DESTRUCTIVE DIELECTRIC CHARACTERIZATION OF MATERIAL USING MICROSTRIP RING RESONATOR.

Hussein Kassem 1 , Hayssam El-Hajj 1 , Rabih Rammal 1 , Ismail El-Sayad 1 , Mohammad Hawila 2 and Ahmad Hamdan 2 . 1. International university of Beirut (BIU), Beirut, Lebanon. 2. Lebanese international university (LIU), Beirut, Lebanon. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History

403 these materials in some applications. The method used here to extract the permittivity is Microstrip Ring Resonator [3][4][5]. To extract permittivity, 2 strategies are used, First the material to be measured is printed on the ring substrate (destructive strategy) and then when the ring resonator is sandwiched between 2 materials (non-destructive strategy). The measurement will be conducted at the resonant frequency.
In this work S11 and S21 parameters are extracted to find the resonant frequency and an equation based inverse problem is used to extract the permittivity of the material.
System Design:-Every material has a special series of electrical characteristics that are dependent on its dielectric properties. So the using of these measurements are precise then it can give researchers and architects commendable data to legitimately use a material into a specific application from high speed circuits to satellite and telemetry application.
There are different methods of dielectric properties measurements like non-resonant and resonant methods [3][4][5]. Resonant methods do not have a sweep frequency capability for the measured frequency, but they are considered more accurate than any other techniques for low loss material and they have possible Q-factors and results in very high sensitivity. So the resonators can be used as sensors of different physical quantities which depend upon dielectric constant like complex permittivity of MUT. A ring resonator structure on a printed circuit board (PCB) can be utilized to deduce the complex permittivity of the substrate material. The measurement rely on S21 parameter of a two-port ring resonator to determine the of the board substrate.
The goal is to extract the unknown permittivity of any material using microstrip ring resonator (MRR) after making several simulations; when the ring is printed on the material (Destructive) and the ring is sandwiched between the 2 materials (Non-Destructive).

System Specifications:-
A design MRR-Ferro is designed using HFSS 3D EM software, High frequency structural simulator. It gives high performance field wave for EM field. The resonance of this resonator follows the below condition: With n = 1, 2, 3…. and " the phase constant along the microstrip line defined by: Where "l" is the resonance length related to the wave length √ " is the average radius of the ring and is the effective permittivity, calculated from: To evaluate the resonance frequency of order s the following formula is used: = [s.c / (2.π )] 2 (5) s.c: radius of the gap The width of the microstrip is chosen such that to get a characteristic impedance of 50 Ω, and the arm length is computed using: Coupling Gap:-So as to have a resonant frequency, a resonator can be fed by microstrip line through coupling gap. These types of coupling are called free coupling. It brings about poor return loss and transmission response, If the gap is reduced, the gap capacitance increases. Under tight coupling gap, capacitance becomes appreciable. This causes the major resonant frequency to deviate from the true value. More tightly the coupling, bigger is the deviation. The result of simulation is displayed in the fig. 3, where resonance appear at the following frequencies: In the second step, the thin film is inserted into the circuit, and simulation is done again. The simulation is done varying the values of the film permittivity (from 50 to 350 by step unit 50) and also to check the effect of the thin film thickness, different values of thickness (from 0.5 to 10 um by step unit 0.5um) are taken and simulated.

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The fig.4 below shows the additional layer added to the model in fig.2. Now, the film is sandwiched between the MRR structure and the dielectric substrate (figure3).

Figure 4:-Destructive Circuit (substrate + thin film) on HFSS Program
The dimension of Ring Resonator we take is shown in the table 2 below:  The plots are fitted to a linear curve, and the results seems comparable. Fig. 8 and Fig. 9 below show the variation of permittivity as function of resonance frequency F1 (GHZ) for thicknesses (e= 6, 9 um).   . 12) is found for the variation at the resonance frequency F1:

Variation of thin film Permittivity 'Ԑ':-
Where y is the permittivity and x is the resonance frequency. The work procedure is conducted as below: For a sample with known thickness, simulation or measurement is done. And depending on the resonance frequency obtained with the thickness previously specified, the above curve is used to extract the permittivity of the thin film.

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To validate the analysis, a simulation is done, for a thin film material of permittivity and thickness e=6.5 um.
Assuming the permittivity is unknown, the simulation lead to a resonance frequency of F1=5252.5.5 GHZ. Using the above curve whose equation is: The value y=200.98 is obtained as the result for the permittivity. This value is not far from the real value. The calculation leads to an error that can be depicted as below: Error= An error of 0.5% is obtained for this test and similar error for other examples.

Variation of Thickness 'e':-
A similar procedure is followed for the thickness versus resonance frequency; and a curve fitting is done for each thickness variation at a specified permittivity. Comparing all the obtained graphs an average linear equation ( fig. 15) is found for the variation at the resonance frequency F1: Where y is the Thickness and x is the resonance frequency. The work procedure is conducted in a similar manner to before, taking sample with known permittivity, simulation or measurement is done. And relying on the value of the resonance frequency obtained with the permittivity previously specified, the above curve is used to extract the thickness of the thin film.
To validate the analysis, a simulation is done, for a thin film material of permittivity and thickness e=3 um.
Assuming the thickness is unknown, the simulation lead to a resonance frequency of F1= F= 52128.5 GHZ, and with the thickness variation equation : , y=3.033 is obtained from calculation Also a small error Error= is obtained from thickness extraction.
Although the calculations are done with high performance commercial Electromagnetic software simulator, testing the method with real measurements with prototype will be very interesting. The simulations results are perfect, but with real life measurements more accurate results are achieved.

Conclusion:-
Simple planar ring resonator is outlined and applied. Simulation results on HFSS are obtained. The method used is an equation based one, that can be used for the MRR sensor of the dimensions specified in the text. Good results are obtained for the permittivity of thin film with an error less than 1%.
The method lacks the real measurement and the dielectric losses measurements described by the loss tangent, which is another important parameter to measure for dielectric materials.
In this research, and in order to get more precise results i.e. a more exact equation representing the variations, more simulation should be done and on a larger range of frequency. The fact that, the simulation time for each step (thickness or permittivity variation) takes very long time (12 hours), has limited the number of steps.
Also, another idea to get higher precision is to switch to more complex form of equation (polynomial and exponential expressions).