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An absorbing material–conductor laminate is widely used for electromagnetic compatibility of electronic circuits at microwave frequencies. Such a laminate when properly designed will exhibit good results in terms of electromagnetic interference and compatibility. In this paper, microwave absorbing materials like 1) Ca-NiTi hexa ferrite composites (Ca (NiTi)x Fe12-2xO19) for x = 0.4, 2) M-Type Barium ferrites (BaFe12-2xAxCoxO19 for the tetravalent A ions, Ru4+ is chosen), 3) MnZn ferrite-Rubber composites with volume fraction vf = 0.4, 4) Carbonyl-Iron particle composites with volume fraction vf = 40% and conducting materials like copper, stainless steel are considered to form the interface in the laminate. Mathematical formulations are carried out for the estimation of reflectivity and shielding effectiveness of absorbing material–conductor laminate at microwave frequencies Analysis is also carried out for various thicknesses of the microwave absorbing material and conducting material in the laminate. The reflectivity and shielding effectiveness depends not only on the type of the selected material in the laminate, but also their thickness in the laminate and frequency of operation.

Electromagnetic compatibility of an electronic circuit at microwave frequencies is of prime concern in the design of microwave circuits. External electromagnetic radiations should not interfere with the basic circuit performance and as well the circuit should not radiate electromagnetic energy to interfere with other neighboring circuits. The best method of achieving such an electromagnetic compatibility is to house the circuit in an enclosure made with a laminate which attenuates the radiations from the circuit and stops the external radiations interfering with the circuit. A laminate of microwave absorbing material-metallic conductor is considered to improve the electromagnetic compatibility capability of the circuit. This laminate is designed such that the radiation from the microwave circuit is attenuated to a very large extent before it propagates out of the circuit housing and simultaneously, also shields the microwave circuit from external radiation inferences. A well designed conducting metal with appropriate thickness provides the required shielding ability and a suitably selected microwave absorbing material with high attenuation constant arrests the radiations from the circuit. The thickness of the material layers in the laminate are so designed such that the reflectivity and shielding effectiveness of the laminate are achieved as per the requirement of the circuit compatibility considerations.

Reflectivity is nothing but the total reflection coefficient of the laminate looked from absorbing material layer direction and shielding effectiveness is the total attenuation offered by the laminate. Appropriate equations are derived for the determination of reflectivity and shielding effectiveness of the proposed laminate. Analysis is carried for the estimation of these parameters for different materials, thickness of the material layers and at different microwave frequencies. Various types of popularly available microwave absorbers and metals are considered for the laminate to give best performance in terms of reflectivity and shielding effectiveness. The thickness of the laminate is to be optimized for the required performance of the electromagnetic compatibility.

Reflectivity of the lamination can be estimated using the transmission line analysis for normal incidence. Reflection coefficient [

where is the intrinsic impedance of metallic conductor and is the intrinsic impedance of the microwave absorbing material.

The intrinsic impedance [

is relative permeability of the absorbing material, is the relative conductivity of the conductor with respect to copper, is free space permeability, is conductivity of copper and is the frequency of operation.

The intrinsic impedance of absorbing material can be derived to be:

Where is the permeability of absorbing material = , is relative permeability of absorbing material and is the propagation constant of the absorbing material [

c is the speed of light in free space._{}

The reflection coefficient at the interface of free spaceabsorbing material is very small and is neglected in this analysis.

The reflectivity at the interface of absorbing materialconducting metal in the laminate, as shown in the figure 1, is the path loss of the electromagnetic energy while it propagates from free space to absorbing material–metal interface and back after reflection by the metal in the interface.

Thus, the reflectivity of the laminate can be derived as:

Where is the thickness of the absorbing material and is the attenuation constant of the absorbing material [

Reflectivity expressed in dB is:

Shielding effectiveness of the laminate of microwave absorbing material and conducting metal is the total attenuation loss of the electromagnetic energy while it propagates through the interface. In other words, the shielding effectiveness is nothing but transmission coefficient of the interface of microwave absorbing material and conducting metal in the laminate.

The transmission coefficient of the interface at two boundaries (absorber-conductor & conductor-free space) [

Where is the free space intrinsic impedance = ohms.

Reflection coefficient [

where, impedance to the right of the absorber-metal interface and can be derived as:

(15)

is thickness of the metallic conductor and is the_{ }propagation constant in the metallic conductor [

The total transmission coefficient [

The Shielding effectiveness of the microwave absorbing material-metal laminate can thus be given in decibels as:

Analysis is carried out for the estimation of reflectivity (Equation (11)) of the laminate of microwave absorbing material-metallic conductor for various types of absorbing materials, conducting materials and thickness of material layers in the laminate. Popular and widely used microwave absorbing materials like 1) Ca-NiTi hexa ferrite composites (Ca(NiTi)_{x}Fe_{12-2x}O_{19}) for x = 0.4 [_{12-2x}A_{x}Co_{x}O_{19} for the tetravalent A ions, Ru^{4+} is chosen) [_{f }= 0.4 [_{f }= 40% [3,7] along with copper as conductor is considered for the estimation of optimum reflectivity.

Figures 3 & 4 show the variations of reflectivity (Equation (11)) with frequency for different absorbing materials at a thickness of 5 and 10 mm respectively. Figures 5 & 6 are the plots for variations of reflectivity with thickness of layer of absorbing materials (BaFe_{12-2x}A_{x}Co_{x }O_{19} for the tetravalent A ions, Ru^{4+} is chosen and ferriteRubber composites with volume fraction v_{f }= 0.4) at different frequencies. Reflectivity is estimated at 12GHz for various absorbing materials at different thicknesses and is presented as in figure 7.

Reflectivity of the laminate mainly depends upon the absorption properties of the microwave absorbing material and its thickness. Thus, the microwave absorbing material, M-Type Barium ferrites exhibits excellent reflectivity (around 20 dB better than Carbonyl-Iron particle composites with volume fraction v_{f }= 40%) over the entire frequency range compared to other types of absorbing materials. Since attenuation constant is very high for that of M-Type Barium ferrites.

It can also be deduced that the reflectivity of BaFe_{12-2x }A_{x}Co_{x}O_{19} for the tetravalent A ions, Ru^{4+} is chosen and MnZn ferrite-Rubber composites with volume fraction v_{f }= 0.4 is better by approximately 20 dB in the X-band range of frequencies and it decreases at high frequencies.

Investigations are carried out to determine the shielding effectiveness (Equation (18)) of the laminate of microwave absorbing material-metal for different combinations of materials at different thicknesses of layers in the laminate. Figures 8 & 9 are the plots for variation of shielding effectiveness of laminate of BaFe_{12-2x}A_{x}Co_{x}O_{19} (for the tetravalent A ions, Ru^{4+} is chosen) and MnZn ferriteRubber composites with volume fraction v_{f }= 0.4 for 1, 5 and 10 mm thicknesses of absorbing material and 1mil layer thickness of copper respectively. Figures 10 & 11 are the plots for variation of shielding effectiveness of laminate of BaFe_{12-2x}A_{x}Co_{x}O_{19} (for the tetravalent A ions, Ru^{4+} is chosen) and MnZn ferrite-Rubber composites with volume fraction v_{f }= 0.4 for 1, 5 and 10mm thicknesses of absorbing material and 1 mil layer thickness of stainless steel respectively.

Shielding effectiveness is also estimated for different layer thicknesses of the copper in the laminate and is presented in figures 12 & 13 for microwave absorbing material layer of BaFe_{12-2x}A_{x}Co_{x}O_{19} for A= Ru^{4+}, MnZn ferrite-Rubber composites with volume fraction v_{f }= 0.4 for x = 0.4 (thickness of the absorbing material = 5 mm). The plot of shielding effectiveness with frequency for different absorbing materials of the interface with copper as conducting layer material is shown in figure 14.

The shielding effectiveness of the conductor dominates that of microwave absorbing material in the laminate and this in turn depends on the thickness of the conducting layer almost linearly. This is because the attenuation constant of the conductor is extremely high

compared that of the absorbing material. The shielding effectiveness of the laminate using stainless steel as conducting layer is much higher than that of a laminate using copper as conducting material layer.

From the above analysis for reflectivity and shielding effectiveness, it may be deduced that laminate comprising of M-Type Barium ferrites as absorbing material layer and stainless steel as conducting material layer exhibits very good reflectivity as well as shielding effectiveness characteristics. It may be concluded that the reflectivity and shielding effectiveness primarily depend upon the material characteristics. The thickness of the material can be selected for a given application according to the requirements of the problem and subject to the availability of the materials and mechanical constraints of the circuit under consideration.

We thank the management of GITAM University for all the support and encouragement rendered in this project. We also extend our thanks to the Vice Chancellor and Registrar of GITAM University for providing the required facilities for carrying out this work. Our sincere thanks are also due to the Principal of GITAM Institute of Technology, Head of the Department of E.C.E and its staff for their kind support.