Design of a compact UWB BPF with a Fractal Tree Stub Loaded Multimode Resonator

Pankaj Sarkar, ECE Department, School of Technology, North Eastern Hill University, Shillong – 793022, Meghalaya, India. Email: pankajsarkar111@gmail.com Abstract This paper presents a novel technique to design an ultra‐wideband bandpass filter (UWB BPF) based on fractal tree stub loaded multimode resonators. Two different topologies are opted to verify the relationships between resonant modes of the multimode resonators with different parameters of the fractal tree stub. UWB bandwidth is acquired by increasing iterations of the fractal tree without a significant effect on the filter's physical size. The proposed topologies provide design flexibility in terms of resonance and bandwidth, which are directly related to the iteration order of the fractal tree used. To verify all the features of fractal‐tree‐based UWB BPF, the proposed UWB BPF is parametrically studied using electromagnetic simulation, and a prototype is fabricated. The measured and simulated results are in close agreement. The actual size of the filters is 11.5 � 9.6 mm. The proposed filter covers the whole band of UWB with a minimum insertion loss of 1 dB and return loss is better than 10 dB. The measured stopband extends up to 16 GHz.


| INTRODUCTION
In wireless communication systems, ultra-wideband (UWB) communication systems create enormous opportunities to have successful transmission of high-speed data, over a short range, due to the availability of a large bandwidth. UWB communication systems could be realised since Federal Communications Commission granted permission to use UWB (3.1-10.6 GHz) for data communication as well as for radar and surveillance applications [1][2][3].
The competence of a UWB system is highly governed by the efficiency of the UWB bandpass filter (BPF) that tremendously assists the front-end subsystems to selectively process the desired band and segregate the undesired frequencies. Beyond the high-performance filtering characteristics, modern UWB BPF demands a high level of circuit miniaturisation to integrate with a compact UWB system. Fractal geometries have been accepted as a viable design approach for this purpose due to their space-filling and self-similarity properties. Fractals are also named as 'space-filling contours' as electrically big structures can be efficiently confined in small areas [4]. The electrical length is one of the most important parameters in the microwave circuit design paradigm. Therefore, the efficient packing of large structures into small areas can be a feasible solution for the miniaturisation technique.
Erstwhile, UWB BPF has been designed using a stepped impedance resonator (SIR) as a multimode resonator (MMR) [5]. Subsequently, numerous works related to stub loaded MMR-based UWB BPFs have been explored in [6][7][8][9][10]. The input/output coupling mechanism in most of the reported works incorporate slots in the ground that introduces circuit mounting constraints. Further investigations have been reported on the use of stub-loaded MMR-based UWB BPF in [11][12][13][14][15][16][17]. A UWB BPF with quintuple mode is presented in [11]. It comprises asymmetric parallel-coupled lines (APCL) loaded with five open stubs and one shorted stub. Defected ground structure (DGS) is also used to improve the coupling between APCL. A compact UWB BPF is reported in [12], which comprises Koch-island-shaped stepped impedance lines and a composite right/left-handed transmission line. An MMR-based UWB BPF consisting of a pair of open-circuited stubs and three pairs of coupling sections to obtain the desired resonant modes is presented in [13]. UWB BPF with dual-stub loaded resonator is reported in [14]. One of the stubs is shortcircuited and the other one is open-circuited. All the desired resonant modes are placed in the UWB range by simply tuning the lengths of both stubs. A multi-stub loaded ring resonator based UWB BPF is reported in [15]. To improve the external coupling, the parallel-coupled lines are used with DGS. Rectangular stub resonator is also explored in this realm to get the desired response [16]. A UWB BPF with a pair of shorted parallel-coupled lines and open parallel-coupled lines in conjunction with a transverse transmission line is investigated in [17]. It is observed that the quest for more transmission poles, to achieve the desired passband for UWB systems, has resulted in the inclusion of more number of stubs in case of stub-loaded MMRs or addition of more resonators in conjunction to a stub-loaded MMR system.
In this work, a novel stub-loaded resonator-based UWB BPF is proposed, which introduces a suitable number of transmission poles with a single-iterated stub structure that has space-filling characteristics. The shape of the stub is implemented with the fractal tree structure to design a compact UWB BPF. The proposed filter structure comprises three iterations of the fractal tree-shaped stub attached with the uniform impedance resonator (UIR). The UWB filter is designed on an FR4 substrate with a height of 1 mm and relative permittivity 4.4.
The fractal geometry, which is used here as a stub, is termed as fractal canopies [18,19]. It is different from other fractal tree geometries because of the sense in its branching nature, which translates to variation in its resonance performance by inclusion of multiple modes, which can be controlled by tuning the geometrical design parameters. This fractal tree is called a binary tree because the branches are flared in two separate directions with different iterations, flare angles as well as dissimilar length ratio between the stem and the branch. These are indicated in Figures 1-3, respectively. This fractal tree is used as a stub to load a UIR resulting in an MMR for designing a UWB BPF.
The rest of the paper is organised as follows. Section 2 describes the development of fractal binary tree. The design of fractal tree stub-loaded MMR structure is analysed and studied in Section 3. The proposed UWB BPF is presented in Section 4.

| DEVELOPMENT OF FRACTAL BINARY TREE
The fractal binary tree opted here is used as a stub that is loaded on a UIR resulting in an MMR. The resonance behaviour of the MMR is investigated to determine the structural dimensions of the binary tree fractal topology. Therefore, two different topologies are adopted here to verify the above fact. The design starts with a stem to create a fractal binary tree, and then it splits into two separate directions with a certain angle θ. For every iteration, the same angle θ is maintained for all iterations. For the first topology, the stem width is kept different for each branch of a given iteration by incorporating a stem width ratio, S i w , of 0.5. In the second topology, the stem width is kept the same throughout the iteration. This new topology is adopted as a stub loaded on a UIR in creating multimode resonances. For both the binary tree topologies, the stem-to-branch-length ratio, also called the scale factor δ s , is changed to tune the resonator characteristics.
The above-mentioned combinations of fractal-tree-shaped stubs are investigated up to the third iteration for a given S i w , as illustrated in Figure 4.

| DESIGN OF FRACTAL TREE STUB-LOADED MMR
In this section, the topological dimensions of the binary fractal tree stub, loaded on to the UIR, are investigated using its transmission line model. To obtain the resonance modes, an in-house MATLAB™ code is developed for the even-and odd-mode analysis of the proposed fractal-shaped MMR. To accomplish this, the scale factor δ s and stem-to-branch-width ratio S i w are translated to electrical parameters like electrical lengths of the binary tree segments as well as the impedance of the stem and branches as indicated in Figure 5(a). This is done using a separate code that synthesises the electrical lengths and impedances [20] from the dimension ratios of the lengths and widths of the transmission line segments like (Z 2 , θ 2 ), (Z 3 ,θ 3 ), (Z 4 ,θ 4 ) and (Z 5 ,θ 5 ) for a third-iteration binary fractal-tree-type stub.

| Even/odd-mode analysis
The basic building block of the proposed MMR is the fractaltree-shaped stub attached with a UIR. The equivalent transmission line model of the proposed MMR is shown in Figure 5 (a) and it is analysed using the even-odd-mode method. The even-mode circuit is developed by adding a magnetic wall along the symmetrical plane (TT ' ) as shown in Figure 5(b), whereas the odd-mode circuit can be achieved by adding an electrical wall along the symmetrical plane TT ' as shown in Figure 5(c). For even-mode excitation, the resulting input impedance can be expressed as For odd-mode excitation, the resulting input impedance can be expressed as By solving Equations (1) and (2), the resonating modes can be obtained. For , the transmission poles are placed at 3.7, 5.9 and 9.67 GHz, respectively. The transmission zeroes (TZs) are located at 2.8 and 10.98 GHz. The fractal tree resonator for different iterations loaded on to a UIR are weakly coupled to 50 Ω lines and the |S 21 | (dB) is plotted for each iteration (branch angle kept at 120°) to examine the changes in the resonating modes. From the |S 21 | (dB) versus frequency plot for identification of the modes by weakly coupling the MMR with a 50 Ω feed line, as shown in Figure 6, it can be observed that the resonant frequencies decrease with an increase in the iterations. The reason behind this is that, when the number of segment increases in each successive iteration, the current travels a longer path. It results in lowering down the resonant modes, which finally contribute to a wide passband bandwidth by insertion of transmission poles at the lower band edge. Table 1 indicates the resonant modes for different iterations. It is seen that the third iteration covers the modes, which can be utilised to achieve the UWB passband. To investigate the design issues in obtaining the UWB passband, an input-output coupling mechanism is designed to form the BPF with a third iteration fractal tree-shaped stub loaded on to a UIR. For understanding the resonance behaviour of the BPF, the branching angle and branch-to-stem-length ratio are parametrically studied.

| Resonance characteristics of the BPF by varying the angle of fractal tree stub
Coupling between the branches is affected by the branching angle. If the length and width of the branches are independent of the branching angle, then the ratio of successive resonant modes is also independent of the branching angle. The simulated S-parameters for three different branch angles (60°, 120°and 180°) are shown in Figure 7. It is seen from the S-parameter plot that the resonance characteristics of the binary fractal tree remains the same with a change in the branch angle. However, for ease of design and to avoid contacts between higher iteration branches, an angle of 120°is used for all designs of the BPF.

| Resonance characteristics of the BPF by varying the length ratios of branch to stem
The stem-to-branch ratio or the scale factor (δ s ) is a pivotal parameter which dominantly controls the resonant characteristics of the proposed resonator. Figure 8 shows the simulated S-parameters of the binary fractal tree resonator for three different scale factors. It can be seen from the S-parameter plot that the resonance characteristics of the binary fractal tree

F I G U R E 7 S-parameters for different branching angles of the fractal tree stub
F I G U R E 8 S-parameters for different branch-to-stem-length ratio (δ s ) of the fractal tree stub 58changes drastically, with a variation of the scale factor. The desirable passband and stopband resonance characteristics are obtained for δ s of 0.9.

| BPF using fractal-tree-shaped stub
Self-similarity is the basic feature of the fractal tree stub, which also contributes to the occurrence of multiple resonances. Transmission poles and zeros, which are obtained from the even/odd-mode analysis of the proposed MMR, are chosen to cover the whole UWB pass band and passband selectivity, respectively. An inter-digital coupled line is used as input-output coupling mechanism for the proposed resonator.
The final layout of the proposed BPF, arrived after the parametric studies, is shown in the inset of Figure 9. From the S-parameter plot, it can be observed that BPF filter has very sharp selectivity because of the two TZs, which are created at 3 and 10.4 GHz, respectively. The simulated passband extends from 3.7 to 9.6 GHz with a return loss less than 10 dB within the desired passband. The stopband is extended up to 14 GHz with minimum attenuation of À 10 dB throughout the stopband.

| UWB BPF by keeping the width of each branch same
From the previous analysis, it is observed that the resonance characteristics of the binary fractal tree are affected by the scale factor but remains the same for different branch angles. All these analyses were performed on the fractal binary tree with S i w ¼ 0.5. However, the extracted S-parameter shows that the structure fails to cover the entire UWB. Therefore, the BPF structure is modified by keeping all branches equal in width, that is, the value of S i w is kept as 1. The input-output feed network remains the same for all variations of the stub-loaded resonators investigated F I G U R E 9 Dimensions of the BPF illustrated in the inset and its passband and stopband characteristics, where l u ¼ 11.55 mm, Layout of the fractal tree stub-loaded uniformimpedance-resonator-based ultra-wideband bandpass filter having the same branch widths, where l u ¼ 11.55 mm, w u ¼ 0.297 mm, l io ¼ 4.52 mm, w io ¼ 0.326 mm, g ¼ 0.1 mm, w ¼ 1.524 mm, l 1 ¼ 5.095 mm, l 2 ¼ 3.303 mm, l 3 ¼ 2.378 mm, l 4 ¼ 1.871 mm F I G U R E 1 1 Photograph of the fabricated prototype of the proposed ultra-wideband bandpass filter F I G U R E 1 2 Comparison of em-simulated and measured S-parameters of the proposed ultra-wideband bandpass filter KUMARI ET AL.
-59 in this work. The layout of the proposed structure is shown in Figure 10. This design provides a passband and stopband characteristics that are suitable for UWB BPF application.

| RESULTS AND DISCUSSION
The photograph of the prototype of the proposed UWB BPF is shown in Figure 11. All the measurements were done using Rhode and Schwarz ZVA 40 VNA. The S-parameters of the proposed UWB BPF obtained from electromagnetic simulation and measurement are compared in Figure 12. The simulated and measured results are in good agreement. From the measured results, it can be inferred that the BPF filter has very sharp selectivity because of two TZs, which are created at 2.4 and 12 GHz, respectively. The measured shape factor of the proposed filter is 0.9. The measured passband range is from 3.3 to 10.7 GHz with |S 11 | below À 10 dB within the desired passband. The stopband is extended up to 16 GHz with minimum attenuation of 20 dB. The overall size of the filter is 11.5 � 9.6 mm 2 . A comparison of the performance of the proposed filter design with previously published works is presented in Table 2. It can be observed that the proposed filter has excellent selectivity compared to filters reported in [11,13,14]. The proposed filter exhibits a compact size compared to the filters presented in [11][12][13][14]. The filter presented in this work has better stopband range (till 16 GHz) compare to the designs in [12,15]. In addition, there are TZs available at both sides of the passband, which are absent in [12,13,15].

| CONCLUSIONS
A novel approach is presented to design a UWB BPF with a fractal-tree-based stub-loaded MMR. Space-filling and selfsimilarity properties of fractal trees used as a stub loaded on a UIR provide a compact topology for obtaining multiple resonances within the UWB passband. This resonator topology enables closely spaced modes for third iteration fractal trees. Investigations reveal that the resonance characteristics can be altered by changing the scale factor as well as the stem-to-branch width ratio. The final design consists of a fractal tree stub that has all branches of identical width, indicating the same impedance as well as having a branching angle of 120°. The proposed filter has high selectivity and it occupies a very little space of 11.5 mm � 9.6 mm. Measurements indicate that the proposed filter covers the whole UWB band with acceptable inband and out-of-band performances. The stopband of the proposed filter is extended up to 16 GHz.