FSS design

The geometry and size of the cell structure, the electrical parameters of the substrate, and the incident angle of the EM waves are all closely related to the performance of the FSS. The metal patch FSS exhibits a capacitive impedance. When the wavelength of the incident wave is consistent with its electrical length, the structure resonates and stop-band characteristics can be realized.

The new, compact single-layer UWB FSS proposed in this study is shown in Fig. 1. The basic unit contains a square loop and multiple metallized vias. The designed FSS structure was printed on an FR-4 substrate with a relative dielectric constant of 4.3; the loss tangent is 0.0025 and the thickness is 1.6 mm. p is the length of the cell's sides and s is the width of the square loop. g is the gap between adjacent cells, and L_via, R_via, and h_via are the spacing, radius, and length of the metallized holes, respectively. It should be noted that the dimensional accuracy of the design can be achieved by general processing. If the processing level is further improved, the unit size is expected to be further reduced.

Fig. 1.

Structure of the proposed FSS unit. p = 4.2 mm, s = 0.4 mm, g = 0.2 mm, L_via = 0.6 mm, R_via = 0.2 mm, and h_via = 1.6 mm.

FSS simulation and measurement results

Figure 2 shows the influence of the number of metallized vias on the transmission coefficient of the proposed FSS unit. It can be observed that when there is signal loop structure, the resonant frequency of the FSS is 12.69 GH, and the corresponding −10 dB BW is 8.6–15.6 GHz (BW = 7 GHz). When the number of metallized vias N_via is 1, the FSS response frequency decreases from 12.69 GHz to 8.67 GHz. As the number of metallized vias increases, the resonance frequency gradually decreases. After all the metallized vias are added, i.e. N_via = 5, the response frequency of the proposed FSS is 6.67 GHz and the corresponding −10 dB BW is 2.8–11.2 GHz (BW = 8.4 GHz). This result indicates that the FSS response frequency is reduced and the operating BW is widened due to the introduction of metalized vias, which increases the equivalent inductance and capacitance. The corresponding value is related to the radius, length, quantity, and spacing of the adjacent metallized vias.

Fig. 2.

Influence of the number of metallized vias on the transmission coefficient.

In order to verify the simulation results, the FSS was processed and measured, as shown in Fig. 3. The sample uses 80 × 80 units and has a total size of 336 mm × 336 mm. Rocker 1, rocker 2, transmitting and receiving antenna are used for reflection coefficient measurement. Rocker 1 and rocker 3 cooperate with transmitting and receiving antenna and are used for transmission coefficient measurement. The 3671E vector network analyzer (China Electronics Technology Instruments Limited Company, Qingdao, 370211, China) provided excitation sources and data records.

Fig. 3.

Fabricated UWB FSS and test environment.

Figure 4 show that the measured results are in good agreement with the simulated results. It can be observed that the FSS has a high attenuation response in the entire frequency range of 3–11 GHz and the reflection phase changes linearly with frequency. When the distance between the antenna and the reflector is $n\lambda /2 ( n = 1, \;2, \;3, \;\ldots ) , \;$ that is, when the co-reflection condition is met, the EM waves reflected by the reflector and the radiated EM waves of the antenna are superimposed in phase to achieve radiation enhancement. The phase of the FSS changes linearly with frequency throughout the operating frequency band, which provides the possibility of achieving broadband radiation enhancement. The transverse electric (TE) and transverse magnetic (TM) modes have the same characteristics at a normal incidence.

Fig. 4.

Simulated and measured results of the proposed FSS.

Angle and polarization-independence are also considerations for the design of periodic structures, which are considerably important in UWB systems. Figure 5 shows the S-parameters of the proposed FSS under different polarization modes and incident angles at 2–12 GHz.

Fig. 5.

S-parameters of the FSS at different incident angles: (a) TE mode, (b) TM mode.

As can be observed from Fig. 5, the FSS has excellent broadband stop-band characteristics in two fundamental modes. In the TE mode (Fig. 5(a)), the resonant frequency is 6.69 GHz at an incident angle of 60°, which is only 0.3% offset relative to the normal incidence. At the same time, in the TM mode (Fig. 5(b)), the resonant frequency is 6.72 GHz and the offset is 0.7%. Thus, the proposed FSS structure has excellent angle and polarization-independence. Similar to the typical characteristics of the conductive element FSS, the resonant BW of the proposed FSS structure in the TE mode widens with an increasing incidence angle; on the other hand, it tends to decrease in the TM mode.

Table 1 compares the size, operating BW, and the angle-independence performance of the proposed FSS with other methods in published literature. In comparison to single-layer single-sided (SLSS) designs [Reference Yahya, Nakamura, Itami and Denidni7–Reference Priyanka and Kaushik9, Reference Kundu15] and single-layer double-face (SLDS) designs [Reference Sayi and Ramprabhu16, Reference Majidzadeh, Ghobadi and Nourinia19,Reference Bashiri, Ghobadi, Nourinia and Majidzadeh20], the structure designed in this study has an advantage in terms of size while ensuring an excellent fractional BW (FBW) performance. Compared with the 2.5-D FSS structure in [Reference Hussain, Cao, Kayani and Majid24–Reference Varikuntla and Singaravelu26], the unit size of the proposed design is 4.2 mm × 4.2 mm, which provides 126% FBW. The resonance frequency under the TE polarization shifts by only 0.003 f ₀ at an incident angle of 60°, while the TM polarization shifts by 0.007 f ₀. Therefore, the structure proposed in this study is simple and compact, easy to debug and process; it has a large FBW and excellent angle and polarization independence.

Table 1.

Comparison of the proposed design with other FSS designs

Equivalent circuit model

The EC model combines closed equations while providing a simple and efficient means for the initial design and performance estimation of the FSS. The EC model corresponding to the EM simulation model is composed of multiple lumped components. The degree of fineness determines the accuracy of the calculation results; however, this reduces efficiency. Therefore, when the designed model is very complex, the accuracy and efficiency of this method are not satisfactory.

The basic unit in this study contains a square loop and multiple metallized vias. The loop unit can be equivalent to the LC series circuit [Reference Hussain, Cao, Kayani and Majid24, Reference Langley and Parker27]. Figure 6(a) shows the EC of a single loop, where L_out is the inductance of the metal patch and C_out is the capacitance between the adjacent metal patches. C_out and L_out can be calculated according to equations (1) and (2) [Reference Langley and Parker27], where θ is the incident angle of EM waves and s, d, p, and g are the structural parameters in Fig. 1. Because equations (1) and (2) have some limitations, such as p/λ ≪ 1, w/p ≪ 1, and p(1 + sinθ) < 1, the accuracy of the calculation depends on the design parameters.

(1)$$\displaystyle{{X_L} \over {Z_0}} = \omega L = \displaystyle{d \over p}\cos \theta F( {\,p, \;2s, \;\lambda , \;\theta } ) , \;$$

(2)$$\displaystyle{{B_c} \over {Y_0}} = \omega C = 4\displaystyle{d \over p}\sec \theta F( p, \;g, \;\lambda , \;\theta ) \varepsilon _{eff}, \;$$

where

(3)$$F( {\,p, \;\omega , \;\lambda , \;\theta } ) = \displaystyle{\,p \over \lambda }\left[{\ln \left({\csc \displaystyle{{\pi \omega } \over {2p}}} \right) + G( {\,p, \;\omega , \;\lambda , \;\theta } ) } \right], \;$$

(4)$$\eqalign {& G( p, \;\omega , \;\lambda , \;\theta ) = \cr& \displaystyle{1 \over 2} \times \displaystyle{{{( {1-\beta^2} ) }^2\left[{\left({1-\displaystyle{{\beta^2} \over 4}} \right)( {A_ + { + } A_-} ) + 4\beta^2A_ + A_-} \right]} \over {\left({1-\displaystyle{{\beta^2} \over 4}} \right) + \beta ^2\left({1 + \displaystyle{{\beta^2} \over 2}-\displaystyle{{\beta^4} \over 8}} \right)( {A_ + { + } A_-} ) + 2\beta ^6A_ + A_-}}}$$

with

(5)$$A_ \pm{ = } \displaystyle{1 \over {\sqrt {\left[{1 \pm \displaystyle{{2p\sin \theta } \over \lambda }-{\left({\displaystyle{{\,p\cos \theta } \over \lambda }} \right)}^2} \right]} }}-1, \;$$

(6)$$\beta = \sin \left({\displaystyle{{\pi \omega } \over {2p}}} \right), \;$$

(7)$$\varepsilon _{eff} = \displaystyle{{\varepsilon _r + 1} \over 2}-\displaystyle{{\varepsilon _r-1} \over 2} \times \exp \left({\displaystyle{{-13h} \over p}} \right)-\left({\displaystyle{{100s^2} \over d}-2g + 10h} \right). $$

Fig. 6.

Equivalent circuit: (a) signal loop, (b) proposed FSS.

According to equations (1) and (2), L_out and C_out are 2.62 pH and 580.13 nF, respectively.

The capacitance C_v and inductance L_v that are introduced by the via are related to g, L_via, R_via, and h_via. The via structure proposed in this study is simple, and the inductance and capacitance can be directly obtained with equations (8) and (9) [Reference Rao28, Reference Savidis and Friedman29].

(8)$$C_v = \displaystyle{{\pi \varepsilon _r\varepsilon _0} \over {cosh^{{-}1}( {g_{via}/2R_{via}} ) }} \times h_{via}, \;$$

(9)$$L_v\displaystyle{{\mu _0} \over \pi }cosh^{{-}1}( {g_{via}/2R_{via}} ) \times h_{via}, \;$$

g_via refers to the spacing of the vias between the adjacent elements, where the value is g_via = g + 2R_via = 0.6 mm. By applying equations (8) and (9), the capacitance and inductance of the metallized vias can be determined as L_v = 0.616 nH and C_v = 0.199 pF. The total capacitance of the proposed structure is ${C}^{\prime}_v = 5 \times C_v$.

The inductors L ₁₁ and L ₂₂ can be regarded as metal micro-strip lines in Fig. 6(b), and the inductance value can be obtained according to equations (10) and (11), where b is the thickness of the metal layer, which is usually 0.02 mm. l ₁ and l ₂ are the lengths of the micro-strip lines corresponding to the L ₁₁ and L ₂₂, and are 0.8 mm and 0.6 mm, respectively.

(10)$$L_{11} = \displaystyle{{\mu _0} \over {2\pi }}\ln \left({\displaystyle{{2l_1} \over {s + b}}} \right)\times l_1, \;$$

(11)$$L_{22} = \displaystyle{{\mu _0} \over {2\pi }}\ln \left( {\displaystyle{{2l_2} \over {s + b}}} \right) \times l_2$$

According to L ₁₁, L ₂₂, L_v, and the EC model shown in Fig. 6(b), the inductance of the proposed structure is equal to ${L}^{\prime}_v$ = 0.443 nH. In addition, the equivalent inductance L _e of the virtual cut-off of the periodic structure is equivalent to infinity.

Equation (8) is used to estimate the mutual capacitance of the metallized vias of the two adjacent metal units and the value is closely related to the spacing and length of the via. If the number of metalized vias is large, the dense array of vias on each side is like a metal plate and the capacitance between the neighboring units is similar to the capacitance of parallel metal plates. By applying equation (12), the equivalent capacitance can be approximated as C_p = 1.218 pF. The structural response calculated by the full-wave EM simulation and the EC model is presented in Table 2. It can be observed that the calculation results that use the metal plate capacitor are closer to the EM simulation results.

(12)$$C_p = \displaystyle{{\varepsilon _r\varepsilon _0 \times S} \over g} = \displaystyle{{\varepsilon _r\varepsilon _0 \times d \times h_{via}} \over g}. $$

Table 2.

Comparison of the EM and EC model calculation results

Antenna design

To evaluate the effect of the designed FSS reflector on the UWB antenna port and radiation parameters, a disc monopole antenna was used as the radiator, as shown in Fig. 7. The antenna structure evolved from the monopole antenna in [Reference Liang, Guo, Chiau, Chen and Parini2]. The difference between the antenna used in this study and the one in [Reference Liang, Guo, Chiau, Chen and Parini2] is that the feed mode is changed from co-planar waveguide feed to stepped microstrip feed and the parameters are optimized. The antenna was printed on the Rogers RT5880 substrate with ɛ _r = 2.2, tanδ = 0.0009, and a thickness of 1.524 mm. When the feeder length is 2.1, 5.0, and 6.5 mm, the feeder width is 2.0, 2.2, and 2.4 mm, respectively. The FSS reflector is installed directly below the antenna at a distance of h, as shown in Fig. 8.

Fig. 7.

Structure of the monopole antenna.

Fig. 8.

Fabricated antenna and FSS reflector.

Antenna loaded proposed FSS

The influence of the reflector on the operating BW and gain of the antenna is closely affected by the distance between the reflector and the antenna. Using the linear relationship between the phase and frequency of the FSS unit, a suitable distance can be determined. In addition, the phase difference can be used to compensate for the wavelength difference. Therefore, the radiated and reflected energy can be superimposed in phase to increase the gain of the antenna within the operating band. The EM wave phase relationship between the FSS reflector and the antenna is given as follows:

(13)$$\phi _{\,fss}-2\beta h = 2n\pi \,\quad n = \cdots -2, \;-1, \;0, \;1, \;2\cdots , \;$$

where ϕ _fss is the phase of the FSS reflection coefficient and β is the free space propagation constant. If ϕ _fss = 0, for example, and the corresponding frequency is 7 GHz, h is equal to 21.42 mm; therefore, 22 mm was selected for this study.

Figure 9 shows the maximum gain and the reflection coefficient of the antenna loaded FSS at different h values. The FSS array that was designed for this investigation uses 20 × 20 units; the overall size of the array is 84 mm × 84 mm.

Fig. 9.

Effect of the FSS reflector on the antennas at different h values: (a) maximum gain, (b) reflection coefficient.

It can be observed from Fig. 9(a) that the gain of the monopole antenna is about 2.5–5.5 dBi in the 3–11 GHz band and the flatness within the band is poor. The closer the distance, the more evident the effect of FSS reflector is on antenna gain enhancement. In addition, because the antennas have different radiation fields at different frequencies, the amplitude of the antenna gain enhancement at the same distance is also different. The monopole antenna has a relatively large back lobe at low frequencies. After the FSS reflector is loaded, the energy of the back lobe is effectively reflected, which greatly enhances the forward radiation; thus, the antenna has an obvious gain enhancement effect. The main radiation of the monopole antenna in the high-frequency band tends to be parallel to the radiating surface and the radiation of the rear lobe is weak. After the FSS reflector is loaded, the gain enhancement effect is not as evident as in the low-frequency band.

It can be observed from Fig. 9(b) that the reflection coefficient of a monopole antenna is substantially <−20 dB in the entire UWB frequency band. When h = 16 mm, the reflection coefficient of the antenna is significantly worse at 3–4.7 GHz and 9–10 GHz, which is about 5 dB or more. This is mainly because the antenna has a strong backward radiation field at low frequencies and the loading of the FSS reflector has a great influence on the EM field distribution. As the distance increases, this effect gradually decreases. When h = 28 mm, the antenna with and without the FSS has a similar reflection performance for the entire UWB band.

Using the reflection coefficient, gain enhancement, and the in-band gain flatness as the evaluation criteria, it is determined that h = 22 mm is an appropriate choice. This value is consistent with equation (13). After the FSS reflector is loaded, the average gain is 8 dBi, the gain variation is <0.5 dB, and the reflection coefficient is <−15 dB over 3–11 GHz.