Can Inst. Food Sci. Techno!. J. Vol. 20, No.4, pp. 279-284, 1987

RESEARCH

A Practical Thermocouple for TemperatureMeasurement in Microwave Ovens!

F.R. van de Voort, M. Laureano,J.P. Smith

Department of Food Science and Agricultural Chemistry

and

G.S.V. Raghavan

Department of Agricultural EngineeringBox 187

Macdonald College of McGill UniversitySte. Anne de Bellevue,

Quebec, CanadaH9X ICO

AbstractA thermocouple capable of measuring temperature in a micro·

wave oven environment without causing discharges or being inter­fered with by the radio frequency field, was developed and tested.Copper constantan thermocouples, shielded with nickel plated copperbraid and using aluminum tubing to form the probe portion of thesensor, worked effectively to prevent the microwave energy frominterfering with the voltage differential generated at the junction.Standard brass Swagelock fittings were used to provide a micro­wave leak-free seal for the holes drilled through the microwave cavitywall and provide a ground for the shielding. Temperature data werecollected using a data logger and temporal variation and heatingrates of water, sulphuric acid, ground meat and skimmilk powderwere studied as a function of power and cavity load. Temperaturesof up to 340°C were successfully recorded. Overall, the thermocouple- based sensor is functional, does not suffer from radio frequencyinterference, and is accurate to within 1°C for convective materi·als. It provides a simple and inexpensive means for the scientist tomake single or multiple temperature measurements in a microwaveoven environment.

ResumeUn thermocouple a ete developpe et veri fie pour mesurer la tem­

perature dans un four a micro-ondes sans causer de decharges ousans etre brouille par Ie champ de frequence de radio. Des thermo­couples en cuivre constantan blinde d'une tresse en cuivre plaqueau nickel et utilisant un tubage en aluminium pour la sonde du sen·seur furent efficaces pour empecher I'interference de l'energie desmicro-ondes avec la difference de voltage genere ala jonction. Desraccords Swagelock en laiton standard furent utilises pour assurerI' etancheite aux micro-ondes des joints aux trous perces dans lesparois du four et pour fournir une prise de terre au blindage. Desdonnees thermiques furent obtenues a I'aide d'un enregistreur dedonnees et la variation temporelle et les taux de chauffage de l'eau,de l'acide sulfurique, de viande hachee et de lait ecreme en poudrefurent etudies en fonction de la puissance et du chargement du four.

I To whom correspondence should be addressed - Dr. F.R. vande Voort.

Des temperatures allant jusqu'a340°C furent enregistrees avec suc­ces. En general, Ie senseur de type thermocouple est fonctionnel,n'est pas affecte par les frequences de radio, et est precis dans leslimites de 1°C pour les produits convecteurs, fournissant ainsi unmoyen simple et peu couteux au scientifique desireux de faire desmesures de temperature simples ou multiples dans un environne­ment de four a micro-ondes.

IntroductionMicrowave energy is of growing importance in food

processing and preparation, and its utilization has beencomprehensively described recently by Decareau(1985). The most common and least expensive micro­wave device available is the microwave oven, whichhas been used extensively for scientific investigationsinvolving the effect of microwaves on food materials.The authors have used it to study the inactivation ofmyrosinase (Maheswari et al., 1980a), the heat stabil­ity of sinigrin (Maheswari et al., 1980b) and themicrostructural changes produced in rapeseed (Ma­heswari et al., 1981). The microwave oven is also beingdeveloped as an auxillary tool in food analysis, themost common uses are rapid moisture determinations(Green and Park, 1980; Karmas, 1980) and accelerat­ing mineral digestion in preparation for atomic absorp­tion analysis (Nadkarni, 1984).

One problem which faces every user of a microwavedevice is temperature measurement. Instinctively, onethinks of using thermocouples; however, our previousattempts to do so (Maheswari et al., 1980a), resultedin spurious signals, electrical discharges, fused ther­mocouples and, finally, the destruction of the oven.The reasons for this behaviour are not that readily dis­cerned; however, Ishii (1983) provides a clear expla-

Copyright 1987 Canadian Institute of Food Science and Technology

279

nation of the discharge phenomena taking place whenmetallic objects are introduced into a microwave cavi­ty. In the case of thermocouple wires in a microwavefield, capacitative and inductive coupling occur,producing currents which interfere with the measur­ing circuit (Chakraborty and Brezovich, 1982).

Under special circumstances, however, thermocou­ples can be used in microwave fields where the micro­wave energy is oriented in a specific direction by thewaveguide. Using a 2450 MHz waveguide in the trans­verse electrical mode, Karmazsin et al. (1984) notedthat thermocouples placed in either the X or Y direc­tion parallel to either the electric or magnetic vectorof the electromagnetic field, did not absorb microwaveenergy; however, orientation in the Z direction causesmaximum absorption of microwave energy. As longas the thermocouple dimensions are small comparedto the waveguide dimensions, field perturbation willbe negligible. However, if higher order modes(TErn. n) are produced by reflections or scattering ofenergy by joints or roughness of the waveguide, tem­perature measurements can be seriously affected andthe thermocouple destroyed (Karmazsin et al., 1984).This is the case in a conventional microwave oven,where the microwave energy emitted from thewaveguide is stirred and reflected randomly off thecavity walls (Ishii, 1983).

The problem of temperature measurement in amicrowave environment has been worked on extensive­ly in the medical field (Cetas and Connor, 1978), wheremicrowaves are being used locally as a means of treat­ing malignant tissues (hyperthermy). Hyperthermyuses lower frequencies, does not involve a reflectingcavity, and requires the direction of microwaves to aspecific locale with the majority of the energy beingin the same mode. Even so, the interaction of micro­wave energy with the tissue perturbs the RF field suffi­ciently to lead to problems with thermocouple usage.A variety of alternate approaches have been under in­vestigation; most attempting to avoid microwave sen­sitive elements, and the majority are not availablecommercially. Some of the experimental approachesinclude: 1. A birefringent crystal optical thermome­ter based on a crystal of lithium tantalate (Cetas, 1976);2. An optical ethalon sensor (Christensen, 1979); 3. Agallium arsenide detector (Christensen, 1979); 4. Adevice based on viscosity change (Cetas and Connor,1978); and 5. The use of a temperature transducer(Karmazsin et al., 1984).

Two commercially available systems are a liquidcrystal optical fiber (LCOF) probe (Rozzell et al., 1974)and a high resistance lead thermistor (Bowman, 1976).The LCOF probe (Ramal Inc.) is costly and requiresfrequent re-calibration due to its inherent long termdrift. The high resistance lead thermistor (Vitek, Inc.)on the other hand is less expensive (approx. $1,000),is relatively stable and not as susceptible to long termdrift (Olson et al., 1982). However, both suffer fromlimited range, the LCOF requiring a number of probesto cover a reasonable temperature range, while thethermistor is limited to a maximum of 100°C. Olsenand Molina (1979) have developed a non metallic ther-

280 / van de Voort et al.

moeouple (NMT), based on the use of low loss nonmetallic 'wires' composed of carbon bearing fluorocar­bon and a conductive elastomer (Olson et al., 1982).The main advantage of the non metallic thermocou­ple would be reduced cost, the use of temperature com­pensation and the ability to use standard voltmetersor data logging equipment generally associated withthermocouple work.

Olson et al. (1982) have criticized the use of metal­lic thermocouples, stating that they are unsuitable formany applications because of reflections and localizedfield enhancement caused by materials of high con­ductivity. In contrast, Chakraborty and Brezovich(1982) supported the use of thermocouples by notingthat conventional thermocouples are rugged, inexpen­sive, and do not require repeated re-calibration. Theypresented a detailed analysis of thermocouple errorsand means to avoid most of them in low frequencydirected electromagnetic fields (13.5 MHz) as relatedto hyperthermy rather than the microwave oven, whichoperates at higher frequencies (912/1250 MHz) andproduces mixed modes (Ishii, 1983).

Domestic microwave ovens can now also be pur­chased equipped with a temperature probe. Due to thedifficulty of obtaining information from the manufac­turers about such probes, one was purchased and test­ed. The probe was found to behave erratically andcause electrical discharges when power was applied toan empty cavity (only the probe present); however,when immersed in liquid or placed in a food product,it appeared to work well up to its operational limit of90°C. When dismantled, it was determined to be ashielded thermistor.

In summary, devices do exist to follow temperaturein microwave environments; however, most are limit­ing either in terms of performance or cost. This paperdescribes the development, construction and opera­tional performance data of a simple and functionalthermocouple capable of operating in a microwaveoven environment.

Materials and MethodsStandard glass wrap/braid coated copper constan­

tan thermocouples AWG No. 30 (Cat No. GG-T30,Omega Engineering Ltd.) were prepared by spot weld­ing the copper and constantan wires at the junction.The thermocouple was shielded using nickel coatedcopper braid, the last 4 em of the probe using stan­dard aluminum tubing having dimensions of 3.18 mm(id), 3.65 mm (od) with a wall thickness of 0.365 mm.

c

~A E F G~

Fig. I. A schematic diagram of the thermocouple sensor: (A) glassbraid copper constantan thermocouple wire; (B) brassSwagelock reduction fitting (bored out); (C) microwave cavi·ty wall; (0) locknut; (E,F) ferrule assembly; (G) cappingnut; (H) copper braid; (I) aluminum probe.

J. Insl. Can. Sci. Techno/. Aliment. Vol. 20, No.4, 1987

120 120

100 l loa mL 300 mL 500 mL

'0'

80 f80 700 mL

60 60 c..

14020' 40

20 20

TIME (MIN)

Fig. 2. The heating profile of 100 mL of distilled water as a func­tion of microwave power (010).

The thermocouple junction was sealed about 3 mm in­side the tip of the tube by crimping the end withsmooth pliers, rounding with a file, and then workedwith emery cloth to form a smooth tapered tip. Thesethermocouples were tested in a conventional mannerto ensure that they gave accurate readings for boilingwater and crushed ice/water. The microwave ovenused in this work was a MDS-81 digestion oven (CEMCorp., Indian Trail, NC 28079), the interior of whichis coated with teflon for working with harsh reagentssuch as acids. Holes were drilled through each of theventing screens located on either side of the microwavecavity to allow passage of the probe. Brass Swagelockadaptor/reduction fittings were drilled out to allowsnug passage of the shielding and the fitting was passedthrough the hole and tightened against the cavity wallusing a retaining nut (Figure I). A ferrule assemblyand ca~ping nut were passed over the shielding afterthe desIred thermocouple length had been passed intothe cavity, and these in turn could be tightened downto prevent microwave leakage, and ground the alumi­num shield to the frame. The shielding was extendedbeyond the exterior of the oven frame to prevent in­terference due to stray RF leakage. The Swagelock fit­tings required good grounding to the metal frame toprevent discharges within the Swagelock orifice or tothe cavity frame. Microwave leakage was monitoredthrough the use of a Holaday model HI-1500 leak de­tector.

TIME IMINI

Fig. 3. The heating profile of water as a function of volume (mL).

The thermocouple wires exiting from the shieldingoutside the microwave oven were attached to a 14channel Campbell Scientific (Logan, UT 84321) CR-7data logger equipped with a magnetic tape for datastorage. The data were transferred to an IBM PC andprocessed using a commercially available APL Stat­graphics program (STSC Inc., Rockville, MD) to al­low the direct plotting of time/temperature data orcarry out any other data transformations.

Thermocouple evaluation consisted of measuringthe heating rates of water, sulphuric acid, hamburgerand skimmilk powder to provide a range of moisturelevels and convective/conductive properties. In allcases, the samples were placed in the geometric centerof the cavity, with the thermocouple being inserted inthe geometric center of the sample. Sulphuric acid wasused to attain significantly higher temperatures andprovide a harsher operating environment. For this sit­uation, the aluminum probe casing was enclosed in aborosilicate glass tube to prevent the aluminum fromcontacting the acid and the top of the glass sheath waswrapped with teflon tape to prevent acid condensatefrom reacting with the metal surfaces. Aluminumoxide powder was used to fill the gap between the twosheaths to improve the thermal conductivity to thethermocouple junction.

Results and DiscussionThermocouple Development

Substantial experimentation was involved in attain­ing the final configuration of a working thermocou-

POWER 1%)

Fig. 4. A rate plot of 100 mL of water as a function of microwaveflower (010)

VOLUME (mLi

Fig. 5. A rate plot of water as a function of volume (mL).

Can. Insl. Food Sci. Technol. J. Vol. 20, No.4, 1987 van de Voort et al. / 281

TIME (MIN)

Fig. 6. The heating profile of 98010 sulphuric acid at 80010 power.

85 ~Tl 'TT,"--'1-'-- r-...---rT'-r--r--l-r-r, -"--l--l'-,,"""J']

c "

R = 0.1979 + 0.2967P + 0.0049p2 (I)

Where: R = rate of heating (dTIdt)P = power setting (010)T = temperature (0C)t = time (min)

Temperature MeasurementFigures 2 and 3 present composite plots of temper­

ature vs. time as a function of power setting andvolume obtained using the thermocouple. All the plotsare smooth and the thermocouple behaves well in bothcircumstances with water indicating the expected tem­perature upon boiling. By calculating the initial linearrate of heating by regression, rate plots (Figures 4 and5) can be obtained to allow one to determine the ef­fect of power and volume for calibration purposes. Ascan be seen from Figure 5, the heating rate as a func­tion of power settings, is not linear for 100 mL ofwater, but quadratic and could be described byEquation 1:

The heating rate as a function of volume (Figure 5)was shown to be biphasic, indicating that convectionand volume were limiting factors in the system athigher volumes. .

To test the thermocouples at higher temperaturesand under harsher conditions, sulphuric acid washeated in the microwave and the temperature meas­ured using a glass-sleeved version of the thermocou­ple. Although the response time suffers somewhatbecause of the glass sleeve and the temperature is quiteclose to the operational limit of the thermocouple, thethermocouple functions adequately (Figure 6), 98010sulphuric acid boiling at 338°C, close to the value of340°C cited in the literature.

In order to study materials which were more non­convective in nature and had substantially differentmoisture contents, ground meat and skimmilk powderwere tested. The heating profile of hamburger ispresented in Figure 7, illustrating a more complex heat­ing pattern showing two inflection points. Figure 8illustrates the heating behaviour of skimmilk powder,the second curve (B) being the temperature profile ofa second thermocouple being suspended in the cavitybut not placed in a sample. Skimmilk, as a low

~-ii1

,-,-,~ ,"-"~,Jo L.~L'J.-L'...L'-L1-e'-'L.L..t.-.Ll.........L..L1 I I I I

o 1

400 f' I I I t iii i i--,--,----r-~.-~---.-r.--r-r-,..,j

t ~~~ ~

L

t200 r

[­

100 l:­fL

pie. Standard thermocouples discharged violently andfused or produced anomoulus readings depending onthe power setting. Based on a suggestion by Chak­raborty and Brezovich (1982) of shielding ancillaryelectronic circuitry from stray microwave radiationthrough the use of aluminum foil as a retlector, a simi­lar approach was attempted using aluminum foil toshield the thermocouples. These versions of the ther­mocouple worked intermittently, but suffered badlyfrom heavy electrical discharges. The reason for thisproblem became apparent based on a study of a paperby Ishii (1983) describing the conditions leading toarcing in microwave ovens containing metallic objects,specifically in relation to thin metal foils or wires whichcan build up the high potentials (> 10,000 V/ cm) re­quired to produce an arc when the load factor on theobject was high (e = 1.0). His equations indicated thatarcing could be avoided in a 700 watt oven, using cylin­drical geometries having radii of greater than 2.2 mm,hence the foil was replaced with an aluminum tube.Major discharges were eliminated with the thermocou­ple in this configuration; however, intermittant gapdischarging was found to occur at the orifice made forthermocouple entry into the microwave cavity. Thisweak "gap" type discharge has also been describedby Ishii (1983) and was prevented by installing brassSwagelock fittings to seal the cavity and make a directground for the aluminum tube to the cavity wall. Sub­stantive trials indicated that the thermocouples workedwell. However, to increase the flexibility of the probethe bulk of the shielding was replaced with nickel plat­ed copper braid, using aluminum tubing only at theend, to provide rigid tip (Figure I).

1j

j3~

1, j

TIME (MIN)

Fig. 7. The heating profile of hamburger at 80010 power.

TIME (MIN)

Fig. 8. The heating profile of skimmilk powder at 35010 power (A)and that of a second thermocouple suspended in air in thecavity (B).

282 / van de Voort et al. J. lnsl. Can. Sci. Technol. Aliment. Vol. 20. No.4, 1987

53t~-T" I ' I I ·..-r~T-'-"'IT'l

48 ~80% ..;

-160'

j

t 43 ~~ 50'

w r~

38 r::>~~

33 r '0' Jw

ia-x~

28i

I ,2~'J23

0 2 10 12

8~, , I , , , I , ,

~rr ~

3 5~~

-j

" c

~----

4 ~u

/w -i>-..

/ "~ I i'" J~ j..

/-iUJ

:Ie C iL "~ J

o [I,..-,-----,- , I , , I I -'--I ~

0 20 40 50 80

TIME (MIN)

Fig. 9. The heating profile of thermocouples suspended in the cavityas a function of power (0J0).

POWER (%)

Fig. 10. A rate plot of thermocouple shield heating as a functionof power.

TIME (MIN)

Fig. II. The heating profile of a suspended thermocouple at 50010power without (A) and with (B) induced air flow throughthe microwave cavity.

moisture powder, is a very good insulator and it wasfound that, in this circumstance, localized heating tookplace around the thermocouple. This was inferred bythe fact that a zone of browning developed around thelocation of the thermocouple. This problem exempli­fies the comments made by Olsen et al. (1982) aboutmetallic thermocouples having limitations due toreflections and localized field enhancements theyproduce. It would appear that in a non-convective sit­uation, at high power levels, the temperature readingscould well be higher in the immediate environment ofthe thermocouple. Regardless, temperature data canbe obtained as a guide to the heating rate of a pow­dered material, such as skimmilk powder, to help de­termine power settings and controlling temperature asa function of weight or volume.

As noted earlier, Figure 8 also contains a secondtemperature profile (B) of a thermocouple suspendedin the cavity as skimmilk powder was heated. As canbe seen, there is some shield heating over time in thepresence of the sample. As the only object in themicrowave oven, the load factor is very high, and eventhough aluminum reflects microwave energy quite ef­ficiently, there is some skin depth penetration ofmicrowave energy resulting in a small temperature rise.

This effect was studied more as a function of power,thermocouple length and rate of air circulation.Although the maximum temperature attained by afree-floating thermocouple was somewhat affected by

37.5152.3279.80

20 0.06 8.2140 2.51 21.3050 4.0960 5.1880 6.46

100

Table 1. Heating rates of aluminum sheathed thermocouples (TC)and 100 mL of water as a function of microwave power.

Power TC Rate H20 Rate(010) (OCImin) (OC/min)

length (surface area), the predominant factor was thepower setting. Figures 9 and 10 illustrate the temper­ature profiles and a rate plot obtained for a ther­mocouple in free space as a function of power. Clearlysignificant shield heating takes place. Figure II illus­trates the heating effect obtained at 50010 power whenair flow is introduced through the cavity by turningon the fan. It is apparent that air circulation dissipatesthe shield heat, effectively limiting the thermocoupletemperature rise to 2.5°C VS. 16°C. Shield heatingwould introduce significant errors in temperaturemeasurement if one were studying low loss samples(i.e., teflon) which would allow the shield heating ef­fect to predominate. Under normal circumstances,there would be competition between the heating effectof the sample and the shield. Table I compares the ratedata for the thermocouple and a 100 mL of water. Ascan be seen, the heating rate of water is approximate­ly one order of magnitude greater than that of the ther­mocouple and will predominate. In addition, shieldheating can effectively be minimized and controlledby air flow through the cavity. It is quite likely thatthe aluminum tube is a greater source of error by virtueof its mass and high heat conductivity characteristics,removing thermal energy from the sample surround­ings, than the overall shield heating effect.

The experiments carried out do not allow for arigorous or conclusive analysis of the accuracy of tem­perature measurements obtained with these ther­mocouples. As has been noted by Cetas and Connor(1978), the proper calibration of thermometers and theevaluation of temperature errors is a problem in itselfand there is no ready method by which to simultane­ously compare the data obtained within and withouta microwave environment by two separate methods.

1210

31 ~

t,27 r

"23

o

Call. Ins!. Food Sci. Technol, J. Vol. 20. No.4, 1987 van de Voort et al.l 283

It would be reasonable to assume that an accuracy of± 1°C could readily be attained with high loss con­vective materials (aqueous systems). This level of ac­curacy would be adequate for most general workrequiring temperature measurement in the microwaveoven. As the convective nature of a material dimin­ishes or its insulative characteristics increase, errorsmay arise due to localized heating of the samplearound the thermocouple. Shield heating may be aproblem with low loss materials; however, this shouldrarely be the case as the sample heating rate wouldgenerally dominate the situation.

ConclusionAlthough this study is not a definitive work on ther­

mometry in a microwave environment, the empericalapproach used has led to a workable sensor which canbe used in a microwave oven. The prototype sensorwhich has been developed works adequately, and be­ing voltage based, makes use of electronic equipmentcommonly found in most laboratories (voltmeters,data acquisition units, strip chart recorders, etc.). Itsconstruction requires only thermocouple wire, copperbraid, aluminum tubing and Swagelock fittings. Ex­trapolating beyond the work carried out, it is clear thatwith additional circuitry, the sensor can also be usedin a feedback mode to control the temperature of thematerial being heated in the microwave oven.

AcknowledgementsThe authors acknowledge and thank the Conseil des

Recherches et Services Agricoles du Quebec CMCA­86-8-1063 and Agriculture Canada for their financialsupport of this project.

ReferencesBowman, R.R. 1976. A probe for measuring temperature in radio

frequency-heated material. IEEE Tran .• MicrowaveTheory Technol. MTT-24 43-45.

Cetas, T.C. 1976. A birefringent crystal optical thermometer formeasurements of electromagnetically induced heating. In:Biological Effects of Electromagnetic Waves. Proc. 1975USNC/URSI Symposium. e.e. Johnson and J.L. Shore

284 / van de Voort et al.

(Eds.). (Bur. Radiological Health, Rockville, MD, 1976).HEW Publ. (FDA) 77-8011. Vol II. p 338.

Cetas, T.e. and Connor, W.G. 1978. Thermometry considerationsin localized hyperthermia. Med. Phys. 5(2): 79.

Chakraborty, D.P. and Brezovich, I.A. 1982. Error sources affectingthermocouple thermometry in RF electromagnetic fields.1. Microwave Power. 17 (I): 17.

Christensen, D.A. 1979. Thermal dosimetry and temperature meas­urements. Cancer Res. 39 2325.

Decareau, R.V. 1985. Microwaves in the Food Processing Indus­try. Academic Press Inc., New York, NY.

Green, W.C. and Park, K.K. 1980. Comparison of AOAC, micro­wave and vacuum oven methods for determining totalsolids in milk, J. Food Prot. 43 (10): 872.

Ishii, T.K. 1983. Theoretical analysis of arcing structure in micro­wave ovens. 1. Microwave Power. 18 (4): 337.

Karmas, E. 1980. Techniques for measurement of moisture con­tent in foods. Food Technol. 6: 52.

Karmazsin, E, Barhoumi, R and Satre, P. 1984. Thermal analysiswith microwaves. Temperature and power control. 1.Therm. Anal. 29: 1269.

Maheswari, P.N., Stanley, D.W., van de Voort, F.R. and Gray,J.1. 1980a. The heat stability of Allyl Glucosinalate(sinigrin) in aqueous and model systems. Can. Inst. FoodSci. Technol. J. 13 (I): 28.

Maheswari, P.N., Stanley, D.W., van de Voort, F.R. 1980b. Micro­wave treatment of dehulled rapeseed to inactivatemyrosinase and its effects on oil quality. J. Am. OilChem. Soc. 57 (7): 194.

Maheswari, P.N., Stanley, D.W., van de Voort, F.R. and Gray,J .1. 1981. Effect of microwave treatment on the micros­tructure of dehulled rapeseed. Cereal Chem. 58 (5): 381.

Nadkarni, R.A. 1984. Applications of microwave oven sample dis·solution in analysis. Anal. Chem. 56 (12): 2233.

Olson, R.G. and Molina, E.A. 1979. The nonmetallic thermocou­ple: A differential temperature probe for use in micro­wave fields. Radio Sci. 14 (6S): 81.

Olson, R.G., Hammer, W.e. and Taylor, J.e. 1982. Coaxial non­metallic thermocouple with electronic ice point for dosi­metric use in electromagnetic environments. J. MicrowavePower. 17 (2): 137.

Omega Engineering. 1985. Temperature Measurement Handbookand Encyclopedia. Omega Engineering Ltd., Stamford,CT 06907.

Rozzell, T.e., Johnson, e.e., Durney, e.H., Lords, 1.L and Ol­son, R.G. 1974. A nonperturbing temperature sensor formeasurements in electromagnetic fields. J. MicrowavePower. 9 (3): 241.

Submitted January 25, 1987Revised April 15, 1987Accepted June 4, 1987

1. InSI. Can. Sci. Technol. Aliment. Vol. 20, No.4. 1987