Design and configuration of FSS-based absorber

The FSS can be used to transmit, reflect, or absorb the plane wave completely or partially, depending on the nature of the array element. The design of FSS-based EM absorbers mainly depends on two sets of design parameters. The first one being the substrate parameter involving the substrate dielectric constant, loss tangent, and its thickness. The second set of parameters is concerned with conducting patch design, its shape, its geometrical parameters, conducting material parameters, and its layout for the other patches. The proposed FSS absorber consists of a periodic pattern of a slot array as shown in Fig. 1(a) printed over a low-cost FR4 dielectric substrate of dielectric constant 4.4, thickness 1.6 mm, loss tangent tanδ = 0.02, and covered with a dielectric sheet of the same thickness having the same material parameter. The bottom part is the conducting ground plane. The FSS is designed with a dielectric cover so that the cover may be used for printing the antenna element for the integration of this FSS absorber with the antenna. The unit cell of the FSS element consists of a simple circular slot etched rectangular patch with the dielectric cover as shown in Fig. 1(b). The equivalent circuit of the proposed structure is shown in Fig. 3(c). As seen in Fig. 1(c) Z_SU is the impedance of the superstrate layer represented in the form of the transmission line TL_SU, Z_FSS is the impedance of the FSS resonant structure and Z_SL is the impedance of the lower substrate layer with a common ground plane represented in the form of a short-circuited transmission line. The geometrical parameters of the unit cell and its periodicity are selected such that the absorber exhibits the absorption characteristics at the desired frequency of operation.

Fig. 1. (a) FSS-based absorber configuration. (b) Unit cell of FSS-based absorber. (c) Equivalent circuit of FSS-based absorber.

The design parameters of the absorber are presented in Table 1. The circuit parameters obtained from the equivalent circuit approach are shown in Table 2. It should be noted that the conventional absorbers are designed to absorb the incoming plane wave falling on the absorbing surface such that the impedance of the absorbing layer is properly matched with the free space impedance. However, in the proposed absorber, since the absorber is sandwiched between the patch and ground plane, the impedance of the absorber is to be matched with 50 Ω instead of free space impedance. This in turn requires the selection of appropriate FSS element and cell dimension. The control of these parameters for 50 Ω impedance matching, while maintaining a compact unit cell is a challenging task. However, an array configuration consisting of a complementary slot pattern accomplishes this requirement. The geometrical parameters of the FSS are, therefore tuned for 50 Ω impedance matching condition. The equivalent circuit of the absorber is shown in Fig. 1(c), where, the superstrate layer depicting an impedance of Z_SU lying over the FSS pattern is equivalent to a transmission line represented as TL_SU, the FSS layer is represented as a series RLC symbolizing an impedance of Z _fss whereas the lowest layer of impedance Z_SC containing the ground plane is represented as a short-circuited transmission line. The RLC circuit can be expressed as a combination of resistance and reactance [Reference Song, Ding and Guo17] which can be obtained analytically using equations (1) and (2)

(1)$$Z_{\,fss} = j\displaystyle{{Z_O} \over {\sqrt {\varepsilon _r} }}{\rm tan}\displaystyle{{2{\rm \pi }f\sqrt {\varepsilon _r} d} \over c}$$

(2)$$\left[{\matrix{ {L_A} \cr {1/C_A} \cr } } \right] = \left[{\matrix{ {\omega_1} & {\displaystyle{1 \over {\omega_1}}} \cr {\omega_2} & {\displaystyle{1 \over {\omega_2}}} \cr } } \right]^{{-}1}\left[{\matrix{ {{\rm im}( {Z_{Fss}( {\omega_1} ) } ) } \cr {{\rm im}( {Z_{Fss}( {\omega_2} ) } ) } \cr } } \right]\;, \;$$

where ω ₁ and ω ₂ are the two angular resonating frequencies. The equivalent circuit model is simulated usingadvanced design system (ADS) software and the design parameters are obtained at an operating frequency of 5.16 GHz. The equivalent circuit model not only offers an insight into the design of the absorber but also helps in tuning the geometrical parameters to obtain the desired results. The absorption characteristics of the proposed absorber can be determined using the reflection characteristics as

(3)$${\rm Absorptivity} = {\rm \;}A( \omega ) = 1-( {\vert {S_{11}( \omega ) } \vert } ) ^2.$$

Table 1. Dimensions of FSS-based absorber (all dimensions are in mm)

Table 2. Equivalent circuit parameters of FSS-based absorbers as shown in Fig. 1(c)

The absorber, thus designed is simulated using Ansys HFSS EM simulation software which uses highly accurate finite element method for analysis. The simulation is performed for the same operating frequency of 5.16 GHz and the results are compared with the results obtained using the ADS simulation tool as shown in Fig. 2. Fairly good agreement is depicted in the figure. Next, the proposed absorber is integrated with the MSA and the radiation characteristics of the composite structure are examined.

Fig. 2. Comparison of absorption characteristic of the proposed absorber.

Design and configuration of an FSS absorber integrated MSA

The FSS absorber thus designed is integrated with the MSA by placing the antenna configuration on the top of the superstrate layer of the absorber. A conventional inset fed MSA consisting of a rectangular patch is placed over the superstrate layer of the absorber symmetrically. The isometric, top, and side views of the proposed structure are shown in Fig. 3(a) and the equivalent circuit of the proposed structure is shown in Fig. 3(b). The equivalent circuit of the proposed structure constitutes two sections, one representing the MSA printed on the top layer of the dielectric and the other one representing the absorber. The dimensions of the patch are selected such that it resonates at the frequency of designed absorber, i.e. 5.16 GHz. However, integrating the antenna with the absorber shifts the resonant frequency to 4.42 GHz indicating that effective absorption is obtained at 4.42 GHz, instead of 5.16 GHz. Therefore, all the characteristics of the proposed structure are examined at 4.42 GHz.

Fig. 3. (a) Isometric, top and side views of the proposed structure. (b) Equivalent circuit of the proposed structure.

The dimensions of the proposed structure as obtained are shown in Table 3. The equivalent circuit of the proposed structure is simulated in ADS simulation software and the design parameters are listed in Table 4.

Table 3. Structural dimensions of the proposed structure (all dimensions are in mm)

Table 4. Equivalent circuit parameters of the proposed structure as shown in Fig. 3(b)