Indian Journal of Radio & Space Physics Vol. 32, April 2003, pp. 108- 113

Comparative study of the methods of measurement of dielectric constant at microwave frequencies for dry and wet soil

o P N Calla

Internati onal Cen ter fo r Rad io Sc ience,"OM- N IWAS" A- 23. Shastri Nagar. Jodhpur 342003

and

S Agarwa l, S K Agarwalla, R Bhattachaljee & A Kalila

Department of Electroni cs and Telecommun ication. Assam Engineering Co llege. Guwahat i 78 1 01 3

Received 6 DeceJllber 200 / ; revised 3 Jllly 2002; accepled 2() SepleJllber 2()02

A n attempt has been made to do the comparati ve study of the three different methods o f mcasuremenl of diclcc lric constant of so il co llec ted from Rajasthan at dirferent gra vimetric moi sture content. The measuremcnts ha ve becn madc us­ing waveguide cell. resonant cav ity and HP network analyzer at X- band.

Introduction The importance of dielectric constant in microwave

remote sensing for the study of wet and dry soil is mllch felt due to the dependence of emiss ivity and backscatter coefficient of so il on thi s particul ar pa­rameter. The knowledge of va ri ab ility o f soil moisture is important for agri culture.

Soil is a mi xture of so lids, liquids and gases mi xed in vari able proportions. Soi I tex ture and so i I structure are the phys ical properti es of so il that influence the amount of pore space in it and the way the pore space are di stributed. Sandy soil lacks water holding capac­ity as in the case of soil of Rajasthan.

I n the present paper, the study o f co llec ted soi I is presented. Table I gi ves the textural data of the soil sample.

The present work includes only the measurement of storage fac tor of dielectric constant of the soil at different grav imetri c moisture contents over a w ide range of frequencies using three different methods I . ] .

M ore work remains to be done on the measurement of imaginary part of complex permitti vity.

2 Sample preparation

The soil samples w ith different moisture content were prepared as given below:

(i) T he samples of the soil were oven-dried and their weights were taken.

(ii ) Then measured quantity of water was added to the samples.

(iii ) The samples were kept for 24 hours for homo­geneous mi xi ng and final settlement.

(iv) The dielectric constant of the samples was then measured at different grav imetric moisture contents at success ive time interva ls. The meas­urements were also made at oven-dry condi ­tions.

3 Methods of measurements

3.1 Waveguide method In the waveguide method, the dielectric constant is

measured by calculating the shift in minima of the standing wave pattern inside a rectangul ar waveguide. This shift takes place due to the change in the guide wavelength when a dielec tric materi al is introduced in the waveguide. The relevant equation is given by

( I )

where, A gl: is found by solving the foll ow ing equati on:

tan {2n (d + L) / Ag,, } tan (2n LI Ag, ) ---=-------=-=- = --------'--

where, a = Width of the waveguide

A" = Wavelength in free space = Vel ocity of light / frequency

A ga = Guide wavelength filled with air A gE = Guide wavelength when fill ed w ith

. . . (2)

CALLA e/ {II.: MEASUR EMENT METHODS OF DIELECTRIC CONSTANT OF SOILS AT X-BAND 109

Table I- Different types of soil and their constituent percentage

Soil type Constituent percentage of Rajasthan soil

Finc sand

Coarse sand

Silt

Clay

Wilting coeffi ci ent

loss less dielectric materi al

83.3%

3.4%

3.33%

9.847%

0.06

d = Displacement of the minima of air

after insertion of the dielectric L = Length of the plane pos iti o n where

the impedance is to be measured .

3.2 Cavity method

In thi s method, a cy lindri ca l cav ity resonator is being used. The cavity is des igned with the he lp of the mode chart whi ch is a family of stra ight lines ob­tained when (jD)2 is plotted agai nst (DIL)2. Here, f is the frequency, D is the diameter of the cavity and L is the length o f the cav ity . The operat ing rectang le is chosen to operate w ithin the frequency range of 7. 1-8.8 GHz in the TE Oil mode. The field equat io ns are deri ved from Max well's equati o n and the resonance conditi on is obta ined by substituting the boundary conditi ons. Here, the dielectric cons tant is measured relative to air and given by k = f.'lEo. w here f.o is the dielectric constant of a ir = 8.854 x 10- 12 Fhn2, and E'

is the dielectric constant of the sample. The parame­ters Eo and E' satisfy the following eq uat ions:

" 2 2 ~o = CD ~Eo - kc

(.1. 2 2 , k " 1-' 1 = CD ~£ - 'c

(3)

(4)

where, ~o and ~ I are the respect ive phase-shift con­

stants, kc is the cut-off parameter in the guide and ~ is the permeab ility of the medium in the resonator. The

parameter ~o is found fro m the equati on

~() =n:/I() . . . (5)

where, 10 is the resonant length of the air filled cavity . The paramete r kc is g i ven by

kc = 3.832/ a ... (6)

where, a is the radiu s o f the cavity.

The paramete r ~I is obtained by so lving the fo llow­ing transcendenta l equation:

-(/, - b)tan f3(J (/, -b)

bf3() (/, - h) . .. (7)

where, Ir is the resonant length of the cav ity with the dielectric sample and b is the thickness of the di e lec­tric materia l. Now E,. is ca lcul ated from

£ = , £'

£0 .. . (8)

To measure the resonant lengths, the measuring c ircuit consis ts of a RF power generator with a fre­quency meter, a slotted line secti on and the cy lindrical resonant cav ity. The probe of the standing wave de­tector is set in a maximum position in the slotted line section, at the load end of which the resonant cav ity is connected . The length of the cavi ty is now changed s low ly and the length at which the pointer o f the standing wave detector shows a dip is noted . Thi s length is the resonant length 10 . Now the di e lec tri c sampl e of he ight b is introduced at one end of the cavity and the same process is repeated to obtain the new resonant length I,..

3.3 Network analyzer method

In this method, dielectric constan t of the sample is measured by simply touching the coax ia l probe o f the network analyzer to the flat face of the soi l surface. The system consists of a swept RF source, a network analyzer (HP 8510C) and associate data processing instrumentat ion.

The value of dielectri c constant of the so il sample is determined from the measurement of the phase and amplitude of the refl ectio n co-efficient of a probe terminated in the material under test.

4 Comparison of the three methods

An attempt has been made to present a comparison of the three methods already menti oned for the meas­urement of dielectric constant. The comparison has been shown in Table 2.

5 Experimental results and discussion

The graphs of die lectri c constant vs frequency as well as mo isture content obta ined from waveguide and netwo rk ana lyzer methods of measurements are shown in Figs 1-3. For the resonant cav ity method the

I I () INDIAN J RA DIO & SPACE PHYS, A PRIL 2003

T able 2 - Compari son of three methods

(i)

( ii)

Network ana lyzer and d ielec tri c probe method

Thi s method g ives data for a w ide fre­quency range, ranging from 2()() M Hz-20 G Hz.

It can provide the permitti vity in complex form, bu( ca nnot rcso lve (an 0 for low loss 1ll ;l teri;li.

( ii i) No s;ullple prepa rati on is needed.

( iv) Very convenient \0 use and direct result is obtained from computer so ft wa re.

(v) Wm Ks very well lo r liquid and semi-li q­uids.

(v i) Ex tremely fast method, especiall y when a \V ide frequency range is \0 be covered.

(v i i) Eq llipmcill s an: very cos tl y .

Waveguide method

T hi s method too gi ves data for a w ide range ranging from SOO MHz- liD G Hz using waveg uide o f different d imen­sions.

It can also measllre both real and imaginary pJrt o f the dielectri c constant and is accurate method for the meas­urement or low ta n o.

Sample preparati on is required.

Easy to lise and its analysis CJn be done manuall y as well as w ith the help o f so ft ware,

Proper design makes it possible to lise for solid s, l iq uids and semi - l iqu ids.

A time consuming method.

Equipment cost is low,

(v ii i ) Acc uracy o f ± S'k for storage factor and Accuracy lies between that o f network

for loss factor it is ± 0.2S%. analyzer and cavity ,

( ix) T his method requires L',,',' lknt craft sman- Limited skill is necessary .

Cavity meti;od

A cavity can be used for a small fre­quency range and diffe rent caviti es arc required to achieve a \V ideI' range. Frequency rnnge can be fro m SO() MH z- IO G Hz.

It ean measure both storage pan and loss part and has high prec ision in measuri ng the (an 0 o f a low loss ma­teria l.

Spec imen material mw,t be des truc­ti vely sampled and be 1(1rIlled in a precise shape,

M easurement o f the storage factor is relati ve ly simple whde calculations in case o f loss fac tor are rather complex.

Suitable for so l ids and semi-so l ids as well as for liquids.

A time consuming method,

Reasonab le cos t.

A nominal accuracy o f ±l'){, for SlOr­

a\!e factor and ± I % for loss factor ca n b~ achieved-'-

Still easier to lise. shi p. • _ _____________________________________ _

relevant data are shown in Table 3, The rea l part, i ,e, r. ' of th e dielectri c constant of the sample showed similar trend in each method , The va lue of r. ' increases with the increase in moisture content. Thi s is due to the presence of free water molecules in the sample,

Though all the methods or measurement show the values of the dielectri c constant very close to each other, the resonant cav ity method, seems to be more accura te due to the absence o f the backlash error pres­ent in the slotted line sec ti on as well as the uncer­tainty in locating very sharp milllma, in the waveguide method, In cavity method, only resonant length s are considered for measurement of dielec tric constant , whi ch reduce the probability of getting un­certain results, It is observed from the study th at the network analyzer produces an accuracy of ±5% (Ref. 4) for £ ' and the resonant cav ity method gives an

accuracy of ±3 9'0 (Ref. I ), whereas it is found th at the waveguide ce ll method gives an accuracy in between that of the resonant cavity and the network analyzer methods. The cav ity method is also found to be most sensitive to tan 8 (Ref I ), The accuracy makes it fea­sible to develop cavity into standalone eq tipment ror fi eld use.

6 Error analysis

6.1 Waveguide method

(i) A number of minima pos itions are sometimes obtained and then it is a matter of choice to se­lec t the correc t minima.

(ii) Error is also introduced in the slotted line sec­tion due to backlash error and improper inserti on of the probe, whi ch can be reduced by careful handling,

-

>

CALLA el 01.: MEASUREMENT METHODS OF DI ELECTRIC CONSTANT OF SOILS AT X-BAND III

3 -

2.5 t= ~ I-Z « I-

2 (fJ z 0 u

1.5 ~ a:: -+- Oven-dry I-u

-Air-dry UJ -' UJ

----0.83% is 0.5

0

8 8.2 8.4 8.6 8.8 9 9.2 9.4

FREQUENCY, GHz

35 .. (b) 30

I-Z ..: 25 I-

--.. en z 0 20 U u --- • --4.72% • • • ---7.61% ir 15 I-U -- 32.28% w 10 -' w --- 22.04% 0

5 . . ---. . . . , , ....

0

8 8.2 8.4 8 .6 8 .8 9 9.2 9.4

FREQUENCY, GHz

Fig . I - Variati on o f dielec tri c constant w ith frequency at vary ing moisture content [both (a) and (b) i obtained from wavegu ide method

35 (a)

I- 30 z ..: I- 25 m z 0 20 0 0 ii 15 I-0 w 10 -' w 0 5

0

0% 5% 10% 15% 20% 25% 30% 35%

GRAVIMETRIC MOISTURE CONTENT

30

I- 25 z ..: I-m 20 z 0 u u 15 ir I-U 10 w ....J W (5 5

0 0% 5% 10% 15% 20% 25% 30% 35%

GRAVIMETRIC MOISTURE CONTENT

Fig. 2- Variati on of die lectric constant w ith grav imetri c moisture content at varying frequency [both (a) and (b) j obtained from waveguide method

11 2

>-z <: >-Vl z a u u rr >-u w --' w (5

f-z <! >-if)

z 0 u u rr f-u w --' w (5

INDIAN J RADIO & SPACE PHYS. APR IL 20D:1

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Fig. 3- (a) Curves showing dielt:ctric constant vs frequency obtained from nelwork analyzer mel hod (so lid curves are for F' and dOlled

curves arc for c") and (b) Curves showing the dielectri c constan t vs grav imetr ic moisture co ntent obtained fro m network anal yze r

mClhocl (solid curves arc for F' and dOlled curves are for E")

Table 3 - Dielectri c constant for oven-dry soil using resonant cav ily method

Soil sample Freq. I, GHz crn

Rajasthan 8.2 3.346

Dala/fJJ' Tuble: Thickness of Ihe specimen. b = 0.5 cm. (kcl~ = n.8:'2 I 2.9 )~ = 1.746. Va lue o f I" at 8.2 GHz = 3.623 Clll. and

11,,= rr / lll= ().X67 I

Ir-b PoUr-b) tan ~[I(lr-b) tan Pt/; cm PoUr-b) Ptb

2.846 2.468 - 0.323 1.84 1 1.1 19

II

5.008 D.752 2.70

CALLA el III.: MEASUREMENT M ETHODS OF DI ELECTRI C CONSTANT OF SOILS AT X- BAND II :\

( iii ) The length of the dielec tri c sample used is a very important parameter and inaccuracy in its meas­urement may lead to cons iderable errors .

( i v) Error is introduced if there is non-consistency in the dimensions 0 1" the waveguide Ll sed in the test bench set-up and the waveguide ce ll carrying the dielect ri c sample.

1i.2 Cavity method

(i ) Errors are, sometimes, caused due to ex traneous modes.

( ii ) From practical aspect, dust deposition on the internal walls of th e cavity res tri cts the resonant conditi on and also changes the Q-factor o f the cav ity.

(iii ) Changes in diameter of the cavity due to inser­tion of end plate also cause some inaccuracy to creep In.

( iv) Errors in th e measurement of dielectric constant may also be caused due to faulty geometry or non-homogeneity of the sample.

Ii .. ~ NetwOI'k analyzer

The measurement errors in network analyzer can be separated in two categori es.

6.3. 1 SyslclllOlic error - Th is error includes leak­age and mi smatch in the tes t set-up, iso lation charac­teri sti c between the reference and tes t signal paths and sys tem freq uency response. Systematic errors are re-

peatable measurement variati on in the tes t set-up that a network ana lyzer can measure.

6.3.2 ROIle/OIll amr- These errors are non­repeatab le and are due to the variati on in nOise. tem­perature and other physica l changes in the tes t se t-up . The phys ical changes to the les t se t-up can happen between success ive measurements or over a peri od of ti me. Agai n temperatu re changes produce dri ft in the measurement results. The impact on measurement results due to noise is determined by th e tes t signal level to noi se rati o.

Acknowledgements T he authors acknowledge wi th thank s the support

gi ven by the Defence Laboratory , Jodhpur and the Elec tronics and Communicati on Engi neering Depart ­ment of Jai arayan Vyas Universit y, Jodhpur. for providing faciliti es for measurements .

References I Choudhury M. Ca lla 0 P . J 111.1'1 o(ElIg (I lldill ). XLIII. No.

5 ( 1963) 47 . 2 Ca lla 0 I' N. Borah M C. Vasi shtha P. Mishra R. Bhat ­

tachaya A & Purohil S P. I lIdi{//1 .I Rlldio 111111 SPIIC(, Ph,'.I'. 2X (1999) 109.

3 Benchimol G & de Bruyen F A. Mell.l'llr('lll elll o( Ihl' f)i l' l l'(' ­Iric CIIII.\,/WII o( Solid MOIeriol.l' ill Cleclmllic M ea.l'/ /rl' llIl'llI in Micmll'lIl'e Noles. Pllilip.l' 190512. pp S-X.

4 HI' 8510 FIIII/il.\' Ne/ll'Ork !l1I{/I.I'~er. 7i:c/llliml Spl'('i/imlioll.l' (45 MH;, - 110 CH:) . Hew lett Packard Illc .. 19X5.