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REFERENCESC. J. Alonzo, R. H. Blackwell, and H. V. Marantz, D irect reading fullyautomatic vector impedance meters, Hewlett Packard J. , pp. 12-20,Jan. 1967.R. J. Reis, Measurement of an unknown impedance in an automatictester, IBM Tech. Disclosure Bu lletin, vol. 24, no. 7A , pp. 3147-3148,Dec. 1981.K. M. Ibrahim and M. A. H. Abdul-Karim, Digital impedance mea-surement by generating two waves, IEEE Trans. Instrum. Meas., vol.IM-34, no. 1, pp. 2-5, Mar. 1985.S.M. R. Taha, Digital measurement of the polar and rectangular formsof impedances, IEEE Transactions on Instrumentation and Measure-ments, vol. 38, no. 1, pp. 59-63, Feb. 198 9.B. M. Oliver and J. M. Cage, Electronic Measurement and Instrumen-tation. New York: McGraw-Hill, 1971.K. Karandeyev, Bridge and Potentiometer Methods of Electrical Mea-surements. Moscow: Peace.K. L. Smith, The ubiquitous phase s ensitive detecto r-application s andprinciple of operation, Wireless World, pp. 361-370, Aug. 1972.D. P. Blair and P. H. Sydenham, Phase sensitive detection as a meansto recover signals buried in noise, Instrument Sci.-J. Physics: Sect. E:Scient@ Instrum., UK , vol. 8 , pp. 621-627, 1975.Embedded Controller Handbook, vol. 1 and 2, Intel, Illinois, 1988.

A High-Resolution, LinearResistance-to-Frequency ConverterKouji Mochizuki and Kenzo Watanabe

Abstract-A resistance-to-frequency converter consisting of a Wheat-stone bridge followed by an integrator and a comparator is described.In concept the circuit represents a relaxation oscillator whose frequencychanges linearly with a resistance change detected by the bridge. Analysesshow that a resolution better than 0.05% is possible with the simpleconfiguration, and an excellent linearity is maintained over the wide re-sistance change by using a simple compensation method. The converter istherefore suited as a signal conditionerof a resistive sensor. Experimentalresults are included to demonstrate its performance.I. INTRODUCTION

Detection of a sm all resistance change is often needed in industrialand process control systems an d medical instrumentation [I], [2]. Insuch systems, m icroprocessors are used exclusively for digital signalprocessing, and thus input data in a digital format is highly desired.A conventional way of detecting the resistance in the digital formis to use a relaxation oscillator whose frequency is determined bythe resistance under measurement and a known capacitor [3],[4].Though simple, this method suffers from nonlinearity. In addition,high sensitivity cannot be expected since the oscillation frequency isinversely proportional to the total resistance.The most sensitive means of detecting the resistance change is aWheatstone bridge. Combining a W heatstone bridge with a relaxationoscillator appears to be a promising approach to the high-sensitivityresistance-to-frequency (R-to-F) converter. Such a scheme has been

Manuscript received March 7, 1994; revised August 30, 1995.K. Mochizuki is with the Department of Electrical Engineering, NumazuK. Watanabe is with the Research Institute of Electronics, ShizuokaPublisher Item Identifier S 0018-9456(96)03092-6.

College of Technology, Numazu 410, Japan.University, Hamamatsu 432, Japan.

NO. 3, JUNE 1996 76 1

uc +VaU b

Fig. 1. A linear resistance-to-frequencyconv erter: Basic configuration.

proposed by Johnson and Richeh [5]. Their circuit is a resistance-to-duty-ratio converter, and the feedback circuit, consisting of anintegrator and a comparator, maintains the balance of the bridgeby controlling the switched resistors incorporated in the arms ofthe bridge. This paper describes a true R-to-F converter designedbased on the above-mentioned approach. Different from the earliercircuit [5], the Wheatstone bridge is used merely to detect theresistance deviation from the offset value. Since no balance operationis involved, the circuit configuration is much simpler. The sensitivityis high enough, because of the differential integration involved, tobe compared to that of the resistance-to-duty-ratio converter [ 5 ] .Therefore, the R-to-F converter described in detail in the followingsections will find wide applicability as the signal conditioner ofplatinum RTDs for temperature measurements, strain gauges forelectronic balances, piezoresistors for pressure detection, and theother resistive sensors for instrumentation and measurements.

11. CIRCUITDESCRIPTIONFig. 1 shows the circuit diagram of the linear resistance-to-frequency (R-to-F) converter. It is essentially a relaxation oscillator

consisting of a Wheatstone b ridge, an integrator, and a zero-crossingdetector. The resistor R, whose resistance change is to be detectedforms one arm of the bridge. The unbalance voltage due to theresistance change is integrated, and its polarity is fed back to thebridge as the bias voltage, to sustain the oscillation.

When op-amps involved are ideal, node voltages are given by

where

an d

. c

R3Rz +R3a ! -

T = C TR T.Output voltage waveforms of the zero-crossing detector and theintegrator are shown in Fig. 2(a). Here,

(7 )is assumed, and Tp nd T, are the periods during which vOut assumesVp an d -Vn, respectively. Referring to these waveforms, one can

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762 IEEE TRANSACTIONS ON INSTRUMENTATIONAND MEASUREMENT, VOL. 45, NO. 3, JUNE 1996

h o u t f w o u t

I-B(Vpt n)

1

(4 @)Fig. 2. Voltage waveforms in Fig. 1, (a) when op-amps are ideal and (b) when the zero-c rossing detector has the response delay Td.

derive the following expressions for Tp nd T,

T, = -( l+a-P

whereY = IVn/Vpl.

The oscillation frequency is thus given by

(9)

whereRo Rs - R1 R2Rl(R2+R3) frfo =

is the offset frequency corresponding to the bridge offset,

is the frequency shift due to the resistance change A R in R,, an d

R, = Ro +AR.Equation (13) indicates that the resistance chang e is linearly convertedinto the frequency.One of the error sources which degrades the linearity is th eresponse delay of the zero-crossing detector. Waveforms when thedelay time is Td are shown in Fig. 2(b). Here,

(15)

Td TdAV,("/")= -( a - 3)voUt = - (a - P)Yp/ ,) (16)

is the voltage change in the integrator output during the delay timeT d . Referring to Fig. 2(b), Ti an d TA are derived as

Tp nd T, given by (8) an d (9), respectively, c hange inversely w ithAR, and thus the nonlinearity due to Td increases with AR.

Waveforms in Fig. 2(b) suggest the compensation method for theresponse delay: Th e effect of the delay time upon the oscillation fre-quency could b e eliminated by replacing the zero-crossing detector bythe comparator which co mpares the integrator output with AV,("").Substituting the com parator threshold voltage AV,("/") iven by (16)into (3) explicitly, one can get the design equation which describesthe required operations

vc - Vout - Td(a - P)vout = -- ( a - P )v ou t d t . (19)The right-hand side indicates the differential integration while theleft-hand side the comparison. The threshold in the comparison is,bout, shifted byThe delay-compensated R-to-F converter thus designed is shownin Fig. 3(a). It should be noted that the voltage at the inverting inpu tterminal @ of op-amp A1 is /3vo,t; an d R3 is split into two parts,6R3 an d (1- S)RB,o shift the threshold voltage. Fig. 3(b) showswaveforms of the integrator output v, and the threshold voltage VTH,which is given by

for the delay compensation.

Referring to these waveforms, one obtains


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IEEE TRANSACTION S ON INSTRUMENTATION AND MEASUREMENT. VOL. 45, NO . 3, JUNE 1996 16 3

Fig. 3. (a) The circuit diagram of the delay-compensated resistance-to-frequency converter, (b) Voltage waveforms at the input terminals ofcomparator A3.

Therefore, if S is chosen such that

then the oscillation frequency changes linearly with A Rf = f o + A f

111. RESOLUTIONAnother error source that influences the converter operation show nin Fig. 3(a) is the offset voltage of an op-amp. Let and VOs2bethe offset voltages of op-amps A1 and A2, respectively. These offsetvoltages produce the constant error voltage. The converter is driven

by its output voltage w,t which assumes the constant value V, orVn . Therefore, the offset voltage is equivalent to the chan ge in uOutand scales Tp an d T, as

Tk (25)1 - A(26)n1 + A / 7TL =

where

an dE1 = v,,,/v,E 2 = VO,2/V,.

The oscillation frequency f ' i s then given by(30)1Ti + TA' = = f ( 1 - A N + A/Y)

where f is the oscillation frequency of the delay-compensated R-to-Fconverter given by (24).It is clear from (27) that if the amplified offset voltage of op-ampA1 cancels the offset voltage of A2 , then no offset error appears. Thiscondition does not always hold true because of the temperature driftsin the offset voltages. The dev iation A f from th e offset frequency f othen consists of two parts; one is A fR due to the resistance change

-4 -2 0 2 4A l t (Q)

Fig. 4. The oscillation frequency change Af of the prototype converter forthe resistance change AR.A R , and the other is A fE due to the offset voltage. A fE s given,to the first order, by

For the resistance change A R to be detected unambiguously, A fRshould be larger than A E . The resolution limited by this conditionis given by

- (1 +2);1 - ;) { E , - (1- Y ) E 2 ) (32)Rowhere ARm in denotes the minimum detectable resistance change.The offset voltage of comparator A3 also affects the converteroperation. Its effect on the oscillation frequency is second-order,because it influences only the delay compensation through shiftingthe threshold voltage. Another factor that limits the resolution is thetemperature drift A f T of the o ffset frequency. A fT can be evaluatedby

a f To = ( ? / a T ) A T (33)where AT represents the operating temperature range of the con-verter. The frequency stability (a o / f o ) / a T of a conventional re-laxation oscillator built using resistors and capacitors with lowtemperature coefficients is typically l o r 5 / "C. Assuming A T =4OoC, the resolution limited by the temperature drift is

(34)


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16 4 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 45, NO. 3, JUNE 1996

-1000 -500 0 500 1000AR (a)

-1000 -500 0 500 lo00Alx (Q)

Fig. 5.and without (6= 0) the delay compensation.The nonlinear error o of the prototype converter with (5 = 0.025)

Assuming Vosl -Vasa = 2 mV, V, = 5 V , y = 0.95,a = 1 1 2 ,Ro M R I , one can estimate the offset-limited resolution given by(32) to be

Summarizing the above estimation, it is concluded that the resolu-tion limited by the offset voltages is comparable to that limited by thetemperature drift of the offset frequency, and the overall resolutionis of the order of 0.05%.

Iv . EXPERIMENTALESULTSTo confirm the principle of operation, the R-to-F converter sho wnin Fig. 3(a) was breadboarded using off-the-shelf components. The

op-amps used are LF411. Its offset voltage is less than 2 mV, and thedelay time is about 2.7 ps. No adjustment was made for the offsetcompensation. The power supplies are f 1 2 V. The other relevantparameters are RI = Rs = 1.6 k R , Rz = 2. 4 kR. The conversionsensitivity was adjusted to be 1 Hz/CL. The integration time constantr = CTRT was then about 110 p s . The oscillation frequency wasmeasured by the frequency counter with 0.1 Hz resolution.Fig. 4 shows the measured frequency changes when R, waschanged in 0.5 R steps from its offset value of Ro = 3. 4 kS2. Theresults indicate that the resolution is higher than 0.015%. Fig. 5showsthe nonlinear error o of the prototype converter with (6 = 0.025)and without (6= 0) the delay compensation. The nonlinear error

is defined here by(35)Af measured - Af given by (24 )c r = Af given by (24)

The results shown in Fig. 5 indicate that a resolution higher than0.1% is achievable over the wide resistance range with the delaycompensation, thus confirming the performance evaluation in theprevious sections. I

V. CONCLUSIONA novel circuit has been presented which provides the frequency

equivalent of a resistance change. The component requirement isminimum. Besides the sim ple configuration, it features a high resolu-tion and an excellent linearity over the wide resistance range. Theseadvantages make the R-to-F converter proposed herein especiallyuseful for signal processing of such transducers as strain gauges,RTDs, and piezo resistive devices.

ACKNOWLEDGMENTThe authors would like to thank S. Katoh, Assistant Professor,Numazu College of Technology, for useful discussions and encour-

agement.REFERENCES

G. Payer, La conversion directe en frequence et son application aupesage numerique, Electronique et MicroElectronique Zndustrielles,no.146, pp 29-31, 1971 .J. A. Vinas, Digital percentage resistance bridge, Elec. Eng., no. 5 ,pp. 15-17, 1973.A. P. Shivaprasad, A wide-range variable-frequency phase-shift oscil-lator, ZEEE Trans. Znstrum. Meas. , vol. IM-21, pp. 180-182, 1972.L. J. Weiss, Measuring resistance deviations quickly and accurately,Elec. Eng., no. 8 , pp. 41-43, 1972.C. D. Johnson and H. A1 Richeh, Highly accurate resistance deviationto frequency converter with programmable sensitivity and resolution,IEEE Trans.Znstrum. Meas., vol. IM-35, pp. 178-181, 1986.

A Simple Measurement Method to Determinethe Burst Acquisition Time of Digital Systeqs

Curtis Hatamoto, Huajing Fu, and Kamilo Feher

Abstract- A cost-efficient solution for measuring fast and ultrafastsynchronization-caused bit errors is disclosed. This invention enables theuser to modify conventional test instruments and to eliminate the needto obtain very expensive test equipment. Ou r new instrumentation imple-mentation concept comprises a gated switch added to a pseudorandombitsequence generator and analyzer. The synchronization time of a coupleof circuits is tested.

I. INTRODUCTIONIn certain applications, such as in the wireless field, synchronizationtime is crucial to the transmission of data. For instance, in frequency-hopping spread spectrum (FH-SS), the c arrier frequency i s constantlyManuscript received May 1, 1995.The authors are with the Digital and Wireless Communications Lab.,Department of Electrica l and Computer Engineering, University of California,Davis, CA 95616 USA.Publisher Item Identifier S 0018-9456(96)03094-X.

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