IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI-19, NO. 4, NOVEMBER 1972

describes the total Seebeck voltage of the sheath withrespect to some reference material (wire A) as a functionof the temperature.

DATA CARD 10 NTr FORMAT (I10)

NT is the number of points on the temperature gra-dient (including the hot and the cold ends).

DATA CARD 11 TEMP (1), POS (1), TOL FORMAT (4E20.5)TEMP (1) cold-end temperature in °CPOS (1) position corresponding to TEMP (1), (USU-

ally taken to be zero)10OL maxiinum error in volts to be allowed at

any of the points on the gradient betweenthe output voltage specified and the out-put voltage determined by the model.

DATA CARDS 12-*NT+10 FORMAT (4E20.5)VOLTS (j), POS (j)

VOLTS (j) output voltage of the thermocouple inmillivolts (VB- VA)

POS (j) position of the thermocouple in centi-meters measured from POS (1), corre-sponding to VOLTS (j).

REFERENCES[1] J. R. McDearman, J. M. Googe. and R. L. Shepard. "A three-wire

insulator-shunting model for high-temperature thermocouple er-rors," IEEE Trans. Ind. Electron. Contr. Instrum., vol. IECI-18,pp. 137-144, Nov. 1971.

[2] G. F. Popper and A. E. Knox, FARET In Core Instrument De-velopment, ANL-7161, July 1966.

[31 J. R. McDearman and J. M. Googe, "Methods to calculate tem-perature profile using data from a thermocouple with high-tem-perature shunting error," Univ. of Tennessee, Knoxville, OakRidge Nat. Lab., Rep. TID-25632, Dec. 1970.

Voltage-to-Frequency Conversion of Signals Suppliedby Physical-Quantity Sensors

ALESSANDRO GANDOLFI, CARLO NOBILI, MARIA PRUDENZIATI,AND ANDREA TARONI

Abstract-The voltage-to-frequency converter presented here isan approach to the problem of realizing the modulation unit of thedata-acquisition system in a computer-controlled industrial process.

Frequency modulation of the electrical signal supplied by physi-cal-quantity sensors was chosen on the ground of some considera-tion pertaining to, among others, the economical convenience, work-ing reliability, interchangeability, and constructive simplicity. Thechoice of the frequency range and the design criteria are also dis-cussed.

The performances, namely sensitivity, response linearity,temperature behavior, working temperature range, as well as thematching of the converter with pressure and temperature sensors, arereported.

NOMENCLATUREB Material constant of a thermistor (K).C Timing capacitance (farad).CT Tr timing capacitance (farad).E Divider bias voltage (volt).f Converter output frequency (hertz).f* Converter output frequency affected by dead time

(hertz).

Manuscript received October 26, 1971. This work was supportedby Pignone Sud (ENI Group) under IMI Contract 23754.

The authors are with the Istituto di Fisica dell'Universiti diModena, Modena, Italy.

GF Gauge factor.R Timing resistance (ohm).R' Voltage divider fixed resistance (ohm).Rr Bias potentiometer.S Strain.T Temperature (degree Celsius).t Time (seconds).ts Switching time (seconds).Vc Voltage across the timing capacitance (volt).VE Timing unit reference voltage (volt).Vi. Input voltage of the converter (volt).Vo Bias voltage of the timing unit (volt).V0* Total voltage across the timing unit (volt).VT Thermocouple EMF (volt).ao Temperature coefficient of thermistors (K-1).0 Temperature (K).p Equivalent resistance of a conducting transistor

(ohm).Po Resistance of a thermistor at infinite temperature

(ohm).pos Resistance of a strain gauge at zero strain (ohm).Ps Resistance of a strain gauge (ohm).PT To timing resistance (ohm).pO Thermistor resistance at the temperature 0 (ohm).

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, NOVEMBER 1972

T = 1/f period of the converter (seconds).TO Oscillation dead time (seconds).

= 1-/f* period of the converter, affected by thedead time (seconds).

INTRODUCTIONT HE USE OF digital computers for the control of

industrial processes, which is spreading more andmore in these last years, involves a critical analysis

of the usual data-acquisition systems and eventually thedevelopment of systems of new types.

These data-acquisition systems necessarily requiresensors of physical quantities in the plant and a systemtransmitting the information supplied by these sensorsto the electronic comiiputer. For clarity's sake, a controlsystemn (for example in a plant that is provided with acentralized unit including a digital computer) can bebriefly exemplified in the following way (see Fig. 1): theprimary sensing element converts the physical quantity(pressure, temperature, etc.) into analogic electricalsignals, which, through appropriate modulator trans-mitters, are sent, usually by cable, to the central controlunit which has, as an essential part, the digital compu-ter.

In the central unit all pieces of information that comefrom the various points of the plant arrive at a multi-plexer, which examines them at different tinmes.The signal of every line is appropriately demodulated

and sent to a converter that performs the essentialanalog-to-digital conversion, and numerically suppliesthe central computer with the information pertaining toevery channel.Such a system should be studied as a xvhole in an in-

vestigation including the sensors, the systems of infor-mation transmission from the peripheral units to thecentral one, as well as the digital computer.

Nevertheless, very often industrial and commercialreasons do not lead to a comprehensive study of thewhole system, but of the various subsystems separately.For example, the optimization of the process-digitalcomputer system has been wvidely studied [1], while lessattention has been devoted in the literature to the trans-mission systems [2 ] and to the primary sensors [3 ]- [5 ],although this attention is especially required for thecontrol of processes that need a numnber of primarysensors greater than a hundred and/or an interrogationtime for every sensor of the order of a millisecond. Infact, for systems so complex, or for systems requiringsuch a short interrogation time, the study of both theprimary-sensor and of the data-transmission subsystemsbecomes as important as that of the digital-computersubsystem that performs the primary function of con-trolling the process itself.

In this framework, we thought it useful to developthe design of a voltage-to-frequency converter match-able through appropriate interfaces to all those pri-mary sensors of conventional type or not whose output

Fig. 1. Basic elements of a centralized instrumentation system.

can be reduced to a voltage signal. We felt that a uniqueconverter matchable to sensors of a different type wouldoffer sure benefits from economical and technical pointsof view, mostly due to the interchangeability amongvarious sensors, so as to justify this work.

Before analyzing in its peculiarities the converter wehave studied, we wish to make a few remarks on thetransmission system, justifying our choice of some of thecharacteristics of the converter itself.

In the system described in Fig. 1, the type of modula-tion of the signal supplied by the primary sensor can bechosen in a range of possibilities that differs consider-ably under the technical point of view and the economi-cal one. Even if, in principle, a transmission system withdigital modulation (e.g., PCM\) is surely to be preferredbecause of the best signal-to-noise ratio, we must, how-ever, remember that, in the case of industrial processeswhere the number of data to collect is very great and thesensors very far from each other and from the centralunit, economical considerations and working reliabilityinduce one to also consider systems of the analogic type,appropriately selected.The so-called analogic transmission systems range

from the well-known AM, to the other FM, pulse posi-tion modulation (PPM), and pulse duration modulation(PDM) systems.The various types of modulation we have talked about

do not modify the major outline shown in the previousexample. Nevertheless, the modulation system associ-ated with the transmitter, the demodulation system thatfollows the multiplexer, and the central converter thatsupplies the numerical information to the computerchange according to the selected type of modulation.

Information theory and communication science [6]-[8] allow us to establish a definite list of merits amongthe various just-mentioned systems, on the grounds ofconsiderations relevant to the bandwidth, the efficency,the required transmission power, and the consequentsignal-to-noise ratio of the system.

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GANDOLFI et al.: VOLTAGE-TO-FREQUENCY SIGNAL CONVERSION

In the applications relevant to the process control,mostly in chemical and petrochemical plants, the AMsystem has been preferred up to now because of itssimplicity, in spite of its limitations in comparison withthe other analogical systems (FM, PPM, PDM), atleast for what concerns the signal-to-noise ratio. Theachievement of a good signal-to-noise ratio togetherwith economical considerations, wxorking security, inter-changeability, and constructive simplicity, guided ustowards the FM\ modulation in developing a system ofthe type previously described in brief.The working frequency of the converter was chosen

because of the following considerations.The frequency range of the transmission system, and

therefore of the converter, is above all linked to the in-formation transimission velocity, and consequently tothe acquisition time by the central unit.

If, for instance, one wants to sample 100 pieces of in-formation in a tenth of a second with an accuracy of 0.1percent, the minimum necessary frequency for thetransmission of the information with an FMN systemturns out to be 1 MHz.The greatest accuracy can, of course, be obtained by

keeping constant, within the same number of channels,the total interrogation time and by increasing the work-ing frequency of the transmission system.We must remember, however, that an increase in fre-

quency much above the given megahertz can require aremarkable increase in the cost of the signal transmis-sion cables that, for high frequencies, should have par-ticular performances.

Moreover, we considered it of primary importancefor the industrial applications, in the study and designof the converter herein described, to accentuate the fol-lowing characteristics:

1) sensitivity;2) response linearity;3) stability with respect to working temperature

fluctuations;4) maximum and minimum operating temperature.

The industrial utilization of a converter of the typestudied here requires that its constructive characteris-tics satisfy the intrinsic safety rules valid for the plantwhere the converter can be employed. These rules varyaccording to the type of the plant and the country wherethe plant is installed. Therefore, we cannot satisfy themin a general way; nevertheless, we have taken these dif-ferences into account, and we think that a few changescan make this converter conform to the rules more com-monly used in industrial plants.

CIRCUIT DESCRIPTIONOur converter circuit can be seen as a relaxation

oscillator whose period is controlled by the voltage (Vin/)(Fig. 2). In fact, a capacitor is charged through a resis-tor to a voltage Ve which is brought to the input of a

Fig. 2. Block diagram of the voltage-to-frequency converter.

voltage comparator circuit D. When Vc equals Vin,t thecomparator D triggers a switch circuit that excites thedischarge of the capacitor, restoring the former opera-tion conditions of the running cycle.

In Fig. 2, the block diagram of the circuit is presented.R and C represent the timing network, Fin the inputvoltage, D the voltage comparator, and S the electronicswitch designed to discharge C in due time.We will report the details of D and S later on.Let us analyze the behavior of the circuit at constant

temperature. The voltage across C is given by

Vc = Vo(l- e-tlC) (1)

If S switches when Vc - Vi, then the charging time ofC is

r RC ln (1 --A.VeX

(2)

If Vo>> Vin, the series expansion of the logarithmic func-tion gives (neglecting higher order terms)

yinr = RC-

Vo(3)

Therefore, the period of the converter is a linear func-tion of Vi,, while the frequency is

1 Vor VinRC

The frequency sensitivity will be

JAf 1 VoAVin V;n2 RC

(4)

(5)

i.e., proportional to Vo and inversely proportional to theRC product and to V,n2.On the other hand, the time sensitivity results pro-

portional to the RC product, inversely proportional toVo, and independent of Vin, according to

Ar RC

AVin V{ (6)

If we choose the working frequency (according to thestandards we have talked about in the Introduction)and the Vin and Vo levels, we can fix the value of the RCproduct.

Let us now describe the details of the blocks shownin Fig. 2. Three types of integrated circuits differingonly in the thermal stability of the threshold were em-ployed for the realization of circuit D. They are LM306

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, NOVEMBER 1972

tv

Fig. 3. Block diagram of the switch unit in the converter circuit.

(NS), LM\4106 (NS), and ,uA710 (SGS). As the operationat constant temperature is concerned, the choice of theelement is not relevant, provided the response time ist<<<r.

In our case, forf-(1 *. 2) MHz we have T(0.5 . 1)/I4S.

All the circuits mentioned satisfy the conditionti <<r, because of t.< 10 ns.

The circuit S is represented in Fig. 3.U.S.M. is a monostable multivibrator of the T118

type or equivalents. When the voltage at the two inputsof D are equal, the output signal of D itself drivesU.S.M., whose output is a square-waveshaped signalwith appropriate amplitude and adjustable width (To).The square signal from U.S.M. leads the MOSFET

transistor T from the off-state to the on-state. Duringthe time To, the discharge of C through the internal(equivalent) resistance p of T takes place. For what con-

cerns the working frequency, (4) holds, provided thatro<<T.

Furthermore, the circuit does work correctly if, dur-ing the time ro, the condenser C can completely dis-charge itself. To this purpose To must be > 3pC.

This condition imposes a lower limit on ro, so that itis not always possible to satisfy the condition thatTo<<T.

In this last case the response of the circuit is therefore

yin

*-T+ To RCV

+To (7)

where T* is the period of the output signal. We see, there-fore, that the period results still linear in Vin and thefrequency results still hyperbolic (in Vin). The followingsensitivities result:

i.r* RC 1= =_-(8)

AVin VO K

Af*= K/(Vin + KO)2. (9)

AVin

Therefore, while the period sensitivity remains un-

changed, that of frequency decreases.

THERMAL STABILITY

We can obtain a good thermal stability of the con-

verter circuit if the following quantities result indepen-dent of the temperature:

1) threshold voltage and input current of the D cir-

cuit;

2) reverse current of the T transistor;3) dead time TO.

0.5

0 25 50T (OC)

75

Fig. 4. Comparison of the temperature dependence of the thresholdvoltage for three comparator micrologic circuits.

As far as the D circuit is concerned, the comparisonbetween the MAA710 C (SGS) and thecircuits LM 306 andLM 106, both of National Semiconductors (Fig. 4)shows that, according to the data sheets, the LM 106circuit is preferable.

For what concerns the dead time ro, in the circuitsT118 (SGS) and SN 15851 (Texas) we have employed,it can be fixed by means of external resistors and capaci-tors with suitable temperature coefficients such as tomake negligible, with respect to the D threshold varia-tions and to the effects of the transistor T, the variationof ro itself with the temperature.

For the switch transistor T we can make the followingconsiderations: during the charge of the condenser C,the reverse current ih the transistor T must be muchsmaller than that of charge of C, or, at least, this currentshould not vary with the temperature. The same con-

sideration holds for the input current of the thresholdcircuit D.

For this reason a MOSFET with a high interdiction re-

sistance [type 3N 128 (RCA)] is to be preferred to a

FET whose junction reverse current (gate-drain) israther sensible to temperature fluctuations.

Unfortunately, generally the MOSFET's present an in-ternal resistance p in the conduction state higher thanthat of the FET's, and consequently To results larger.

NEGATIVE INPUTSAll the previous considerations apply to the case when

C and the MOSFET source are referred to VE =0. If in-stead they are referred to V= VE <0, all the argumentsare valid if we put Vo0= Vo*, with VO*= Voo- VE.So Vin can assume all the values allowed by the char-

acteristics of the circuit D.The complete circuit for either positive or negative

inputs is shown in Fig. 5, where, in addition to the ele-ments we have already discussed, the numerical valuesof all elements of the circuit are quoted. Besides thesymbols already used in the previous figures, in thisfigure, PT and CT are, respectively, the resistance and thecapacity that fix the dead time rO. To the aims of ther-mal stability these two elements must have a controlledtemperature coefficient (6 X 10-6 P/°C). G, Dr, Sr are

gate, drain, and source, respectively, of the MOSFET 3N128. R and C are the timing elements; also they are tobe chosen with a high thermal stability (6 X 10-6 P/°C)

-±A710 SGS VO=10.68VD=---LM306 NS C =260pF--LM 106 NS VIN=O V

USM=T 118(SGS)T =3N 128 (RCA)

A

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GANDOLFI et al.: VOLTAGE-TO-FREQUENCY SIGNAL CONVERSION

1.2 kQ

+7V v+12V 0

,3j3QOpF TiT=lOk5O tR=22kQ106 ilS3N15

*VINM - 1tlOk!Q -CT=68pF Dr r +6V-6.V r LC=130PF

-1 i47n22k0 T220-5V

-12V

R1=lkQ

Fig. 5. Converter circuit suitable for both input polarities,

Fig. 6. Measured voltage-to-frequency response of the converter.

C -130PF3 USM = T 118 (SGS) /V5V =10V

T = 3N 128 (RCA)D LM106(NS)

=15

0 ~~~~~~~~=20V

VIN (Volt)

Fig. 7. Measured voltage-to-period response of the converter.

DP is a silicon diode with a high inverse resistance (typeFD 100), which has the only function to protect theinput of LM 106 from possible dangerous over-voltages.R1 is a bias potentiomneter for the MOSFET.

The experinmental results are shown in Figs. 6 and 7.

The general characteristics are summarized in the fol-lowing table:

Input resistance 65 250 kgvin -4 +5 VSensitivity 50 1000 Hz/mVFrequency 0.5 2 MHzAf/f +0. 15 percent in the temperature range

0°C 500CWorking temperature -300C+ +1000CPower suppliesa f1-12, +25 V1100 mAa Vo and VE should be kept constant within ± 1 mV.

MATCHING WITH THE SENSORS

In order to test the versatility of the above-describedconverter we carried out measurements of the responseof the circuit-transducer system by means of three dif-ferent sensors: a thermocouple, a high-sensitivity ther-mistor, and a semiconductor strain gauge.The choice of these three sensors has been guided by

the following considerations.Temperature and pressure (whose measurement is

equivalent to a force measurement) are the physicalquantities more frequently controlled in industrialplants.The most widely employed sensors for temperature

measurements are the thermocouples whose response is,to a first approximation, a voltage linearly varying withtemperature. On the other hand, the utilization of semi-conductor thermistors permits a greater temperaturesensitivity, while the resistance (or tension or current)versus T curve is highly nonlinear (exponential).The pressure measurement by means of piezoresistive

devices offers two advantages. The first one is repre-sented by the linearity of the resistance versus pressure(force or strain) curve. The second one consists of thegreater sensitivity of the piezoresistive devices withrespect to the strain gauges of conventional type, whoseresistance variations are mainly due to geometry varia-tions.Both these solid-state sensors, though they were

brought out some years ago, are only now consideredfully developed from the point of view of their possibleuses [3], [4].These three sensors require different matchings to the

converter circuit. In fact, we can consider the thermo-couple as a voltage generator; therefore, it can be di-rectly matched to the converter circuit input (except forthe introduction of a suitable amplifier). The thermistorand the strain gauge are instead variable resistors and,therefore, can be inserted in an appropriate interfacecircuit that performs the resistance-to-voltage conver-sion.

RESULTS AND DISCUSSIONResponse of the Converter-Thermocouple SystemThe converter has been matched to the thermocouple

through a dc amplifier (10 times gain). The amplifiergaini is high enough to allow an accuracy better than 1

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, NOVEMBER 1972

T(°C)

Fig. 9. Computed T versus T response of the converter circuitmatched to a thernmistor. The insert shows the interface circuit.

Fig. 8. Measured f versus T response of the converter circuitmatched to a thermocouple (curve a) and comparison with thethermocouple characteristic (curve b).

percent, with an interrogation time of 50 ns. The ex-

perimental results are shown in Fig. 8, where curve a

represents the frequency-to-temperature response of thethermocouple-converter system, while curve b representsthe voltage-to-temperature response of the thermo-couple alone. It is worthwhile to notice that, as alreadysaid, for a limited range of frequency variations, the con-

verter response is a linear function of the input voltage.

Response of the Thermistor-Converter SystemIt is well known that the resistance of a thermistor

po is a function of the temperature 0 according to therelation Po po exp (B/6), where 0 is the temperature indegrees Kelvin, po the therm-istor resistance for 06-* ,

and B is a clharacteristic coefficient of the thermistorthat specifies its sensitivity. In fact, this last quantitycan be shown by the relation ao = (Ape/poA) (- B/02).Wlhen the thermiistor is inserted in a voltage divider

witlh a constant bias voltage E, so chosen as to respectthe zero power limnits of the thermistor [3], the voltagedrop across po (case a) or R' (case b) can he expressedthrough the simple relations

Yin = E (case a)RI + P6

RIVi, = ER---- (case b). (10)

RI + pa

Keeping into account relation (3), we can obtain somecurves T (T),1 as shown in Fig. 9.

1 r(T) represents the frequency inverse of the pulses supplied bythe converter and not their width.

1.6

_ju) 1.5

E

PeoVIN

E =-1V

R'=68Q

1.4

100 200 300 400T(°C)

500 600

Fig. 10. Experimental data of r* versus T response for the convertermatched to a thermnistor.

These curves refer to five differenit values of the fixedresistance R', so chosen as to maximize the sensitivityAVi,,/AT of the divider itself in correspondence of fivedifferent temperatures. In fact, it is easily shown thatthe divider maxinmim sensitivity (A Vi//AT) is ob-tained for a value of the resistance R' equal to the ther-mistor resistance po. It is therefore possible to changethe divider maximum sensitivity through a simple com-

mutation to a different value of the resistance R'. InFig. 9 the R' values are chosen so as to maximize(AVi,/lAT) for the following temperature values: 200,250, 300, 350, 400°C. Fig. 10 shows the experimental

400T(°C)

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GANDOLFI et al.: VOLTAGE-TO-FREQIJENCY SIGNAL CONVERSION

curves of T* (T) obtained by using the same resistancevalues of those already used in the calculations of thetheoretical behaviors shown in the previous figure.The comparison of Figs. 9 and 10 shows that the ex-

perimental results and the t;heoretical expectations arein good agreement. The difference in the ordinates mustbe ascribed to the term To [appearing in (7) ], which inthis case is not negligible in respect of T. 1Ioreover, boththe theoretical and the experimental curves show thepresence of various linearity ranges of r as a function ofthe temperature. Such ranges extend for temperatureintervals of (50 . 100)°C, and can easily be fixed arounda desired temperature by simply changing the value ofthe divider fixed resistance. The average accuracy of thetemperature measurements results better than 1 per-cent for interrogation times of about 25 ms.

Response of the Converter-Strain-Gauge SystemAs is well known, the resistance ps of a strain gauge

subjected to a strain S is a linear function of the typeps=pos (1+GFS), where Pos is the unstrained sampleresistance and GF is the gauge factor. So the strain gaugecan be considered a linear transducer.

In performing our measurements we have biased thestrain gauge with a constant current supply and thevoltage across the sensor is the converter input VinThe current choice is not arbitrary, but is restricted

to the rating values supplied by the sensor manufac-turer.To increase its sensitivity, a dc amplifier with a gain

once more equal to 10, has been inserted between thetwo elements of the system. Figs. 11 and 12 show theexperimental results obtained with this arrangement.The frequency versus load curve shows that non-

linearity effect is limited to 1 percent. Such effect is dueto the converter nonlinear frequency versus voltagecharacteristic. On the other hand, the period versusload curve has a linearity better than 0.05 percent,according to the converter theory. The average measure-ment accuracy is better than 1 percent for interrogationtimes greater than 20 nis.

CONCLUSIONSThe aimii of this work was an approach to the problem

of introducing electronics of the digital type, or easilydigitizable, to control industrial processes. Particularly,we have faced the first problem in the field; i.e., thevoltage-to-frequency conversion of the signal suppliedby the sensor. We have designed a converter with goodcharacteristics and a sufficiently low cost to allow itsmatching to each sensor placed in the field.The converter has been tested and matched with three

different sensors chosen among the types more suitableto measure the quantities of greater interest in the indus-trial field.The quality of the results obtained is like the one ob-

tainable through an instrumientation of analogic type

380

370

NeZ; 360

350

340200 400 600

Loadi(gr)800

Fig. 11. Experimental frequency versus load response for theconverter matched to a strain-gauge sensor.

3.0 1

2.9

32.8

2.7-

261-0 200 400 600 800

Load (gr)

Fig. 12. Experimental period versus load response for theconverter circuit matched to a strain-gauge sensor.

[2 ]. This comparison is made on the basis of the resultsobtainable in loco; therefore, due to the advantages ofinformation transmission with frequency modulation inrespect of amplitude modulation, the system we haveproposed can be considered without any doubt verysuitable for the control of industrial processes.

In particular, we feel it worthwhile to underline thefollowing performances of the converter presented, also,on the grounds of the characteristics we intended totake into consideration and about which we have talkedin the Introduction.

1) High stability of the characteristics with respect toambient temperature fluctuations.

2) Versatility of use (the converter can be matched tosensors of different type simply by changing the inter-face).

3) The converter response is linear on the whole in-terval of input voltages when we consider l/f versusVj, and, of course, for small ranges of input voltagesthe f versus Vi,, characteristic is also linear. This char-

I

I

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1EEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL iNSTRUMENTATION, VOL. IECI-19, NO. 4, NOVEMBER 1972

acteristic allows us, therefore, to keep the system re-sponse linear for large dynamic intervals of the quantityunder control, when the sensor response is linear.

4) The nonlinearity effects of the sensors whose re-sponse is exponential can be compensated by takingadvantage of the circuit nonlinearity effects through thematching with an appropriate interface. Such compensa-tion extends over large intervals of the quantity undermeasurement. Especially for a thermistor, the system-response linearity over intervals of the order of 100°C isparticularly interesting.

ACKNOWLEDGMENTThe authors wish to thank Prof. A. Alberigi Quaranta

for his constant interest and support in this work, Dr. E.Pupillo, M. Dondi, and R. Volta for valuable help inperforming the electronic circuit and taking the mea-

surements. They also wish to thank Prof. F. Baracchifor some helpful suggestions.

REFERENCES[1] R. A. Klososky, "Computer architecture for process control,"

IEEE Trans. Ind. Electron. Contr. Instrum., vol. IECI-17. pp.277-281, June 1970.

[2] D. M. Considine, Ed., Process Instruments and Controls Hand-book. New York: McGraw-Hill, 1957.

[3] M. Prudenziati, A. Taroni, and G. Zanarini, "Semiconductorsensors: I-Thermoresistive devices," IEEE Trans. Ind. Elec-tron. Contr. Instrum., vol. IECI-17, pp. 407-414, Nov. 1970.

[4] A. Taroni, M. Prudenziati, and G. Zanarini, "Semiconductorsensors: II -Piezoresistive devices," IEEE Trans. Ind. Electron.Contr. Instrum., vol. IECI-17, pp. 415-421, Nov. 1970.

[5] K. Arthur, Transducer Measurements, Tektronix, Inc., Beaver-ton, Ore., 1970.

[6] H. S. Black, Modulation Theory. Princeton, N. J.: Van Nostrand,1953.

[7] J. C. Hancock, An Introduction to the Principles of Communica-tion Theory. New York: McGraw-Hill, 1961.

[8] C. E. Shannon, "A mathematical theory of communications,"Bell Syst. Tech. J., vol. 27, pp. 3.79-656, Oct. 1948.

Optimum Design of a Position Detection System witha Sinusoidal Perturlation Signal

J. H. AYLOR, EDWARD A. PARRISH, JR., ANI) GERALD COOK

Abstract-In a paper by McVey and Chen [I] the effect of theamplitude of a sinusoidal perturbtion signal on the accuracy of aposition detection system was presented. However, the amplitudesconsidered were chosen arbitrarily, and no optimum value wasspecified. This paper presents a method for determining an optimumamplitude for a sinusoidal or, for that matter, any other perturba-tion signal. In addition, the method may be used to eliminate certainfunctional forms of a perturbation signal from consideration for agiven receptor geometry.

Manuscript received August 24, 1971; revised July 16, 1972. Theresearch on which this paper is based was supported by the ResearchInstitute of the U.S. Army Engineer Topographic Laboratories,Department of the Army, Fort Belvoir, Va., under Contract DAAK02-70-C-0280.

The authors are with the Department of Electrical Engineering,School of Engineering and Applied Science, University of Virginia,Charlottesville, Va.

I NT1RODUCTIONN A PAPER by McVey and Clheni [1], a method ofimproving detection accuracy of a discrete-outputreceptor composed of photosensitive elements was

presented. The output of each element is assumed to be1 if illuminated by an amount equal to or greater thansome threshold, and 0 otherwise. This being the case,the transfer characteristic of an infinitely long, one-di-mensional receptor is nonlinear.The system proposed in [1 ] to smooth the nonlinear

characteristic is shown in Fig. 1. The elements are as-sumed square (MXM) and are separated by an amountg. Smoothing is obtained by moving the target imageback and forth across the receptor with a perturbation

114