In recent years, multiband bandpass filters (BPFs) have attracted considerable interest in modern fast-growing wireless communication technologies, such as GSM (global system for mobile communications), WLAN (wireless local area network) and RFID (radio-frequency identification) systems, because microwave filters are the key element to passing the desired electromagnetic signal and blocking the undesired frequency band signal. For this, multiband bandpass filters with excellent performance—such as high 3 dB roll-off skirts through the generation of transmission zeros (TZs) between the passbands—that are lightweight, low cost, compact size, and have high design flexibility are in strong demand [1–3].

To cope with the development of new era, dual-mode characteristics can be implemented using the step impedance technique, open-short-circuited stubs, substrate integrated waveguide (SIW), SIW with mushroom resonators, and quantic mode resonators [1–16]. For example, a dual-band filter centered at 2.4 GHz and 4 GHz based on a step impedance ring-loaded resonator is modelled in [1]. The presented filter shows a narrow bandwidth for the first passband and a wide bandwidth for the second passband. A drawback of a larger circuit area and poor selectivity is seen by exciting only two TZs between the passbands. A selectivity enhancement method is introduced in [2] using step impedance resonator (SIR) to design a two-band filter; however, the structure fails to reduce insertion loss (IL) and increase fractional bandwidth (FBW), which degrades the overall performance. A low-cost and lightweight SIW-based first-order dual-band filter centered at 1.94 GHz and 4.84 GHz is designed in [3]. The presented structure has a compact circuit area, but greater in-band IL and poor sharpness are observed by introducing two TZs between the passbands. A dual-band filter for Wi-Fi and WLAN applications is modeled in [4] to overcome the drawbacks mentioned in [1–3]; however, the proposed design has a larger circuit area. A first-order dual-band filter with controllable bandwidth and wide stopband is designed in [5]. The filter shows a good FBW, but a complex larger circuit area and poor 3 dB roll-off skirts are the major drawbacks associated with the design. A hexagonal-shaped second-order dual-band filter with a simple topology is designed and fabricated in [6] based on a modified split ring resonator. The presented filter has good IL; however, a larger circuit dimension and poor selectivity degrade the filter performance by introducing two TZs in the passbands. A second-order filter centered at 2.25 GHz and 4.1 GHz is designed in [7], utilizing two mushroom resonators loaded inside in the cavity of SIW. However, the structure has the drawback of poor selectivity and larger circuit dimensions. To overcome the problems of poor sharpness and a larger circuit area in [5–7], a high selectivity first-order dual-band BPF based on the self-coupled resonator is designed in [8]. However, the proposed structure has the drawback of a narrow bandwidth and poor IL, especially in the second passband, which is greater than −3 dB. Second-order dual-band BPFs utilizing dual-mode dual loop resonators and multimode SIW cavity are reported in [9] and [10]. The proposed filters have good sharpness, but a narrow bandwidth, poor in-band ILs, and greater structural dimensions are the major problems related to these designs. A two-passband filter based on magnetically coupled resonators centered at 2.45 GHz and 5.6 GHz is designed and fabricated in [11]. However, the proposed structure has greater ILs and poor selectivity, consisting of only two TZs in the passband. Recently, high selectivity dual-band filters based on quantic-mode resonator and hairpin line resonators have been presented in [12] and [13]; however, the reported filters have poor ILs, narrow FBW, and larger structure size. The authors of [14] designed a second-order dual-band filter with controllable bandwidths at 2.1 GHz and 3.43 GHz based on a quintuple-mode resonator. The presented filter has the advantage of a wider bandwidth, but high IL, poor selectivity, and a larger circuit area are the drawbacks of this filter. A compact dual-band response for Wi-Fi and WLAN applications using SIR and shorted stub-loaded resonators was presented in [15]. The proposed filter has the advantage of high return loss and high selectivity by exciting five TZs near the passbands, but the drawbacks are a larger circuit dimension, a narrow bandwidth, and high in-band losses. Recently, a high selectivity dual-band response at 3.7 GHz and 4.8 GHz using the transversal signal interaction concept was designed in [16]. The proposed design shows good stopband performance by introducing a dozen TZs between 5.2 GHz and 40 GHz. However, the proposed filter has the drawback of high IL, narrow bandwidth in the first passband, and a larger circuit size.

This research designs a compact and lightweight dual-band filter for GSM and GPS (global positioning system) applications to overcome the above challenges. The presented structure is designed on a shorted T-shaped λ/4 resonator. A direct feed resonator provides the first passband and provides the source to load coupling for a higher frequency band internal resonator. The coupled resonators generate a pair of TZs in the passbands, which guarantees high-frequency selectivity. Resonators A and B are folded and connected to a metallic via to minimize the filter size. The key benefit of this design is that it controls all TZs without altering the central frequencies, which is later shown in the paper. A symmetrical arrangement was used to achieve the two passbands, i.e., 850 MHz and 1.57 GHz, using the method of even-odd-mode analysis. The filter was designed and tested for authentication to measure the level of matching between the experimental and measured data.

In total, three stubs exist in the T-shaped resonator, in which two are open ended while the third one is short circuited and can be seen in Fig. 1, where Y₁ is admittance of the open-ended stubs with length L₁, and Y₂ is admittance of the short-ended stub with length L₂.

Since the topology obtained for this structure is symmetrical in nature with respect to plane A-A′, an even-odd mode analysis will be performed for both resonators (i.e., A and B) for characterization of the two passbands. The corresponding circuits of the odd and even modes are depicted in Figs. 2 and 3. For the lower band, outer resonator A is directly fed to achieve source-to-load coupling for the inner one, which is B in our case and which is operating for the higher band. Therefore, the resonance frequency equations of the fundamental even and odd mode can be calculated using the procedure mentioned in [17] and [18] and is given as follows:

In the above equations, c = 3 × 10⁸ m/s and ɛ_eff show the effective permittivity of the substrate material. From Eqs. (1)–(4), the fundamental resonance frequencies can be obtained and are verified in Section IV.

Based on the geometrical study described in the previous section, a dual-band BPF, with a size of 22 × 21 mm² or 0.10 λ_g × 0.99 λ_g, is simulated in the High Frequency Structure Simulator (HFSS) 15 software, designed on the Rogers RO-4350 substrate having a height of 0.762 mm and relative permittivity of 3.66. The filter consists of two quarter-wavelength resonators with dual-mode symmetry. Both resonators are folded to minimize the circuit size. Fig. 4 illustrates the topology of the dual-band filter, and Table 1 sets out the geometric dimensions.

To evaluate the corresponding resonance frequencies of the dual-band filter, the physical length of each resonator is determined using an even-odd-mode method. The first passband is created by resonator A, which is used as the feed mechanism for the internal resonator B working at a higher band. As the dual band filter is based on a quarter wavelength resonator, there are two modes in each passband: one is even, and one is odd. The resonance frequency of the first even mode is 0.90 GHz and is found using Eq. (1) and Fig. 2(a). The fundamental odd-mode frequency (i.e., 0.86 GHz) is found using Eq. (2) and Fig. 2(b). Similarly, Eqs. (3)–(4) and Fig. 3(c)–3(d) are utilized for the even-odd resonant frequencies of the second passband, i.e., f_effen = 1.53 GHz and f_odd = 1.57 GHz. The slight difference in frequencies is due to the resonator coupling, and they are adjusted in the HFSS software to our desired band applications.

As seen in Fig. 5(a), length L₃ is the controlling parameter of the first passband, and by altering, only the first passband is shifted while the second passband is unaffected. Similarly, in Fig. 5(b), length L₆ controls the second passband, and by changing, it will shift only the second band while keeping the first band fixed. Thus, it is confirmed that the proposed filter is capable of independently controlling the two passbands.

The second advantage of the proposed filter is that the transmission zeros on either side of the passbands can be regulated according to the appropriate stopband frequency. As shown in Fig. 6, only the position of TZs is influenced by changing parameter t₁, while the central frequencies remain fixed. This property makes the proposed filter unique compared to other published dual-band BPFs in the existing literature. We generate four transmitting zeros in the following manner. TZ₁ is produced through source-to-load coupling, TZ₃ is the inherent transmission zero, and TZ₂ and TZ₄ are excited with the help of two coupled symmetrical open-ended stubs.

The coupling coefficient (K_e) and external quality factor (Q_ext) is determined using the following equations [18–22];

In Eqs. (5) and (6), K_e denotes the coupling coefficient, Q_ext represents the external quality factor, f₂ and f₁ represent the higher and lower frequencies of each passband, f_c is the central resonance frequency, and B. W_3dB is the absolute bandwidth at central frequency. K_e can be determined by the coupling between the two resonators, while Q_ext could be measured according to the outer resonator and the feedlines. As shown in Figs. 7 and 8, the coupling coefficient decreases as gap G₁ and d₁ increases with an increasing external quality factor [16, 17, 23]. Fig. 9 indicates the relationship between Q_ext and parameter t₁, and by increasing t₁, Q_ext also increases according to Eq. (5). Figs. 7 and 8 present graphical plots of Q_ext and Ke with respect to parameters G₁ and d₁. The figures show that if gap G₁ increases, K_e decreases accordingly, while Q_ext improves in Eqs. (5) and (6).

The proposed technique has been simulated and tested for a compact dual-band BPF. The filter is modelled in the following way. First, the sample is designed in the ANSYS HFSS 15 electromagnetic simulator, and parametric analysis is performed to obtain the required dual-band frequencies. The simulated model is then checked for authentication using the Agilent E5071C network analyzer. In Fig. 10, a significant match can be found between the experimental and fabricated results. For feeding, two 50-Ω feedlines of 1.7 mm width are connected on both sides of the filter. The filter consists of two resonators A and B to control both bands separately. The first operational band is generated by resonator A, which provides the load-to-source coupling for the second resonator, which creates the second passband. For wireless applications such as GSM and GPS, the presented dual-band filter resonates at fundamental frequencies, i.e., 850 MHz and 1.57 GHz. The absolute bandwidth for each passband was 16.84% and 3.5%. A return loss of more than −15 dB was seen for each passband. Four controllable TZs were excited at different frequencies (i.e., 1.04 GHz, 1.16 GHz, 1.82 GHz, and 2.22 GHz) to increase the sharpness and the stop band performance of the filter. For the GSM and GPS frequency bands, the minimum ILs (−20 log|S₂₁|) are 0.98 dB and 1.11 dB, respectively. Moreover, Table 2 provides a detailed comparison datasheet with the most recent published work in terms of IL, FBW, TZs, and circuit area [3–14]. The comparison shows that the presented structure has the potential to compete in the market with existing ones for wireless applications.

In this article, a symmetric T-shaped dual-mode λ/4 resonator is employed for designing a compact dual passband filter for wireless applications such as GSM and GPS systems. The dual-band filter with four controllable transmitting zeros was obtained using λ/4 wavelength (A and B) resonators. The fabricated filter has a total size of 22 × 21 mm² independent of the feedline. Finally, the filter has been fabricated to check the simulated results with the measured one. Owing to the planar structure, low losses, and compact size, the designed filter has good integration ability in the existing emerging wireless multiband applications.