Bandwidth deficiency is a major challenge because of the exponential rise in data usage and transmission on wireless devices and multimedia applications [1]. Frequencies ranging from 300 MHz to 3 GHz (ultra-high-frequency band) are widely used in television, cellular global positioning system, Zigbee/Bluetooth, radio, and satellite communications. The wide spectrum in the 3–300 GHz range remains unoccupied, referred to as the millimeter-wave band [2], which supports the promising demand for services based on the spectrum. This unoccupied spectrum fascinates researchers’ attention worldwide, resulting in explorations of the millimeter-wave frequency band to overcome the global bandwidth shortage [1]. A millimeter-wave communication system is capable of accommodating a larger bandwidth, which can be directly translated into a higher data transfer rate of up to multiple gigabits per second [2–4]. The usage of the 24.25–86 GHz millimeter-wave band has been considered a 5G spectrum. Hence, the millimeter-wave communication technique is recognized as a feasible technology that can be used as the backbone to satisfy and support the demand for services based on the spectrum for next-generation 5G applications.

Filters are one of the most significant devices that play a vital role in wireless communications. The major problem with filter designs is that the passband insertion loss is inversely related to the filter bandwidth. To realize the design of a compact, sharp filter with a low passband insertion loss useful for narrowband applications becomes challenging at high frequencies.

Many techniques are used to realize bandpass filters at higher 5G frequencies to satisfy the present scenario demands. For example, metal cavity-type bandpass filters are used for millimeter-wave bandpass filters [5], and with the advantage of easy integration to a printed circuit board, substrate integrated waveguide filters have been expanding their application [6]. However, the former type is too large, and the latter is insufficient in terms of electrical performance. A bandpass filters at 28 GHz frequency are designed, taking advantage of hybrid architecture planar/non-radiative dielectric waveguide technology, although the size of the filter is large [7]. Bandpass filter using a quartz crystal waveguide in a 28-GHz band was proposed in [8], taking advantage of temperature stability and power durability, but the size is also large. Waveguide topology has been used to design a dual bandpass filter at 26 GHz and 28 GHz, taking advantage of specifying bandwidths accurately for each passband and its inner band frequency selection provided by the chained response method; however, the problem remains the large size for millimeter-wave communications [9]. Bandpass filters are designed using a broadside coupled meander line resonator with a defective ground structure, taking advantage of small size using on-chip technology, although with a high fabrication cost [10].

Some of the filter structures that apply coupled transmission lines act as coupled resonators. Researchers are taking advantage of coupled resonator theory to design new models of coupled transmission lines [11]. Metamaterial structures can exhibit novel electromagnetic properties at microwave and millimeter-wave frequencies that cannot be obtained using conventional materials. By employing metamaterial units, it is possible to achieve extensive miniaturization in filters based on coupled resonators [12].

Based on this background, we designed a novel, compact, and simple dual bandpass filter using a dual split ring resonator as a metamaterial structure coupled to the microstrip transmission line on Rogers RT/Duroid 4003C substrate material at millimeter-wave frequencies useful for higher 5G upper microwave flexible use services.

A dual-split rings resonator was designed, and dimensions were optimized to obtain better performance of the bandpass filter by following the metamaterial structure homogeneity condition of a unit cell size less than one-fourth of the guided wavelength (Fig. 1). The dimensions of the dual-split ring resonator are shown in Table 1.

The feed lines were designed to match the 50-Ω microstrip transmission lines. The feed lines had a width of 0.825 mm. The dual-split rings resonator filter was designed on Rogers RT/Duroid 4003C substrate material with a relative permittivity of 3.55 and a thickness of 0.813 mm. The length and width of the dual-split ring resonator filter were 14 mm and 10.75 mm, respectively. The proposed dual-split ring resonator filter layout is shown in Fig. 2. Two dual-split ring resonators were coupled along the transmission line and resonated at two resonant frequencies (also called eigenfrequencies). The strength of coupling is expressed using the coupling coefficient, which can be calculated from the following formula [11]:

where f₁ and f₂ are the coupled resonance resonant frequencies. The resonant frequencies can be observed in electromagnetic simulations. The resonant frequencies can be calculated by analyzing half of the coupled resonator structure with the perfect electric or magnetic wall introduced in the symmetry plane. Depending on the type of coupling, the eigenfrequency f₁ can be lower or higher than f₂. Let us assume that the electric type of coupling results in f₂ > f₁ and that the magnetic type of coupling produces a reverse relation between eigenfrequencies. For this study, we assume that f₂ > f₁. Then, formula (1) can be written without an absolute value sign.

After a simple transformation, Eq. (1) becomes

where g means the function, which is the same for any coupled resonator. Thus, one can state that the coupling coefficient depends on the ratio between resonant frequencies.

Both dual-slit ring resonators had maximum electric field density at the sides with open gaps at resonance. Given that the fringe field exhibits an exponentially decaying character outside the region, the electric fringe field is stronger near the side with the maximum electric field distribution. Electric coupling can be obtained if the open sides of the two coupled resonators are placed proximately. The coupling between resonators is proximity coupling, which occurs through fringe fields. The nature and expansion of the fringe fields determine the nature and strength of the coupling.

The lumped element equivalent circuit of the proposed dual split ring resonator dual band-pass filter is shown in Fig. 3.

The T-circuit of L₁/2, L₂/2, and 2C₁ and 2C₂ represents the transmission line on each side. L₃C₃, L₄C₄, L₅C₅, L₆C₆ resonators represent equivalent dual split rings resonators. The coupling of transmission lines and resonators is represented using C₇ and C₈ and Inductance is represented using L₇ and L₈. Open slit gaps are represented using C₉, C₁₀, C₁₁, and C₁₂. The coupling gaps are represented using C_13, C₁₄. Mutual inductance between coupling gaps is represented using L₁₃ and L₁₄. Inductance and mutual inductance due to a T-shaped patch between open slits of proximately coupled resonators are represented using L₁₅, L₁₆, M₁₅, and M₁₆.

The equivalent lumped element values of the proposed dual split rings resonator dual bandpass filter were L₁ = L₂ = 0.0004 nH, C₁ = C₂ = 0.0375 pF, L₃ = L₄ = L₅ = L₆ = 0.8 nH, C₃ = C₄ = C₅ = C₆ = 0.02115 pF, C₇ = C₈ = 0.029 pF, L₇ = L₈ = 0.85 nH, C₉ = C₁₀ = C₁₁ = C₁₂ = 0.02115 pF, L₁₃ = L₁₄ = 1.9 nH, C₁₃ = C₁₄ = 0.008 pF, L₁₅ = L₁₆ = 0.65 nH, and M₁₅ = M₁₆ = 0.707 nH.

The proposed dual-split ring resonator dual bandpass filter was simulated using the HFSS simulator (ANSYS Inc., Canonsburg, PA, USA) and the finite element method. The equivalent circuit of the proposed dual-split ring resonator dual bandpass filter was simulated using an AWR design environment (Cadence Design Systems Inc., San Jose, CA, USA). The comparison of S-parameters S₁₁, S₂₁, S₂₂, S₁₂ for HFSS simulation and lumped element equivalent circuits are shown in Figs. 4 and 5. The proposed design resonated in the frequency range from 23.6 to 25.6 GHz and 27.9 to 28.25 GHz using an HFSS simulation. The frequency of the lumped equivalent circuit ranged from 23.8–24.35 GHz and 27.7–28.2 GHz. The center frequencies were 24.6 GHz and 28 GHz, respectively, for the HFSS simulation and 24.075 GHz and 27.95 GHz for equivalent circuits. The fractional bandwidth of the proposed design was 8.1% and 1.1% for both bands, respectively, using the HFSS simulation and 2.28% and 1.78% using the AWR simulation. The insertion loss was less than 1 dB in both bands for the HFSS simulation and less than 0.5 dB in the AWR simulation for lumped element equivalent circuits.

The proposed dual-split ring resonator dual bandpass filter was fabricated and measured to validate its performance using the network analyzer N5222A. The fabricated prototypes of the proposed dual-split ring resonator dual bandpass filter are shown in Figs. 6–8. The comparison of S-parameters S₁₁, S₂₁, S₂₂, S₁₂ for HFSS simulation and measurement are shown in Figs. 9 and 10. The proposed design resonated in the frequency range of 23.6–25.6 GHz and 27.9–28.25 GHz using HFSS simulation. The frequency range for the measurement results was 23.8–25.98 GHz and 28.05–28.7 GHz. The center frequencies were between 24.6 GHz and 28 GHz, for the HFSS simulation, and 24.79 GHz and 28.37 GHz with the measurement. The fractional bandwidth of the proposed design was 8.1% and 1.1% for first band and second band respectively, using HFSS simulation. The fractional bandwidth of the proposed design was 8.8% and 2.2% for first band and second band, respectively, with the measurement. The insertion loss was less than 1 dB in both bands for the HFSS simulation and less than 4.2 dB for the measurement results.

Due to the use of proximity coupling for microstrip dual-split ring resonator dual bandpass filters, insertion loss with less than 4.2 dB was observed even at higher frequencies. The main design occupies the area of 2.6 mm × 1.8 mm, which is 0.4λ_g × 0.27λ_g, where λ_g is the guided wavelength at a center frequency of the first band. The overall circuit size of the filter was 14 mm × 10.75 mm. From the comparison in Table 2 [6–11, 13, 14], we can conclude that the proposed design is compact, and dual bands can be observed using microstrip technology, which is compact and economically feasible.

A novel, simple, and compact dual bandpass filter was designed using dual-slit ring metamaterial resonator structures by proximately coupling along the microstrip transmission line. The proposed filter centered at two resonant frequencies, 24.79 GHz and 28.37 GHz, is useful for terrestrial wireless operations, fixed-satellite service earth stations, and mobile communications. A minimum insertion loss of 4.2 dB was obtained in the overall passband for both bands, even at a higher 5G band, using Microstrip Technology. Thus, our proposed dual split ring resonator dual bandpass filter had good performance characteristics.

Future studies can fabricate the prototype of this filter using additive manufacturing, which can improve the design freedom and productivity of compact designs required at the millimeter-wave frequencies, offering more time and cost savings.