Parametric Optimization and Performance Analysis of a Compact Dual-Band Split Square Loop FSS for X-Band and Ku-Band

Frequency Selective Surfaces (FSSs) are filters based on the use of microwave filters to provide band-pass or band-stop behaviour in frequency space. These periodic structures are periodic structures with frequency-dependent transmission and reflection characteristics that act as filters that consist of an array of elements [1]. In microwave and millimeter-wave applications, FSSs are utilised to improve the quality of a received signal, gain and directivity. They have been designed with communication systems in a number of forms, and they include dipole, Jerusalem crosses, rings, tripods, cross dipoles, and square loops [2, 3]. There are two basic types of FSS (array of wires (dipoles) and array of slots) both generally placed on a dielectric substrate. Figure 1 is a diagram of a spatial band-stop filter comprising of resonant dipole and a spatial band pass filter comprising of slots. For clarity, except for microwave filters, a FSS's frequency response is affected by polarization and incidence angle in addition to frequency [4].

The design of FSS depends on choosing appropriate parameters, as the center frequency is affected by several factors, including polarity response, element shape, and frequency bandwidth in transmission and reflection [5]. A significant care must be taken to select the appropriate element to achieve the desired mutual polarization and bandwidth [6]. The operating range of a FSSs unit cell is determined in the resonant state and depending on the shape, size of the element, and the periodicity of the cell [7]. A common geometry for doubly infinite periodic FSSs in the x−y plane is shown in Figure 2. Their transmission and reflectivity properties are sensitive to the frequency of the electromagnetic field that incident upon them due to their periodic nature. In the vicinity of the element resonance, they usually show a significant reflection [8].

By altering the frequency periodicities along the x, y, or z axes, the frequency response can be managed. To enhance the directivity of the electrically small antenna covered by the FSS, FSS screens are occasionally utilized both above and below the sides of a diffraction grating. This creates a uniform aperture distribution of the near-field [8, 9].

FSSs analysis and design, as well as parameter calculation, are inherently multidisciplinary, necessitating awareness of antenna, electromagnetic theory, and FSS analysis and modeling disciplines. For instance, when a parameter in an FSS is changed, it may have some electromagnetic consequences and thus impact the frequency filtering [10]. Generally, FSS can be engineered utilizing transmission line theory to forecast the intended transmission attributes, and it performs a filtering operation, as the name suggests. Hence, as shown in Figure 3, they are classified on their physical construction into [11, 12]:

- Low-pass FSS filters pass low frequencies.

- High-pass filters pass high frequencies and block low frequencies.

- Stop-band filters reject unwanted frequencies.

- Pass-band filters allow specific frequencies to pass.

Figure 1. Basic Frequency Selective Surface (FSS) configurations: (a) dipole array, (b) slot array, and (c) frequency responses [1]

Figure 2. Regular morphology of a doubly infinite periodic Frequency Selective Surface (FSS) in the x−y plane

Figure 3. A Frequency Selective Surface (FSS) is adopted as a notch filter [11]

Antenna systems leverage FSSs as reconfigurable electromagnetic filters to tailor electromagnetic wave (EM) properties (frequency/polarization), benefiting from their thin profiles and manufacturability [13]. Key implementations comprise:

•   Reflector antenna systems, where FSS reflectors isolate feeds operating in different frequency bands [14].

•   Antenna radomes, which enhance control over transmitted and reflected waves [15].

Additional FSS applications in sixth-generation (6G) networks include interference mitigation, improved channel quality, and enhanced coverage compared to Intelligent Reflection Surfaces (IRS), with emerging use cases such as adaptive spectrum [16] as well as its use in substrate-integrated waveguide (SIW) technology, which was specifically developed for airborne radar dome applications to achieve high selectivity, low input loss, and stable angular performance [17]. Finally, electromagnetic shielding and radar cross-section reduction, where they act as slotted wideband frequency selective reflectors designed specifically for sub-6 GHz 5G devices to achieve wideband reflection performance and angular stability [18].

Modern dual-passband FSSs achieve independently tunable bands by incorporating unit cells with two distinct transmission poles [19]. A miniaturized FSS unit cell was achieved using a meandered or fractal geometry to increase the electrical length within a compact footprint [20]. This design approach ensures polarization insensitivity due to symmetrical geometry and provides angular stability because of the reduced unit cell size relative to the wavelength for Ku-band satellite communication applications. U-shaped resonator with a ground via to generate dual-band responses through multiple resonant modes. The concept relies on the U-shaped structure to provide two distinct electrical paths, enabling independent frequency tuning and polarization selectivity. As a result, the design achieves compact size, stable angular performance, and dual-band operation suitable for wireless communication applications [21], while polarization-insensitive dual-band FSSs deliver EMI shielding using compact unit cells [22]. Despite advances in optimization techniques. Recent studies indicate that dual-band FSS designs can be optimized using advanced algorithms [23]. A graphene-based reconfigurable FSS is introduced for cognitive radio applications [24]. By applying a DC bias voltage, the conductivity of the graphene layer is dynamically tuned, enabling continuous frequency shifting of the resonant response. The design achieves a tunable range of 2.1–5.2 GHz with 10–15% bandwidth and maintains polarization insensitivity and angular stability up to 50°. However, it suffers from high insertion loss and complex fabrication due to the integration of graphene with biasing networks. To address these challenges, further research is needed to optimise the fabrication process and enhance the overall efficiency of the device. Additionally, exploring alternative materials or hybrid systems could potentially reduce insertion loss while maintaining the desired performance characteristics.

This work presents a split-loop topology that supports tunable dual-band resonance at 8 GHz and 18 GHz, achieving a 44% bandwidth, as demonstrated through systematic parametric optimization.

3.1 Simulation results

Simulations were performed using Computer Simulation Technology (CST) Microwave Studio, a comprehensive software package for high-frequency electromagnetic analysis. The simulator employs hexahedral grids with unit cell boundary conditions, as illustrated in Figure 6. For simplicity, the FSS was simulated as an infinite structure using master/slave boundary condition to impose periodic symmetry on the cell's sides, thus ensuring the electromagnetic field repeats as if the matrix were infinite. Floquet ports were used to simulate infinite periodic matrices by modeling a single, unary cell. These ports act as an excitation source for planar waves, enabling the precise calculation of the transmission and reflection coefficients (S21, S11).

A 3 × 3 array configuration minimized edge diffraction effects while maintaining computational efficiency, exhibiting less than 0.5 dB deviation in S-parameters compared to larger arrays (5 × 5). A 3 × 3 matrix is sufficient for modeling performance in a simulation environment to reduce computation time without sacrificing accuracy [13]. The FSS frequency response (band-stop or band-pass) depends on the element shape and type [25]. Figure 7 demonstrates that the split square loop FSS with s = 0 functions as a band-stop filter for varying gr values to understand the behavior of the single band before moving to the dual band. Here, the operating frequency is the resonant frequency (fr).

Figure 6. Computer Simulation Technology (CST) simulation setup with unit cell boundary conditions

Figure 7. (a) Split Square Loop Frequency-Selective Surface (SSL-FSS) with length of SSL legs (s = 0), (b) The effect of varying the Length of gap (gr) between the SSL sides

Signals at frequencies lower or higher than fr are transmitted by the structure's surface, but it also reflects signals at this frequency. In theory, bandwidth (BW) is determined by the difference between lower and upper frequencies at an S-parameter of -10 dB divided by the resonant frequency [26]. Table 2 lists the parameters of SSL FSS as the length of the ring gap (gr).

Table 2. Parameters of Split Square Loop Frequency-Selective Surface (SSL-FSS) with varying the Length of ring gap (gr)

Figure 8 depicts the transmission response dependence on the length of the legs of the SSL element length (s) (all the parameters are unchanged). Variations in leg length (s) directly alter resonant frequencies, inducing dual-band behavior when s > 0. Increase of the length of legs(s) of SSL-FSS leads to decrease resonant frequency, but when (s > 0) there are two resonant frequency appear and meanwhile the bandwidth becomes narrower as illustrate in Table 3.

Figure 8. The effect of varying the length of the legs (s) of Split Square Loop Frequency-Selective Surface (SSL-FSS)

Table 3. Parameters of Split Square Loop Frequency-Selective Surface (SSL-FSS) with varying the length of the legs (s)

Figure 9 depicts the variation in resonant frequency caused by a change in copper width. Except for the element width, all of the parameters remain unchanged. The resonant frequency rises proportionally to the width. The resonant frequency increases as the width increases. Meanwhile, as shown in Table 4, the bandwidth increases.

Table 4. Parameters of Split Square Loop Frequency-Selective Surface (SSL-FSS) with varying the width of the SSL (w)

Figure 9. The impact of changing the copper width

Figure 10 depicts the variation in resonant frequency caused by changes in substrate thickness (n). As the thickness of the substrate increases, the resonant frequency and bandwidth decrease slightly as shown in Table 5.

Figure 10. The impact on modifying the thickness of the substrate

Table 5. Parameters of Split Square Loop Frequency-Selective Surface (SSL-FSS) with varying the substrate thickness (n)

3.2 Analysis for dual-band design

1. Gap Length (gr): Increasing gᵣ raises the first resonant frequency (fr1) but narrows bandwidth due to reduced capacitive coupling (fr $\propto$ 1/√LC) [3, 5]. For dual-band operation, (gr) should be moderate to balance resonances between the two bands. Optimal value (gr = 0.5 mm) balances dual-band performance.

2. Copper Width (w): Increasing (w) increases the resonant frequency (fr1), bandwidth, and supports the second resonance needed for dual-band operation. A higher (w) value facilitates the second resonance appearance. Thicker substrates increase the effective permittivity (εₑff), which lowers (fr $\propto$ 1/√εₑff) and reduces bandwidth due to higher dielectric loss [27]. Preferred (w = 2 mm), because it is permitting broader bandwidth and can be operated in dual-band mode.

3. Substrate Thickness (n): Thickness of substrates decreases resonant frequencies and bandwidth [28]. Both frequency and bandwidth are favored with thin substrates (n = 0.05 mm).

A small increase in (n) decreases resonant frequencies and decreases bandwidth. To operate in dual band mode, thinner substrates are better in order to retain the higher frequency bands and bandwidth [29, 30]. Value (n = 0.05 mm) recommended because it supports a higher resonant frequency.

4. Leg Length (s): As s increases there is a second resonance frequency (fr2). The extra inductance (s) of legs induces a second LC resonance. The structure also acts like two resonators at s = 0 that are coupled to each other (fr1 loop, fr2 leg-dominated path) [8, 31]. As presented in Table 3, with a 2-band mode, with fr1 = 8 GHz and fr2 = 18 GHz, recommended value (s = 3 mm).

Contemporary communication systems demand a high capacity and multifrequency band (dual-band) but existing designs are affected by either sophisticated design or poor performance.

This paper presents an SSL design that has been optimally refined by analyzing four main factors (gᵣ, s, w, n). An “independent control mechanism” uses legs of length (s) to bring about innovation. At s > 0, the architecture becomes a pair of resonators which are coupled together:

◦ The core loop controls the first band (fr1 8 GHz).

◦ The second band (fr2 18 GHz) is due to the extra inductance of the legs (s). This enables the second frequency to be controlled and restricted without greatly impacting the first frequency, thereby being able to overcome the "control deficit."

According to Table 6, this study is outstanding in three ways together:

• Bandwidth: The design had a bandwidth of 44% higher than expected in the table in previous works, with similar designs [16, 18, 21] having a range between 20% and 30%.

• Compactness: The design achieves high performance using a single passive layer. Designs offering wider bandwidth [12] are multi-layered, and those offering flexibility [17] lack dual-band functionality.

• Control: The experiment showed that besides increasing the frequency, the width of the copper (w), is also the secret to a huge increase in bandwidth.

Consequently, this novelty of the research is not just a parametric study but the discovery of the best engineering combination that enables a simple structure (SSL-FSS) to attain a tremendous bandwidth (44%) and the capacity to modulate the frequencies of the two (X and Ku) independently, which previously had to be done with complex or active structures.

Table 6. Comparison to the previous design