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Fig. 1 Geometry of the circular loop FSS and its ECM (a) Perspective view, (b) Top view, (c) ECM

Figure 1 Geometry of the circular loop FSS and its ECM (a) Perspective view, (b) Top view, (c) ECM

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square-loop array. Accordingly, a lumped-element ECM can be obtained for the circular loop array.
square-loop array. Accordingly, a lumped-element ECM can be obtained for the circular loop array.
Fig. 2 Plane wave incidence upon an inductive strip grating [21]. For a capacitive strip grating, replace the incident electric field (E) with a magnetic field (H)
Fig. 2 Plane wave incidence upon an inductive strip grating [21]. For a capacitive strip grating, replace the incident electric field (E) with a magnetic field (H)
where a factor z/2 owing to the length of the half circular loop (zd/2) is compared with the straight line for the square loop (), €et¢ is the effective permittivity of the substrate, and g, is the average gap between two adjacent unit cells and can be calculated as The capacitance between two adjacent circular loops can be modelled to a pair of parallel plate capacitance. The capacitance value is determined by the average gap width between the two adjacent loops, the half loop length, and the effective dielectric constant of the substrate. Therefore, the susceptance B, of the capacitance C, for TE and TM incidence is given by
where a factor z/2 owing to the length of the half circular loop (zd/2) is compared with the straight line for the square loop (), €et¢ is the effective permittivity of the substrate, and g, is the average gap between two adjacent unit cells and can be calculated as The capacitance between two adjacent circular loops can be modelled to a pair of parallel plate capacitance. The capacitance value is determined by the average gap width between the two adjacent loops, the half loop length, and the effective dielectric constant of the substrate. Therefore, the susceptance B, of the capacitance C, for TE and TM incidence is given by
there was a close agreement at the resonant frequencies. The resonant frequencies are adequately predicted (to within 3%) in all 12 cases by the equivalent circuit.
there was a close agreement at the resonant frequencies. The resonant frequencies are adequately predicted (to within 3%) in all 12 cases by the equivalent circuit.
Fig. 3 Reflectivity and transmission response of the FSS calculated from the ECM and CST (a) Reflectivity response, (b) Transmission response Table 2 Simulated and calculated results for different arrays of circular loop FSSs
Fig. 3 Reflectivity and transmission response of the FSS calculated from the ECM and CST (a) Reflectivity response, (b) Transmission response Table 2 Simulated and calculated results for different arrays of circular loop FSSs
Fig. 4 Unit cell of the double circular loop FSS and its ECM (a) Geometry of FSS, (6) ECM
Fig. 4 Unit cell of the double circular loop FSS and its ECM (a) Geometry of FSS, (6) ECM
parameters including the substrate thickness, h, dielectric constant, é,, Outer diameter, d, width of the circle, w, and gap between two elements, g, through which significant characteristics of the circular loop FSS can be determined. All the simulations are performed using the CST microwave studio software and the results of the proposed ECM are compared with the CST ones to show the validity of the proposed approach.
parameters including the substrate thickness, h, dielectric constant, é,, Outer diameter, d, width of the circle, w, and gap between two elements, g, through which significant characteristics of the circular loop FSS can be determined. All the simulations are performed using the CST microwave studio software and the results of the proposed ECM are compared with the CST ones to show the validity of the proposed approach.
Fig. 5 Transmission response of the DCL FSS calculated from the ECM and CST
Fig. 5 Transmission response of the DCL FSS calculated from the ECM and CST
Fig. 7 Comparison between the resonant frequency of a circular loop FSS as a function of circle outer diameter with the geometrical parameters: p = 10mm, w = 0.5mm, substrate: €, = 4.3, h = 0.127 mm Fig. 6 Effective permittivity as a function of thickness and relative permittivity of the substrate with the geometrical parameters p = 10 mm, w =0.5mm, d=9mm (a) ¢+ = 4.3, h= variable, (b) h=0.127 mm, e; = variable
Fig. 7 Comparison between the resonant frequency of a circular loop FSS as a function of circle outer diameter with the geometrical parameters: p = 10mm, w = 0.5mm, substrate: €, = 4.3, h = 0.127 mm Fig. 6 Effective permittivity as a function of thickness and relative permittivity of the substrate with the geometrical parameters p = 10 mm, w =0.5mm, d=9mm (a) ¢+ = 4.3, h= variable, (b) h=0.127 mm, e; = variable
Fig. 9 Comparison between the resonant frequency of a circular loop FSS as a function of inter-elements gap with the geometrical parameters d= 9mm, w = 0.5mm; substrate: €, = 4.3, h = 0.127 mm Fig. 8 Comparison between the resonant frequency of a circular loop FSS as a function of circle width with the geometrical parameters p = 10mm, d = 9mm; substrate: e, = 4.3, h = 0.127 mm
Fig. 9 Comparison between the resonant frequency of a circular loop FSS as a function of inter-elements gap with the geometrical parameters d= 9mm, w = 0.5mm; substrate: €, = 4.3, h = 0.127 mm Fig. 8 Comparison between the resonant frequency of a circular loop FSS as a function of circle width with the geometrical parameters p = 10mm, d = 9mm; substrate: e, = 4.3, h = 0.127 mm
Fig. 10 Comparison between the transmission response of the circular loop FSS at different incidence angles for TE and TM modes obtained with the geometrical parameters p = 10 mm, d= 9 mm, w = 0.5 mm substrate: &, = 4.3,h =0.127mm f(a) Incident anole is 30°. (Hh) Incident anole is 60°
Fig. 10 Comparison between the transmission response of the circular loop FSS at different incidence angles for TE and TM modes obtained with the geometrical parameters p = 10 mm, d= 9 mm, w = 0.5 mm substrate: &, = 4.3,h =0.127mm f(a) Incident anole is 30°. (Hh) Incident anole is 60°
Fig. 11 Photographs of the FSS structures with the substrate of ¢, = 4.3, h = 0.127 mm LN + man wv rmnmtoran
Fig. 11 Photographs of the FSS structures with the substrate of ¢, = 4.3, h = 0.127 mm LN + man wv rmnmtoran
Fig. 12 Measured and ECM transmission coefficients of the both FSS prototypes 7.) Ot. .1.. 122. TOC Ainnt roa
Fig. 12 Measured and ECM transmission coefficients of the both FSS prototypes 7.) Ot. .1.. 122. TOC Ainnt roa
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