Analysis of Reflectivity and Shielding Effectiveness of Absorbing Material–conductor Laminate for Electromagnetic Compatibility

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 Fe 12-2x O 19) for x = 0.4, 2) M-Type Barium ferrites (BaFe 12-2x A x Co x O 19 for the tetravalent A ions, Ru 4+ is chosen), 3) MnZn ferrite-Rubber composites with volume fraction v f = 0.4, 4) Carbonyl-Iron particle composites with volume fraction v f = 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.


Introduction
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
Reflectivity of the lamination can be estimated using the transmission line analysis for normal incidence.Reflection coefficient [1] at an interface of absorbing materialconducting metal can be given as where c  is the intrinsic impedance of metallic conductor and A  is the intrinsic impedance of the microwave absorbing material.The intrinsic impedance [2] of metallic conductor can be estimated as Where permeability of themetal, rc  is relative permeability of the absorbing material, r  is the relative conductivity of the conductor with respect to copper, o  is free space permeability, o  is conductivity of copper and f is the frequency of operation.
The intrinsic impedance of absorbing material can be derived to be Where A  is the permeability of absorbing material  is relative permeability of absorbing material and A  is the propagation constant of the absorbing material [3] which can be given as Relative permeability, rA Relative permeability, rA rA 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 A t is the thickness of the absorbing material and A  is the attenuation constant of the absorbing material [3]

Shielding Effectiveness
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) [2] is given as Where o  is the free space intrinsic impedance = 120 ohms.
Reflection coefficient [2] at absorbing material-metal interface, 1 q and that at conductor-free space interface 2 q can be given as where   z c , impedance to the right of the absorber-metal interface and can be derived as c t is thickness of the metallic conductor and c  is the propagation constant in the metallic conductor [2] given as The total transmission coefficient [2] across the laminate of the two interfaces can thus be derived to be The Shielding effectiveness of the microwave absorbing material-metal laminate can thus be given in decibels as   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.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.

4 .
Results and ConclusionsAnalysis 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[4], 2) M-Type Barium ferrites (BaFe 12-2x A x Co x O 19 for the tetravalent A ions, Ru 4+ is chosen)[5], 3) MnZn ferrite-Rubber composites with volume fraction v f = 0.4[6] and 4) Carbonyl-Iron particle composites with volume fraction v 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.Fig- ures 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 ferrite-Rubber 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.

Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .
Figure 3.The variation of the reflectivity as a function of frequency for different microwave absorbers at absorber thickness of 5 mm

Figure 8 .
Figure 8.The variation of the Shielding effectiveness as a function of frequency of BaFe 12-2x A x Co x O 19 -copper laminate for different thicknesses of microwave absorber