Suspended microstrip patch resonator sensor for ... - IEEE Xplore

Suspended Microstrip Patch Resonator Sensor For Determination Of Complex Dielectric Constant Of Liquid And Paste A K Venna', Nasiinuddin , R K Garg, and A S Oinar'

Department of Electronic Science, University of Delhi South Campus, New Delhi-1 10021, INDIA 'Microwave and Coinmunication Engineering, University of Magdeburg, Magdeburg, Germany Abstract - We report a new accurate suspended microstrip patch resonator to determine dielectric constant and loss tangent of petrol, kerosene, Vaseline and wax. Our results shows good agreement with available results. No calibration liquid is used and its use will further improve accuracy.

I. INTRODUCTION The accurate measurements of the permittivity and loss-tangent of diclcctric materlals are very important for their industrial application and remote sensing. However, as compared to work on solid materials, comparatively less work has been reported for the measurement of the materials in the paste and in the liquid forms [I-41. The microstrip patch resonator has not been used to dcterminc the complex permittivity of paste and liquid. In this work we report a suspended microstrip parch resonator sensor to determine accurately the complex permittivity of petrol, kerosene, Vaseline and wax. We extract the diclectric constant and the loss tangent of these materials from the measurement of resonance frequency and the bandwidth of thc rcsonator with sample. II. SUSPENDED MICROSTRIP SENSOR A two layer suspended cavity rcsonator is shown in Fig.1. The first layer is air filled metallic cavity which is fillcd with the sample liquid or paste. We can put wax also and heat thc cavity so that it is uniformly filled in by the wax. The patch is printed on the dielectric substrate and is known as thc base substrate 111. FORMULATION FOR DETERMINATION OF COMPLEX PERMITTIVITY OF DELECTRIC MATERIALS

The resonancc frequency and thc total i.e loadcd Q-factor of the two layer microstrip cavity resonator can bc computcd accurately with the help a generalized multilayer cavity model, called the modificd Wolff model (MWM) [6-9].The MWM is based on the mode dependent dynamic relative perimittivity of the multilayer structure. It also treat the multilayer substrate as an equivalent singlc layer substrate. The MWM computes the complex rcsonance frequency. From these information we compute the total Q-factor and transfer all the losses to the single laycr substrate with help of effective loss tangent of the substrate. The thcorctical rcsonance frequency of the suspended microstrip patch resonator computcd by using the modificd Wolff model (MWM) is,

Where E ,

dyn

is the complex dynamic effective relative permittivity. It takes care of the modal

field variation by the modal number m, n and losses in all dielectric layers.

vI,is the velocity of

an clcctromagnctic wavc in the free space. The L,m and Wen are the effective length and the

effcctivc width respectively of a rectangular patch. Due to fringe field.they are different from the physical length,L and width, W. The computation of complex dynamic permittivity &;mn(E;I

,E;2,hl,,h2,kf‘, L ) of two

layer rcctangular patch resonator is discussed in reference [9]. The total Q-factor (Q.) of a multilayer microstrip cavity resonator is computed by

Where Q,,, Qo QSw, and Q, are the Q- factors, due to dielectric loss, conductor loss (both in patch and ground plane) surface-wave loss and radiation loss respectively. The computation of the Q-factors are again discussed in the reference [7-S]. If we transfer all losses of the structure to equivalent single layer substrate, we can obtain the equivalent loss-tangent of the single layer substrate, tan 6eq = 1/ Q,, The total theoretical Q-factor, Qttdiffers from the measured loaded Q-factor, Qlmof the cavity. The corrected total Q-factor is Q,,, = Qlt +AQ,,. The correction factor for the suspended patch resonator as function of the aspect-ratio (WIL) is, dQ

,, = 118.88

- 187.47

(F) +

($:I2

115.86

- 31.97

(a)’ +

3.24

( F ) 4 (3)

All the needed expressions for development of an algorithm to extract the dielectric constant

and the loss-tangent are mentioned above. The functional relations for the theoretical resonance frequency, f,, and the theoretical total Q- factor, Q,, are given by,

s,,= . f ( ~ , ~ , ~ , , , t a n 6 , ,qh2,,,t a n 6 , , h , , a.)

Once the measured resonance frequency, f,,

and the measured total Q-factor,

(4)

Q,, are

obtained from a scalar network analyzer the unknown dielectric constant and loss tangent of sample layer can be obtained form the two-dimensional optimization subroutine. Fig. 2 (a) and Fig. 2 (b) show the variation in various kinds of Q-factors due to change in normalized thickness of the base substrate. These figures show the study of Q-factors on both = 9.8 ) dielectric constant substrates. We have taken the low ( E,hase= 2.2 ) and high ( Erbase

tantirbdSe= 0.00 1 for both the substrates. These figures help us to determine thickness of the sample cavity. We have taken it 1.0 nun for simplicity of machining. It provides enough space for holding the sample material. The cavity with thickness 0.5 mm provides higher Q-factor, as the radiation loss is low. However, its machining is difficult and it provides less space to hold the sample material. The cavity with 2.0 nun or 3.0 mm thickness is easier to machine and it also give more space to hold liquid and paste, however, for this thickness Q-factor of the cavity is very low. For the typical cavity thickness 1.0 mm the total Q-factor is about 33 for E,,,,,

= 2.2 and it is 40

= 9.8, when

hIo.01. h,

IV. EXPERIMENTAL DETERMINATION : We have fabricated a microstrip fed suspended cavity resonator on the base substrate 2.2, h2= 0.25 mm with the patch dimension, W = 59.293 mm, L= 49.996 mm. The photograph of the fabricated sensor is shown in Fig.!. This patch resonator without sample has theoretical resonance frequency f, = 2.618GHz and the total Q-factor, Q,= 35.22. The Table-I shows the experimental results on the resonance frequency and the total Q-factor of the patch resonator without sainple and with sample. Every time with the change of sample we have E,>=

652

measured the resonance frequency and the Q-factor. The Q-factor did not repeat exactly. This may bc due to absorption of sample material in the base substrate and also due to some deformation in the base substrate, affecting characteristics of the cavity. The nominal value of the dielectric constant and the loss tangent for the sample materials has been taken from the data given by Hippcl [ I ] . TABLE 1

1

~

Petrol (1.92, 0.0014)

1 1 1 1 !!1 1

Experimental Data Without Sample

Nominal valuc of sample &,,/tanGI

fn(GHz) 2.61 18

Experimental Data With Sample

Qe

frdGHz)

34.39

2.0869

Recovered value of sample

3;3:

Kerosene (2.09, ,0045)

2.6093

30.78

2.0362

31.78

Wax (2.21.0.0054)

2.6107

29.62

1.9665

59.08

Vaseline (2.10, 0.001)

2.6168

32.23

2.0501

58.58

0.0167

2.22

0.0039 0.0027

These data are for specific samples at a certain temperature and frequency diffcrent from ours. The sample obtained from the market can differ very much from the sample tabulated by Hippel. Especially any kind of adulteration or moisture absorption can lead to the increase in the loss-tangent. Thus we find higher loss-tangent for petrol and kerosene. Other two cases also differ from the nominal value of Hippel.. In case the dielectric constant situation is much better. The dielectric constant of pctrol, kerosene, wax and Vaseline differs from the nominal value of Hippel by l.56%, 0. 96%. 0.45% and 5.6% respectively. These data appears to be reasonable in view of the imperfect sample and different measurement condition. There can be other sources of errors too, like deformation in cavity, air-gap between base substrate and the sample, error in dielectric constant and loss-tangent of the base substrate, dimension of cavity, measurement of resonance frequency and the total Q-factor. V.CONCLUSION The suspended.patch resonator is an effective and simple method to determine the complex relative permittivity of material available in liquid, paste and powder forms

REFERENCES: [ I I A . V. Hippcl, Dielectric materials and application,Artech House, USA, 1995. [?]A. Raj. W. S. Holmes and S. R. Judah, “Wide bandwidth measurement of complex permittivity of liquids using coplanar lines, Proc. IEEE Instrum. Meas. Tech. Conf IM7C 2000, vol. 2, pp. 802-809. [3]K. A JOSC,V. K. Varadan and V. V. Varadan, “Wideband and noncontact characterization of the coinplex pcnnittivity of liquids,” Microwave and Optical Technology Letters, vol. 30. no. 2, pp. 75-19. (41 D. Misra, “On the measurement of the complex pennittivity of materials by open-eneded coaxial probe, It~EL~Micrwave andGaided Wave Letters, Vol. 5 , pp. 161-163, 1995. [SI I. Q. Howcll, “A quick accurate method to Ineasurc the diclcctric constant of microwave mtegratcd circuit substrates”,lEEE Truns. Micruwave Themy Tech. Vol. 21. Mar. 1973, pp. 142-143. [61Y. K. Venna and A. K. Verma, “Accurate deiennination of dielectric constant of substrate materials using modified Wolffmodel”, IEEE M T S , 2000. [7] A. K. Venna and Nasimuddin, “Resonance frequency and bandwidth of rcctangular microstrip antenna on thick substrate,”IEEE Microwave and Wireless Components Lefters, Vol. 12, No. 2, pp. 60-62.

Nov. 2002. [SI A. K. Verma, Nasimuddin, V. Tyagl and D. Chakraverty, “Input impedance of probe-fed multilayer rectangular patch antenna using the modified Wolff model,” Microwave and Optical Tech. Lriters, vol. 31, no. 3, 2001, pp. 237-239

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[9] A. K.. Venna. and 2. Rostamy. "Resonance frequency of uncovered and covered rectangular inicrostrip patch using inodified Wolffmodcl," IEEE TPOIIS... Micwwuve Theon, Tech.. Vol. 41, pp. 109I 16, Jan. I993

I

I

-.

Fig. I.

Suspended patch (SUS) resonator

Fig.3. Fabricated Sensor

Fig. 2(bJ Q of suspended (SUS) patch resonator with substrate thickness.

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