IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. SC-22, NO. 3, JUNE 1987 335 A CMOS Chopper

CHRISTIAN C. ENZ, STUDENT MEMBER, IEEE, ERIC A. VITTOZ, MEMBER, IEEE, AND FRAN~OIS KRUMMENACHER

Abstracf —This paper describes a highly sensitive CMOS chopper Section II will review different low-frequency noise and amplifier for low-frequency applications. It is realized with a second-order offset reduction techniques, emphasizing the fundamental low-pass selective amplifier using a continuous-time filtering technique. differences between the autozero and chopper techniques. The circuit has been integrated in a 3-pm p-well CMOS technology. The chopper amplifier dc gain is 38 dB with a 2@-Efz bandwidth. The equiv- Section III will present the realization of the selective alent inpnt noise is 63 nV/dHz and free from l/~ noise. The input offset amplifier, whereas the theoretical performances of the is below 5 VV for a toning error less than 1 percent. The amplifier chopper amplifier will be discussed in Section IV. Finally consumes only 34 ~W. the circuit implementation and the experimental results will be presented in Sections V and VI. 1. INTRODUCTION II. LOW-FREQUENCY NOISE AND OFFSET N SPITE OF the evolution of scaled-down digital REDUCTION TECHNIQUES [3] Iprocesses, analog circuits will always be needed to per- form a variety of critical tasks required to interface the 4. Input Device Optimization digital with the external world. One of these functions is high-precision amplification with low power consumption. The classical approach to reduce the l/f noise is to The amplifier must be fully compatible with a process enlarge the gate area of the input devices [3]. This method basically tailored for digital requirements like the CMOS is area costly and inefficient because offset and l/f noise technology. subsist at low frequency. A second approach is to use It is well known that highly sensitive CMOS MOS input operated in the lateral bipolar mode are always limited by offset and I/j noise. An offset [4], [5]. This mode of operation provides a reduction of voltage of 10 mV and a comer frequency of 10 kHz are more than 40 dB for the l/f noise with an offset typically typical values for a CMOS amplifier. A combination of comprised between 1 and 10 mV. Further improvements of autozero and chopper techniques was used by Poujois and the l/f noise and the offset require special circuit tech- Borel [1] to realize a fully integrated MOS amplifier with niques. typical offset of 5 pV and an equivalent input noise of 2.5 pV/~Hz. However, two external capacitors were required B. A utozero Technique and the amplifier consumed 240 mW! Good noise perfor- mance was obtained by Hsieh et al. [2] in a CMOS The principle of the autozero technique is represented in differential chopper amplifier for SC filter applications. Fig. 1. In the sampling phase @l the output and the input The equivalent input noise was 40 nV/~Hz for a chopper of the amplifier are shorted together, so that the input frequency of 128 kHz. The amplifier displayed a 15-MHz noise is sampled in capacitor C. In the amplification phase gain-bmdwidth product and 4-rnW power dissipation with @2 the noise sample is subtracted from the instantaneous k 7.5-V supplies. noise of the amplifier. Since the sampled noise and the This paper presents a highly sensitive CMOS chopper low-frequency continuous noise are highly correlated dur- amplifier realized with a second-order low-pass selective ing a sampling period, the l/f noise is removed. “Thesame amplifier. The objective is to reach the microvolt level for is true for the amplifier offset, except that offset will both offset and noise, while keeping the total power con- subsist due to charge injection. In the case of a–single-pole sumption below 100 ILW.The bandwidth is then limited to amplifier, the transfer function is given by a few hundred hertz by the fundamental thermal noise. AO A(f)=— (1)

Manuscript received October 14, 1986,; revised January 5, 1987, This l+j~ work was supported by the Fends National Suisse pour la Recherche Jc Scientifique,.PN13. C. C. Enz and F. Krummenacher are with the Electronics Laboratory, where AO is the dc gain and f, the cutoff frequency. The Swiss Federrd Institute of Technology-. (EPFL), CH-1OO7 Lausanne, equivalent amplifier input noise can be expressed as’ Switzerland. E. A. Vittoz is with the Centre Suisse d’Electronique et de wcrotech- fk nique S.A. (CSEM,), CH-2000 Neuchiltel 7, Switzerland. (2) IEEE Log Number 8713955. ‘N’”= ‘“0 ()1+ m 0018-9200/87/0600-0335 $01.00 01987 IEEE

/ 336 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. SC-22, NO. 3, JUNE 1987

m,(t) ~ ,=,,2 r----% m,(t) t m2(t ) * 9 9 -y+++ vi 1 “ o J

LfTLfTkfTkfT

Fig. 1. Autozero amplification principle Fig. 3. Chopper amplification principle.

However, the output noise is dominated by the amplifier undersampled w~te noise. Thus the l/f noise is removed at the cost of an increase of the white-noise component by -1 /0 a factor ~fCT,. The offset cancellation is limited by charge injection due to the autozero switch. It can be reduced to a mismatch of charge injection by using a fully differential implementa- tion. The basic autozero principle described above can be improved by storing the offset and the noise information at the output of a first amplifier stage [8]. Effects due to . .. ~ o 1 2 3 4 5 charge injection and noise undersampling are thus reduced by a factor proportional to the gain of this first amplifier. fT, However, the need of a two-stage amplifier gives rise to Fig. 2. Baseband transfer function lHO(~) 1. potential stability problems. Another possibility & to use an amplifier with a low-sensitivity auxiliary input con- where S~Ois the amplifier white-noise component and f~ trolled by the compensating voltage [9], [10]. the corner frequency. Assuming that AO >>1, fCT, >>1, The alternative to the autozero method is the chopper f~~ < 1/2, and (~1/~2) <<1, the avera~e output noise technique, which will be described in the next section. power spectrum is given by [6] C. Chopper Technique [2] fk Sivo.t(.f) ‘4%0 1+ fi l~o(.f)l’ The chopper amplification principle is illustrated in Fig. (( ) 3. Suppose that the input signal has a spectrum limited to + nfc~sine’ ( nf T, ) (3) fChOP/2and that the amplifier has neither noise nor offset. } This input signal is multiplied by the square-wave modulat- where ion signal ml(t) with period T= l/fChOP.After this mod- ulation, ‘the signal is transposed around the odd harmonic fr~quencies of the modulation signal. It is then amplified l~o(f)l’ =(l-sinc(mfl,))’+ and demodulated back to the original band. Because of the (1-’%7)2 ‘4) finite bandwidth of the amplifier, the output signal con- (5) tains spectral components aroun,d the even harmonics of the chopper frequency. The bilateral Fourier transform (BFT) of the output voltage Uo(t) is given by The first term in (3) represents the baseband noise attenua- tion, while the second term comes from the undersampling of the amplifier white noise [7]. The transfer function Vo(f) = y Hk(f”)~ f –,; (7) kk=e;ec l~o(f )1 is represented in Fig. 2. For ~fl$ <1, it can be (1 approximated by a differentiator function where

~fls 2 l~o(f)12= y . (6) () Because of the double zero introduced by the baseband transfer function [HO(f) 12, the l/f noise is removed. for k even (8) ENZ d a[.: CMOS CHOPPER AMPLIFIER 337

+Vinj

t

‘Vinj T I!zfT (a)

. infinite bandwidth 2 ~ t E ideal low-pass a A

103 , , 10= m % ~ fT 1 3 579 11

(b) z Fig. 5. (a) Spikes’ signal (b) Spikes’ signat and modulated signaf spec- Yi tra with amplifier transfer function characteristics. g

10 10 tively, the chopper amplifier schematic and the measured 1 10 10= 103 10’ equivalent input noise. The measured input white noise Froquoncy [Hz] without the chopper is 37 nV/~Hz and the theoretical input white noise given by (11) is 50.5 nV/~Hz for &OP= (b) f~ = 1 kHz, which is very close to the measured result. Fig. 4. (a) Expenm@af chopper amplifier schematic. 0,41 and OA 2 were, respectively, a CA 3420 and a pA 741 and the switches were Equation (11) shows that if f~ >>fCkOPthe equivalent MC 14016. ~chOP= fk=1 klfz. (b) Measured equivalent input noise. low-frequency input noise of the chopper amplifier is equal to the original amplifier white-noise component. Contrary ~.(~) is the BFT of the input voltage, and tO is a possible to the autozero techmque, the white noise is not aliased delay between the input and output modulation signals to because there is no sample-and-hold process. This suggests compensate for the phase shift introduced by the amplifier. that the autozero technique is more suitable for sampled- After low-pass filtering at &OP/2, (7) becomes data circuits like SC filters [11] where the undersampling process is unavoidable and that the chopper technique is vo[f)=Ho(f)fi(f) (9) better used in continuous:time applications. The high-frequency components, which also include the where HO(~) represents the baseband transfer function amplifier l/f noise and offset, can easily be removed by a and is given by (8) for k = O. simple low-pass fiiter. The noise and the offset of the amplifier are only As is the case for the autozcwo technique, the offset of modulated once and translated tb the odd harmonics of the chopper amplifier is lirriited by charge injection r&- the output chopping square wave. The output noise spec- match. T&s charge injection and parasitic coupling in the trum is given by input modulator cause spikes to appear at the input of the amplifier. As only the components at the odd harmonics of the chopper frequency contribute to the offset after de- modulation, the positive and negative spikes can be as- (lo) sumed to be symmetrical as represented in Fig. 5(a). If care is taken to limit the time constant ~ of those spikes to where S~,. ( ~ ) is the amplifier equivalent input noise a value much smaller than T/2, most of the energy re- spectrum given by (2). In the case of a single-pole ampli- mains at frequencies higher than the chop$er frequency. fier with a transfer function given by (l), the low-frequency The spectrum of the spikes’ signal is represented in Fig. output noise spectrum given by (10) can be summed and 5(b) by impulses at the odd harmonics of the chopper approximated by frequency with an equivalent bandwidth proportional to l/~ and much larger than fchop. On the other hand? Fig. 5(a) shows the spectrum of a modulated signal. Since the spectral envelope is inversely proportional to the frequency, ‘NOut=A:snO(l+a)’11)the output signal after amplification and demodulation is where it is assumed that ml(t) = rn2(t) (tO = 0) and ~C>> essentially reconstituted by the fundamental component. ~CbOPto preserve a sufficient overall gin for the chopper This sets the problem of choosing the amplifier bandwidth amplifier. Equation (11) has been verified experimentally such as to have sufficient gain for the modulated signal on a breadboard circuit. Fig. 4(a) and (b) shows, respec- while rejecting most of the spikes’ spectral components. 338 IEEE JOURNAL OF SOLID-STA’JZ CIRCUITS, VOL. SC-22, NO. 3, JUNE 1987

V(.*V.”,. 2C “

VW, = + vi” Input stag- Cmtr.1 cell output Stage

(a) (b) Fig. 6. (a) Basic integrator. (b) Low-pass selective amplifier principle.

Assuming that the output modulator is ideal, the output ~’,, offset is given by Fig. 7. Low-pass selective amplifier schematic.

vOffOut= — ~=–mjm5 ~ex’(’2mn+}A(~)~p~e(~) 2) the central cell which fixes the resonance frequency n odd f,; and (12) 3) the output stage which realizes the current-to-volt- age conversion while providing a defined quality where factor Q. It can be shown that the optimum dynamic range is obtained for g~2 = g~~ = gn and Cl = C2= C. The transfer function is then given by is the. BFT of the spike signal of Fig. 5(a). In the case of an ideal amplifier with gain A~ and infinite bandwidth (16) (12) reduces to

(14) where A ~ = g~l/g. and Q = gm/gm4. The resonance frequency aO and the gain at tiO are, respectively, given by where it is assumed that ~ <

(15) Because of the lack of a positive transconductance ele- ment, the selective amplifier is implemented in a fully It can be shown that this result is already obtained with differential structure, which also offers an increase in the a second-order low-pass selective amplifier, assuming that common-mode signal rejection and an easy implemen- the resonance frequency is locked to the chopper frequency. tation of the modulators. Fig. 7 shows the selective ampli- This means that the output offset is not further reduced by fier schematic with the input and output modulators. Pair using a higher order selective filtering characteristic. T1/T{ forms the itiput stage, pairs T2/T~, T3/T~, and Therefore second-order selective amplification is the best capacitors C form the resonator, while pair T4/ T/ is the trade-off between circuit complexity and residual offset. termination. A controlled gain at the resonance frequency requires matching of pairs Tl, T; and T4, T4’. On the contrary a good matching of pairs T2, T2~and T3, T3’ is not III. THE SELECTIVE AMPLIFIER necessary because the resonance frequency is given by the mean of their transconductances. To obtain an indepen- The selective amplifier is realized using the continuous- dent control of Ao, @o,and Q, half of currents 11 and 14 time filtering technique described in [12]. It is based on the are subtracted from the appropriate branches as is shown g~ /C integrator represented in Fig. 6(a) and made of a in Fig. 7. positive or negative transconductance element and an in- TO obtain a sufficient gain A~= and to optimize the tegrating capacitor. The second-order low-pass selective offset and the white noise at a given current, the input pair amplifier represented in Fig. 6(b) is composed of three Tl, T{ is biased in weak inversion [13]. It is realized in parts: PMOS because of the better flicker noise of those devices. 1) the input stage which realizes the voltage-to-current Thus g~l is proportional to 11 whereas g~i are propor- conversion and provides the dc gain A ~; tional to & (i = 2,3,4). To keep the dc gain A. constant ENz et a[.: CMOS CHOPPER AMPLIFIER 339 .1“’Y*F; “vi”F:ww:wt Fig. 8. Chopper smplifier dc gain. for small variation of the current 12 when adjusting the the relative error on the dc gain can be expressed as resonance frequency ~0,II is set to two times 12. AA~c The complete chopper amplifier will be described in — = (2Qt)2 (21) Section IV. A DC max where it is assumed that Q >>1 and A~c ~= = (8/7r2)A~m. IV. THE CHOPPERAMPLIFIER Since the gain error is proportional to the square of the quality factor, a high-precision de gain implies a very A. DC Gain and Transfer Function accurate tuning or a low Q.

To evaluate the dc gain of the chopper amplifier, let us B. Noise assume that the resonance frequency is ideally locked to the chopper frequency (~. = ~C~OP).Note that because of The output noise spectrum given by (10) is essentially the 90° phase shift introduced by the selective amplifier, composed of spectral Components around fchOP(n = 3 1). the input and output modulation signals have to be in The low-frequency output noise becomes quadrature as illustrated in Fig. 8. Supposing that the input signal is a dc signal with amplitude Vi., the signal fk s AA’ S I+_...._ (22) after the first modulator is a square wave with amplitude Nout = ~2 max nO Mfchop “ Vi. and period T (Fig. 8). The signal after selective ampli- fication is approximately a sine wave with amplitude Since A.> 1, the noise is mainly due to the input pair and (4/m) A~=Vti, period T, and a 90° phase shift. The output can be expressed as signal after demodulation is a rectified cosine wave with a S~o= 4kTRN1 (23) dc component equal to (8/~ 2)A~mVin. In order to achieve maximum gain for the chopper amplifier, one has to where R N1= n~/g~l is the thermal noise of the input realize gain peaking in the selective amplifier at the chopper transistors (nl is the weak inversion slope factor [5]). frequency, which implies that Q>> 1. The overall baseband Using (19) the equivalent low-frequency input noise transfer function (k= O) can be evaluated using (8) and becomes to= (16) with T/4 and ~0= ~C~OP.For Q>> 1 and s<< aO, fk only the fundamental component can be taken into account SNin = :4kTRN1 1+ — (24) (n’t= *1): ()fchop “ 8 Am= Equation (24) shows that to eliminate the contribution of Ho(s)=~— (19) the l/f noise to the residual noise, the chopper frequency n 1+: fchop must be much larger than the corner frequency fk. In this case the original amplifier white noise is only increased by a factor of T2/8 (2 dB). where ~.= Q. /(2Q ) is the cutoff frequency. Note that (24) holds only if the source impedance is The resonance frequency can be locked to the chopper resistive. As a matter of fact, in the case where the source frequency by using a reference amplifier [12] or a PLL [14]. impedance is capacitive, the broad-band noise undersam- In practice, a certain difference between ~0 and ~C~OPwill pling process discussed previously will reappear. subsist due to the nonidealities of the tuning circuit. Be- cause of this residual error, the dc gain will decrease. C. Offset Defining the tuning error by There are many possible causes for residual offset, but fo. _l (20) the most fundamental is the charge injection and parasitic ‘ = fcho, coupling in the input modulator. Fig. 9 represents the 340 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. SC-22, NO. 3, JUNE 1987

-! J Fig. 9. Chopper amplifier input modulator.

input modulator where R, is the source resistance and C; Fig. 10. Photomicrograph of the chip. and Ci; are the selective amplifier input capacitances. At each switching, a certain amount of charges Aql and Aq3 will flow, respectively, into capacitors C: and Ci~, while can easily show that the product AqRon is independent of charge Aq2 will flow through the source resistance R$. the switch width W and is minimum for a minimum These charges Aqi(i = 1,2, 3) result from mismatches be- channel length. Thus we can assume that for a given tween the different switches realizing the input modulator. process the product AqROn remains approximately con- Assuming that half of the charges forming the switch stant with respect to W. On the other hand, a proper channel flow into source and drain, Aqi can be expressed working of the input modulator requires R ~nCin to be as much smaller than T = (l\fchop).As Q is considered to be much larger than one, the second term in (26) will usually Aqi= dominate. Furthermore, (24) and (26) show that there is a %(%+3VD--AVT1 trade-off between the noise and the offset with respect to ACOU the chopper frequency. A good choice is to take fchOP= fk. + CO”(VDD–vJ~, i=l,2,3 (25) In the case where the source impedance is much larger 00 than the ON resistance of the switches, the input offset is still given by (26) where ROn must be replaced by the where source resistance R,. For c = O, the input offset increases W, L dimensions of the switches, quadratically with respect to R, and thus this chopper c overlap capacitance, amplifier is no longer suited for high-precision dc amplifi- A?OJCOU relative overlap capacitance mis- cation. match, A~./~, ALi/Li relative geometric mismatch (i= 1,2, 3), and V. CIRCUIT IMPLEMENTATION A“, threshold-voltage mismatch. To avoid saturation of the second stage while keeping To evaluate the output offset, let us first assume that sufficient gain at fo, zto and Q were both set to 10. This gives a gain A~a of 40 dB and a chopper dc gain of 38 dB. Aq1=Aq2=– Aq3=Aq To maintain the theoretical input offset below 1 pV, a ROni= ROn, for i=l,2,3,4 chopper frequency of 4 kHz is chosen. The chopper amplifier cutoff frequency is then equal to 200 Hz. To respect the condition f~h~p> fk, g~l is set to 15 pA/V. Capacitor C is then equal to 30 pF. The theoretical input and that the clock rise and fall times are much smaller noise estimated by (22) is 47 nV/{Hz with fk = 645 Hz than the spikes’ time constant ~, the output modulator is and T = 300 K. The resulting theoretical input offset given ideal, and the resonance frequency is locked to the chopper by (26) is 0.57 pV, assuming that AW/ W = AL/L = frequency. The output offset is then given by (15) with ACou/Cou= 30 percent, lAV~l = 100 mV, Ron= 90 kfl, Ci. ~.~j = (2A q)/Cin, ~ = RonCin, and AO= A~=. Using (12) = 1 pF, and c = 1 percent. and taking into account the tuning error discussed previ- The chopper amplifier has been integrated using a 3-pm ously, it can be shown that the input offset is given by p-well CMOS technology. A photomicrograph of the chip is presented in Fig. 10. The total chip size is 0.95 mm2.

voff ~ 2~fchOP AqR m{ 2 ‘fchop R onCm +2Q(} (26) Care was taken to respect the symmetry of the circuit in designing the layout. Note that the input pair was cascoded where c represents the tuning error defined by (20). One and realized as a quad. ENZ et al.: CMOS CHOPPER AMPLIFIER 341

50- supplementary parasitic coupling. The circuit consumes - 180” 12.690nA 40 . only 34 pW.

30 - 12=1PA l,= 1.2PA

20 VII. CONCLUSION m’ ~ A highly sensitive amplifier for low-frequency applica- G o - tions has been described. To reach the microvolt range it is necessary to eliminate both the l/~ noise and the offset of -lo - the amplifier. The chopper modulation technique was cho- -20 - sen to avoid aliasing of the amplifier broad-band noise.

-30; The residual offset due to charge injection and parasitic 345 m Frequency [kHz] coupling in the input modulator is minimized at first by Fig. 11. Selective arnpfifier measured transfer functions. spreading most of the spikes’ energy to high frequency and then by choosing selective amplification to amplify the modulated signal and reject most of the spike components. To minimize the contribution of the I/f noise to the TABLE I chopper amplifier residual noise, the chopper frequency CHOPPER AMPLIFIER MEASURED RESULTS must be larger than the amplifier corner frequency. But since the residual offset increases with the chopper Test condition: VDD = +2 V v~~ = -2 v f~ = fc~OP= 4 kHz frequency, there is a trade-off between offset and noise. A

DC gain : AK= 38dB good compromise is to choose the chopper frequency equal c utmff frequency : fc = 200 Hz to the corner frequency. low-frequencyinputnoise : ~.63nV/~ The integrated chopper amplifier has a 38-dB dc gain, a typicalinputoffset: Voff=5 WV 200-Hz bandwidth, and a input offset below 5 pV for a pouw consumption: P=34pw tuning error smaller than 1 percent. In a future design, which will include the clock generator and the tuning circuit on the chip, we can expect that an offset less than . 1 pV will be reached. The input low-frequency noise is free from l/~ noise and equal to 63 nV/~Hz. This amplifier was originally designed for a temperature sensor using a thermocouple, but it can be used for any low-frequency application.- ensuring that the source impedance is resistive : and much smaller than the ON resistance of the switches. ~-1200 5 10 o Frequency [HZ] REFEMNCES Fig. 12. Chopper amplifier measured output noise s ectnrm. V~~ = 2V, Vs~=-2V, fO=4kHz, fChOP=4k& . [1] R. Pouiois and J. Borel. “A low drift fullv integrated MOSFET operati&ml amplifier,” IEEE J. Solid-State ~ircuit;, vol. SC-13, pp. 499-503, Aug. 1978. [2] K. C. Hsieh et al., “A low-noise chopper-stabilized differential switched-car3acitor filtering technique.” IEEE J. Solid-State Cir- cuits. vol. SC-16. rm. 708–~15. Dec~1981. VI. EXPERIMENTALRESULTS [3] H. W. Klein ~d ‘W. L. Engl, “Design techniques for low-noise CMOS operational amplifiers,” in ESSCIRC ’84 Dig. Ted-z. Papers, The measured transfer functions of the selective ampli- Sept. 1984, pp. 27-30. [4] E. Vittoz, “ MOS transistors oDerated in lateraf biDohr mode and fier are presented in Fig. 11 for different bias currents. their armlications in CMOS te;hnolo~v.” IEEE J. ‘Solid-State Cir- Note that AO and A~w are kept constant for a t 25-per- cuits, ~~1.SC-18, p . 273–279,,June 1383. [5] E. Vittoz, “The /’eslgn of hrgh-performance analog circuits on cent variation of $.. The measured output noise at j.= 4 digitaS CMOS chips,” ZEEE J. Solid-State Circuits, vol. SC-20, pp. kHz is 5.5 pV/~Hz; the CMRR and the PSRR at ~.= 4 657-665, June 1985. [6] C. Enz, “Analysis of the low-frequency noise reduction by autozero kHz are better than 50 dB. technique;’ Electron. Left., vol. 20, pp. 959-960, Nov. 1984. Table I shows the measured performance of the chopper [7] C. A. Gobet, “Spectraf distribution of a sampled lst-order lowpass filtered white noise;’ Electron. Lett., vol. 17, pp. 720-721, Sept. amplifier. As expected, the measured dc gain is 38 dB and 1981. the cutoff frequency is 200 Hz. Fig. 12 shows the output [8] R. C. Yen and P. R. Gray, “A MOS instrumen- tation amplifier,” ZEEE J. So[id-State Circuits, vol. SC-17, pp. noise spectrum of the chopper amplifier measured between 1008-1013, Dec. 1982. O and 10 Hz. The noise is free from I/f noise and [9] E. Vittoz, “Dynamic analog techniques,” in Design of MOS VLSI Circuits for , Y. Tsividis and P. Antognetti, Eds. corresponds to an equivalent input white noise of 63 Emzlewood Cliffs. NJ: Prentice-Hall. 1985. DD. 145-171. nV/4Hz. The input offset is below 5 NV for a tuning error [10] M.- Degrauwe et al., “A micropower’ ~MOS-instrumentation amplifier’ IEEE J. Solid-State Circuits, vol. SC-20, pp. 850–807, less than 1 percent. One reason that the input offset is June 1985. above 1 pV is that the measurement system, including the [11] F. Krummenacher, “ Micropower switched capacitor biquadratic cell; IEEE J. So[id-State Circuits, vol. SC-17, pp. 507–512, June clock generator, was external and thus introduced some 1982. 342 IEEE JOURNAL OF SOIID-STATE CIRCUITS, VOL. SC-22, NO. 3, JUNE 1987

[12] H. Khorranrabadi and P. R. Gray, “High-frequency CMOS con- After spending one year as a Research Assis- tinuous-time filters.” IEEE J. Solid-State Circuits. vol. SC-19. ,..DV. tant, he joined the Centre Electronique Horloger 939-948, Dec. 1984. SA (CEH), Neuch2tel, Switzerland, in 1962, [13] E. Vittoz and J. Fellrath, “CMOS analog circuits based on weak where he became involved in micropower in- inversion operation,” IEEE J. Solid-State Circuits, vol. SC-12, pp. tegrated circuit developments for the watch, while 224-231, June 1977. preparing a thesis in the same field. In 1971 he [141. . M. Banu and Y. Tsividis. “An ellictic continuous-time CMOS filter with on chip automatic tuning,” IEEE J. Solid-State Circuits, vol. became Vice-Director of CEH, supervising ad- SC-20, pp. 1114-1121, Dec. 1985. vanced developments in electronic watches and other micropower systems. Since 1984 he has been Director of the Centre Suisse d’Electro- nique et de Microtechnique SA, Neuch?itel, Switzerland, which was cre~ted by merging CEH laboratories with other institutes, and he is in charge of the Division of Circuit and System Design. His field of personal research is the design of low-power analog circuits in CMOS technologies. Since 1975 he has also been lecturing and supervising student work in design at EPFL, where he became Titular Professor in 1982. Christian C. EHZ(S’83) was born in Ziirich, Switzerland, on December 24, 1957. He received the MS. degree in electrical engineering from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1984. Since 1984 he has been a Research Assistant at EPFL, where he is currently working towards the Ph.D. degree on the subject of micropower ana- log CMOS integrated circuit design. Fran$ois Krnmmenacher was born in Lausanne, Switzerland, on April 29, 1955, He received the MS. and Ph.D. degrees in electrical engineering from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1979 and 1985, respectively, Since 1979 he has been with the Electronics Laboratory of EPFL, working in the field of low-power and high-performance analog CMOS integrated circuit design. From ADril to October 1987 he was with the %lectrical E~gineering De- Eric A. Vittoz (A’63-M72) was born in Lausanne, Switzerland, on May partment of the University of California, Los Angeles, where he was 9, 1938. He received the M.S. and Ph.D. degrees in electncaf engineering involved in the design of MOS switched-capacitor circuits, He is currently from the Federal Institute of Technology (EPFL) in Lausanne, Switzer- responsible for the research activities at the Electronics Laboratory of land, in 1961 and 1969, respectively. EPFL.