2 = &mi Vin
`I + (2m2+ 8mo2)Rp
`
`eeSee (3.117)
`
`
`
`ects occur: (1)
`rops below V;,
`nsions and the
`V, is relatively
`ode region, Vx
`
`assuming both
`of a common-
`ow through the
`is independent
`
`
`
`The voltage gain is therefore given by
`
`_ Bm (82 + 8mb2)Re Rp
`1 + (8m2 + 8mb2) RP
`ae
`
`(3.118)
`
`Ay =
`
`Animportantproperty ofthe cascodestructureis its high output impedance. As illustrated
`in Fig. 3.55, for calculation of Royr, the circuit can be viewed as a common-source stage
`with a degeneration resistor equal to ro,. Thus, from (3.60),
`
`Rout = (1 + (gm2 + &mb2)ro2lro1 + roe.
`
`(3.119)
`
`
`
`
`
`Chap. 3
`
`Single-Stage Amplifiers
`
`Figure 3.55 Calculation of output re-
`sistance of cascodestage.
`
`Figure 3.56 ‘Triple cascode.
`
`then Gm 8ml and Rou ~ (2m2 + &mb2)FO2"01s yielding Ay = (8m2 + &mb2V028m1401:
`
`Assuming gmro >> 1, we have Roy: © (8m2 + 8mb2)ro2ro1- That is, Mz boosts the output
`impedance of M, by a factor of (gma + 8mb2)ro2- AS shown in Fig. 3.56, cascoding can
`be extended to three or more stacked devices to achieve a higher output impedance, but
`the required additional voltage headroom makes such configurations less attractive. For
`example, the minimum output voltage of a triple cascode is equal to the sum of three
`overdrive voltages.
`To appreciatethe usefulness of a high output impedance,recall from the lemmain Section
`3.2.3 that the voltage gain can be written as Gy, Rou. Since G,, is typically determined
`by the transconductance ofatransistor, e.g., M) in Fig. 3.50, and hence bears trade-offs
`with the bias current and device capacitances, it is desirable to increase the voltage gain by
`maximizing Ro,;. Shown in Fig. 3.57 is an example. If both M@, and M2 operatein saturation,
`
`Vop
`
`fy
`
`| M,
`
`Vine M,
`
`Figure 3.57 Cascode
`current-source load.
`
`stage with
`
`
`
`Sec. 3.5
`
`Cascode Stage
`
`
`
`87
`
`
`
`Thus, the maximum voltage gain is roughly equal to the square ofthe intrinsic gain of the
`transistors.
`
`Example 3.15
`
`
`
`Calculate the exact voltage gain of the circuit shown in Fig. 3.57.
`
`Solution
`
`The actual G,, of the stage is slightly less than g,,.; because a fraction of the small-signal current
`produced by Mjis shuntedto ground by ro. As depicted in Fig. 3.58:
`
`Vop
`
`i
`
`Vout
`
`n
`
`Mo
`Ve
`
`loa
`
`- Im1'o1 Vin
`
`For
`
`(b)
`
`
`
`ut
`an
`ut
`or
`ee
`
`on
`
`ed
`ffs
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`by
`on,
`
`
`
`rorouSm2 + &mb2) + roi + re2
`
`
`
`
`
`If we had assumed Gy, © gm, then |Ay| © gmi {ll + (gm2 + 8mb2)rozlroi + roz}.
`Another approachto calculating the voltage gain is to replace Vj, and M; by a Thevenin equivalent,
`
`reducing the circuit to a common-gate stage.Illustrated in Fig. 3.58(b), this method in conjunction
`
`with (3.104) gives the sameresult as (3.123).en —————
`
`__Smiroilror(Sm2 + &mb2) + 1] (3.121)
`
`Figure 3.58
`
`rol
`lout = 8m1 Vin7 —
`
`ro, + ———— |ro2
`8m2 + Smb2
`
`(3.120)
`
`It follows that the overall transconductance is equal to
`
`and hencethe voltage gain is given by
`
`|Ayl| = GmRour
`
`= gmiroil(gm2 + &mb2)ro2 + 1).
`
`(3.122)
`
`(3.123)
`
`
`
`
`
`
`88
`
`Chap. 3
`
`Single-Stage Amplifiers
`
`Ip
`Vine, &
`L
`
`Ip
`Yak =
`4L
`
`Ip
`
`Vp2e— *
`Ww
`Vine
`7
`
`—=
`
`(a)
`
`(b)
`
`(c)
`
`Figure 3.59 Increasing output impedanceby increasing the device
`length or cascoding.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`It is also interesting to compare the increase in gain due to cascoding with that due to
`increasing the length of the input transistor for a given bias current (Fig. 3.59). Suppose,
`for example, that the length of the input transistor of a CS stage is quadrupled while the
`width remains constant. Then, since Ip = (1/2)(4nCox(W/L)Ves — Vrq)*, the overdrive
`voltage is doubled, and the transistor consumes the same amount of voltage headroom as
`does a cascodestage. Thatis, the circuits of Figs. 3.59(b) and (c) impose equal voltage
`swing constraints.
`Nowconsider the output impedance achieved in each case. Since
`
`&ulo = picost.,
`
`Ww
`
`l
`
`(3.124)
`
`and A « 1/Z, quadrupling Z only doubles the value of g,,ro while cascoding results in an
`output impedanceof roughly (g,,'9)*. Note that the transconductance of M,in Fig. 3.59(b)
`is half that in Fig. 3.59(c), leading to higher noise (Chapter 7).
`A cascodestructure need not operate as an amplifier. Another popular application of
`this topology is in building constant current sources. The high output impedance yields a
`current source closerto the ideal, but at the cost of voltage headroom. For example, current
`source J, in Fig. 3.57 can be implemented with a PMOScascode(Fig. 3.60), exhibiting an
`impedanceequal to [1 + (£m3 + 8no3)"o3lroa + ros. If the gate bias voltages are chosen
`
`‘ Current
`Source
`
`Vout
`
`Vop : Cascode
`
`=
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Figure 3.60 NMOS cascode ampli-
`fier with PMOS cascode load.
`
`
`
`
`
` Sec. 3.5
`
`
`
`we have |Ay| © g1 Rou. For typical values, we approximate the voltage gain as
`
`
`
`
`
`
`(3.125)
`
`Cascode Stage 89
`
` properly, the maximum output swing is equal to Vpn — (Ves) — Vri) — Vos — Vr2) —
`|Ves3 — Vru3| — |Vosa — Vrual.
`
`
`Wecalculate the voltage gain with the aid of the lemmaillustrated in Fig. 3.25, Writing
`Gm © 8m and
`
` Rout = {11 + (m2 + 8mv2)ro2Ir01 + roo} |{f1 + (8m3 + 8mb3)ro3lroa +103},
`
`
`(3.126)
`|Avl © &mil(m2ro2ro1)II(Gm3r03r04)].
`
`
`Shielding Property Recall from Fig. 3.23 that the high output impedance arises from
`the factthat if the output node voltage is changed by AV,the resulting change at the source
`
`
`
`
`
`of the cascode device is muchless. In a sense, the cascode transistor “shields”the input
`
`
`
`device from voltage variations at the output. The shielding property of cascodes proves
`
`
`useful in manycircuits.
`
`
`Example 3.16
`
`
`
`
`
`
`Two identical NMOStransistors are used as constant current sources in a system [Fig. 3.61(a)].
`However, dueto internal circuitry of the system, Vy is higher than Vy by AV.
`
`
`
`
`
`
`ag with that due to
`ig. 3.59). Suppose,
`adrupled while the
`rH), the overdrive
`tage headroom as
`pose equal voltage
`
`(3.124)
`
`oding results in an
`“My,in Fig. 3.59(b)
`
`ular application of
`mpedanceyields a
`yr example, current
`.60), exhibiting an
`oltages are chosen
`
`
`
`
`
`
` Figure 3.61
` (a) Calculate the resulting difference betweenJp1 and [pz ifr 40.
`
`
`
`(b) Add cascode devices to MW1 and Mp and repeatpart (a).
` Solution
`
`
`(a) We have
`
` WwW
`
`Ibi ~ Ip2=SUnCox —(Vp — VrY(AVps1 — AVps2) (3.127)
`
`
`2
`L
`ampli-
` 1
`
`Ww
`= 5Cox = (Vb ~ Vr#YQAY).
`(3.128)
`5
`
`
`
` 90
`
`Chap. 3
`
`Single-Stage Amplifiers
`
`(3.129)
`
`(b) As shown in Fig. 3.61(b), cascoding reduces the effect of Vy and Vy upon Jp; and Ipo,
`respectively. As depicted in Fig. 3.23 and implied by Eq. (3.63), a difference AV between Vx and
`Vy translates to a difference AVpg between P and Q equalto
`
`AVpo = AV-
`of!
`[1 + (gm3 + 8ub3ro3lroi +fo3
`AV
`
`(83 + 8mb3)F03
`
`Y————, (3.130)
`
`Thus,
`
`I
`
`D
`
`
`I
`Lac Wy, Vray
`AeY
`2= 5b
`x
`b
`TH
`»
`20" OL
`(23 + 8mb3 "03
`
`.
`
`(3.131)
`3.
`
`In other words, cascoding reduces the mismatch between Ip1 and Ip2 by (23 + &mb3)r 03+
`
`ee ————
`
`The shielding property of cascodes diminishes if the cascode device enters the triode
`region, To understand why, let us considerthe circuit in Fig. 3.62, assuming Vy decreases
`fromalarge positive value. As Vx falls below Vio -- Vr2, M2 requires a greater gate-source
`
`stage.
`
`Figure 3.62 Output swing of cascode
`
`overdrive so as to sustain the current drawn by M;. We can write
`
`j
`
`WwW
`
`(3.132)
`Ip = gnCox (7) [2(Vn2 — Ve — Vrn2)(Vx — Vp) — (Vx — Vey],
`concluding that as Vx decreases, Vp also dropsso that [pz remains constant. In other words,
`variation of Vy is less attenuated asit appears at P. If Vx falls sufficiently, Vp goes below
`Vn. — Vrwi, driving M,into the triode region.
`
`2
`
`3.5.1 Folded Cascode
`The idea behind the cascode structure is to convert the input voltage to a current and
`apply the result to a common-gate stage. However, the input device and the cascode device
`need not be of the same type. For example, as depicted in Fig. 3.63(a), a PMOS-NMOS
`combination performs the same function. In order to bias M, and M2, acurrent source must
`be added as in Fig. 3.63(b). The small-signal operation is as follows. If V;, becomes more
`positive, |/p;| decreases, forcing Ip to increase and hence Vou to drop. The voltage gain
`and output impedance of the circuit can be obtained as calculated for the NMVOS-NMOS
`
`
`
`
`
`Sec.3-5
`
`Cascode Stage
`
`(a)
`Figure 3.63 (a) Simple folded cascode, (b) folded cascode with proper biasing, (c) folded cascode
`with NMOSinput.
`
`cascodeof Fig. 3.50. Shownin Fig. 3.63(c) is an NMOS-PMOScascode. The advantages
`and disadvantagesof these types will be explainedlater.
`The structures of Figs. 3.63(b) and (c) are called “folded cascode” stages because the
`small-signal currentis “folded” up [in Fig. 3.63(b)] or down [in Fig. 3.63(c)]. Note thatthe
`total bias current in this case must be higher than that in Fig. 3.50 to achieve comparable
`performance.
`It is instructive to examinethe large-signal behavior of a folded-cascode stage. Suppose
`in Fig. 3.63(b), Vin decreases from Vpp to zero. For Vix > Vopo — |Vrail, Mi is off and
`Mycarriesall of I,’ yielding Vou = Vop — Rp. For Vi, < Vop — |Vruil, M1 turns on
`in saturation, giving
`
`Ipp = 1) — 57HCox (Z) (Vop — Vin - Vr)’
`
`1
`
`WwW
`
`1
`
`As V,, drops, /p2 decreases further, falling to zero if Ip; = J). Forthis to occur:
`
`nplifiers
`
`and Ip2,
`1 Vx and
`
`(3.129)
`
`(3.130)
`
`(3.131)
`
`the triode
`decreases
`
`ate-source
`
`(3.132)
`
`other words,
`, goes below
`
`21 I, is excessively large, Mz may enter deeptriode region, possibly driving 7; into the triode region as well.
`
`2h,
`1
`DD
`1)CoxCW/L)i
`\Vril
`(
`)
`
`
`If V;,, falls below this level, Jp, tends to be greater than 7, and M,enters the triode region
`so as to allow Ip, = 1;. The result is plotted in Fig. 3.64.
`What happens to Vx in the above test? As Ip drops, Vy rises, reaching V, — Vrx2 for
`Ino = 0. As M,entersthetriode region, Vx approaches Vpp.
`
`1
`
`WwW
`
`5ltpCox (7) (Vpp — Vint —|Vrmil= Ne
`
`1
`
`(3.133)
`
`(3.134)
`
`
`
`Vint = Vop —,|—— V. ; 3.135
`
`
`
`, current and
`iscode device
`MOS-NMOS
`it source must
`yecomes more
`e voltage gain
`IMOS-NMOS
`
`
`
`
`
`92
`
`Chap. 3
`
`Single-Stage Amplifiers
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`V;in1 Ypo-|“tHi]
`
`Vin
`
`Vint Yoo-|Mtri| Vin
`
`Figure 3.64 Large-signal characteristics of folded cascode.
`
`/ —
`Example 3.17 «
`Calculate the output impedance of the folded cascode shownin Fig. 3.65 where M3 operates as a
`current source.
`
`V
`
`pp
`
`|
`
`Rout
`
`Ms, } Vy
`
`Via Ah Ms
`
`=
`
`Figure 3.65
`
`Solution
`
`Using (3.60), we have
`
`Row = Uh + (gm2 + Snb2)F02)r01 ro3) + Fo2-
`
`(3.136)
`
`Thus, the circuit exhibits an output impedance lowerthan that of a nonfolded cascode.
`
`In orderto achieve a high voltage gain, the load of a folded cascode can be implemented
`as a cascodeitself (Fig. 3.66). This structure is studied more extensively in Chapter9.
`Throughout this chapter, we have attempted to increase the output resistance of voltage
`amplifiers so as to obtain a high gain. This may seem to make the speed ofthe circuit
`quite susceptible to the load capacitance. However, as explainedin Chapter 8, a high output
`impedanceper se doesnot pose a serious issue ifthe amplifieris placed in a proper feedback
`loop.
`
`
`
`3.6 Choice of Device Models
`In this chapter, we have developed various expressions for the properties of single-stage
`amplifiers. For example, the voltage gain of a degenerated common-source stage can be as
`simple as —Rp/(Rs + g,,') or as complexas Eq.(3.71). How does one choose a sufficiently
`accurate device modelor expression?
`
`
`
`
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