I. INTRODUCTION
In modern wireless communication systems, bandpass filter (BPF) with miniaturized dimensions, minimum insertion loss, and enhanced selectivity is highly desirable and challenging constraints. Extensive research works and several techniques have been reported in the literatures to meet these requirements. The design of dual-band filters employing the conventional stepped-impedance resonator (SIR) has become a popular approach [Reference Zhang and Zhu1–Reference Weng, Wu and Su4]. The resulting dual-band behavior can easily control the second passband frequency by varying the impedance ratio and electrical lengths of SIR. Furthermore, the design of dual-band BPFs based on modified and open stub loaded SIRs has also been reported in [Reference Mo, Song, Tao and Fan5–Reference Chu and Chen7]. Compact dual-band BPFs with high selectivity have also been designed using the quadruple mode (QMR) [Reference Gao and Zhang8–Reference Xu, Wu and Miao11]. Spiral resonators have been adopted to realize compact dual-band BPFs [Reference Xu, Wei, Cao, Guo, Zhang, Heng, Jiang, Zheng and Wang12, Reference Luo, Jin, Sun and Li13].
On the other hand, the conventional SRRs and complementary split-ring resonators (CSRRs) have been reported in [Reference Aznar-Ballesta, Garcia-Perez, Gonzalez-Posadas and Segovia-Vargas14–Reference Liu, Fan, Zhang, Zhao, Xu, Guan, Sun and He20] to design compact bandpass filters and microwave planar circuits. A defected ground structure (DGS) based on Hilbert fractal curve has been used in the design of a microstrip lowpass filter operating at the L-band microwave frequency [Reference Chen, Weng, Jiao and Zhang21]. The Sierpinski fractal geometry has been used in the implementation of a CSRR [Reference Crnojevic-Bengin, Radonic and Jokanovic22]; where split-ring geometry using square Sierpinski fractal curve has been proposed to reduce the resonant frequency of the structure and achieve improved frequency selectivity in the resonator performance. It has also been reported that Minkowski, Koch, and Peano fractal geometries have been successfully applied to the conventional square ring resonators to produce high-performance miniaturized dual-mode microstrip BPFs [Reference Ali23–Reference Ali, Alsaedi, Hasan and Hammas25]. Sierpinski fractal curve has also been applied to design a dual-mode microstrip BPF based on the conventional square patch [Reference Weng, Lee, Yang, Wu and Liu26]. Recently, other fractal geometries have also been applied in the design of miniaturized dual-band dual-mode BPFs [Reference Ahmed27, Reference Liu, Liu, Yeh, Liu, Zeng and Chen28].
Furthermore, split-ring resonators (SSRs), CSRRs, and complementary single split-ring resonators (CSSRRs) have been adopted in the design of BPFs and band reject filters. On the basis of complementary split-ring resonator (CSRR) using Koch fractal curve, a bandpass filter based on such a structure is designed [Reference Li, Wang, Lu, Xu, Liao and Zong29]. Hilbert fractal geometry has been applied as a DGS to produce miniaturized fractal spiral resonators [Reference Palandoken and Henke30]. A comprehensive study of the effects of the conventional SRRs and CSRRs on their resonant frequencies has been reported in [Reference Solymar and Shamonina31]. It has been concluded that the resonant frequency is predominantly determined by the rings dimensions, the inter-ring separation, and the rings gap widths, since the CSRR self and mutual inductances and capacitance are highly attributed by these parameters. However, smaller split rings have higher resonant frequencies.
In this paper, a compact dual-mode dual-band microstrip BPF is introduced. The ground plane of the proposed filter has been defected using fractal-based CSRR. The inner ring of the conventional square CSRR has been modified by applying Minkowski-like pre-fractal curve to its sides. This results in more compact microstrip BPFs with dual passbands. Higher resonant band is attributed to the dual-mode ring structure, while the other is a result of the embedded CSRR structure in the filter ground plane. The application of different iteration levels to the inner ring results in filter responses with different resonant frequency ratios. Measured results carried out on fabricated filter prototypes, corresponding to different iteration levels, are in good agreement with those theoretically predicted.
II. THE FILTER STRUCTURE
The structure of the proposed filter consists of two parts; the first part is the conventional microstrip dual-mode BPF configuration, which constitutes the upper side of the whole structure, whereas the second part represents the proposed CSRR as a DGS in the ground plane. In this paper, the Minkowski-like pre-fractal geometry has been applied to both parts. Figure 1 demonstrates the generation process of the Minkowski-like pre-fractal geometry as applied to a squared shape ring.
Fig. 1. The generation process of the Minkowski-like pre-fractal structure: (a) the generator, (b) the square ring, (c) the first iteration, and (d) the second iteration [23].
For simplicity, the same fractal geometry has been applied to both the dual-mode resonator filter and CSRRs DGS. It has been shown that shape modification of the structure depicted in Figs. 1(c) and 1(d) are ways to increase the surface current path length compared with that of the conventional square ring resonator; resulting in a reduced resonant frequency or a reduced resonator size, if the design frequency is to be maintained [Reference Ali23]. For the nth iteration, the Minkowski-like pre-fractal structures depicted in Figs. 1(c) and 1(d) have been found to have the perimeters given by [Reference Ali23, Reference Lee, Soh, Hashim, Vandenbosch, Volski, Adam, Mirza and Aziz32, Reference Alqaisy, Ali, Chakrabarty and Hock33]

where P n is the perimeter of the nth iteration pre-fractal structure, and w 2 and L 0 are as depicted in Fig. 1. Equation (1) and Fig. 1 imply that, at certain iteration level, a wide variety of structures with different perimeters can be obtained by varying w 1, w 2, or both.
It is expected then that further miniaturization can be achieved when applying fractal geometries to the conventional square CSRR. This means that higher iterations will result in further miniaturization possibility owing to its extra space filling property. The increase in length decreases the required volume occupied for the pre-fractal bandpass filter at resonance. Theoretically, as n goes to infinity the perimeter goes to infinity. The ability of the resulting structure to increase its perimeter in the successive iterations was found very triggering for examining its size reduction capability as a microstrip bandpass filter. It should be reminded again that the same fractal has been applied to the dual-mode ring resonator (on the top of the filter structure) and the CSRR in the ground plane (on the bottom of the filter structure). However, this does not prevent the possibility to use other types of space filling fractal curves for the same task.
III. THE FILTER DESIGN
It is worth to mention here that, a dual-mode fractal-based ring resonator, as shown in Fig. 2(a), has been adopted by one of the authors to produce a miniaturized dual-mode microstrip BPF [Reference Ali23], where the Minkowski-like fractal geometry has been applied for this purpose. In this paper, the same dual-mode filter structure is recalled again. What is new here is that the filter ground plane is perforated with fractal-based CSRRs shown in Figs. 1(c) and 1(d) in an attempt to produce a miniaturized dual-band dual-mode BPF. Figure 2 demonstrates the details of the proposed filter structure. The top view of this structure, Fig. 2(a), represents the dual-mode BPF with the associated input/output feed lines. The ring resonator of this filter has the structure corresponding to the second iteration Minkowski pre-fractal geometry. The bottom views, Figs. 2(b) and 2(c), show the fractal-based CSRR structures corresponding to the first and second iterations Minkowski pre-fractal geometry that have to be embedded in the proposed filter ground plane.
Fig. 2. The proposed microstrip dual-band dual-mode BPF structure: (a) the dual-mode fractal-based ring structure (top view), (b) and (c) CSRRs with Minkowski fractal-shaped inner ring of the first and second iterations, respectively (bottom views).
The first step, the filter structure of Fig. 2(a) has been designed for the ISM band applications at 2.45 GHz with its ground plane not defected. The filter structure has been etched using a substrate with a relative permittivity of 2.2 and thickness of 0.787 mm. The input/output ports have characteristic impedances of 50 Ω. This corresponds to a transmission line width of about 1.12 mm. At resonance, the dual-mode resonator side length is found to be equal to 13.52 mm with the ratios of w 1/L 0 and w 2/L 0 of about 0.1 and 0.34, respectively.
Based on this filter, two other filters with their ground planes being defected with CSRRs fractal structures corresponding to those depicted in Figs. 2(b) and 2(c) have been modeled using the prescribed substrate. As these structures imply, the inner split rings are in the form of Minkowski-like fractal geometry of the first and second iterations, respectively. In both cases, the dimensions of the CSRR are such that the side length of the outer ring is approximately equal to that of the dual-mode resonator. The corresponding inner fractal-shaped rings are scaled such that the inter-ring separations between the outer and the inner rings are found to be 0.65 and 0.37 mm to achieve the required coupling. The gaps in the two split rings, for the two iterations, have been made equal to about 0.65 and 0.55 mm, respectively to reach the specified performance.
IV. PERFORMANCE EVALUATION
The filter structure, depicted in Fig. 2(a) with no CSRR in its ground plane, has been modeled and analyzed at the design frequency, using the commercially available EM simulator, CST Microwave Studio [34]. The dual-mode resonator side length is found to be equal to 13.52 mm at resonance. This length represents about 0.11 the guided wavelength, λg, which is given by

where εeff is the effective dielectric constant and can be calculated by empirical expressions reported in the literature [Reference Pozar35]. For the present case, λg has been found to be 89.35 mm at the design frequency. Figure 3 shows a photo of a prototype of this filter fabricated with mentioned dimensions and substrate parameters. Measured and simulated return loss and transmission responses offered by this filter are shown in Fig. 4.
Fig. 3. A photo of the dual-mode microstrip filter prototype based on Fig. 2(a) without CSRR DGS.
Fig. 4. Measured and simulated return loss and transmission responses of the filter shown in Fig. 3.
The bottom right of the fractal-based filter depicted in Fig. 3 has been modified to introduce a dissymmetry in the resonator structure. This dissymmetry is important because it makes possible controlling the coupling between the filter two orthogonal modes [Reference Ali23]. This topology introduces two transmission zeros, one on each side of the passband; enhancing the selectivity of the filter as shown in Fig. 4. This filter is therefore a second order with two transmission zeros. The equivalent circuit of this filter is composed of two similar LC sections connected in cascade; with input and output couplings. Each LC section represents a resonant mode of the dual-mode filter. The input coupling produces the transmission zero on the left side of the passband, whereas the output coupling creates the transmission zero on the right side of the passband. The positions of the transmission zeros can be controlled by varying the input/output coupling. The transmission zero frequency on the left side of the passband can be controlled by varying the input coupling without changing the position of the transmission zero on the right side of the passband and vice versa.
Results shown in Fig. 4 imply that the filter offers good return loss response with an in band level of more than −20 dB, and a transmission response with two transmission zeros almost symmetrically located around the design frequency and an out of the band response of more than −25 dB. In addition, measured and simulated results are in good agreement.
Moreover, two other BPF filters have been designed; both with the same dual-mode resonator depicted in Fig. 3. The first filter has the CSRR DGS structure based on the first iteration Minkowski-like fractal geometry as shown in Fig. 2(b), whereas the other filter has the CSRR DGS shown in Fig. 2(c) which is based on the second iteration of the same fractal geometry. Figure 2 demonstrates the dimensions of the simulated filters. Detailed dimensions of the dual-mode resonator, which is the same for the three filters, are depicted in Fig. 2(a). The details of CSRRs of the filters with DGS of the first and second iterations are shown in Figs. 2(b) and 2(c), respectively.
In this context, the topology of the introduced CSRR DGS has an equivalent circuit model composed of parallel combination of the ring inductance L r and ring capacitance C r in series with a coupling capacitance C r [Reference Wu, Mu, Dai and Jiao19]. It is expected then, that the filter structure will have a third transmission zero. The position of this transmission zero is given by the frequency that nulls the shunt impedance as follows:

The prototype photo of the first filter is shown in Fig. 5. The corresponding measured and simulated results of return loss and transmission responses offered by this filters are shown in Fig. 6. As it is implied in this figure, the upper resonant band which is attributed by the dual-mode structure is maintained; as if this resonator performs alone regardless of the existence of the CSRR DGS. The effect of the embedded CSRR DGS is assured by the appearance of the lower resonant bands. There is no such a resonant band associated with the response of the filter with non-defected ground plane. Higher fractal iteration level of the CSRR leads reduced lower resonant frequency, and consequently, makes the filter gains further miniaturization or, in other word, provides the designer with a practically useful means to tune the resulting filter response to the specified frequencies.
Fig. 5. Photos of the fabricated filter prototype with its CSRR DGS structure is based on the first iteration Minkowski-like fractal geometry: (a) top view and (b) bottom view.
Fig. 6. Measured and simulated return loss and transmission responses of the filter depicted in Fig. 5.
This is confirmed by the other filter shown in Fig. 7, where its CSRR DGS structure is based on the second iteration Minkowski-like fractal geometry. The corresponding measured and simulated return loss and transmission responses of this filter are shown in Fig. 8. Here, it has been noted again that the upper resonant band is almost maintained unchanged, as compared with those observed in Figs. 4 and 6 for the filters without CSRR DGS and first iteration fractal-based CSRR DGS shown in Figs. 3 and 5, respectively. On the other hand, the lower resonant frequency of this filter is lower than that produced by the filters with first iteration fractal-based CSRR DGS shown in Fig. 5. This is, of course, due to the extra length provided by the second iteration fractal structure compared with that provided by the CSRR DGS based on the first iteration fractal structure, as equation (2) implies.
Fig. 7. Photos of the fabricated filter prototype with its CSRR DGS structure is based on the second iteration Minkowski-like fractal geometry: (a) top view and (b) bottom view.
Fig. 8. Measured and simulated return loss and transmission responses of the filter shown in Fig. 7.
In this respect, more miniaturization could be obtained when using higher iteration levels as long as fabrication tolerances permit [Reference Ali and Hussain36]. Furthermore, as Fig. 1 implies, varying the ratios of w 1/L 0 and w 2/L 0 will lead to different values of the inner split-ring perimeters, which in turn result in a wide range of the lower resonant frequencies. The lower resonating bands as a result of the CSRRs depicted in Figs. 2(b) and 2(c) are 1.81 and 1.45 GHz, respectively. These are equivalent to size reductions, in terms of the corresponding guided wavelengths, of about 0.12 and 0.09λg, respectively. For the sake of comparison, the measured and simulated return loss and transmission responses of the three presented filters are summarized in Figs. 9 and 10, respectively.
The ratio of the lower resonant frequencies attributed by the split rings depicted in Figs. 2(b) and 2(c) is equal to 1.25 which is very close to the ratio of their corresponding perimeters, 1.42 as calculated using equation (1). This ratio becomes closer, 1.33, if the slight change in the guided wavelength is to be taken into account. This interesting result indicates that increasing the perimeter of the inner split ring, due to the higher fractal iteration level, results in lowering the CSRR resonant frequency. Based on this, for different values of w 1 and w 2, Fig. 3(a), a wide range of the inner split-ring perimeters will result in. It is then expected to design dual-band filters with fixed higher frequency and wide range of lower resonant frequencies. Consequently, this indicates that using inner split rings with structures based on fractal geometries having higher space-filling properties such as Hilbert and Peano fractal curves will result in lower resonant frequencies.
Figure 11 shows the surface current distribution on the top and the bottom of the filter structure at the centers of the two passbands. It is clear again that the two resonating bands are independent of each other; in Fig. 11(a), the surface current density on the surface of the dual-mode structure is high at the upper band, whereas it approaches zero at the lower band. The reverse is true in Fig. 11(b), for the surface current density on the bottom ground plane. It is worth to note that the same color scale is adopted for all figures.
Fig. 11. Simulated surface current distributions at the lower and the upper passbands on (a) the dual-mode ring on the top structure and (b) bottom of the ground plane containing the CSRR.
V. CONCLUSION
A compact dual-band dual-mode microstrip BPF has been presented in this paper, where two miniaturization techniques have been simultaneously applied to construct it. These include the use of the conventional dual-mode square ring resonator together with the application of a fractal-based CSRR as a DGS in the filter ground plane. Measured and simulation results show that the proposed filter offers a transmission response with two passbands; the first one is that originally produced by the dual-mode ring resonator and the other is a result of the DGS. The lower passband is that attributed by the CSRR, which means that the CSRR provides further miniaturization besides that conventionally produced by the dual-mode ring resonator. Furthermore, results show that two bands are independently produced.
Moreover, measured results carried out on three filter prototypes corresponding to different fractal iterations of the CSRR DGS, confirmed that the application of higher fractal iteration levels results in further miniaturization. Depending on limitations imposed by the fabrication technique adopted to produce the filter prototype, more miniaturization could be achieved. The proposed filter design technique can be generalized to include other types of dual-mode BPFs to provide a suitable means of adding further resonant bands of these filters while maintaining their original sizes unchanged.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the Center for Radiofrequency and Microwave Engineering, University Tenaga National for its financial support for the research. Also, they would like to express their thanks to the head of Microwave Research Group, University of Technology, Iraq for the valuable discussions and support, and also wish to thank the reviewers for their useful and constructive comments.
Mushtaq Alqaisy was born in Baghdad, Iraq in June 1971. He received his B.Sc. and M.Sc. degrees in Electrical Engineering/Communication Engineering from Al-Rasheed College for Science and Technology, Iraq in 1996 and 2005, respectively. He is currently working toward his Ph.D. degree in Microwave Communication Engineering in the faculty of graduated study, Tenaga National University. His research interests include the analysis and design of microwave passive circuits. He is a student member of IEEE.
Chandan Chakrabraty was born in Malaysia. He received the Bachelor of Science (Hon.), Physics in 1986 and Master of Science, majoring in Plasma Physics in 1989 from University of Malaya and Ph.D. in Radiofrequency Plasma in 1996 from Flinders University of South Australia. He is currently involved in the research of developing ultra-wideband antennas for partial discharge detections in MV and HV underground cables, meta-materials microwave antenna and filters, and FPGA-based partial discharge location and detection system for power distribution assets. He is currently a Professor in the Electronics and Communications Engineering Department at University Tenaga Nasional and also the Head of the Research Center for Radiofrequency and Microwave engineering.
Jawad Ali was born in Baghdad, Iraq in November 1956. He received his B.Sc. and M.Sc. degrees in 1979 and 1986, respectively from Al-Rasheed College for Science and Technology, Iraq. From 1989 to 1991, he joined a Ph.D. study program at AZMA Academy, Brno, former Czechoslovakia. Since 2010, he has been a Professor at the University of Technology, Iraq. Currently, he is the Deputy Dean for postgraduate studies and scientific affairs at the Department of Electrical Engineering. His fields of interests are microwave antenna miniaturization and design, and passive microwave circuits design. He has more than 80 published papers in local and international conferences and peer-reviewed journals. Prof. Ali is a member of IEEE and IET.
Adam R. H. Alhawari was born in Jordan. He acquired the B.Sc. degree in Communication Engineering from Hijjawi Faculty for Engineering Technology of Yarmouk University, Jordan in 2003. He had an internship program done for couple of months in Cairo, Egypt for Industrial Training of his B.Sc. Meanwhile the M.Sc. and the Ph.D. degrees were both pursued later in 2009 and 2012, respectively, in Wireless Communications Engineering from Universiti Putra Malaysia, Malaysia. That was after a double 2-year duration working in Jordan and then Saudi Arabia. Currently, he is a Senior Lecturer at the Department of Computer and Communication Systems Engineering, Universiti Putra Malaysia since December 2012. His main research interests are in metamaterial antennas, microwave absorbers, and RFID.