**2.1 Ferrite absorbers**

The simplest type of ferrite absorbers is ferrite tiles, where the whole desired surface can be covered by installing multiple tiles next to each other. This type of absorber is shown in **Figure 1(a)**, backed by a PEC layer. Ferrite tile ceramics are realized by heating powders under pressure at 1000–1500°C. Thus, brittle and thin tiles between 4 and 7 mm are commonly used because of the heavyweight of iron,


### *Analysis and Design of Absorbers for Electromagnetic Compatibility Applications DOI: http://dx.doi.org/10.5772/intechopen.100543*

**Table 1.**

*Typical reflectivity of a specific absorber series in different frequency bands for normal incidence [20].*

**Figure 1.** *(a) Ferrite tile absorber [24] and (b) its typical reflectivity [25] (The photos used with permission of ETS-Lindgren).*

manganese, and other metal oxides [1]. The typical surface area of the tiles is 100 mm<sup>2</sup> , and they are usually installed onto plywood panels leading to an extremely fire-retardant installation [5]. Due to the low operation frequency, the homogenization of the entire structure and later using the transmission line method gives reasonable results for the associated absorption rate. Thus, the surface impedance of the shortened ferrite slab is [14]:

$$\eta\_t = \eta\_0 \sqrt{\frac{\mu\_r}{\varepsilon\_r}} \tanh\left(\frac{2\pi t}{\lambda\_0} \sqrt{\mu\_r \varepsilon\_r}\right) \tag{1}$$

where *t* is the thickness of the tile, *η*<sup>0</sup> is the free-space intrinsic wave impedance, *ε<sup>r</sup>* ¼ 14 is the relative permittivity of the tile, and *μ<sup>r</sup>* is the relative permeability calculated by the Drude model, which reads as [26]:

$$\mu\_r = 1 + \frac{1101.4}{1 + j\frac{f}{7.066 \times 10^6}}\tag{2}$$

where *f* is the operating frequency. Using the aforesaid surface impedance, the reflectivity of the ferrite tile absorbers can be calculated readily. **Figure 1(b)** shows the typical reflectivity of a ferrite tile.

An inherent problem of installing the ferrite tiles is the small-sized air gaps between the adjacent cells. The air gaps result in performance degradation due to the significant difference between the permeability of the air gaps and ferrite material. The impact of air gaps on the performance of the ferrite tile absorbers can be approximated *via* their similarity to the air gaps in the core of power transformers to obtain the equivalent permeability as [14]:

$$
\mu\_r^\epsilon = \frac{\mu\_r}{1 + \frac{\Delta}{l}(\mu\_r - \mu\_{air})} \tag{3}
$$

*Analysis and Design of Absorbers for Electromagnetic Compatibility Applications DOI: http://dx.doi.org/10.5772/intechopen.100543*


**Table 2.**

*Different homogenization approaches for modeling ferrite tiles with air gaps [29].*

where Δ is the size of the air gap perpendicular to the magnetic field and *l* is the width of the ferrite tile. Some gap-filling materials, such as ferrite rubber or developed plastic material called REC 65, are proposed to obviate this issue [27]. Moreover, ferrite absorbers are fabricated in other geometries such as grids, where they have an additional degree of freedom to adjust the resonant frequency through the filling factor. Therefore, synthetized capacitance and synthetized inductance models can be used to determine the effective permeability of the ferrite grids and ferrite grids with air gaps [28]. Furthermore, due to the lower amount of utilized ferrite material in the fabrication, the performance sensitivity to the air gaps is lower in the ferrite grids with respect to the ferrite tiles. Different homogenization approaches for modeling ferrite tiles with air gaps are summarized in **Table 2**. Note that these approximate mixing rules do not always work well, especially for hollow and wedge shapes (or other complicated shapes). A full numerical model using a unit cell/periodic boundary (Floquet ports) and full-wave modeling is fast and easy. The full-wave model can account for air gaps and complicated shapes [29]. As a final comment, due to ferrite tile's heavyweight and expensive cost, its minimum usage, which is predicted by the optimization tools, is preferred [30–32].

#### **2.2 Pyramidal absorbers**

Different types of dielectric absorbers having lossy permittivity (electric loss) or permeability (magnetic loss) are commonly used for the wideband electromagnetic wave absorption above 1 GHz [5]. Organic materials (such as rice straw, oil palm empty fruit bunch, sugar cane bagasse, and coconut shell [33]), magnetic materials (such as NiZn spinel ferrite, Co2Z hexaferrite, and RuCoM hexaferrite [34]), and dielectric materials (such as foam (carbon-based), polyurethane, polystyrene, polyethylene, and thin film [30]) can be used for this purpose. The absorption capability of each material can be evaluated using its constitutive parameters. To this end, the attenuation constant of the incoming wave is calculated to guarantee that the wave can penetrate the device. Therefore [2],

$$a = a\sqrt{\varepsilon\_0 \mu\_0} \left( a^2 + b^2 \right)^{1/4} \sin\left(\frac{1}{2} \tan^{-1}\left(\frac{a}{b}\right)\right) \tag{4}$$

where prime and double prime, respectively, denote the real and imaginary parts of the permittivity (*ε*) and permeability (μ). Also, the parameters *a* and *b* in Eq. (4) are defined as follows:

$$\mathfrak{a} = \left( \varepsilon\_r' \mu\_r' - \varepsilon\_r'' \mu\_r'' \right) \tag{5}$$

$$b = \left(\varepsilon\_r' \mu\_r'' + \varepsilon\_r'' \mu\_r'\right) \tag{6}$$

Note that the real and imaginary parts of the constitutive parameters cannot change arbitrarily, and the Kramers–Kronig relationship should be satisfied [2]. Above 1 GHz, absorbers are fabricated in the form of pyramidal (standard, twisted, or hollow), wedge, convolved, or multilayered geometries, the pyramidal shape being the most common one [5]. Pyramidal absorbers are fabricated in different lengths, depending on the lower limit of the operating band. Specifically, with the optimized carbon loading, the one and eight wavelength absorber's reflective is around �33 dB and �51 dB [5]. Also, for mechanical reasons, the base-to-height ratio is about 2.5 [1]. The product is commonly black after fabrication and is painted with blue latex to improve light reflectance. The tips are retained unpainted to prevent absorption degradation in the millimeter-wave band. The measured data do not seem to support such a common practice, and the whole absorbers should be unpainted to achieve improvements at the millimeter band [35]. Moreover, pressure-sensitive adhesives can be used for the installation, and fire-retardant chemical loading is used to meet the current fire retardancy requirements [5].

At the low-frequency limit, when the period of the array is small compared to the wavelength, homogenization of the transversely periodic structure in **Figure 2** with a transversely uniform medium with anisotropic permittivity and permeability can be used for the analysis. Thus, the longitudinal and transverse components of the constitutive parameters can be approximated as [36]:

$$
\varepsilon\_{\mathbf{z}} = (\mathbf{1} - \mathbf{g})\varepsilon\_0 + \mathbf{g}\varepsilon\_d \tag{7}
$$

$$
\mu\_x = (\mathbf{1} - \mathbf{g})\mu\_0 + \mathbf{g}\mu\_a \tag{8}
$$

$$\varepsilon\_{t} = \varepsilon\_{0} \left[ \mathbf{1} + \mathbf{g} \frac{\mathbf{2}(\varepsilon\_{t} - \varepsilon\_{0})}{(\mathbf{1} + \mathbf{g})\varepsilon\_{0} + (\mathbf{1} - \mathbf{g})\varepsilon\_{a}} \right] \tag{9}$$

$$\mu\_t = \mu\_0 \left[ \mathbf{1} + \mathbf{g} \frac{\mathbf{2}(\mu\_a - \mu\_0)}{(\mathbf{1} + \mathbf{g})\mu\_0 + (\mathbf{1} - \mathbf{g})\mu\_a} \right] \tag{10}$$

where the subscripts *t* and *a* respectively indicate the transverse component and parameters referring to the absorbing material. Also, the parameter *g* is defined based on the pyramid length *L* and the distance of the layer from the tip *z* as *g* = (*z*/*L*) 2 . The accuracy of the aforesaid equations for practical materials is around 5% [36]. In another low-frequency approach, the pyramid is divided into multiple layers

**Figure 2.** *The schematic view of the pyramidal absorber [24] (The photo used with permission of ETS-Lindgren).*

*Analysis and Design of Absorbers for Electromagnetic Compatibility Applications DOI: http://dx.doi.org/10.5772/intechopen.100543*

**Figure 3.**

*(a) Spatial meshing of the pyramidal absorber for its analysis based on FDTD and (b) its return loss in comparison with the homogenization model and capacitor model ([16], reproduced courtesy of The Electromagnetics Academy).*

with label *i*, and then, each layer is approximated with the permittivity and permeability of [37]:

$$
\varepsilon\_{ieq} = (\mathbf{1} - K\_i) + \frac{K\_i \varepsilon\_a}{K\_i + (\mathbf{1} - K\_i)\varepsilon\_a} \tag{11}
$$

$$
\mu\_{iq} = (\mathbf{1} - K\_i) + \frac{K\_i \mu\_a}{K\_i + (\mathbf{1} - K\_i)\mu\_a} \tag{12}
$$

where the parameter *Ki* represents the normalized area of the absorber in the *i*th layer. The transmission-line model can be used to calculate the multiple reflection and transmissions coefficients by starting from the metal-backed bottom layer. Note that surface fraction models have been used in another homogenization approach, called the synthesized capacitance model [38].

Apart from low-frequency approximate techniques, various full-wave numerical and quasi-analytical methods such as the finite element method (FEM), the integral-equations-based method of moments (MoM), and the FDTD technique can be used for the pyramidal absorber analysis. In this regard, time-domain methods are more reasonable choices due to the wideband nature of the problem [39]. Thus, for accurate wideband modeling of pyramidal absorbers, the FDTD method can be used. The required spatial meshing for this approach is illustrated in **Figure 3(a)**, and its return loss in comparison with the homogenization model and capacitor model is included in **Figure 3(b)**, where good agreement with the former approach is attained [16].

Importantly, the bi-static or off-angle behavior of the absorbers is an important factor affecting the validity of the indoor facilities for RE/RI measurements. Therefore, polynomial approximations are proposed to predict reflected energy from pyramidal RF absorbers in different incident angles [1, 40, 41].

#### **2.3 Hybrid absorbers**

To design an absorber covering the sub-GHz and GHz frequencies, hybrid absorbers, simultaneously exploiting both technologies mentioned above, are proposed. Hybrid absorber design is not just putting the pyramidal absorbers above the

**Figure 4.**

*(a) Hybrid absorber designed by controlling the amount of carbon loading and using pyramid's tip truncation [24] and (b) typical reflectivity of a hybrid absorber at low-frequencies [3] (The photos used with permission of ETS-Lindgren).*

ferrite tiles [42]. Adjusting the carbon loading of the dielectric pyramidal absorbers, making the pyramidal absorbers hollow, or using shaped coatings of lossy paint are some solutions to improving the impedance matching of hybrid absorbers. Also, the absorption degradation due to a lower amount of carbon material is compensated by truncating the pyramid's tip, and some small-sized elements are included to improve the high-frequency performance, as in **Figure 4** [24]. Moreover, using a matching layer between the pyramidal and ferrite absorbers is another method. Fourier analysis and the mode-matching technique have been used to analyze this absorber efficiently [17]. Note that when several thousands of hybrid absorbers with complex material parameters are used in the facility design, a thin-surface impedance sheet with the same reflectivity can be used to provide time and memory efficiency instead of simulating the hybrid absorber. For this purpose, the reflectivity of the absorber must be approximated by optimizing the material parameters and thicknesses in the equivalent multilayered model [43, 44]. Modeling the absorber arrays as multilayered media through homogenization aids in analyzing the chambers using Green's function of the layered media [45].

#### **2.4 Millimeter-wave absorbers**

With the development of fifth-generation (5G) communication technology utilizing massive multiple-input multiple-output (MIMO) phased array antennas for high-speed communication, the use of millimeter-wave absorbers (30–300 GHz) with high-power handling capability is necessary for test facilities [46–48]. Convoluted (egg-carton) absorbers with the typical absorption of 50 dB at normal incidence at 30 GHz are primarily useful in millimeter-wave bands [1, 2]. The manufacturers also suggest convoluted absorber in this frequency spectrum because of tolerating wide incident angles and suggest ordering them without paint [49]. Moreover, pyramidal structures with vent holes and heat sinks are proposed, and associated power-handling capability is analyzed using multi-physics simulations [50]. Also, a millimeter-wave metamaterial absorber bandwidth is widened by embedding one of the resonators inside another in the unit cell. The device is fabricated by a standard optical photolithography process, and the measurement is done by a custom-made spectrometer, as shown in **Figure 5** [51]. Furthermore, the optical transparency requirement for some special EM protections, demanding large *Analysis and Design of Absorbers for Electromagnetic Compatibility Applications DOI: http://dx.doi.org/10.5772/intechopen.100543*

**Figure 5.**

*Measurement setup of the millimeter-wave absorber ([51], reproduced courtesy of The Electromagnetics Academy).*

light transmittance and high absorptivity, can also be satisfied [52–54]. As a final note, naturally thin and transparent graphene material has great potential in the millimeter-wave absorber design [55].
