IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 1, MARCH 1979

Digital Ventilated PsychrometerYASUO NANTOU

Abstract-A digital ventilated psychrometer for direct reading ofthe relative humidity (RH) from the digital indicator by meam oftwoidentical type thermistors is described. The method is based on thetemperature to linear voltage converter, the calculator ofthe dry andwet bulb temperature ratio, the converter from the ratio to thevoltage proportional to RH, and the analog to digital (A/D) conver-ter. The experimental result by the digital ventilated psychrometershows that the apparatus makes the direct indication ofRH possible.The accuracy of the apparatus is estimated to contain an RH error ofless than 2 percent and it is almost the same as that ofthe Assmannpsychrometer. The principal advantage of the apparatus is the directindication of RH and the capability to use the data directly for theinput of the digital data processor.

I. INTRODUCTION

THE VENTILATED psychrometer indirectly measuresI the relative humidity (RH) by reading the temperatureofthe wet and dry bulbs [1], [2]. This paper describes a directreading digital ventilated psychrometer (hereafter referredto as the experimental psychrometer). It is based on themeasurement of the temperature ratio between the dry andwet bulbs, and the detection of the temperature by a linearvoltage converter. The various methods of linearlizing thenonlinear resistance of a thermistor to temperature havebeen devised [3], [4]. The linearlizing method of this exper-imental psychrometer is characterized by the use of atemperature to linear voltage converter. It is achieved by theuse of an operational amplifier with the input circuit of acombined thermistor and two resistors. The temperatureratio of the dry and wet bulbs is calculated by an integratedcircuit (IC) divider. The detected voltage of the IC divider isproportional to the dry- and wet-bulb temperatures. In thetemperature range from 0 to 50°C, the temperature ratio ofthe dry and wet bulbs is simply reduced to a function ofRH.The experimental result shows that the experimental psych-rometer can measure the RH from 20 to 100 percent, in thetemperature range from 0 to 50°C, with an RH error of lessthan 2 percent and the response time of less than 1 min.

II. PRINCIPLE OF MEASUREMENTIn the case of an Assmann ventilated psychrometer and if

Sprung's formula is used to convert the dry and wet bulbtemperatures into relative humidity, the formula may begiven as

e= ew- AP(Od-Ow)/755 (1)where A is a constant which becomes 0.5 at temperaturesabove 0°C, P is the atmospheric pressure in millibars (mb) or

Manuscript received November 22, 1977; revised November 6, 1978.The author is with the Industrial Research Institute of Kanagawa

Prefecture, Yokohama, Japan.

millimeters of mercury (mm Hg), e is the vapor pressure inthe air, ew is the saturated vapor pressure in the air at the wetbulb temperature, fld is the dry bulb temperature, and Ow isthe wet bulb temperature in degrees Celsius, respectively.The relative humidity H in percent becomes

H = e/e, x 100 (2)

where es is the saturated vapor pressure at the dry bulbtemperature. In practice, a table is used to convert the dryand wet bulb temperatures of an Assmann ventilated psych-rometer to units of RH.The purpose of this paper is to report an experimental

psychrometer which gives a direct indication of RH re-gardless of the environmental temperature.One can define the temperature ratio Q ofthe dry and wet

bulbs of the ventilated psychrometer as

Q= (Ow - C)/(Od - C) (3)where C is a constant in degrees Celsius. If the value of theconstant C equals - 16, the RH will simply become afunction ofQ under the condition oftemperature range from0 to 50°C and humidity range from 20 to 100 percent, withthe error less than 2-percent RH. Accordingly, ifthe dry andwet bulb temperature ratio can be calculated by the elec-tronic circuit design, it is possible to give a direct indicationof RH.

III. DESCRIPTION OF DRY AND WET BULB TEMPERATUREDETECTION METHOD

A thermistor is generally used as adetector oftemperaturefor the thermometer. The relation between temperature andresistance of the thermistor is usually nonlinear. It is neces-sary that the relationship between temperature and resist-ance of the thermistor be linearized since thermistors areused in the ventilated psychrometer.A suggested circuit to convert the temperature linearly to

voltage is shown in Fig. 1. In Fig. 1,

R,(T) = RQ exp B(1/T - 11To)where Ro is the thermistor resistance at temperature Toaround which the linearization is to be obtained. B is thecharacteristic constant ofthe thermistor. The output voltageof the circuit can be shown to be (see Appendix)

Vw(T)/lV(T0) =(a + 1)[a + b + exp {B(1/T - 1/To)}](a + b + 1)[a + exp{B(1/T-1/To)}] (4)

where VW,,(T) is the output at temperature Tand VW(To) is theoutput at temperature To.

0018-9456/79/0030-0042$00.75 (9 1979 IEEE

42

NANTOU: DIGITAL VENTILATED PSYCHROMETER

+ Vcc(constant voltage)

/i

vi

Vw(T)F , 1

Fig. 1. Thermistor temperature to linear voltage converter.

connector

35-

straight line(m=0.02)

'e'%1 agmesured

deviation

water bath

Fig. 3. Internal configuration of the dry and wet bulbs.

Thermistor Temperature to

linear voltage converter

+15v

Q Calculator

200

273.15 298.11 323.15 Temp. ( K)

Fig. 2. The relationship between thermistor temperature and normalizedvoltage at T. = 298.15 K.

Factors a and b ofthe combined resistances are chosen inaccordance to the relationships given by (5) and (6).

B-2Toa

B + 2To

4BmTo(B + 2TO)(B + 2To - 2mTr)

where m represents the desired slope of a straight line.Equation (4) behaves nearly as a linear function of

temperature with a slope m around the temperature To.Equation (4) will, however, deviate from a straight line. Thedeviation is given as

D(T) = V.(T)/V.(T0) - 1- m(T - TO).

Fig. 4. Simplified circuit diagram of the experimental psychrometer.

(7)

IV. CIRCUIT DESCRIPTION AND EXPERIMENTALRESULT

The experimental results of the digital ventilated psych-rometer were measured and were determined at T = 298.15K.The relationship between thermistor temperature and

normalized voltage at To is shown in Fig. 2. The deviationfrom the straight line in the temperature range from 273.15to 323.15 K is less than one degree. The dry and wet bulbconfiguration for the experimental psychrometer is shown inFig. 3. The thermistors for the dry and wet bulbs are ofbeadtype which have the same dimensions: 2.5-mm diameter and13-mm length. The value of Ro and the characteristicconstant B of the two thermistors are 4.63 kS, 5.13 kS2 and3745 K, 3770 K, respectively. An electric fan is used tocirculate the air around the wet bulb with an air speed ofmore than 2.5 m/s.

Fig. 5. Front view of experimental psychrometer.

A simplified circuit diagram of the experimental psy-

chrometer is shown in Fig. 4 and the view of it is shown inFig. 5.The wet-bulb temperature is always below the dry-bulb

temperature due to evaporization, except for the case of100-percent RH. The descending rate of wet-bulb tempera-ture depends upon the environmental RH. Accordingly, theabsolute value of the voltage for the temperature ofthe wetbulb V,,, is smaller than the voltage for the temperature ofthe

2.0-

+5--

g O - 1.0-0 >

-5 -co aCs

IOU

241)

100

43,(5)

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-28, NO. 1, MARCH 1979

o . 9t

0.94.-

0.60-

0.5

calculated

/

2() ) 40 5u) 60 70 80 9i) 1038. .i. 33O

Fig. 6. The measuring result of the dry and wet ratio by the experimentalcircuit at 25°C.

dry bulb Vd except also for the case of 100-percent RH. Asmentioned in the preceding section, the absolute values ofthe output voltages, Vd and Vw, are each proportional to thedry- and the wet-bulb temperatures, respectively. The vol-tages, V,w and Vd, are applied to the terminal of switches, SIand S2, of the dry and wet ratio calculator.The voltage corresponding to the detected voltage at the

dry bulb was applied to terminal S2. The wet-bulb ther-mistor was inserted into the constant temperature bath,having been maintained at the temperature correspondingto each RH.The voltage required to satisfy the constant C in (3) can be

set by the variable 1-kQ resistor. The ratio Q is calculated bythe IC divider. The output voltage of the divider, which isproportional to the ratio Q, is converted to a voltage that isproportional to RH by the diode linearlizer using a break-point method. Finally, the analog output of the diodelinearlizer is converted to digital value by the A/D converter.The RH is directly indicated by the counter.The measured results of the temperature ratio of the dry

and wet bulbs at 250C by this circuit is shown in Fig. 6. TheRH deviation from the calculated value is less than 2 percentover the temperature range from 0 to 50°C and covering a

humidity range from 20 to 100 percent. The characteristicsof the total system of the experimental psychrometer as wellas the associated errors are shown in Fig. 7. The horizontalaxis is the calculated RH using Assmann psychrometer'stable and the vertical axis is the measured value. The relativehumidity error is also shown at the vertical axis. As it can beseen the error of the total system is less than 1.5-percent RH.The calibrated result of the experimental psychrometer is

shown in Fig. 8. The environmental constant humidity wasmade by using a salt constant humidity bath such as

MgCl2 - 6H20 for the 33-percent RH, NaBr 2H20 for the58-percent RH, and ZnSO4 7H20 for the 90-percent RH.After the dry and wet bulbs had been inserted into the bathfor about 2 h when a stable humidity condition was reached,the RH was read. The calibration error has been proved tobe less than 2-percent RH. The response time of the exper-

imental psychrometer is less than 1 min. Comparing thiserror with the Assmann psychrometer, the error is almost

Fig. 7. The characteristics of the total system and the associated errors.

lxu +

aL)

co

aL)

I/

2J t

20 5( 1)(v)True ..(/D

Fig. 8. Calibration of the experimental psychrometer.

the same while the response time is faster because of lowerheat capacity with the dry and wet bulbs. A practical test wasmade to measure the RH in a room by using both theexperimental psychrometer and the Assmann psychrometer.The results are shown in Fig. 9. The deviation from theAssmann's psychrometer is 2-percent RH and proves thatthe application of Sprung's formula is correct.

V. CONCLUSIONA direct reading digital ventilated psychrometer has been

designed and developed. The apparatus measures RH with adigital readout regardless ofthe environmental temperature.It is significant in that it is a direct reading digital ventilatedpsychrometer. It can be used in an automatic control systemfor measuring and recording RH by remote control andprovides direct input to the digital data processor.

Further development of an automatic water supplymethod to the wet bulb, a measuring method at tempera-tures below 0°C and above 50'C, and a measuring method ofRH below 20 percent, is needed.

100 +

+ 2- ta)

+ 1- I'

3-1

-

- 2 - -e

20Q

measurea

A, /\1,

.l ror

20 50 LJ)

44

,x'

RtO

0

hAr.I

.4

NANTOU: DIGITAL VENTILATED PSYCHROMETER

For T = To (A4) becomes

V"(To-= -R (a+b+ 1))w~) bRO(a + 1) (A5)

") t Deviation to A.osmanri's

oa..uroU 0.11. x sign is Ass:aailn's j

I'- - _0, v -s

!'enperatureL

Measured Nio.

Fig. 9. Comparison of the experimental results between the digital andan Assmann's psychrometers.

APPENDIX

Derivations of (4), (5), and (6) are given below.Referring to Fig. 1, if the operational amplifier is ideal,

VW(T) can be given by

VW(T) -Rf/Z* Vi (Al)

where Rf is the feedback resistance and Vi is the constantvoltage.

Generally, the thermistor resistance R,(T) is related to theabsolute temperature by

R,(T) = Ro exp B{(l1/T - /To)} (A2)

where To is the reference temperature, B is the thermistorconstant, both in kelvins, and Ro is the thermistor resistanceat temperature To. Accordingly, Zj(T) is

Z(T) = +bR[a + exp {B(1/T - 1/T0)}] (A3)

a±+b±+exp{JB(I/T -l/TO)}

Consequently, (Al) is given by

Vw(T) _ -Rf[a + b + exp {B(/T - l/To)}]Vw(T) bRO[a + exp {B(l/T - l/To)}]

Normalizing (A4) with reference to the quantities at thereference temperature To we obtain

V'(T"lVwT' =

a+1 [a+b +exp{tB(1/T -1/T0)}]w( )/ °) -a + b + 1 a + exp{B(1/T-1/To)}

(A6)

which is (4) in the text. In order to represent a straight-linecharacteristic, the above equation should be of the form as

follows:

Vw(T)/Vw(To) = 1 + m(T - To)

where m represents the desired slope of the straight line.Obviously it means that

d{Vw(T)dVw(T0)| = mdT T=To

dn{Vw(T)lVw(TO)l = 0.

dTn =T

(A7)

(A8)

(n> 2) (n> 2)

Substituting n = 2 in (A8) and solving (A8) with regard tothe parameters a and b, we obtain

B-2Toa =

B + 2To4BmTg2

(B+2TO)(B+2TO-2mT2)

which are (5) and (6) in the text.

(A9)

(A10)

REFERENCES[1] K. Shiba, T. Ichinose, and S. Mizumura, "Ventilated psychrometer,"

Trans. Soc. Instrum. Contr. Eng. (Japan), vol. 9, pp. 499-503, Oct. 1973.[2] T. Tozawa, "Wet-and-dry-plate hygrometer," J. Soc. Instrum. Control.

Eng. (Japan), vol. 2, pp. 182-185, May 1963.[3] M. Ikeuchi, T. Furukawa, and G. Matsumoto, " A linear temperature-

to-frequency converter," IEEE Trans. Instrum. Meas., vol. IM-24, pp.233-235, Sept. 1975.

[4] S. Natarajan, "Wide linear temperature-to-frequency converters,"IEEE Trans. Instrum. Meas., vol. IM-24, pp. 235-239, Sept. 1975.

s +2

-1

.1 -2

45

I

.s -1,I

co

r-0a)P,