This paper analyzes the advantages and limitations of using the floating- (or flying-) capacitor technique as a building block with differential input and either differential or single-ended output to implement voltage amplifiers, multiplexers,
and coherent amplitude demodulators. Theoretical analysis, supported by experimental results, shows that the fully differential configuration has a better common-mode rejection ratio (CMRR). However, if the output signal, once amplified, must be
single ended, then it may be better to have a floating capacitor with single-ended output in amplifiers and some multiplexers
whereas in demodulators a floating capacitor with differential output yields a better CMRR.Peer Reviewe

Gasulla Forner, Manuel

Jordana Barnils, José

Pallàs Areny, Ramon

Torrents Dolz, Josep M.

IEEE Transactions on Instrumentation and Measurement

English

This paper analyzes the advantages and limitations of using the floating- (or flying-) capacitor technique as a building block with differential input and either differential or single-ended output to implement voltage amplifiers, multiplexers,

and coherent amplitude demodulators. Theoretical analysis, supported by experimental results, shows that the fully differential configuration has a better common-mode rejection ratio (CMRR). However, if the output signal, once amplified, must be

single ended, then it may be better to have a floating capacitor with single-ended output in amplifiers and some multiplexers

whereas in demodulators a floating capacitor with differential output yields a better CMRR.Peer Reviewe

UPCommons

The floating capacitor as a differential building block

Pallàs-Areny, Ramon

UPCommons. Portal del coneixement obert de la UPC

26 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 1, FEBRUARY 1998The Floating Capacitor as aDifferential Building BlockManel Gasulla-Forner, Student Member, IEEE, Josep Jordana-Barnils, Student Member, IEEE,Ramo´n Palla´s-Areny, Fellow, IEEE, and Josep Maria Torrents, Member, IEEEAbstract— This paper analyzes the advantages and limita-tions of using the floating- (or flying-) capacitor technique as abuilding block with differential input and either differential orsingle-ended output to implement voltage amplifiers, multiplex-ers, and coherent amplitude demodulators. Theoretical analysis,supported by experimental results, shows that the fully differ-ential configuration has a better common-mode rejection ratio(CMRR). However, if the output signal, once amplified, must besingle ended, then it may be better to have a floating capacitorwith single-ended output in amplifiers and some multiplexerswhereas in demodulators a floating capacitor with differentialoutput yields a better CMRR.Index Terms—Capacitor switching, CMRR, data acquisition,differential amplifiers, multiplexing, sampling methods, syn-chronous detection.I. INTRODUCTIONTHE floating- (or flying-) capacitor technique is a com-mon method for low-level signal amplification [1] andmultiplexing [2]–[4]. Fig. 1 shows the basic floating-capacitorcircuit. First, switches and close and charges tothe differential input voltage (assumed constant). Next,and open and and close, so that, except forstray capacitances to , the charge stored by isshared by , assuming it was previously fully discharged,in accordance with(1)And therefore(2)This means that the differential output voltage ideallydepends only on the differential input voltage , thus yieldinga very high common mode-rejection ratio (CMRR) without thenecessity of any component matching.When the floating-capacitor technique is used for amplifi-cation [1] or demodulation [5] or multiplexing [2], the circuitoutput in Fig. 1 is usually grounded and connected to the inputof a single-ended amplifier that provides gain and low outputimpedance [1], [5]. This is a considerable advantage becauseit allows us to use an op-amp-based amplifier, which is lessManuscript received June 1, 1997; revised March 27, 1998. This work wassupported by the Spanish DGICYT, Project PB93-0961.The authors are with the Divisio´ d’Instrumentacio´ i Bioenginyeria, Depar-tament d’Enginyeria Electro`nica, Universitat Polite`cnica de Catalunya, 08034Barcelona, Spain.Publisher Item Identifier S 0018-9456(98)05492-8.Fig. 1. Floating capacitor circuit. Cs1 to Cs4 are stray capacitances.expensive than an instrumentation amplifier. Furthermore, byusing switches able to withstand high voltages it is possible topick out small differential voltages superimposed on very highcommon-mode voltages. In multiplexers, however, sometimesnone of their output terminals are grounded [3], [4] but areconnected to an instrumentation amplifier.Therefore, the question arises as to whether it is better touse the floating capacitor as a building block with differentialinput but single-ended output, or as a fully differential circuit.A satisfactory answer can only be given by considering thefact that an amplifier must follow the floating capacitor.II. THEORETICAL ANALYSISA. Fully Differential Floating CapacitorAnalog switches have stray capacitances to ground, whichaccording to switch technology can change from the ON tothe OFF state. These changes are disregarded here. In Fig. 1,parallel capacitances are grouped together. Let the switcheshave zero ON resistance.is defined as the charge on the top plates of , ,, ; and as the charge on the top plates of ,, plus the charge on the bottom plates of , . At anyrandom time period , first , are closed and ,are opened. The charge will result from the actual inputvoltages on the top plates of , plus the charge storedon the top plates of , , at the previous time period(assuming that has not been reset between samples). Thesame will apply for , giving(3)0018–9456/98$10.00  1998 IEEEGASULLA-FORNER et al.: FLOATING CAPACITOR AS A DIFFERENTIAL BUILDING BLOCK 27When and close, the electric charge will quicklyredistribute among capacitances. As the total charge at eachside, and , cannot change, we have(4)Equating expressions (3) and (4) in the transform domain [6]shows that after many clock cycles the voltage at each outputterminal equals that at the respective input terminal, which areassumed to be constant. That is , .Input and output signals can be described in terms ofdifferential and common-mode voltages, ,, , .Fully differential circuits can be described by four transferfunctions as follows [7]:(5)Here, , , , and .The CMRR (CMRR ) is therefore infinitebecause the input common mode voltage cannot produce anydifferential output voltage.In practice, the input voltage will not be truly constantand when closing and there will be some chargeredistribution to “update” the voltage across . But if theswitching rate is fast enough as compared with the rate ofchange of the input signal, a steady state will be reachedrather quickly.B. Floating Capacitor with Single-Ended OutputIn Fig. 1, if the bottom side of the output circuit is grounded,then when and are closed, (3) is still valid (with). However, when and close, the chargewill remain constant, but part of will run to the ground.The output voltage will then fulfill the condition(6)As before, the output voltage after many clock cycles canbe calculated by assuming the input voltages to be constant,(7)If the input signals are again described by differential andcommon mode voltages, can be written as(8)From (7),(9)Therefore, the CMRR is now,CMRR (10)which is smaller than that of a fully differential floatingcapacitor circuit.C. Effect of Output Amplifier on the CMRRBoth the fully differential and the single-ended circuits needan output amplifier to provide gain and low output impedance.If this amplifier has a differential input, the overall CMRRwill be [7],CMRR CMRR CMRR (11)where CMRR and CMRR are the respective CMRR’s forthe floating capacitor circuit and the amplifier. This means thatCMRR will be smaller than that of each stage, if they havethe same sign, and will be the largest of them all, if they haveopposite signs. Hence, if the fully differential floating capacitoris used because of its high CMRR, then CMRR must be veryhigh too, otherwise it could yield a low CMRR .For low-frequency signal amplification, amplifiers providea high CMRR with differential input and differential outputbuilt from matched op amps, without requiring any matchedresistor [8]. Therefore, if a fully differential amplifier withhigh CMRR is already available, there is no need for aninput amplifier stage based on the floating capacitor. However,differential amplifiers with single-ended output have a muchsmaller CMRR than that of fully differential amplifiers. Inaddition, CMRR decreases for low gain. Therefore, for low-gain applications, a floating capacitor circuit with single-endedoutput may have a larger CMRR than a common differentialamplifier.If the floating capacitor circuit is used as a coherent am-plitude demodulator [5], its switches typically operate at thecarrier frequency. For frequencies about 1 kHz or higher, tran-sients, ON resistance, and limited OFF isolation in switchescan yield a CMRR that is lower than CMRR for a dif-ferential amplifier working at low-frequency (demodulatedsignal). Consequently, in this case it should be advantageous toplace a fully differential floating capacitor demodulator aheadof a differential amplifier, rather than using a single-endeddemodulator following a differential amplifier working at thecarrier frequency [5].The floating capacitor is also used in fully differential mul-tiplexers [3], [4]. In Fig. 2, using a floating capacitor makesit possible to simultaneously sample all input signals and thensequentially amplify each sampled signal by using a commondifferential (or fully differential) amplifier. Just as in low-frequency amplification, a floating capacitor with single-endedoutput may have a larger CMRR than a common differentialamplifier but only for low-gain applications requiring a single-output.On the other hand, if for the fully differential circuitand , then according to (5), . Therefore,the amplifier (and input switches) must withstand the inputcommon mode voltage present at any input channel. In case28 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 1, FEBRUARY 1998Fig. 2. Fully differential multiplexer.of large common-mode voltages, it may be better to use anamplifier with single-ended input after the floating capacitorcircuit because this only applies the differential input voltageto the amplifier. Alternatively, if there is galvanic isolationbetween signal ground and amplifier ground, it is feasibleto use standard switches and a differential amplifier after thefloating capacitor circuit because most of the signal commonmode voltage will be applied across the insulation barrier.In summary, it is better to use a fully differential floatingcapacitor circuit rather than a floating capacitor with a single-ended output for coherent amplitude demodulators, and itmay be even better for simultaneous multiplexing. For largecommon mode voltages, either in multiplexers, amplifiers ordemodulators, it is better to use a floating capacitor withsingle-ended output.III. EXPERIMENTAL RESULTS AND DISCUSSIONThe circuit shown in Fig. 1 was built using CMOS switches(CD4053B and MAX303). As the results were similar for bothmodels, only those for the CD4053B are presented. The circuitoutput was connected to an instrumentation amplifier. Thesame circuit was used either as an amplifier or as a coherentdemodulator. When working as an amplifier, the switchingfrequency must be much higher than the frequency of the(differential) input signal. When working as a coherent de-modulator, the switching frequency was the carrier frequency.The reference circuit had F, duty cycle10% for the clock signal (10% sample, 90% hold) and theunknown parasitic capacitances inherent to components andcircuit layout. Both output configurations, fully differential andsingle ended, were tested for each circuit.Table I shows the CMRR for the demodulator when thefollowing amplifier was the INA 110 with a gain of 500 (forthe fully differential demodulator) or 100 (for the demodulatorwith single-ended output). Here the amplifier works at DC and,from the data sheet, its typical CMRR at dc is 110 dB for gainsof 100 and higher. We first measured the reference circuit. Thefirst row in Table I shows that if the carrier frequency is low,the amplifier according to (11) limits the CMRR for the fullydifferential circuit. But from 10 kHz up, there is a reductionTABLE IFREQUENCY DEPENDENCE OF THE CMRR (dB) OF A COHERENT DEMODULATORBASED ON A FLOATING CAPACITOR CIRCUIT. FD: FULLY DIFFERENTIALFLOATING CAPACITOR; SE: FLOATING CAPACITOR WITH SINGLE-ENDED OUTPUTin CMRR attributable to the demodulator. Nevertheless, theCMRR is very high. When the output of the floating capacitorcircuit is grounded the demodulator determines the overallCMRR. It decreases by 8 dB at 10 Hz, as predicted by (10),and 30 dB at 100 kHz.Next, it was verified that, as predicted by the theoreticalmodels, had no influence on the CMRR. A reducedduty cycle , however, resulted in a reduced CMRR at highfrequencies. Table I shows the results for %. An analysiswas then made of the influence of . When was reducedfrom 1 F to 100 nF, the low-frequency CMRR for the fullydifferential demodulator first increased by about 20 dB, from107 to 126 dB. This can be explained by (11) if each stage hasa CMRR with opposite sign. By the same token, if the inputterminals for the amplifier are inverted, the CMRR shoulddecrease. Effectively, it reduced to 107 dB, the same as forthe reference circuit. For the single-ended demodulator, whennF the CMRR reduced by about 20 dB, as predictedby (10).The parasitic impedance was then increased by connecting a100 pF capacitor, first from the top side to ground, in parallelwith , and next from the bottom side to ground, in parallelwith . Again, the CMRR increased (or decreased) for thefully differential demodulator and was smaller for the single-ended demodulator, as predicted by (10). Note that invertinginput connections for the instrumentation amplifier works inopposite ways for and . In addition, should notaffect the results for the single-ended circuit, but from 1 kHzup, a large reduces the CMRR.When the floating capacitor was used to amplify low fre-quency signals (0.1 Hz), the results for the frequency depen-dence of the CMRR (Table II) were similar to those for thedemodulator, as expected. For 1 Hz and 10 Hz input signals itis necessary to increase the minimal sampling frequency, butotherwise the results are the same.The INA114 was also used as a differential amplifier. Forthe fully differential circuit the CMRR increased to about 120dB at low frequencies because the INA114 has a better CMRRat dc than the INA110. The CMRR for the fully differentialcircuit at higher frequencies and for the single-ended circuitwas similar.GASULLA-FORNER et al.: FLOATING CAPACITOR AS A DIFFERENTIAL BUILDING BLOCK 29TABLE IIFREQUENCY DEPENDENCE OF THE CMRR (dB) OF AN AMPLIFIER BASEDON A FLOATING CAPACITOR CIRCUIT WHEN THE INPUT SIGNALIS 0.1 HZ. FD: FULLY DIFFERENTIAL FLOATING CAPACITOR;SE: FLOATING CAPACITOR WITH SINGLE-ENDED OUTPUTIV. CONCLUSIONSThe floating-capacitor circuit provides an excellent CMRRwhen used as fully differential amplifier or demodulator. TheCMRR for the floating-capacitor circuit with single-endedoutput, depends on the ratio between the capacitance of thesampling capacitor and stray capacitance from the circuithigh side to ground (10). Second-order effects reduce theCMRR at frequencies above 1 kHz. This reduction is greaterfor the single-ended circuit.Whatever the application, the floating-capacitor circuit re-quires a following amplifier providing voltage gain and lowoutput impedance. If the signal, once amplified, must be singleended, then it may be better to have a floating capacitor withsingle-ended output in amplifiers and some multiplexers whilein demodulators a floating capacitor with differential outputyields a better CMRR. For large common mode input voltages,it is also better to use a floating capacitor with single-endedoutput.REFERENCES[1] J. Williams, “Applications for a switched-capacitor building block,”Application Note 3, Linear Technology Inc., Milpitas, CA, July 1985.[2] R. C. Jaeger, “Tutorial: Analog data acquisition technology, PartIII—Sample-and-holds, instrumentation amplifiers, and analog mul-tiplexers,” IEEE Micro, vol. 2, pp. 20–35, Nov. 1982.[3] D. H. Sheingold, Ed., Analog-Digital Conversion Handbook, 3rd ed.Englewood Cliffs, NJ: Prentice-Hall, 1986.[4] P. H. Garrett, Advanced Instrumentation and Computer I/O Design.New York: IEEE Press, 1994.[5] R. Palla´s-Areny and O. Casas, “A novel differential synchronous de-modulator for ac signals,” IEEE Trans. Instrum. Meas., vol. 45, pp.413–416, Apr. 1996.[6] K. R. Laker and W. M. C. Sansen, Design of Analog Integrated Circuitsand Systems. New York: McGraw-Hill, 1994.[7] R. Palla´s-Areny and J. G. Webster, “Common mode rejection ratio forcascaded differential amplifier stages,” IEEE Trans. Instrum. Meas., vol.40, pp. 677–681, Aug. 1991.[8] , “Common mode rejection ratio in differential amplifiers,” IEEETrans. Instrum. Meas., vol. 40, pp. 669–676, Aug. 1991.Manel Gasulla-Forner (S’97) received the En-ginyer de Telecomunicacio´ degree in 1992 fromthe Universitat Polite`cnica de Catalunya, Barcelona,Spain, where he is currently pursuing the Ph.D.degree in electronics.In 1993, he joined the Department of ElectronicEngineering, Universitat Polite`cnica de Catalunya,as a Lecturer. His current research interest is inthe field of electrical impedance measurement andsubsurface imaging.Josep Jordana-Barnils (S’93) received the En-ginyer de Telecomunicacio´ degree in 1990 fromthe Universitat Polite`cnica de Catalunya, Barcelona,Spain, where he is currently pursuing the Ph.D.degree in electronics.In 1993, he joined the Department of ElectronicEngineering, Universitat Polite`cnica de Catalunya,as a Lecturer. His current research interest is inthe field of electrical impedance measurement andsubsurface imaging.Ramo´n Palla´s-Areny (F’98) received the Inge-niero Industrial and Doctor Ingeniero Industrial de-grees from the Universitat Polite´cnica de Catalunya,Barcelona, Spain, in 1975 and 1982, respectively.He is a Professor of Electronic Engineering at theUniversitat Polite´cnica de Catalunya, and teachescourses in several areas of medical and electronicinstrumentation. In 1989–1990, he was a Visit-ing Fulbright Scholar at the University of Wiscon-sin, Madison. He does research on instrumentationmethods based on electrical impedance measure-ments, high resolution ECG and electromagnetic compatibility in electronicsystems. He is the author of Basic Electronic Instruments (1987), Sensors andSignal Conditioning, 2nd ed. (1994), and Signal Acquisition and Distribution(1993), coauthor of An Introduction to Bioengineering (1988) and of Electro-magnetic Interference in Electronic Systems (1991), all published in Spanishby Marcombo, Barcelona, Spain. He is also coauthor (with John G. Webster)of Sensors and Signal Conditioning (New York: Wiley, 1991).Dr. Palla´s-Areny was a recipient, with John G. Webster, of the 1991 AndrewR. Chi Prize Paper Award from the IEEE Instrumentation and MeasurementSociety. He is a member of the Biomedical Engineering Society, and theInternational Society for Measurement and Control.Josep Maria Torrents (M’90) received theEnginyer de Telecomunicacio´ and Doctor Enginyerde Telecomunicacio´ degrees in 1989 and 1996respectively, from the Universitat Polite`cnica deCatalunya, Barcelona, Spain.In 1989, he joined the Department of ElectronicEngineering as a Lecturer, and currently heis an Associate Professor at the UniversitatPolite`cnica de Catalunya. His research interestsare in electronic instrumentation, nondestructivetesting, and electrical impedance spectroscopy,mainly applied in soil and ceramic structures.

https://upcommons.upc.edu/bitstream/2117/1398/4/GASULLA.pdf

The floating capacitor as a differential building block

Abstract

Similar works

Full text

Available Versions

UPCommons

UPCommons. Portal del coneixement obert de la UPC