--
`
`published monthly by the Institute of Electrical and Electronics Engineers, Inc.
`
`--
`November 1996 Vol. 84 No. 11
`IIRl=IAAV G~av" ,
`~ ~f\OWN DRAu ~
`'j-'v<?Y-..
`
`1579
`
`SCANNING THE ISSUE
`
`\
`
`NO\J 20199~-
`K~
`'lUBi.JFlN UN\\JE-~5\
`
`1581
`
`1584
`
`1617
`
`1625
`
`1640
`
`1659
`
`1684
`
`1705
`
`EDITORIAL
`85th Anniversary Celebration, R. B. Fair and J. Cal d-- --
`
`PAPERS
`Circuit Techniques for Reducing the Effects of Op-Amp Imperfections:
`Autozeroing, Correlated Double Sampling, and Chopper Stabilization
`(Invited Paper), C. C. Enz and G. C. Ternes
`1582 Prolog, R. O'Donnell
`Antennae, G. W. Pickard
`1615 Prolog, J. E. Brittain
`
`SPECIAL SECTION ON SIGNALS AND SYMBOLS
`Edited by Martin D. Levine
`
`Knowledge-Directed Vision: Control, Learning, and Integration, B. A. Draper,
`A. R. Hanson, and E. M. Riseman
`1623 Prolog, H. Falk
`Recognizing Object Function Through Reasoning About Partial Shape
`Descriptions and Dynamic Physical Properties, L. Stark, K. Bowyer, A. Hoover,
`and D. B. Goldgof
`1638 Prolog, F. Caruthers
`A Hybrid System for Two-Dimensional Image Recognition (Invited Paper)
`F. Roli, S. B. Serpico, and G. Vernazza
`1657 Prolog, R. O'Donnell
`Environment Representation Using Multiple Abstraction Levels, G. L. Dudek
`1682 Prolog, J. Esch
`
`COMMENTS
`Corrections to "Optical Scanning Holography," T.-C. Poon, M. H. Wu, K. Shinoda,
`and Y. Suzuki
`
`BOOK REVIEWS
`1706 Managing Innovation and Entrepreneurship in Technology Based Firms
`by M; J. C. Martin, Reviewed by J. K. Pinto
`Technology and Strategy: Conceptual Models and Diagnostics, by R. A. Goodman
`and M. W. Lawless, Reviewed by J. K. Pinto
`
`1707
`
`SCANNING THE PAST
`Harris J. Ryan and High Voltage Engineering, J. E. Brittain
`FUTURE SPECIAL ISSUES/SPECIAL SECTIONS OF THE PROCEEDINGS
`
`1709
`1711
`
`LG Ex. 1007
`LG Electronics Inc. v. ParkerVision, Inc.
`IPR2022-00245
`Page 00001
`
`

`

`PROCEEDINGS OF THE IEEE
`1996 EDITORIAL BOARD
`Richard B. Fair, Editor
`James E. Brittain. Associate f;ditor, History
`
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`G. M. Borsuk
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`Giovanni DeMicheli
`E. K. Gannett
`T. G. Giallorenzi
`J. D. Gibson
`Bijan Jabbari
`Dwight L. Jaggard
`Peter Kaiser
`M. H. Kryder
`Mural Kunt
`
`C. G. Y. Lau
`Chen-Ching Liu
`Massimo Maresca
`K. W. Martin
`Theo Pavlidis
`George Pearsall
`P. B. Schneck
`Marwan Simaan
`L. M. Terman
`Fawwaz T. Ulaby
`A. N. Vcnetsanopoulos
`Paul P. Wang
`Jeannette M. Wing
`H. R. Wittmann
`
`1996 IEEE PUBLICATIONS BOARD
`W. Kenneth Dawson, Chair
`Tariq Durrani, Vice Chair
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`
`--
`
`Sc
`
`Circ'
`Ami:
`Sam
`Enz
`In
`nolo
`offsc
`men
`and
`com
`effec
`and
`and
`tech
`ing
`per
`issu
`
`Ant
`!'icl
`pag,
`Ir
`tion
`sele
`oft
`Piel
`tecl
`Adi
`mir
`Ins1
`
`Ha
`(Sc
`I
`ing
`res
`anc
`
`SP!
`
`ap1
`by
`of
`
`PR
`
`IPR2022-00245 Page 00002
`
`

`

`Circuit Techniques for Reducing the Effects of
`Op-Amp Imperfections: Autozeroing, Correlated
`Double Sampling, and Chopper Stabilization
`
`CHRISTIAN C. ENZ, MEMBER, IEEE, AND GABOR C. TEMES, FELLOW, IEEE
`
`Invited Paper
`
`In linear !C's fabricated in a low-voltage CMOS technology,
`the reduction of the dynamic range due to the de offset and low(cid:173)
`frequency noise of the amplifiers becomes increasingly significant.
`Also, the achievable amplifier gain is often quite low in such a
`technology, since cascading may not be a practical circuit option
`due to the resulting reduction of the output signal swing. In this
`paper, some old and some new circuit techniques will be described
`for the compensation of the amplifier most important nonideal
`effects including the noise (mainly thermal and I/ f noise), the
`input-referred de offset voltage, as well as the finite gain resulting
`in a nonideal virtual ground at the input.
`
`I.
`
`INTRODUCTION 1
`In linear active circuits, the active element most often
`used is the operational amplifier (op-amp), whose main
`function in the circuit is to create a virtual ground, i.e.,
`a node with a zero (or constant) voltage at its input
`terminal without sinking any current. Using op-amps with
`MOS input transistors, the op-amp input current at low
`frequencies can indeed be made extremely small; however,
`the input voltage of a practical op-amp is usually signif(cid:173)
`icantly large (typically of the order of 1-10 m V), since
`it is affected by several nonideal effects. These include
`noise (most importantly, 1/ f and thermal noise), the input(cid:173)
`referred de offset voltage, as well as the signal voltage
`needed to generate the desired output voltage of the op-amp.
`Normally, the thermal noise occupies a wide frequency
`band, while the 1 / f noise, offset and input signal are
`narrowband low-frequency signals.
`
`Manuscript received April 18, I 996; revised September 5, 1996. G.
`Temes's work was supported by U.S. National Science Foundation though
`the NSF Center for the Design of Analog-Digital ICs (CDACIC).
`C. C. Enz is with the Swiss Federal Institute of Technology, Lau(cid:173)
`sanne (EPFL), Electronics Laboratory (LEG), ELB-Ecublens, CH-1015
`Lausanne, Switzerland (e-mail: enz@leg.de.epfl.ch).
`G. C. Ternes is with the Department of Electrical and Computer
`Engineering, Oregon State University, Corvallis, OR 97331-3211 USA
`(e-mail: temesg@ece.orst.edu).
`Publisher Item Identifier S 00 I 8-92 I 9(96 )08690-2.
`1 This work is dedicated to Prof. Karoly Simonyi on his 80th birthday.
`
`The purpose of the circuit techniques discussed in this
`paper is to reduce the effects of the narrow-band noise
`sources at the virtual ground of an op-amp stage. By
`reducing the low-frequency noise and offset at the op-amp
`input, hence the dynamic range of the circuit is improved;
`by reducing the signal voltage at the virtual ground ter(cid:173)
`minal, the effect of the finite low-frequency gain of the
`op-amp on the signal-processing characteristics of the stage
`is decreased. Both improvements are especially significant
`for low-supply voltage circuits, which have limited signal
`swings and where the op-amp gain may be low since
`headroom for cascoding may not be available. The proposed
`techniques are applicable to such important building blocks
`as voltage amplifiers, ADC and DAC stages, integrators and
`filters, sample-and-hold (S/H) circuits, analog delay stages,
`and comparators.
`Sections II and III present the two basic techniques that
`are used to reduce the offset and low-frequency noise of op(cid:173)
`amps, namely the autozero (AZ) and chopper stabilization
`(CHS) techniques. A clear distinction is made between
`autozeroing, which is a sampling technique, and CHS,
`which is a modulation technique, mainly with respect to
`their effect on the amplifier broadband noise. The correlated
`double sampling (CDS) technique is described in Section 11
`as a particular case of AZ where, as its name indicates,
`the amplifier noise and offset are sampled twice in each
`clock period. Then, Section IV treats the most important
`practical issues at the transistor and circuit level that
`are faced when implementing the offset and noise reduc(cid:173)
`tion techniques discussed previously. Section V presents
`fundamental building blocks that are used for sampled(cid:173)
`data analog signal processing. They are all realized as
`switched-capacitor (SC) circuits and therefore exploit the
`CDS technique not only for reducing the offset and the
`1/ f noise, but also to lower the sensitivity of the circuit
`performance to the finite amplifier gain. Examples of SC
`S/H stages, voltage amplifiers, integrators, and filters are
`
`1584
`
`PROCEEDINGS OF THE IEEE. VOL. 84, NO. 11, NOVEMBER 1996
`
`0018-9219/96$05.00 © 1996 IEEE
`
`IPR2022-00245 Page 00003
`
`

`

`S&H = Sample & Hold
`
`SAR = Successive
`Approximation
`Register
`
`Fig. I. Basic autweroed stages. (a) Analog offset control storage and (b) digital offset control
`storage.
`
`(a)
`
`(bl
`
`Q):_i ---✓-~Ot--------+-[ I _____._0-.--, -· t
`
`mT5
`
`(m+1)Ts
`
`Voltages
`
`RC<< TAz
`
`Fig. 2.
`
`(al Basic AZ circuit and autO/crned signal: (bJ shows volta~es in (a).
`
`(a)
`
`(bl
`
`presented. An example of the use of the CHS technique
`to realize a low-noise and low-offset micropower amplifier
`for intrumentation applications is presented in Section VI.
`Finally, a summary is given in Section VII, where the two
`techniques discussed in this paper are compared.
`
`II. AUTOZEROJNG AND CORRLLATED
`DOUBLE SAMPLING TECHNIQUES
`In this section, the principle of AZ and CDS techniques
`will be introduced and their effect on offset and noise
`analyzed.
`
`A. Basic Principle
`The basic idea of AZ is sampling the unwanted quantity
`(noise and offset) and then subtracting it from the instanta(cid:173)
`neous value of the contaminated signal either at the input
`or the output of the op-amp. This cancellation can also be
`done at some intermediate node between the input and the
`output of the op-amp, using an additional input port defined
`as the nulling input and identified with the letter N in the
`schematics of Fig. I.
`If the noise is constant over time (like a de offset) it
`will be cancelled, as needed in a high-precision amplifier
`or high-resolution comparator. If the unwanted disturbance
`
`is low-frequency random noise (for example, 1 / f noise), it
`will be high-pass filtered and thus strongly reduced at low
`frequencies but at the cost of an increased noise floor due
`to aliasing of the wideband noise inherent to the sampling
`process. The general principle of the AZ process will first
`be described considering only the input referred de offset
`voltage V08 and will then be extended to the input referred
`random noise voltage \/.iV.
`The AZ process requires at least two phases: a sampling
`phase ( </> i) during which the offset voltage ½,, and the noise
`voltage V N are sampled and stored, and a signal-processing
`phase ( </>-i) during which the offset-free stage is available
`for operation. The two major categories of AZ are shown
`in Fig. I. During the sampling phase (shown in Fig. 1), the
`amplifier is disconnected from the signal path, its inputs
`are short-circuited and set to an appropriate common-mode
`voltage. The offset is nulled using an auxiliary nulling input
`port N by means of an appropriate feedback configuration
`and/or a dedicated algorithm. The control quantity :re is
`next sampled and stored, either in an analog form as a
`voltage using a S/H stage [Fig. l(a)] or in a digital form,
`using for example a register !Fig. l(b)]. The output V, 11 , is
`forced to a small value in these particular configurations.
`The input terminals of the amplifier can afterwards be
`connected back to the signal source for amplification. If
`
`ENZ AND TEMES: CIRCUIT TECHNIQUES FOR REDUCING THE El'FECTS OF OP-AMP IMPERl'ECTIONS
`
`1585
`
`IPR2022-00245 Page 00004
`
`

`

`1.4
`
`1.2
`
`1.0
`
`C 0.8
`:z:::
`i:.
`~ 0.6
`C.
`
`0.4
`
`0.2
`
`-- -...
`0.0 L - - - ' - - - - - - - ' ' - - - - - - ' - - - " - - -...... - -......
`2.5
`0.0
`0.5
`1.0
`1.5
`2.0
`3.0
`f Th
`
`Fii:. 3. Autozero baseband and foldover bands transfer functions.
`
`reset to zero and the noise source voltage V N appears
`across resistor R and capacitor C. Assuming RC « 1Az,
`at the end of the sampling phase (when switch S opens)
`the noise voltage V:v is sampled onto capacitor C. The
`output voltage becomes equal to the difference between
`the instantaneous voltage VN and the voltage ½ stored
`on capacitor C. This eliminates the de component of V N,
`but not its time-varying part. It can be shown [8] that if
`source voltage VN(t) corresponds to a stationary random
`noise with a PSD SN(!), the PSD of the autozero voltage
`across the switch can be decomposed into two components:
`one caused by the baseband noise (which is reduced by
`the AZ process) and the other by the foldover components
`introduced by aliasing. Thus
`
`baseband
`
`foldCJver
`
`Sr..1<1(1) = f IHn(f)l 2 SN(f- ;J.
`
`(I)
`
`(2)
`
`n=-oo
`n,!O
`The foldover component results from the replicas of
`the original spectrum shifted by the integer multiples of
`the sampling frequency. The baseband transfer function
`IH0 (f) 12 is given by (see (3) at the bottom of the page)
`where d = Th /T., is the duty cycle of the clock signal
`[Fig. 2(b)]. The magnitude of H0 (f) normalized to the
`duty cycle d is plotted as a function of fTh in Fig. 3,
`which shows its high-pass characteristic. Note that for
`1r fTh « 1, Ho (f) acts like a differentiator
`IHo(f)I ~ 1r JT,,.
`It imposes a zero at the origin of frequency axis that
`cancels out any de component present in Vv ( t). The other
`transfer functions I H,, (f )12 for n =f O are derived in the
`Appendix. Their shape depends on the duty cycle d, but
`they all merge to a common function in the case the AZ
`time TAz can be considered much smaller than the hold
`time (TAz « T1i)
`IHn(f)l 2 ~ [d · sinc(1rfTh)] 2
`for n i O and TAz « T1,
`(5)
`where sinc(:.c) = sin(x)/:i:. IHn(f)I is plotted in Fig. 3.
`The PSD at the output of the AZ circuit clearly de(cid:173)
`pends on the PSD of the source which is autozeroed. The
`low-frequency input-referred noise PSD of an amplifier
`generally contains both a white and a 1 / f noise component.
`It can be written in the following convenient form:
`
`(4)
`
`it is used under the same conditions as during sampling,
`the amplifier will ideally be free from any unwanted offset.
`
`where
`
`B. The Effect of AZ on the Noise
`The autozero principle can be used not only to cancel
`the amplifier offset but also to reduce its low-frequency
`noise, for example 1/ f noise. But unlike the offset voltage,
`which can be considered constant, the amplifier's noise
`and particularly its wideband thermal noise component is
`time-varying and random. The efficiency of the AZ process
`for the low-frequency noise reduction will thus strongly
`depend on the correlation between the noise sample and
`the instantaneous noise value from which this sample is
`subtracted. The autocorrelation between two samples of
`1 / f noise separated by a time interval r decreases much
`slower with increasing r than it does for white noise,
`assuming they have the same bandwidth. The AZ process
`is thus efficient for reducing the 1 / f noise but not the
`broadband white noise.
`Another way of looking at the effect of AZ is to note that
`it is equivalent to subtracting from the time-varying noise
`a recent sample of the same noise. For de or very low(cid:173)
`frequency noise this results in a cancellation. This indicates
`that AZ effectively high-pass filters the noise.
`In addition to this basic high-pass filtering process, since
`AZ is a sampling technique, the wideband noise is aliased
`down to the baseband, increasing the resulting in-band
`power spectral density (PSD) unless the system is already
`a sampled-data one.
`The effects of AZ on the amplifier's noise can be better
`understood by analyzing the simple circuit shown in Fig. 2,
`where source V N may represent the noise at the output of
`the amplifier in the autozero phase [see, i.e., Fig. 21(a)].
`Each time switch S is closed, the output voltage VAz is
`
`1Ho(f)l 2 = rP{ [i _ sin (27r JT1,] 2 + [ 1 - cos (21r JT1i)] 2
`
`21rfT1,
`
`27rfTh
`
`(6)
`
`(3)
`
`}
`
`1586
`
`PROCEEDINGS OF THE IEEE, VOL. 84, NO. 11, NOVEMBER 1996
`
`IPR2022-00245 Page 00005
`
`

`

`Normalized PSD
`
`N=4
`
`~
`n =-1
`
`n = -4
`--r--+------r-,--r--f"""-,,-,--r--"'1'-LL,.LLµ...'+-A'-4----,-,...fTS
`-7 --6 -5 -4 -3
`
`Fig. 4. Aliasing of an ideally low-pass filtered white noise having
`a bandwidth equal to twice the sampling frequency.
`
`where 8 11 represents the white noise PSD and .h is the
`comer frequency, defined as the frequency for which the
`1/.f noise PSD becomes equal to the white noise 8 0 . The
`comer frequency of amplifiers having MOS input devices
`can be relatively high (typically ranging from I kHz to
`as high as 100 kHz), which means that in the absence of
`aliasing the input noise is often dominated by the 1 /.f noise
`component in the frequency range of interest. The effect
`of AZ will be examined separately for each of these PSD
`components, starting with the white noise.
`The foldover component defined by (2) can easily be
`calculated if the amplifier's broadband white noise is con(cid:173)
`sidered as an ideally low-pass filtered white noise having
`a bandwidth equal to fl. The aliasing effect introduced by
`the sampling process in this case is illustrated in Fig. 4
`for BT., = 2 (i.e., for a noise bandwidth fl = four times
`the Nyquist frequency). Fig. 4 clearly shows the effect of
`undersampling the broadband white noise: the original noise
`power spectrum is shifted by multiples n of the sampling
`frequency and summed, resulting in a white noise of PSD
`value approximately equal to NS0 , where JV is the integer
`closest to the undersamplingfactor defined by '2flT_,. Thus
`
`n~ c-o SN (1- ;J =" 2UTsBo-
`
`(7)
`
`The signal conesponding to (7) has no physical reality
`since its power is infinite. The power is actually bounded by
`the sinc2 ( 1T f T.,) function introduced by the hold operation.
`The foldover component in the Nyquist range is then simply
`derived from (7) by subtracting the original band ( n = 0)
`and multiplying the remainder by the sinc 2 ( ?T JT.,) function:
`Srotd-whit..Cl) = (2flT., -
`l)Sosinc 2 (rr.fT.,).
`This result can be extended to the case of a first-order
`low-pass filtered white noise with a PSD
`
`(8)
`
`So
`
`SlV-wl,itc,(f) = ··
`1+(J)
`
`:2
`
`(9)
`
`where f c
`is the 3-dB noise bandwidth, which typically
`corresponds to the amplifier gain-bandwidth product when
`the noise is sampled with the op-amp in a unity-gain
`configuration. Therefore, .fc is generally much larger than
`
`the sampling frequency .f., = 1/T,. The detailed analysis
`given in [8] shows that (8) also holds for the foldover
`component of a first-order low-pass filtered white noise if
`n is replaced by the equivalent noise bandwidth defined by
`1 1·+=
`fl = 0
`1T = 2 .fc-
`If the undersampling factor 2nr_, = 1r.f. T, is much larger
`than unity, the foldover component dominates, since the
`baseband term IHo(.{)12 is bounded by 1.6. The autozeroed
`white noise is thus dominated by the aliased broadband
`noise component and can be approximated by
`
`.
`
`-CX)
`
`,:,o
`
`8N-white(f) rf,f
`
`(10)
`
`8Az - white(f) =" SfoJJ - white(./)
`=" (pifcTs - 1 )So sinc2 (7r./T_,).
`
`(11)
`
`The PSD of a first-order low-pass filtered white noise
`having a bandwidth five times larger than the sampling
`frequency2 UcT., = 5) and the different PSD components
`resulting from the AZ process are plotted in Fig. 5. It clearly
`shows that the autozeroed noise PSD is dominated by the
`foldover component in the Nyquist band (lfT.,I::; 0.5).
`A similar analysis can be carried out for a first-order
`low-pass filtered 1/f noise having a PSD given by
`
`C ,,-,;J. ~ III [1+ (D T (12)
`
`_,.
`
`(f)
`
`So.h
`
`As shown in Fig. 6, the input 1/.f noise is zeroed,
`removing the original divergence of the 1/ f noise occurring
`at the origin of frequency. Although 1 / f noise has a narrow
`bandwidth, it still has a foldover component due to the
`aliasing of all the tails of the 1/.f noise. This foldover
`component and the original baseband PSD are plotted in
`Fig. 6 for f cTs = 5 and for a comer frequency equal to the
`sampling frequency (.hT., = I).
`The foldover component for the 1/.f noise can be ap(cid:173)
`proximated [8] in the Nyquist range by
`
`Srotd-1// =" 2So.h1\[l + !11 (ifrTs)]sinc 2 (1rfTs)-
`
`(13)
`
`Comparing Sfold-l ;r to the conesponding term obtained
`for the white noise (8), it can be seen that it increases
`proportionally to f,,T_, for the white noise, but only log(cid:173)
`arithmically for the 1/f noise. The effect of aliasing on
`the 1/ f noise is thus not as dramatic as on the broadband
`white noise.
`The PSD at the output of the AZ circuit at low frequen(cid:173)
`cies, considering both the white and the 1 / f component
`given by (6) and assuming 1T fcT., » 1, can simply be
`obtained from (11) and (13):
`SAz(f) = IHo(f)l2S,v(f) + Sro1<1
`
`(14)
`
`'This seleclion reflects the requirement f,.T, 2'. 'i needed for the full
`settling of an SC stage [10].
`
`ENZ AND TEMES: CIRCUIT TECHNIQUES FOR REDUCING THE EFFECTS OF OP-AMP IMPERFECTIONS
`
`1587
`
`IPR2022-00245 Page 00006
`
`

`

`10
`
`"' a.
`j
`ii
`E 0 z
`
`8
`
`6
`
`4
`
`2
`
`•• -
`
`......
`.
`/
`.
`/
`.
`.
`:
`.
`:
`.
`/
`:
`,/
`./ /
`
`Baseband
`component
`
`Foldover
`component
`
`\
`
`\
`
`... ...
`-----·
`\
`.
`.
`.
`.
`.
`.
`\
`••
`\,
`\,
`
`AZ input PSD
`
`--
`
`10----------------------------
`mCTS - 1----... 1--------------....,...-.,.....---------------1
`14
`jt,T, = s1
`//
`
`C 12
`
`--
`-
`?.. -
`-
`-
`-
`-
`-
`/
`-
`-
`-
`-
`-:-·- -
`-
`-
`..... , ............. , ... '"-c .... - .. ..
`... ,.-,A ........................... .,,. • ..., ..................................................... ,.,... ..... -
`.. ..
`.... ....
`0 _,.._._. ----------------..__ ...... ___________ ..... _____ •• _ . ..._.
`-0.5
`0.5
`1.0
`0.0
`-1.0
`f T5
`l<'ig. 5. Effect of the AZ process on a first-order low-pass filtered white noise with a bandwidth
`five times larger than the sampling frequency.
`
`C u,
`a..
`"C
`Cl)
`N ·--ca
`E ... 0 z
`
`16
`
`14
`
`12
`
`10
`
`8
`
`Foldover
`component
`
`\
`
`AZ. input PSD
`
`\I
`
`\
`'
`\ AZ?utPSD
`
`6
`
`4
`
`2
`
`..
`... ...
`.... ·-.. ~·-.
`.....
`.... ·• ....
`,. . ._....
`...,
`"•:.~ ... __
`zeroed 1/f noise
`__ - _;;,:.•~'"
`--
`···-:::i,:.,.. ...
`....
`,,.._,.! ... :.-··
`... .... '
`., , -
`-
`-
`. ., ....................... _ .
`... ':': ................. ---
`······.••:"'
`,,
`..
`--
`'..
`........ _ ............... .
`',
`___ ..
`,"
`,.
`' ;
`.............. _
`........
`0 ..._.,a.a..;.. _ _ _ _ ..,__ _ _ _ _ _ _ _ _ _ _ _ _ _ _,1,. ____ ;;.:.:.,....,J
`0.0
`-0.5
`0.5
`-1.0
`1.0
`f T9
`
`;
`
`'Fig. 6. Effect of the AZ process on a first-order low-pass filtered 1 / f noise having a bandwidth
`five times larger than the sampling frequency.
`
`where the total foldover component is given by
`
`Braid =So{ ('rr.f/I'., -1) + 2.fi,Ts[l +ln(U,,7\)]}
`· sinc2 (1r]T8 ).
`(15)
`The comer frequency for which the 1 / f noise foldover
`component [given by (13)] is equal to the foldover compo(cid:173)
`nent coming from the white noise [as given by (8)] is plotted
`against the normalized white-noise bandwidth in Fig. 7. The
`
`total foldover term given by (15) is thus dominated by the
`I/ .f noise contribution for parameter values (11-J'.s, le 1',)
`falling in the region above this curve, while it is dominated
`by the broadband white noise contribution below the curve.
`For example, an amplifier auto zeroed at 100 kHz and
`having a gain-bandwith product equal to 7 x ls = 700
`kHz should have a comer frequency larger than 4.13 x
`f, = 113 kHz for the 1/ f noise foldover to dominate.
`
`1588
`
`PROCEEDINGS OF THE IEEE. VOL. 84, NO. 11. NOVEMBl'R 1996
`
`IPR2022-00245 Page 00007
`
`

`

`1 0 0 i ; - - - - - - - - - - - - - - - -~
`
`input referred offset
`
`1/f noise foldover
`component dominates
`
`1-: 10
`....
`
`white noise foldover
`component dominates
`
`1 ~-------'--'--L......L..L...;.-'----L.J___------1_-'-__._--'--'---'-..W..
`1
`100
`
`Fig. 7. Compari,on between the 1/.f and white noise contribu(cid:173)
`tion to lhe Lola I foldovcr component a, a function or Lhc whitc-rn1i,c
`bandwidth
`
`This demonstrates that in most practical cases the foldover
`component is dominated by the broadband white noise.
`In conclusion, it was shown in this section that the
`AZ process not only cancels the amplifier's offset. but it
`also strongly reduces the amplifier 1 /.f noise thanks to
`the double zero introduced by the AZ baseband power
`transfe;-
`function. This improvement is obtained at the
`cost of an increased white noise foldover component due
`to the aliasing of the amplifier's thermal and as well as
`1/ .f noise. In most practical cases, this foldover term is
`dominated by the aliased thermal noise component. which
`is approximately equal to the amplifier's original broadband
`thermal noise multiplied by the ratio of the cqui valent noise
`bandwidth to the Nyquist frequency.
`
`C. Residual Offset
`Next. the effectiveness of the stages of Fig. I in eliminat(cid:173)
`ing the effects of Vrn will be discussed. Since the additional
`input used in the amplifiers of Fig. I for nulling the offset
`can either be a voltage or a current, it will generally be
`denoted as a control variable :r,.. Changing this input when
`the amplifier is in the sampling phase, as shown in Fig. 1,
`allows the zeroing of the output voltage for a particular
`value of the control variable.
`Let the input-referred offset Vios be defined as the output
`voltage during the offset sampling phase divided by the
`differential gain of the amplifier in the amplification mode.
`The relation between this input-referred offset and the
`control variable is schematically plotted in Fig. 8. and is
`first assumed to be linear (see the continuous straight line
`in Fig. 8). Assume that the amplifier has an initial offset as
`shown in Fig. 8(a). The appropriate feedback configuration
`or the dedicated algorithm will have to bring this offset very
`close to zero. When the loop has settled or the algorithm
`is completed, the control information is stored. During the
`storage process, there might be some error ~:r,. introduced
`into the control variable, due for example to charge injec(cid:173)
`tion by the sampling switch, or to the quantization error
`of the AID converter, that leads to a residual offset Vins-lin
`or Vios-01L depending if the compensation characteristic is
`linear or not. It is important to notice that the characteristics
`
`residual offset Vos-NL
`Vos-lin
`
`initial offset ,
`
`(a)
`
`input referred offset
`
`residual offset
`
`dXC
`
`I
`
`I
`
`Fig. 8.
`lnput-refen-ed offset versus nulling control variable: (a)
`large initial oll,ct and (b) small initial offset.
`
`(b)
`
`between the control variable and the input-referred offset
`voltage is not