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A non destructive method for measuring the Complex permittivity of Dielectric Materials using a resonator Transmission Line Brahim ATROUZ laboratoire Micro-ondes/Radar U.E.R. d'Electronique E.M.P, B.P. 17 Bordj El Bahri, Alger Algérie Tel: 213 2 86 34 69 Fax:213 2 86 32 04, e-mail: reatrouz@ist.cerist.dz Or: reatrouz@yahoo.fr Contact

ABSTRACT

A non destructive method for the determination of dielectric constant (e'_r) and the loss tangent (tand ) of dielectric materials using a transmission line resonator is presented in this paper.

The method is based on the perturbation of the electromagnetic field of the transmission line by the unknown dielectric material. The measure is undertaken with the help of an oscillator (or V.C.O.), building around (or exciting) a microstrip resonator.

This "active probe" is connected to a microcomputer by the intermediary of a specific card to this application. This probe allows, from the measure of the frequency and the amplitude of oscillation (or resonance), to determine the complex dielectric permittivity of materials studied.

The total control of the device and the exploitation of data are insured by a P.C through the parallel port (Centronics). The system, so formed, can be considered as a "collector of complex permittivity". The measure is based on calibration from a bank of reference samples.

The unknown complex dielectric constant is obtained by approximation (mean square). The system can be used for the control of materials during process (polymerisation, chemical reaction etc. .) and for determining the profile of non homogeneity of a structure because to fact that the measure is punctual.

The experimental results obtained for some solid dielectrics materials and liquids, show that the method has sufficient accuracy for most applications.

INTRODUCTION

So as to characterise homogeneous and non homogeneous materials, we have been brought to develop a punctual measure method that uses the perturbation of the discontinuity of an open coaxial line (Fig.1).

Fig 1: Perturbation of the discontinuity of an open coaxial line by a dielectric

From resonance frequency and quality coefficient without and with presence of the material on the probe, obtained with an automatic acquisition program, it is possible to calculate e'_r and tgd of the unknown material.

This measure can be rendered more sensitive by profiting the resonance of a coaxial element feebly coupled to the entry of a network analyser. (Fig. 2), [1], [2].

Fig 2: Perturbation of a coaxial line length by a dielectric

A same resonator can be used on several harmonic frequencies (resonance Kl / 2).

No complex manufacturing the material is necessary; the alone constraint is that the sample has to present a plan with a good state of surface and a volume minimal according with the dimensions of the probe.

The method is applicable not only for solid dielectric materials but also for liquids.

This concept of measure necessitates nevertheless a heavy environment understanding especially an automatic network analyser and a probe whose realisation makes call in mechanical precision.

These various considerations have made us develop a complete autonomous system of measure, realising a collector of permittivity.

PRINCIPLE OF THE AUTONOMOUS SYSTEM USING A COAXIAL PROBE

From presented general concept, an autonomous collector using an oscillator coupled to a coaxial resonator has been realised (Fig. 3).

Fig 3: autonomous Collector of dielectric permittivity using a coaxial resonator

The complex permittivity is deduced from the numerical measure of the frequency and a measure of amplitude of the signal by a program of management of the system implanted in a P.C.

The coaxial discontinuity (probe loaded by the material) has been modeled using a static analysis based on the method of relaxation (finished differences).

The curve of the figure 4 represents variations of the capacity of discontinuity of a coaxial line ended by a dielectric according to e'_r of the material for a value of tgd of 10^-3. It appears that the variation is quasi linear.

Fig 4: Capacity of the discontinuity according to e'r

The curves of the figure 5 represent variations of the conductance G/w according to tgd for giving values of e'_r. There also, the function is linear.

Fig 5: (G / w) according to tgd, for e'r given

The variation of the frequency Df due to the presence of the dielectric allows to determine DC of the equivalent electric circuit of the figure 2 and, as a result, e'_r of the material.

On the other hand DG, which is function of the frequency, e'_r and tgd, has to be deduced from the amplitude of oscillations and a non linear analysis of the oscillator.

In order to eliminate the influence of the various dispersions due to components, we have prefered to calibrate the system by a bank of reference samples and to determine values of e'_r and tgd, by a program of interpolation [3].

More than that, such an approach allows us to renew the calibration and to spread the area of measure by adding a plastic adhesive film between the probe and the sample. This plastic film allows a protection of the probe, in the case of the corrosive material measure or materials with strong losses, by realising a serial capacity limiting the load of the oscillator

PRINCIPLE OF MEASURE

First we have to calibrate the system with the help of known samples (bank of reference samples). This operation allows us to plot curves e'_r(DF) and G(DV) then to determine the parameters allowing the characterisation of the unknown dielectric by approximation (mean squares).

The way to follow is therefore:

• We measure the frequency F₀ and the amplitude of oscillation V₀ for the line without any dielectric sample on the probe.
• We measure then the frequency F and the amplitude of oscillation V for each sample of reference placed in the end of the line which we compare to the frequency F₀ and the amplitude V₀ , measured without sample, to obtain the quantities DF=F₀- F and DV = V₀ - V.

A capacity C can then be calculated from characteristic relationships linked to the used electronic circuit (oscillator). C and G being elements of the same physical structures, the conductance G will be deduced of the expression:

G = C.w.tgd

(1)

where tgd. represents the angle of loss of the samples of reference. It is possible then to trace curves representing e'_r and G in function respectively of the deviation of frequency (DF) and the variation of amplitude (DV).

Once the calibration undertaken, it suffices to place the unknown material to be characterised on the probe and to notice the corresponding frequency and amplitude variations (DF and DV) that allow to find e'_r and G of the material to characterise, by approximation.

Knowing C by calculation, tgd is deduced by the relationship (1).

Fig 6: demarch of resolution

AREA Of APPLICATION

No complex manufacturing of the material is necessary; the only constraint is that the sample has to present a plan with a good state of surface and a minimal volume. To evaluate the minimal volume that the sample to be measured has to present so as the lines of field remain confined inside the material, we have calculated, by the finished difference method, the capacity of discontinuity for a given material of variable thickness steady by a layer of air.

The various tests have shown that the method presents a good sensitivity for the determination of e'_r. This sensitivity is put in obviousness through the possible characterisation of a material such the polystyrene whose constant dielectric e'_r is very close to 1.

This sensitivity is due to the very good stability of the oscillator used and to the great precision of the numerical frequencemeter .

Various materials have been able to be characterised by this method. Table 1 gives some results of measures obtained on some samples.

The samples referenced by an asterisk have been used during the calibration.

The comparison of the results obtained with those measured or published furthermore allows to confirm the principle we have used.

Matériaux	mesurés par ailleurs		Mesurés par l'auteur
Dépron	1.03	<10-4	1.05	0
Téflon (*)	2.04	<10-4	2.13	0
Plexiglas	2.65	6.10-3	2.61	310-3
Polyéthylène	2.32	_	2.3	0
Air (*)	1	0	1	0
Alumine (*)	9	10-4	9.3	0
"bois"	2.5	7.10-2	2.4	5.10-2
Table 1: Experimental results

Other tests with industrial origin materials have allowed us to validate the method for the dielectrics such as:

With the studied system, it is possible to characterise materials whose relative permittivity is in the order of 50.

On the other hand, a lack of sensitivity of the system for the measure of dielectric losses (tgd,) has appeared during tests. It is thus very difficult to determine the value of tgd, for materials with important losses; variations of amplitude (DV) linked to the presence of the dielectric on the probe remain too feeble to be detected by the system (the measurable minimal tension by the voltmeter being 5 mv).

For the dielectrics whose permittivity is too large, the conditions of oscillation can no longer be filled and the oscillator ceases to function. This difficulty can be overcame by placing on the probe a thin adhesive film with feeble losses that would decrease its sensitivity but would spread the area of application.

It is necessary, of course to realise a new calibration using the bank of samples.

MEASURES PERMITTIVITES USING A PRINTED PROBE

The limits of the utilisation of the coaxial probe have been indicated in the preceding paragraph. On one hand, its lack of sensitivity to losses of materials under test does not allow the reliable and complete characterisation of lossy materials; on the other hand, the nature of the oscillator makes that the conditions of oscillation are not fulfilled for materials whose imaginary or real parts of the permittivity is too high.

So we have oriented the study to the utilisation of a resonant microstrep line associated with an oscillator functioning around 1Ghz.

PRINTED PROBE ASSOCIATED WITH AN OSCILLATOR

The principle of measure remains the same as for the coaxial probe and the numerical acquisition card of data is unchanged.

An open microstrip line forming the element resonating for an oscillator is disturbed to its extremity by the sample to characterise.

This perturbation is going to modify the frequency of oscillation. The determination of e'_r is made from the measure of the deviation of frequency (DF) provoked by the dielectric permittivity of the unknown material. (Fig. -6-).

Fig 6: Autonomous collector of dielectric permittivity using a printed. resonator

DESCRIPTION OF THE PROBE

The probe of measure is formed of two parts:
1. a resonating microstrip line of 50 W characteristic impedance engraved on a substrat with a relative permittivity e'_r=2.51 and an angle of loss tgd =0.0017; the thickness of the layer of copper t being equal to 0.035 mm.
2. A microstrep structure of coaxial form engraved on the quoted "plan of mass" of the same substrat composed of an internal conductor (R_a=3.5 mm) and an external conductor (R_b=5.5mm). The structure, thus formed, is superposed to the open extremity of the microstrip line through the substrat (Fig. 7).

Fig 7: Descriptive of the printed probe

The structure formed by the two concentric conductors, engraved on the side "plan of mass" can be considered as an open coaxial line whose dielectric e₀ is the air (8.8419.10-12 F/m) of length t (thickness of the copper) with an impedance characteristic Zc function of R_a, R_b and the permittivity e₀ (Fig. 10).

Fig 10: Printed probe loaded by the dielectric

This coaxial line is ended on a side by the unknown material of dielectric permittivity (e'_r, tgd) put on the probe and the other by a media formed by the substrat of permittivity e'_r=2.51, and tgd =0.0017.

The presence of a dielectric on the open extremity of the coaxial line is translated into a capacity DC proportional to the value of the permittivity and a conductance DG function of losses of the material (Fig. 9).

Fig 9: equivalent Circuit of the printed probe loaded by a material

This admittance is coupled to the extremity of the microstrip line by the intermediary of a capacity C_c formed by the surface S₁ of the central conductor of the coaxial and S₂of the microstrip line through the dielectric of the substrat given by:

where:

h is the thickness of the substrat.
S is the common surface to S₁ and S₂.

The capacity DC comes to be added to the capacity C_f of end of line formed by the open microstrip line [4].

Indeed, an open microstrip line gives place, in its extremity, to a capacity C_f function of the characteristic impedance of the line Z₀, the width of the band W, the height of the substrat h and the effective permittivity e_eff. (Fig. 8).

Fig 8: Effect of edge of an opened line

According to [4], the capacity C_f and the corresponding additional length DL are given by:

The perturbation of field lines, caused by the material to measure put on the probe, can be modelled by the fictitious increase of the length of the resonant microstripe line (DL). DL is proportional to the permittivity of the dielectric.

ADMITTANCE OF DISCONTINUITY OF THE PRINTED PROBE ENDED BY A DIELECTRIC

We want to evaluate the admittance of discontinuity of the structure of the figure 10. To do this, it is necessary to bring the problem to that of the coaxial line of the precedent paragraph and to determine the admittance of discontinuity of an open coaxial line, length t (thickness of the copper), disturbed to its two extremities by the dielectrics. The resolution of the equation of Laplace, with the limit conditions corresponding to the new system, allows to calculate the capacity of discontinuity of the structure.

The curve of the figure 11 represents variations of the capacity of discontinuity of the printed probe realised on a substrat of glass Teflon TLX030 presenting a height h =0.762mm, a thickness of copper t=0.035 mm, a relative permittivity e'_r=2.51 and an angle of loss tgd=0.0017, according to e'_r of the material for a value of tgd=0. It appears that the variation is quasi - linear.

Fig 11:printed Probes: Capacity of the discontinuity according to e'r

A mathematical model expressing the relationship between e'_r and DC is given by:

The capacity DC due to the presence of the material on the probe, coupled to the extremity of the microphone line, is going to increase the length of the resonator and therefore to modify the frequency of oscillation.

The conductance DG, translating the losses of the dielectric is going to modify the amplitude of oscillation.

The study of detailed oscillation conditions of the circuit's oscillator, allows to deduce the frequency of oscillation according to DC (Fig.12).

Fig 12:frequency of oscillation according to the capacity of discontinuity

PRINCIPLE OF MEASURE AND RESULTS

The step to follow is identical to that used for the coaxial probe. A preliminary calibration with the help of a bank of reference samples allows to determine by approximation the permittivity of the material under test.

The configuration retained for the oscillator doesn't allow to establish an exploitable relationship between variations of amplitude DV and the admittance of the probe loaded by the dielectric, it is not foreseeable to measure the losses of materials by this method.

But the system presents a very great sensitivity for the determination of e'_r.

Tests have shown that the range of measure is very extensive. It is thus perfectly possible to characterise materials such as the Depron (e'_r=1.03) or water (e'_r =78) without having the oscillator cease to function.

Materials to be measured or samples used for calibration have to present a surface sufficiently plane to insure a good contact with the probe. In order to avoid the appearance of a layer of air between the probe and the sample that would falsify results.

Some experimental values are indicated in the table 2.

Matérials	### f (Mhz)	###'r (measured)	###'r (Published)
air (*)	0	1	1
Depron	0.42	1.03	1.06
Téflon	3.06	2.05	2.07
P.V.C	4.81	2.5	2.59
Plexiglas (*)	4.92	2.65	2.61
"wood"	4.12	-	2.35
Alumine	15.41	9.5	9.42
Pure water	79.6	--	--
Salted water	77.3	--	--
Table 2: Experimental results

The permittivity of the water has not been able to be measured by lack of reference samples which cover the range of measure; nevertheless, we can notice the corresponding drift of frequency.

References with an asterisk have participated to the calibration of the system

CONCLUSION

The presented autonomous system is very simple to use. Because of its conversational management program, it can be employed by any operator, even inexperienced. The device can be used for the rapid characterisation of homogeneous materials. The measure being quasi-punctual, it allows to find a profile of non homogeneousity by the sweeping of a surface. It is also usable for the study of materials presenting variations of e'_r and tgd according to time (polymerisation for example).

This method allows to characterise solid and liquid materials. It is useless to give to samples a precise form by a rigorous manufacturing. The alone constraint is that it has to present a flat surface with a good surface state allowing to insure a good contact with the probe.

On the other hand, it is necessary that the element to study presents a sufficient volume in order that lines of field remain confined inside the material. Otherwise, the calibration is realised with samples having the same thickness as the dielectric to be characterised.

The method of measure is based on an approximation, it results that it is necessary to avoid to explore a too great range of values for an unique calibration that would give then bad results. It is preferable, in this case, to fraction the area of study after having situated the material to characterise in the good range of measure.

BIBLIOGRAPHY

1. J. DAVID, I. IDRISS, and J.C. MATHEAU, "Homogeneous material microwave dielectric constant automatic measurement by contact plan", International Fifth conference one microwave solid electronics", Gdansk (Poland), 27 march 1980.
2. I. IDRISS, "Contribution à la mesure de constantes diélectriques en hyperfréquences", Thesis of Doctorate, INP de TOULOUSE (France) , 17 July 1979.
3. B. ATROUZ," Conception et réalisation d'un capteur autonome de permittivités diélectriques à résonateur coaxial ou micro bande" These de Doctorat, INP de TOULOUSE, 07 September 1993.
4. WHINNER. JAMIESON and ROBBINS," Coaxial line discontinuities" - Proc. I.R.E. Flight. 32, November 1944.

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