Unit cell geometry

A convoluted square loop slotted structure has been utilized to build this CFSS. The proposed geometry has been derived from a complementary square loop (CSL). The next development regarding the improvement of electrical length has been accomplished by the sequential development of CCSL denoted as CCSL-1 to CCSL-4 as illustrated in Fig. 1. The geometrical configuration of the single-layered one side printed CCSL-4 design has been developed on ultrathin FR-4 substrate (ɛ _r = 4.4, h = 0.2 mm & tanδ = 0.02). The dimension of CCSL-4 unit cell configuration is 0.105λ ₀ × 0.105λ ₀ × 0.0023λ ₀ (λ ₀ being the free space wavelength) which mainly contributes to achieving two narrow passbands separated by a wide stopband.

Fig. 1. Geometry of (a) CSL-FSS (b) CCSL-1 (c) CCSL-2 (d) CCSL-3(e) proposed CCSL-4 (f) Transmission coefficient of Figs 1(a)–1(e).

Evolution of unit cell with design synthesis

In the design steps of the unit cell, initially, a narrow slotted square loop has been etched to the one-sided metallic surface which contributes to the hybrid L ₂C ₂ resonator in parallel with the external wired grid and predicted as an inductor L. The transmission coefficient response of the CSL-FSS illustrates one transmission pole and one transmission zero as shown in Fig. 1(f). The impedance (Z) of the above mentioned equivalent circuit of basic CSL-FSS can be expressed as

$$Z = \displaystyle{{\,j\omega L( {1-\omega^2L_2C_2} ) } \over {1-\omega ^2( {L + L_2} ) C_2}}.$$

Hence the transmission pole (ω_p) and transmission zeros (ω_z) can be calculated as

(1)$$\omega _p = \displaystyle{1 \over {\sqrt {( {L + L_2} ) C_2} }}$$

and

(2)$$\omega _z = \displaystyle{1 \over {\sqrt {L_2C_2} }}$$

Hence [Reference Nauman, Saleem, Rashid and Shafique2]

(3)$$C_2 = \displaystyle{1 \over {L_2\omega _Z^2 }}$$

and

(4)$$L = \displaystyle{1 \over {C_2}} \times \displaystyle{{\omega _Z^2 -\omega _p^2 } \over {\omega _Z^2 \omega _p^2 }}$$

The structural development of CCSL-1 provides the enhancement of the slotted length as shown in Fig. 1(b). The interspacing between the curved slots introduces an additional parallel resonating circuit L ₁C ₁ while the intra spacing metallic part inside the four individual curved slots contributes largely to its capacitance of the series L ₂C ₂ resonator. Hence the equivalent circuit of CCSL-1 can be empirical modeled as a parallel combination of L = 2.94 nH, L ₁ = 0.56 nH, C ₁ = 2.1 pF are in parallel connection with series resonating circuit L ₂ = 0.82 nH, C ₂ = 1.24 pF as shown in Fig. 2(a). The fascinating feature of the transmission coefficient response of Fig. 1(f) shows that the modification of the CCSL structure development influences the shifting of the transmission zeros (ω _z) in the vicinity of the transmission pole (ω _p). Based on the ECM of Fig. 2(a), the transmission matrix of CCSL geometry can be constructed as

(5)$$\eqalign{\left[{\matrix{ A & B \cr C & D \cr } } \right] = & \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {\,j\omega L}}} & 1 \cr } } \right]\left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {\,j\omega L_1}}} & 1 \cr } } \right]\left[{\matrix{ 1 & 0 \cr {\,j\omega C_1} & 1 \cr } } \right] \cr & \times \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {( {\,j\omega L_2 + ( 1/( j\omega C_2) ) } ) }}} & 1 \cr } } \right]}$$

(6)$$\eqalign{& = \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {\,j\omega ( ( L \times L_1) /( L + L_1) ) }}} & 1 \cr } } \right]\left[{\matrix{ 1 & 0 \cr {\,j\omega C_1} & 1 \cr } } \right] \cr & \times \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {( {\,j\omega L_2 + ( 1/( j\omega C_2) ) } ) }}} & 1 \cr } } \right]}$$

Fig. 2. (a) Equivalent circuit model of proposed single layer CFSS (CCSL-4) (b) Transmission and reflection coefficient of CST-MWS & ADS.

For simplification purpose, let L × L₁/(L + L₁) = L_X; hence the ABCD matrix can be written as

(7)$$\left[{\matrix{ A & B \cr C & D \cr } } \right] = \left[{\matrix{ 1 & 0 \cr {\displaystyle{{( {1-\omega^2L_XC_1} ) ( {1-\omega^2L_2C_2} ) -\omega^2L_XC_2} \over {\,j\omega L_X( {1-\omega^2L_2C_2} ) }}} & 1 \cr } } \right]$$

Using the transformation between S parameters and ABCD parameters, the transmission coefficient (S ₂₁) between the two ports can be determined by using the reference [Reference Guo, Li, Su, Song and Yang43]:

(8)$$S_{21} = \displaystyle{{2Z_0} \over {AZ_0 + B + CZ_0^2 + DZ_0}}$$

Where Z ₀ is the characteristics equation. In order to evaluate the passband pole │S ₂₁│ = 1, equation (8) can be rearranged as

(9)$$\omega ^4L_XC_1C_2L_2-\omega ^2( {L_XC_1 + L_XC_2 + L_2C_2} ) + 1 = 0.$$

Hence two poles ω_{p 1} and ω_{p 2} are

(10)$${\eqalign{& \omega _{\,p1} = \cr & \sqrt {\displaystyle{{( {L_2C_2 + L_XC_2 + L_XC_1} ) -\sqrt {{( {L_2C_2 + L_XC_2 + L_XC_1} ) }^2-4L_XC_1C_2L_2} } \over {2L_XC_1C_2L_2}}}}} $$

(11)$${\eqalign{&\omega _{\,p2} = \cr & \sqrt {\displaystyle{{( {L_2C_2 + L_XC_2 + L_XC_1} ) + \sqrt {{( {L_2C_2 + L_XC_2 + L_XC_1} ) }^2-4L_XC_1C_2L_2} } \over {2L_XC_1C_2L_2}}}}} $$

In order to determine stopband zero, the transmission coefficient │S ₂₁│ = 0. Hence the condition can be established as

(12)$$j\omega L( {1-\omega^2L_2C_2} ) = 0\;{\rm and}\;\omega _z = \displaystyle{1 \over {\sqrt {L_2C_2} }}$$

The stopband zero completely depends on L ₂ and C ₂. However, transmission poles are shifted with the varying L ₁, C ₁, L ₂ and C ₂ as illustrated in Fig. 3. According to the abovementioned expression of equations (8)–(11), the lumped equivalent circuit elements L ₁, C ₁, L ₂ and C ₂ can be expressed in terms of two poles and one zero as

(13)$$L_2 = \displaystyle{1 \over {\omega _z^2 C_2}}.$$

Fig. 3. Frequency response of Equivalent circuit with (a) varying C ₁ (L ₁ = 0.56 nH, L ₂ = 0.82 nH, C ₂ = 1.24 pF) (b) varying L ₁ (C ₁ = 2.1 pF, L ₂ = 0.82 nH, C ₂ = 1.24 pF) (c) varying C ₂ (L ₁ = 0.56 nH, C ₁ = 2.1 pF, L ₂ = 0.82 nH) (d) varying L ₂ (L ₁ = 0.56 nH, C ₁ = 2.1 pF, C ₂ = 1.24 pF).

The design synthesis concerning poles is

(14)$$( {1-\omega_p^2 L_XC_1} ) \times ( {1-\omega_P^2 L_2C_2} ) = \omega _p^2 L_XC_2$$

Now, this equation can be modified as

(15)$$( {1-\omega_p^2 L_XC_1} ) \times ( {\omega_Z^2 -\omega_p^2 } ) = \omega _p^2 \omega _z^2 L_XC_2$$

Further rearranged expression is

(16)$$\omega _p^4 L_XC_1-\omega _p^4 ( {1 + \omega_Z^2 L_XC_1 + \omega_Z^2 L_XC_2} ) + \omega _Z^2 = 0$$

$${\eqalign{\omega _{\,p1}^2 = & \displaystyle{{( {1 + \omega_z^2 L_XC_1 + \omega_Z^2 L_XC_2} ) + \sqrt {{( {1 + \omega_Z^2 L_XC_1 + \omega_Z^2 L_XC_2} ) }^2-4L_XC_1\omega _Z^2 } } \over {2L_XC_1}} \cr \omega _{\,p2}^2 = & \displaystyle{{( {1 + \omega_Z^2 L_XC_1 + \omega_Z^2 L_XC_2} ) -\sqrt {{( {1 + \omega_Z^2 L_XC_1 + \omega_Z^2 L_XC_2} ) }^2-4L_XC_1\omega _Z^2 } } \over {2L_XC_1}}}} $$

Replacing the value of L _X,

(17)$$C_1 = \displaystyle{{4\omega _Z^2 } \over {( ( L \times L_1) /( L + L_1) ) \Big[ {{( {\omega_{\,p1}^2 + \omega_{\,p2}^2 } ) }^2-{( {\omega_{\,p1}^2 -\omega_{\,p2}^2 } ) }^2} \Big] }}.$$

Here the optimum value of L can be determined from equation (4) of the CSL-FSS circuit model. L ₁ and C ₁ have been introduced due to the interspacing of slots. In order to synthesize both L ₁ and C ₁, both the transmission pole and transmission zero are the key factors. However, the values of L ₂ and C ₂ of the lumped element model can be adjusted independently with ω_Z. In the further development of CCSL-2 and CCSL-3 geometry, the intra space meandered slot length increases in stepwise structural development and the narrow separation between the nearby meandered slots enhances the capacitive coupling effect which in turn enhances the value of C ₂. On the other hand, the longer narrow metallic gap between etched curvatures is mainly responsible for large inductive cross-coupling. The enhanced inductive nature of the narrow metallic span maximizes L ₂. Therefore, the shifting of poles and the zero toward the lower frequency can be observed in Fig. 1(f) and it can be validated by the ECM results as illustrated in Fig. 3 where the alteration of L ₂ and C ₂ sweep the position of zero though the poles position shifting is relatively lower. This variation illustrates a noticeable development of the frequency gap reduction between the primary transmission pole and transmission zero. This ultimately leads to the improvement of the roll-off criterion (ROC) of the right-handed slope of the passband. Since the magnitude of the transmission coefficient (in dB) is varying with respect to the change of frequency (in GHz), therefore the ROC be defined as

$$ROC = \displaystyle{{\Delta _{dB}} \over {\Delta _{GHz}}}, \;$$

where, △_dB = − 3 dB passband to − 10 dB stopband magnitude difference and △_GHz is the difference between −3 dB passband cut-off frequency to −10 dB cut-off frequency in GHz.

In the proposed CCSL-4 structure, four arrow-shaped slotted extended loops are connected with each of four large slotted curvatures. These four symmetrical closer arrows shaped extended loop produce a very high capacitive coupling effect which results in the enhancement of C ₁. As observed from Fig. 3 that the raised C ₁ value shifts transmission poles toward the lower frequency. However, the rate of shifting of the transmission pole is quite lower as compared to the variation of L ₁. The inductive effect of the interspacing region deteriorates sharply which ultimately leads toward the sharp decrement of L ₁ and due to that a noticeable shifting of the primary pole of the transmission characteristics is observed. On the other hand, the frequency position of transmission zero is almost constant due to the negligible variation of L ₂, C _2, so that the gap between the primary pole and primary zero reduces significantly. In effect of that ROC of CCSL-4 becomes significantly high as compared to CCSL-3. The proposed CCSL-4 structure is mounted over an ultra-thin dielectric FR-4. The ultrathin dielectric substrate of thickness h₁ can be modeled in transmission line equivalent circuit as L_d C_d combination where, L _d = μ ₀μ _rh ₁, C _d = ((ɛ ₀ɛ _rh ₁)/2) and “μ ₀” is the free space permeability, “μ _r” is the relative permeability of the dielectric material, “ɛ ₀” is the absolute permittivity and “ɛ _r” is the relative permittivity. To validate the abovementioned design, the synthesis procedure is carried on the calculated optimized parametric values of L = 2.94 nH, L ₁ = 0.56 nH, C ₁ = 2.1 pF, L ₂ = 0.82 nH, C ₂ = 1.24 pF, L_d = 0.25 nH and C_d = 0.15 pF and the simulation is performed in ADS solver. The comparative transmission and reflection coefficient curves by CST electromagnetic solver and ADS simulation are illustrated in Fig. 2(b). It is observed that the curves agree with each other very well for ω_{p 1} and ω_Z. Although a little disagreement arises for ω_{p 2}, the discrepancy may be ignored.

Topology and demonstration

High order mode coupling effects are ignored due to the simplification of the design synthesis. The main objective of this design is to achieve a wide second-order passband response along with the wide second-order stopband response. The simulated transmission and reflection coefficient responses of Fig. 5(c) exhibit the two nearby transmission passband poles and also nearby stopband zeros. The air space (h ₀) between the ultrathin dielectrics is playing a key role where the increasing h ₀ certainly reduces the gap between two successive poles in order to maintain the flat and steep passband response with enhanced fractional bandwidth of 20.35%. Two successive passband poles are generated due to the top CCSL-4 and bottom CCSL-2. It can be noticed that the shifting of the second pole is completely controllable by varying the dielectric spacer length. Besides the magnitude of the second transmission pole improves significantly with the increasing air gap. The optimum air gap matching has been compromised to its maximum value of h ₀ = 11 mm which is equivalent to λ ₀/8 transmission line length where λ ₀ can be defined as the central passband frequency. At the optimized air gap separation, almost flat passband response has been realized with significantly sharp passband to stopband ROC as shown in Fig. 6. The peak magnitude of both the passband poles is above −1 dB which illustrates the excellence of air gap coupling between top CCSL-4 and bottom CCSL-2 CFSS array. In addition to this, the steep passband could improve the passband Selectivity Factor (SF) which can be defined as

(18)$$SF_{\,passband} = \displaystyle{{Transmission\,Bandwidth\;_{{-}3\,dB}} \over {Transmission\,Bandwidth\;_{{-}10\,dB}}}.$$

Fig. 6. Influence of air gap variation on frequency response on double-layer CFSS.

To improve passband SF, the proposed cascaded dual metallic layered CFSS structure helps in achieving wider bandwidth of the passband with higher-order response. Figures 5(d) and 5(e) illustrate the individual simulated transmission and reflection characteristics of the CCSL-2, CCSL-4 and the proposed dual-layer CFSS structure. The fascinating features of dual-layer structure as compared to independent ultrathin single-layer CCSL-2 or CCSL-4 are the enhanced passband (20.35%), enhanced stopband (63.5%), improved ROC (70 dB/GHz) and improved SF(0.692).

Equivalent transmission line model of a double layer structure

Figure 3 depicts a crucial feature of the increased C ₂ and L ₂ which is also responsible for the emergence of the sharp passband. This increasing sharpness lowers the passband SF. Dual-layer structure with free space may resolve this problem by generating the enhanced SF. The ultrathin dielectric substrate of thickness h₁ on both sides of the air foam spacer sand witched air space between the ultrathin dielectric can be modeled as a transmission line with characteristics impedance Z ₀ = 377 Ω with free space isolation gap h ₀. The top complementary metallic structure is CCSL-4 and the bottom structure has been predicted as CCSL-2 has the impedance denoted as Z_T and Z_B respectively. CCSL-4 and CCSL-2 are mounted on ultrathin substrates of impedance

$$Z_d = \displaystyle{{Z_0} \over {\sqrt {{\varepsilon }_r} }}$$

where “ɛ _r” is the relative permittivity of the ultrathin substrate and Z_T can be expressed as

(19)$$Z_T = \displaystyle{{\,j\omega L_X( {1-\omega^2L_2C_2} ) } \over {( {1-\omega^2L_XC_1} ) ( {1-\omega^2L_2C_2} ) -\omega ^2L_XC_2}}$$

(20)$$Z_B = \displaystyle{{\,j\omega L_X^{\prime} ( {1-\omega^2L_2^{\prime} C_2^{\prime} } ) } \over {( {1-\omega^2L_X^{\prime} C_1^{\prime} } ) ( {1-\omega^2L_2^{\prime} C_2^{\prime} } ) -\omega ^2L_2^{\prime} C_2^{\prime} }}$$

The single-layered ultrathin CFSS comprises CCSL-4 on the top of ultrathin dielectric material. The ABCD parameter of the subsection-1 of transmission line model shown

(21)$$\left[{\matrix{ {A_T} & {B_T} \cr {C_T} & {D_T} \cr } } \right] = \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {Z_T}}} & 1 \cr } } \right]\left[{\matrix{ {\cos \beta h_1} & {\,jZ_d\sin \beta h_1} \cr {\displaystyle{\,j \over {Z_d}}\sin \beta h_1} & {\cos \beta h_1} \cr } } \right]$$

Since h ₁ is ultra-thin substrate thickness and hence it can be assumed that sin βh ₁ ≈ 0 and cos βh ₁ ≈ 1

(22)$$\therefore \left[{\matrix{ {A_T} & {B_T} \cr {C_T} & {D_T} \cr } } \right] = \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {Z_T}}} & 1 \cr } } \right]\left[{\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right] = \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {Z_T}}} & 1 \cr } } \right]$$

Similarly, the bottom CCSL-2 with the ultra-thin dielectric of subsection-2 can be simplified as

(23)$$\left[{\matrix{ {A_B} & {B_B} \cr {C_B} & {D_B} \cr } } \right] = \left[{\matrix{ 1 & 0 \cr {\displaystyle{1 \over {Z_B}}} & 1 \cr } } \right]$$

Therefore ABCD of the transmission line model of dual-layer CFSS can be expressed as

(24)$$\eqalign{\left[{\matrix{ A & B \cr C & D \cr } } \right] & = \left[{\matrix{ {A_T} & {B_T} \cr {C_T} & {D_T} \cr } } \right]\left[{\matrix{ {\cos \beta h_0} & {\,jZ_0\sin \beta h_0} \cr {\displaystyle{\,j \over {Z_0}}\sin \beta h_0} & {\cos \beta h_0} \cr } } \right] \cr & \times \left[{\matrix{ {A_B} & {B_B} \cr {C_B} & {D_B} \cr } } \right]}$$

Since in this work, h ₀ is approximated to λ/8 on the stopband resonance in order to simplify, so that βh ₀ = 2πh ₀/λ = π/4, therefore rearranging equation (24), we have

(25)$$\left[{\matrix{ A & B \cr C & D \cr } } \right] = \left[{\matrix{ {A_T} & {B_T} \cr {C_T} & {D_T} \cr } } \right]\left[{\matrix{ {\displaystyle{1 \over {\sqrt 2 }}} & {\displaystyle{{\,jZ_0} \over {\sqrt 2 }}} \cr {\displaystyle{\,j \over {\sqrt 2 Z_0}}} & {\displaystyle{1 \over {\sqrt 2 }}} \cr } } \right]\left[{\matrix{ {A_B} & {B_B} \cr {C_B} & {D_B} \cr } } \right]$$

Therefore equating the ABCD, we can solve the ultimate value of S ₂₁ from equation (4). In this regard, multiple simulations have been performed in ADS to extract the value of the parameters are L = 2.94 nH, L ₁ = 0.56 nH, C ₁ = 2.1 pF, L ₂ = 0.82 nH, C ₂ = 1.24 pF, L ^′₁ = 2.13 nH, C ^′₁ = 0.0187 pF, L ^′₂ = 0.7 nH, C ^′₂ = 1.12 pF. It can be noted that C ₁ > C ^′₁ and L ₁ < L ^′₁ that indicates the noticeable reduction of metallic interspacing and intense capacitive coupling between four arrow-shaped slots. The comparative CST and ADS transmission coefficient depict the good agreement between those results with an excellent exhibition of two passband poles and two stopband zeros as depicted in Fig. 7(b).

Fig. 7. (a) Equivalent circuit model of proposed double-layer CFSS (b) Transmission coefficient of CST-MWS & ADS (c) Reflection coefficient of CST-MWS & ADS.

Circuit model analysis of conformal single-layer complementary FSS

The comprehension of the bending mechanism can be assisted by the explanation and illustration of the modified ECM. The radius of curvature in the apex region of the convex curved surface is 200 mm has cell induced by the incident plane wave. The surface current distribution around the reduced circumference of the central element or apex region of the CCSL-4 array is highly influenced by the normalized plane wave on its slightly curved unit cell area which has less circumference as compared to the planar one, which actually introduces the change of impedance due to the inclusion of the series inductive effect in the intra-spacing region. This series inductor ultimately shifted the transmission zero toward the lower frequency range. However, the angle of the incident to the nearby tilted cell array element on the curved CFSS is becoming large as compared to the planar CFSS, which creates an increasing phase difference in the magnetic field concerning the incident plane wave and therefore inter-element coupling among the unit cells are deteriorates noticeably. The weak coupling among the unit cell boundary contributes to the parallel inductive effect which is ultimately responsible for the sharpness of the passband [Reference Lee, Park, Chun, Kim and Hong44, Reference Savia and Parker45]. The shifting of transmission zero toward the pole ultimately enhances the ROC to 75.7 dB/GHz as compared to the planar structure with ROC 16.28 dB/GHz. However, the −3 dB bandwidth of the passband of transmission coefficient is reduced significantly to 6.7% as compared to planar CCSL-4 of 23.75% as shown in Fig. 10(b). Figure 10 exhibits the modified equivalent circuit with additional lumped reactive components (L_{c 1} = 0.55 nH, L_{c 2} = 0.5 nH) and its corresponding transmission coefficient which clearly illustrates the better parity with the simulated result and validates the hypothesis regarding the conformal structure equivalent circuit.

Fig. 10. (a) Modified ECM for conformal single-layer CFSS (b) Comparative transmission coefficient of CST-MWS & ADS for both planar and conformal FSS.

Conformal structure of double-layered complementary FSS

The proposed double-layer conformal CFSS structure illustrates the little degraded fractional bandwidth of passband (16.51%) as compared to the planar structure passband (20.35%). On contrary, conformal stopband (65.14%) is quite better as compared to stopband (63.5%). The passband to stopband one-sided ROC of the curved CFSS is 76.14 dB/GHz as compared to the planar double-layer structure (70 dB/GHz) as shown in Fig. 11. The SF of the double layer curved structure is 0.648 which is almost similar to the SF of planar (0.692). The study reveals that the passband and stopband responses of planar and conformal structures are almost in better agreement in spite of the little disagreement in ROC, passband and stopband regarding simulated transmission coefficient.

Fig. 11. Comparative transmission coefficient of the planer and conformal at normal incidence for double layer CFSS.

Measurement setup

The measurement of the transmission coefficient of proposed single and dual-layer fabricated prototypes have been carried out by using two horn antenna setup pair are connected to a network analyzer (Rohde & Schwarz ZND20). Two types of horn antennas pair for different frequency ranges are utilized in the laboratory as transmitter and receiver measurement setup separately. The assigned frequency ranges of these antennas are 2–4 GHz and 4–8 GHz. Each antenna pair has a different flared cross-sectional area. Passband and stopband measurement for both the planar and conformal structure has been accomplished with the help of transmitter/receiver antenna setup with 2–4 GHz and 4–8 GHz correspondingly. Besides, the power sensor and power meter have also been incorporated along with the horn antenna to evaluate side lobe radiation. It has been observed that the abovementioned antenna setup uses with different specific frequency ranges made the side lobe radiation insignificant. Initially, calibration of setup has to be ensured with the transmission coefficient measurement without placing the CFSS array. The Horn antenna of the measurement setup is so arranged that it ensures the separation distance ≥2D²/λ where D is the maximum dimension of the antenna and λ denotes the operating wavelength [Reference Anwar, Wei, Mao and Ning31].

Since the flexible nature of ultrathin single layer CCSL-4 generates misalignment for the normal incident, the air foam sheet along with wood frame fixture for measurement support is taken carefully to accomplish adequate measured results. The single-layer measurement has been carried out for a one-sided metallic CCSL-4 CFSS array. The single-sided conductor part of CCSL-4 is directed toward the transmission antenna. Due to the availability issue of an anechoic chamber, some new mechanisms have been adopted to measure the transmission coefficient in free space. The FSS array has been placed in a wood frame where the rear part of the wooden fixture is completely embedded with an electromagnetic wave absorber material sheet in order to prevent the reflected ray effectively back to the antennas. The wide periphery of the wooden frame with wave absorbing sheet may also reduce the multipath effect. The planar FSS array has been placed approximately at the midpoint in between the transmission and receiving horn antenna gap in order to measure the transmission coefficient at the normal and oblique incident with θ = 45°. However, measurement regarding the conformal structure has been carried out in such a way that the position of the FSS array has been moved closer to the receiving horn antenna without any separation changes between the transmitting horn and receiving horn antenna. Therefore the flared cross-sectional aperture area can entirely cover the aperture area of curved FSS circumference thus collecting radio waves of the main lobe more efficiently and simultaneously avoiding the multi-path effect.

Measured results

The comparative simulated and measured transmission coefficient of single and double layer structures in both the planar and conformal modes are illustrated in Figs 13 and 14 respectively. Though the experimental ripple can be seen, yet the envelop of the experimental results are in good agreement with the simulated results. The comparative simulated and measured results of both the planar and conformal modes are listed in Table 3. The little discrepancy observed between simulated and measured responses in parametric comparison may be due to the fabrication error of complex structure and the free space measurement environment. Otherwise, the better parity of the measured and simulated results can be seen.

Fig. 13. Simulated vs Measured frequency response of planer (a) single layer (b) double layer CFSS array.

Fig. 14. Simulated vs Measured frequency response at normal incidence of conformal (a) single layer (b) double layer CFSS array.

Table 3. Comparative simulated and measured values

Figure 15 shows the angular stability for TE polarization at two incident angles, θ = 0° and 45° have been investigated experimentally. The wooden fixture with embedded CFSS array is angularly rotated horizontally to obtain the transmission coefficient response at θ = 45°. It can be observed that the single and the double layer passband and stopband do not change significantly. The double-layer angular transmission coefficient response provides a stable passband and good stopband. Besides, two transmission poles of the passband and two transmission zeros of the stopband can precisely be determined from the measured results. Moreover, the remarkable angular stability regarding measured ROC and SF can also be observed where ROC = 68.3 dB/GHz and SF = 0.764 for θ = 45°.

Fig. 15. Simulated vs Measured frequency response at various incident angles under TE polarization for (a) single layer (b) double layer CFSS and (c) Block diagram of the oblique incidence measurement setup.