·Table of Contents ·Materials Characterization and testing | A non destructive method for measuring the Complex permittivity of Dielectric Materials using a resonator Transmission LineBrahim ATROUZlaboratoire 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 |
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.
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.
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
The way to follow is therefore:
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 |
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.
So we have oriented the study to the utilisation of a resonant microstrep line associated with an oscillator functioning around 1Ghz.
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 |
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 e_{0} 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 e_{0} (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 S_{1} of the central conductor of the coaxial and S_{2}of 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 S_{1} and S_{2}.
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 Z_{0}, 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.
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 |
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
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.
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