IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL IM-27, NO. 3, sEPTEMBER 1978

+ 75"

390p 3k3BD 139

F- BA 219

lR7 L To XLM3OIA- AA--0

9D140@3k3

Fig. 5. Circuit of the amplifier used for link compensation. The letters F,H refer to Fig, 3(b)

about 100 n; with the active link compensation it is notnecessary.The amplifier of Figs. 2 and 3 was made using an LM301A

to which a simple class B power stage was added to increasethe permissible operating currents; the circuit is shown inFig. 5. The measured gain G of the amplifier was 160000 sothat the L4(G + 1) term in the effective link resistance wasnegligible even for a link of 200 Q. With a current in theunknown of 20 mA and a supply voltage of + 15 V to theamplifier of Fig. 5 a maximum link resistance ofabout 7000is permissible. Once the active network is connected bridge

balance procedure is unchanged from that required in abridge using conventional compensation arms except thatthe precision needed in adjustment of these arms is thatcorresponding to a small link resistance.The twenty resistors of Fig. 4 were measured against a 10

n standard with a discrimination of 1 ppm. The timerequired for a complete run was less than 1 h and thereproducibility was within 1 ppm.

CONCLUSIONThe problems of using the Kelvin bridge with large link

resistance have been considered. A method ofcompensatingfor the effects of this large link resistance using an opera-tional amplifier has been described and its practical im-plementation demonstrated.

REFERENCES[1] D. Rameley, "A method of controlling the effect of resistance in the

fink circuit ofthe Thomson or Kelvin double bridge," J. Res. Nat. Bur.Stand, vol. 64C, pp. 267-270, Oct.-Dec. 1960; also in "Precision mea-surement calibration, electricity-low frequency," Spec. Publ. 300, vol. 3,U.S. Dep. Commerce, NBS, Dec. 1968.

[2] F. K. Harris, Electrical Measurements. New York: Wiley, 1952, pp.282-287.

[3] J. L. Williams, Melbourne, Australa, Kelvin Bridge Type KBLC6.

Manometer for Measurement of DifferentialPressure ofthe Order of 2 Millibars

JURAJ POLIAK

Abstract-Exarnining the functioning of sensors for mesunuug3pressure shows that most of them make we of a displacement. Thelinearty an the semitivity of this type of sensor are closely 2dependent on thevle of this dispcement. For the sake of linearity ,.and repeatabiity of largeuip,gag the displacement has to be smalL.Consequently the output signals obtained are weak.

INTRODUCrlONASCHEMATIC diagram of the proposed solution is

depicted in Fig. 1. It has a "pressure-displacement"transducer of a classic type with a metal diaphragm, but theconversion "displacement-electric signal" is performed bymeans of interference and a photosensitive device. The _Iprinciple of operation can be described as follows.

Manuscript received February 17, 1978.The author is with the Ecole Polytechnique Fed6rale Lausanne, Chaire

d'Electrom6trie, 16 Chemin de Bellerive, CH-1007 Lausanne, Switzerland.

Fig. 1. 1. Monochromatic source. 2 Beam splitter. 3. Fixed mirror. 4.Diaphragm with mirror. 5. Detector. 6. Up/down counter. 7. Multiplica-tion constant introduction. 8. Multiplier. 9. Display of the differentialpressure. 10. Display of the number of interferences.

0018-9456/78/0900-0227$00.75 (D 1978 IEEE

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IIEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. tM-27, No. 3, SEPTEMBER 1978

~~~~-

-

-

-

- D,

20mm

Fig. 4. Light beams as seen by the detectors.

Y (.-I)IiSI "S2 d X

SrnF S2 d

rig. z. Lnapnragm witn mirror.

laser

20mm

Fig. 3. Optical system.

PRINCIPLE OF OPERATIONA monochromatic light beam of known wavelength is

divided by a beam splitter (Fig. 1), semitransparent mirror,into two parts-one being reflected and the remaindertransmitted. The reflected beam is again reflected at mirror(3), so that it travels back towards the detector (5). Similarly,the transmitted beam is reflected from a mirror (4) on thediaphragm (Fig. 2). Both beams will recombine at thedetector level, producing interference fringes. The displace-ment of the fringes is a function of the movement ofthe diaphragm, therefore of the pressure.

In order to obtain interferences, the difference in the twobeam-lengths has to be smaller than the length I of coher-ence. This coherence length is defined as the ratio of thespeed of light c to the spectral width of the source

c A2

Av AA

If the light source is a helium-neon laser, the variation inthe beam length due to the movement of the diaphragm ismuch smaller than the length of coherence, which is sometenth of a centimeter. The interference patterns at the levelof the detectors are defined by the optical system shown inFig. 3.

Fig. 5. Estimation of the diameter of the first interference fringe if there isa maximum in the middle.

Fig. 4 represents the light beams as seen from the screen.The surface of constant phase difference of the two

coherent point sources S1 and S2 are revolution hyperbol-oids. Their intersections with a plane perpendicular to theline connecting the two foci are concentric circles. In orderto place the two photodetectors correctly, it is necessary toestimate the radius ofthe first circle, which corresponds to amaximum of the light intensity assumed that there is amaximum in the center (Fig. 5). If the distance SI S2 is anintegral multiple of the wavelength, there is a maximum inthe center of the circles. The equations are as follows:

y2 X2 + d2

(Y + (n - )A)2 = x2 + (nA + d)2.From these equations one obtains

X=|(2nd+ A(2n-1)) 2X 2(n -1) d.

The term in A can be neglected; and the wavelength isinvolved only in the determination ofthe number ofinterfer-ences n:

n = A/A, where A is a difference in the beam lengths.Fig. 6 gives the radius X ofthe circle as a function ofn and

A. This curve shows that the maximumrVariation ofx occurswhen n and A are small. To assure a correct functioning atthe level of the detectors, it is therefore necessary to providesufficient offset in the distance between the mirror and thediaphragm, in order to avoid the critical part of the curve.Two photodetectors are arranged in such a way that their

mutual distance is equal to I or - ofthe distance between theadjacent maxima of the interference and give two out ofphase signals corresponding to the movement of the dia-phragm in either direction (see Fig. 7). The direction of themovement of the interferences depends upon the sense ofvariation in the pressure.

228

POLIAK: MANOMETER FOR MEASUREMENT OF DIFFERENTIAL PRESSURE

Xcm

6 1.2

Fig. 6 Diameter of the first circle as a function of n and A.

Fig. 7. Arrangement of the two detectors.

If the signals from the detectors are applied to the X andY inputs of an oscilloscope, the resulting curve is an ellipsewhich rotates clockwise. One of the signals is counted by areversible counter and gives the number of interferencefringes: the other signal is used for the estimation of thecounting modes-counting-up or counting-down. Theoret-ically the two signals form two sine curves which are out ofphase. In realiy, random disturbances, mainly of mechani-cal nature, are superimposed on the two sinusoidal signals.After a minor shock or variation in pressure, the diaphragmstarts to vibrate on its natural frequency and its harmonics.The disturbances can be classified into three groups depend-ing upon the detectors output amplitude as follows:

1) disturbances with amplitudes smaller than half themaximum of the sine-wave signal;

2) disturbances between half that amplitude and the fullamplitude;

3) disturbances higher than the total amplitude of thesine-wave signal.

In the first two cases, one can eliminate their effect by usingadetector with hysteresis and properly adjusted thresholdlevels (Fig. 8).

If the disturbances are too severe, the signal is ofno value.Electrical filtering cannot be used, because it would affectthe counting of faster or slower pressure variations and thiswould limit the performance of the system. Excluding a very

-t

Fig. 8. Random disturbances superimposed upon the two sinusoidalsignals.

complicated signal processing, some elimination of thedisturbances or noise can be done by proper selection ofthediaphragm. Several types of capsules and diaphragms withdifferent possibilities of fittings were tested. The diaphragmwas excited by a loudspeaker till a maxima amplitude wasobtained. The diaphragm giving maximum amplitude smal-ler than one half of the amplitude corresponding to theinterference fringe was chosen.From the detectors with hysteresis two logic signals (Fig.

8)pass through the direction discriminator and the up/downcounter. The binary coded decimal (BCD) signal, corre-sponding to thenumber ofthe interference fringes per unit ofpressure, is collected at the output of the up/down counter.The ratio between the state of the up/down counter and thepressure is defined by the wavelength of the laser and themechanical parameters of the diaphragm.The calibration factor of the instrument can be set

according to the required display unit chosen in advance bythe user.One could adapt the characteristics ofthe manometer by

changing thediaphragm or the wavelength ofthe laser; thesemethods would be complicated and expensive. The problemwas solved as follows: The number of interference fringescorresponding to the pressure is multiplied by a constantfunction of the selected unit of pressure chosen for thedisplay. The multiplication is performed automatically, inthis particular case in 2.3 s: the introduction ofthe constant

0o6 i

229

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-27, NO. 3, SEPTEMBER 1978

Fig. 9. Manometer mounted in a 19-in box, front view.

0 10 20

Fig. 10. Calibration curve.- mm H20

is performed by means of a keyboard before the measure-ment starts.

REALIZATIONBecause the complete apparatus (monochromatic source

of light, optical system, detectors and diaphragm) is sensitiveto disturbances and noise, it has to be assembled as solidly aspossible. For this reason a compact monochromatic source,the helium-neon laser model 136 of Spectra Physics waschosen. The complete system-laser, optics, diaphragm-was built into a 19-in rack tray (Fig. 9), in such a way thatthere is a possibility of adjusting the position of the fixedmirror by three micrometric screws.

UNITES DE CONSTANTE FACTEURMESURE

-3mbar 56 8 50 10

-2mm H20 5 7 9 71 10

-3Torr 42640 10

Pa-1

N/rn 56850 10Fig. 11. Multiplication constants.

Estimation of the multiplication constants was based onthe calibration performed by the "Bureau Federal des Poidset Mesures" (Federal Bureau of Standards of Switzerland).The calibration has been made both for increasing anddecreasing pressure. The results of this calibration are givenin Fig. 10; Fig. 11 gives the values of some multiplicationconstants. The principal characteristics ofthe equipment areas follows.

Available ranges2 mbar20 mm H202 Torr200 Pa (200 N/M2)

Resolution6 - 10' mbar

or 6- 10-2 mm H20or 4- 103 Torror 6- 10-1 Pa (N/m2)

Precision0.5 percent of full scale

Linearity 0.3 percent

Hysteresis1 digit.

CONCLUSIONSThe differential manometer presented in this paper is able

to function in a large range of pressure, independent of thenature ofthe gas. Themaximum differential pressure and thesensitivity, depend on the diaphragm chosen. The displace-ment of the diaphragm changes with the exponent 1.2through 1.6 of its thickness and with the exponent four of itsdiameter [1]; this gives the possibility to adjust the requiredsensitivity of the apparatus and its range of measurement.

REFERENCES[1] H. H. Norton, Handbook of Transducers for Electronic Measuring

Systems. Englewood Clffs, NJ: Prentice-Hall, 1969.[2] D. Mange, "Analyse et synthese des systemes logiques," Cahier de la

C.S.L, no. 4 EPFL[3] A. Finn, Physique Geinrale. Reading, MA: Addison-Wesley, 1967.M4] J. L. Dion, "Ondes et vibrations," Centre Educatif et Culturel, Inc.,

Montreal, P.Q., Canada, 1974.

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