HDIROCCEEDHNGETWEIEEE published monthly by the Institute of Electrical and Electronics Engineers, Inc. November 1996 Vol. 84 No. 11 1579 SCANNING THE ISSUE EDITORIAL vteSAOWN DRAIT7 5) I IRR ARV ‘4/9041NOV 2 0 ustiRNuNive 1581 85th Anniversary Celebration, R. B. Fair and J. Calder" PAPERS 1584 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. Temes 1582 Prolog, R. O’Donnell 1617 Antennae, G. W. Pickard 1615 Prolog, J. E. Brittain SPECIAL SECTION ON SIGNALS AND SYMBOLS Edited by Martin D. Levine 1625 Knowledge-Directed Vision: Control, Learning, and Integration, B. A. Draper, A. R. Hanson, and E. M. Riseman 1623 Prolog, H. Falk 1640 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 1659 A Hybrid System for Two-Dimensional Image Recognition (Invited Paper) F. Roli, S. B. Serpico, and G. Vernazza 1657 Prolog, R. O’Donnell 1684 Environment Representation Using Multiple Abstraction Levels, G. L. Dudek 1682 Prolog, J. Esch COMMENTS 1705 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 1707 Technology and Strategy: Conceptual Models and Diagnostics, by R. A. Goodman and M. W. Lawless, Reviewed by J. K. Pinto SCANNING THE PAST 1709 Harris J. Ryan and High Voltage Engineering, J. E. Brittain 1711 FUTURE SPECIAL ISSUES/SPECIAL SECTIONS OF THE PROCEEDINGS (cid:149)(cid:149)(cid:149)11(cid:149)(cid:149)(cid:149)(cid:149)1.. NOVEMBER
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`00 PROCEEDINGS OF THE IEEE 1996 EDITORIAL BOARD Richard B. Fair, Editor James E. Brittain, Associate Editor, History Winser E. Alexander Roger Barr Albert Benveniste G. M. Borsuk Bimal K. Bose S. Joseph Campanella Giovanni DeMicheli E. K. Gannett T. G. Giallorenzi J. D. Gibson Bijan Jabbari Dwight L. Jaggard Peter Kaiser M. H. Kryder Murat 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. Venetsanopoulos Paul P. Wang Jeannette M. Wing H. R. Wittmann 1996 IEEE PUBLICATIONS BOARD W. Kenneth Dawson, Chair Tariq Durrani, Vice Chair John B. Anderson Frederick T. Andrews Joseph Boykin Gerald L. Engel Richard B. Fair Donald Fleckenstein Antonio G. Flores Randall Geiger W. Dexter Johnston, Jr. Deborah Flaherty Kizer Prasad Kodali PROCEEDINGS STAFF Jim Calder, Managing Editor Margery Scanlon, Editorial Coordinator Gail S. Ferenc, Transactions Manager Valerie Cammarata, Editorial Manager Geraldine E. Krolin, Managing Editor, TRANsAcrioNs1JouRNALs Desiree Rye, Associate Editor Frank Lord William Middleton Lloyd Morley M. Granger Morgan Robert T. Nash Allan C. Schell Leonard Shaw Friedolf Smits James Tien George W. Zobrist Frank Caruthers, Jim Esch, Howard Falk, Richard A. O’Donnell, Kevin Self, Contributing Editors Stephen Goldberg, Cover Artist Susan Schneiderman, Richard C. Faust, Advertising Sales
`IEEE, 445 Hoes Lane, Piscataway, NJ 08855-1331 USA. (Telephone: 908-562-5478,fax: 908-562-5456, email: j.calder@ieee.org.) COVER This issue contains a Special Section on Signals and Symbols. The cover was inspired by the blocks used to demonstrate simulated objectspaper: Recognizing Object Function through Reasoning About Partial Shape Descriptions and Dynamic Physical Properties by Stark, et al. Ciro Amy Sam Enz In nolo offse incrc and corn effec and and tech ing per isSU Ant Pici pag,It tion sele of t Plc tect Ach mir Insi Ha (Sc ing res an SPI api by of PR
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`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 IC’s fabricated in a low-voltage CMOS technology, the reduction of the dynamic range due to the dc offset and low-frequency noise of the amplifiers becomes increasingly significant. Also, the achievable amplifier gain is often quite low in such a technology, since cascoding 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 1I f noise), the input-referred dc offset voltage, as well as the finite gain resulting in a nonideal virtual ground at the input. I. INTRODUCTION’ 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-icantly large (typically of the order of 1-10 mV), since it is affected by several nonideal effects. These include noise (most importantly, 1/f and thermal noise), the input-referred dc 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, 1996; 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-sanne (EPFL), Electronics Laboratory (LEG), ELB-Ecublens, CH-1015 Lausanne, Switzerland (e-mail: enz@leg.de.epfl.ch). G. C. Temes 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 0018-9219(96)08690-2. 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-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-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 II 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-tion techniques discussed previously. Section V presents fundamental building blocks that are used for sampled-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 0018-9219/96$05.00 ' 1996
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`4)
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`yin
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`Vos+VN
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`A2
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`S&H = Sample & Hold
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`4))
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`Vos+VN
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`SAR = Successive
`Approximation
`Register
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`(a) Fig. 1. Basic autozeroed stages. (a) Analog offset control storage and (b) digital offset control storage.
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`C S
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`VAz
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`Voltages
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`VN(li
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`mTs
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`(m+1)Ts
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`t
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`RC « TAz
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`TAZ
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`(m+1)Ts
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`VAz(t)
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`Fig. 2. (a) Basic AZ circuit and autozeroed signal: (b) shows voltages in (a). 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. 11. AUTOZEROING AND CORRELATED 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-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. 1. If the noise is constant over time (like a dc offset) it will be cancelled, as needed in a high-precision amplifier or high-resolution comparator. If the unwanted disturbance mTs
`( b ) 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 dc offset voltage Vos and will then be extended to the input referred random noise voltage Vv. The AZ process requires at least two phases: a sampling phase (01) during which the offset voltage V(cid:132), and the noise voltage VN are sampled and stored, and a signal-processing phase (02) 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 is next sampled and stored, either in an analog form as a voltage using a S/H stage [Fig. 1(a)] or in a digital form, using for example a register [Fig. l(b)1. The output Vo(cid:132), 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 EFFECTS OF OP-AMP IMPERFECTIONS 1585
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`1.4
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`;'—differentiator
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`n = 0
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`Fig. 3.
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`n 0 and TAz « TA
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`•
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`Autozero baseband and foldover bands transfer functions. it is used under the same conditions as during sampling, the amplifier will ideally be free from any unwanted offset. 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 7 decreases much slower with increasing 7 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 dc or very low-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 VN 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 reset to zero and the noise source voltage VN appears across resistor R and capacitor C. Assuming RC << TAz, at the end of the sampling phase (when switch S opens) the noise voltage VN is sampled onto capacitor C. The output voltage becomes equal to the difference between the instantaneous voltage VN and the voltage Ve stored on capacitor C. This eliminates the dc component of VN, 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( f), 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 SAz(f) = 1Ho(f)12SN(f )+ Sf
`f Th << 1, Ho( f) acts like a differentiator I-1/0(f fTh(cid:149) (4) It imposes a zero at the origin of frequency axis that cancels out any dc component present in VN(t). The other transfer functions IHn(f )12 for n 0 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 TA z can be considered much smaller than the hold time (TAZ << Th) 11-1(cid:132)(f)12 ’.1=2[d (cid:149) sinc fTh)j2for n 0 and TAZ << Th (5) where sine (x) sin (x)/x. in(f)1 is plotted in Fig. 3. The PSD at the output of the AZ circuit clearly de-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: 11/0(/ )12 = d2 [1 sin (27 fTh 1 227rfThSN(f) So(1+ If I 11 (6) + 1 (cid:151) cos (27 fTh )12} (3) fTh
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`old _
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`where baseband foldover +00 sfo.d(f) E IHn(f)12sN(f (cid:151) (2) Ts= (cid:151) CX) n#0 The foldover component results from the replicas of the original spectrum shifted by the integer multiples of the sampling frequency. The baseband transfer function 11/0(f )12 is given by (see (3) at the bottom of the page) where d ThIT, 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
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`Normalized PSD N= 4 n = - n = +3
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`n=+2
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`2 1 + ()L. where f, 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, f, is generally much larger than (9) the sampling frequency f, 1/T(cid:132). 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 B is replaced by the equivalent noise bandwidth defined by T, 1 = (cid:151) SN-white(f ) SO . 7r = 2- f(cid:132). (10) If the undersampling factor 2BT, = 7r f,T, is much larger than unity, the foldover component dominates, since the baseband term 11/0(f )12 is bounded by 1.6. The autozeroed white noise is thus dominated by the aliased broadband noise component and can be approximated by SA z (cid:151) White( f)= Sf01,1 White(/’ ) (Pi fcTs - 1)S0 sinc2 (7rfT(cid:132)). (11) The PSD of a first-order low-pass filtered white noise having a bandwidth five times larger than the sampling frequency ( f, T, = 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 (L fTI < 0.5). A similar analysis can be carried out for a first-order low-pass filtered 1/f noise having a PSD given by
`4--BT, 3 4 5 6 I’ frs 7 Fig. 4. Aliasing of an ideally low-pass filtered white noise having a bandwidth equal to twice the sampling frequency. where So represents the white noise PSD and fk is the corner frequency, defined as the frequency for which the 1/f noise PSD becomes equal to the white noise So. The corner frequency of amplifiers having MOS input devices can be relatively high (typically ranging from 1 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-sidered as an ideally low-pass filtered white noise having a bandwidth equal to B. 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 B = 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 N50, where N is the integer closest to the undersampling factor defined by 2BT,. Thus +00 E SN(f -
`SokIP + (1- j- 2(12) 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 L.T. = 5 and for a corner frequency equal to the sampling frequency (fhoT, = 1). The foldover component for the 1/f noise can be ap-proximated [8] in the Nyquist range by Sfold--1/f 250.477,[1 In (if,,T(cid:132))]sinc2 (7i - fT(cid:132)). (13) Comparing Sfold-1/f to the corresponding term obtained for the white noise (8), it can be seen that it increases proportionally to feT, for the white noise, but only log-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-cies, considering both the white and the 1/f component given by (6) and assuming r feT, > 1, can simply be obtained from (11) and (13): SAZ(f) = I f )12 SN(f)+ stoic’ (14) 2This selection reflects the requirement f.T.,
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`2BT,So. Ts (7) The signal corresponding to (7) has no physical reality since its power is infinite. The power is actually bounded by the sinc2 (7r fTs) 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 sinc2 (7r f Ts) function: sfuld-whit,,(f) _ (2BT, - 1)S0 sinc2 (7r fT(cid:132)). (8) This result can be extended to the case of a first-order low-pass filtered white noise with a PSD So S N
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`EM! AND TEMES: CIRCUIT TECHNIQUES FOR REDUCING THE EFFECTS OF OP-AMP IMPERFECTIONS
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`icfcT s -
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`AZ output PSD
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`•
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`Foldover
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`Baseband
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`AZ input PSD
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`---
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`1
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`Fig. 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. a co
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`Ow.
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`fcTs = 5
`fkIs = 1
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`. ....... .... ....... (cid:149)(cid:149)(cid:149)(cid:149)(cid:149)(cid:149) ... ....................... ......
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`•••
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`-0.5
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`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 Sfold = S0{ (71- feTs - 1) + 2 fkTs[l + In (:ifeTs)]1 (cid:149) since (71-f T8 ).
`falling in the region above this curve, while it is dominated by the broadband white noise contribution below the curve. For example, an amplifier autozeroed at 100 kHz and having a gain-bandwith product equal to 7 x fs = 700 kHz should have a corner frequency larger than 4.13 x f, = 413 kHz for the 1/f noise foldover to dominate.
`(15) The corner frequency for which the 1/f noise foldover component [given by (13)] is equal to the foldover compo-nent coming from the white noise [as given by (8)] is plotted against the normalized white-noise bandwidth in Fig. 7. The
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`total foldover term given by (15) is thus dominated by the 1 / f noise contribution for parameter values (fkTs , f eTs)
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`AZ input PSD
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`AZ output PSD
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`Foldover
`component
`
`Baseband
`component
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`_ -
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`•••
`
`......
`
`......
`zeroed 1/f noise
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`12
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`Q. 10
`V a)
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`8
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`O
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`6
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`4
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`2
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`0
`-1.0
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`TCL & Hisense Ex. 1007
`Page 7
`
`V
`

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`100
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`input referred offset
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`1/f noise foldover
`component dominates
`
`white noise foldover
`component dominates
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`I
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`I
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`I
`
`I
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`I I 11111
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`residual offset Vos-NL
`V
`•
`os-lin
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`initial offset
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`control
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`__Control
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`errors
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`1
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`Fig. 7.
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`10
`fcTs
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`Comparison between the 1// and white noise contribu-tion to the total foldover component as a function of the white-noise bandwidth. 100 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 transfer 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 equivalent noise bandwidth to the Nyquist frequency. C. Residual Offset Next, the effectiveness of the stages of Fig. 1 in eliminat-ing the effects of V(cid:132), will be discussed. Since the additional input used in the amplifiers of Fig. 1 for nulling the offset can either be a voltage or a current, it will generally be denoted as a control variable 3:(cid:132).. 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 Ax,. introduced into the control variable, due for example to charge injec-tion by the sampling switch, or to the quantization error of the A/D converter, that leads to a residual offset Vi(cid:132)s_ii(cid:132) or 17;,,,,,_NL depending if the compensation characteristic is linear or not. It is important to notice that the characteristics
`
`(a)
`
`input referred offset
`
`Axc
`
`Axc
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`residual offset
`
`Vos-lin
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`Vos
`
`control
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`control errors
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`initial offset
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`Fig. 8.
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`Input-referred offset versus nulling control variable: (a) large initial offset and (h) small initial offset. between the control variable and the input-referred offset voltage is not required to be linear. An example of a nonlinear characteristic is illustrated in broken lines in Fig. 8(a) and (b). Let AV be defined as the difference between the initial offset and the offset corresponding to the point where the incremental gain on the nonlinear characteristic equals the slope of the linear characteristic. The resulting residual offsets of the linear (Vios_ii(cid:132)) and the nonlinear (Vi,-N-1,) characteristics resulting from equal control errors Axe are compared in Fig. 8(a) for an initial offset larger than A V. The residual error of the nonlinear characteristic is obviously larger. On the other hand, if the initial offset is already small compared to AV [Fig. 8(b)], the residual offset of the nonlinear characteristic becomes smaller. A nonlinear offset-nulling characteristic can thus potentially reduce the sensitivity to control errors and hence reduce the residual offset.
`But this only happens if the initial offset is already small. The choice between a linear or a nonlinear control characteristic depends on the anticipated initial offset reduction strategy and the test methodology. D. Correlated Double Sampling In the AZ principle described in Fig. 1, the amplifier has to be disconnected from the signal path during phase 01 in EN/.
`
`AND TEMES: CIRCUIT TECHNIQUES FOR REDUCING THE EFFECTS OF OP-AMP IMPERFECTIONS
`
`1589
`
`TCL & Hisense Ex. 1007
`Page 8
`
`(b)
`

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`V n
`
`►fT
`
`1 2 3 4 5
`
`- (cid:149) A f m2(t) At VAm2(t)
`1 2 3 4 5 Vin(cid:149)miml (t) mi (t) 1 2 3 4 5 Fig. 9. The chopper amplification principle [19]. Vin(t) mi(t). Vin(t) +VinT/2 T/2 (cid:151)yin-Vos VN V(cid:132)+VN
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`VA(t)
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`+4/16•Ao•Vin
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`- 4/1t.Ao•Vin
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`