ULTRAWIDEBAND BANDPASS FILTERS BASED ON COUPLED ELECTROMAGNETIC BAND GAP STRUCTURES Ursula Martinez-Iranzo, Bahareh Moradi, and Joan Garcia-Garcia noma De Barcelona Edificio Electronic Department, Universidad Auto Q, Campus De La UAB, Cerdanyola Del Valles, 08193 Barcelona, Spain; Corresponding author:
[email protected] Received 4 May 2015 ABSTRACT: In this letter, an ultrawideband (UWB) bandpass filter design, using coupled electromagnetic band gap structures, is proposed. Theoretical analysis is used to establish clear relations between physical parameters and the main filter characteristics. UWB bandpass filter C 2015 Wiley from 3.1 to 10.7 GHz has been fabricated and measured. V Periodicals, Inc. Microwave Opt Technol Lett 57:2857–2859, 2015; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.29458 Key words: ABCD matrices; dispersion relation; electromagnetic band gap structures; high coupling resonator; ultrawideband bandpass filters 1. INTRODUCTION
The ultrawideband (UWB) standard was developed in 2002 for commercial uses at frequencies between 3.1 and 10.6 GHz [1]. As one of the essential components in UWB communication systems, the UWB bandpass filter has been developed rapidly in recent years [2–5]. The most commonly used technique to generate UWB filters is the microstrip multiple-mode resonator that distributes the resonant modes evenly within the UWB band [6]. However, other approximations have been used with the aim of improving the performance. For instance, in [7], parallel-coupled microstrip lines are used to design an UWB bandpass filter with a wide spurious-free stop band, at the cost of introducing chip capacitors that hinders the fabrication process. More recently, in [8], a very complex structure based on composite right/left handed transmission-line unit cell has been proposed. In this case, although the performance of the filter is reasonably good (with some drawbacks in the out-band rejection level), the structure becomes too complex to establish direct relations between the filter performance and the physical dimensions of the designs. Another recent research [9], shows a very compacted UWB filter using a quarter-wave short circuited stubs model with a well-described design process based on a theoretical transmission
Figure 1 a) Layout of the proposed EBG basic cell and b) equivalent circuit model obtained using the Richards’s transformation and the Kuroda equivalences
DOI 10.1002/mop
Figure 2 Dispersion relation between 0 and 13.5 GHz in the case of 2, 3, and 4 stages, respectively, for w 5 0.2 mm, s 5 0.03 mm, Lv 5 1.5 mm, and Lh 5 5.5 mm. The conducting regions are determined by the frequency in which the dispersion region is between 1 and 21. fH and fL are high and upper limits of the bandwidth, respectively
lines analysis but with high insertion losses (3 dB) and fabrication disadvantages like vias to the ground. In this letter, an UWB bandpass filter based on a simple electromagnetic band gap (EBG) structure with coupling sections is proposed. The periodic structure allows designing bandpass filters with controllable characteristics using analytical expressions. As illustrative example, a 110% fractional bandwidth (FBW) filter with threestages EBG has been designed, fabricated, and measured. Parametric analyses of the structure using the developed analytical expressions are discussed. A key aspect of the proposed design is the utilization of small separation distances between transmission lines, around 30 lm, to enhance the coupling coefficients.
Figure 3 Low and upper limits (fL and fH) of the BW as a function of the horizontal stub (Lh), with fixed Lv value at 1.6 mm, and vertical stub (Lv), with fixed Lh value at 5.4 mm
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Figure 5 Slopes of UWB filters according to the number of stages
Figure 4 3 results
FBW as a function of the Lh and Lv parameters from Figure
2. THEORETICAL FRAMEWORK
One of the advantages of the periodically loaded filtering structures is the possibility to control the limits of the transmission bands through the dispersion relation. The dispersion relation can be analytically evaluated from the ABCD matrix in a conceptually simple process [10]. In our case, the basic cell can be described as the combination of the transmission matrix corresponding to the different basic cell sections as can be observed in Figure 1. The proposed basic cell [Fig. 1(a)] is composed by three sections. Two coupled microstrip lines at the extremes and a cross-shape resonator in the center. The coupled microstrip sections are characterized by the impedance Zu, the electrical length u, and the distance between microstrips s. The central cross section is characterized by the impedance Z0 and the electrical length h. All the transmission lines used in the cell have the same width w. The corresponding equivalent circuit model observed in Figure 1(b) can be obtained by applying the Richards’s transformation and the Kuroda equivalences. The process to obtain the ABCD matrix of the equivalent circuit model of the basic cell that is depicted in Figure 1(b) is conceptually simple but difficult to handle in practice. As can be observed in (1), the basic cell ABCD matrix is the result of the multiplication of the nine ABCD matrices corresponding to the elements of the equivalent circuit model in Figure 1(b).
Figure 6 a) Layout of the proposed and fabricated EBG structure. Geometric values correspond to Lv 5 5.5 mm and Lh 5 1.56 mm. b) Picture of the fabricated EBG structure. P1 and P2 are input and output port, respectively. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com]
the ABCD matrix. It has been possible to obtain the dispersion relation according with the expression (2) [10] as a function of the physical dimensions of the design. In (2), b is the propagation constant in the case of lossless assumption and d is the length of the transmission line. The confinement of the right side of the Eq. (2) between 21 and 1 determines the allowed transmission bands in the EBG. cos ðbdÞ5ðA1DÞ=2
(2)
10 10 1 1 0 1 1 cos u jZu sin u 1 1 B C B C B j Yu tan u C @ A5@ j Yu tan u A@ A@ A jsin u cos u C D 0 1 0 1 Zu 1 0 Z0 0 1 0 1 cos h jZ0 sin h 2 cos h j sin h C 1 j Z0 sin h B 3 CB B CB C 3 C@ @ jsin h AB A A @ 3jsin h cos h 0 1 cos h Z0 Z0 0 10 1 10 1 1 cos u jZu sin u 1 1 B j Yu tan u CB CB j Yu tan u C @ A@ jsin u A A@ cos u 0 1 0 1 Zu (1) 0
A B
Due to the complexity of the analytical expression (1), it has been convenient the utilization of the Maple software to deal with
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Figure 7 Simulated and measured S-parameters and measured group delay of the filter prototype
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DOI 10.1002/mop
TABLE 1 Performance Comparison of UWB Filters Ref. This work [7] [8] [9]
Size
Bandpass Freq. (GHz)
|S21| (dB)
|S11| (dB)
Fab. Drawback
3 3 3 3
3.1–10.1 3.1–10.6 3.0–10.0 3.1–10.6
2.0 2.6 3.0 0.5
13.0 12.5 12.5 11.0
NO Chip cap/slot Vias to the ground Vias to the ground
0.29kg 0.72kg 0.52kg 0.63kg
1.55kg 1.02kg 0.15kg 0.46kg
kg is the guided wavelength of the 50 X microstrip lines on the substrate at the center frequency.
As can be observed in Figure 2, by a proper combination of the geometric parameters of the basic cell, it is possible to keep the dispersion relation confined between 21 and 1 in a very wide frequency range to perform an UWB bandpass filter between 3.1 and 10.7 GHz. The limits of the bandpass observed (fH and fL) in Figure 2 can be analytically determined from the design physical dimensions. Figure 3 plots the dependence of fH and fL with the parameter Lv and Lh. Through these bandpass, in Figure 4, can be observed the range of FBW that is obtained with variations of Lv and Lh. The wide range that can be obtained, from 40% to 90% of FBW, from the studied values with one basic cell, provides a large design margin. Besides the bandwidth, other filter parameters can be also controlled in the proposed EBG structure. Figure 5 shows the relation between the filter sharpness and the number of stages of the EBG, pointing out a selectivity improvement as the number of stages is incremented. The results show linear slopes that go from 9.0 to 18.4 dB/GHz below fL and from 25.9 to 43.8 dB/ GHz over fH. Conversely, the slope for each number of EBG stages can also be modified by controlling the position of two transmission zeros depending of the electrical lengths h and u. Eventually, this relation could be analytically expressed using the equivalent circuit model expressed in Figure 1(b). 3. FILTER IMPLEMENTATION
An UWB filter has been fabricated in a RO3010 0.635 mm Rogers substrate characterized by a loss tangent d 5 0.0022 and er 5 10.2 using a laser milling machine. Figure 6(a) shows the final layout of the proposed device after an optimization process by combining momentum and ADS optimization tools. Figure 7 shows the comparison between the predicted and measured frequency responses of S21 and S11 magnitudes, and group delay. As can be observed, the proposed device exhibits a welldefined bandpass between 3.1 and 10.7 GHz. The measured inband return loss is mostly better than 13 dB and the measured insertion loss is less than 2.5 dB over the 3.1–10.1 GHz range. Certain filter performance degradation is observed above 9 GHz, probably due to the fabrication and measurement process. The UWB filter has a flat measured group delay within its passband, whose variation is less than 0.3 ns. Table 1 shows the performance comparison of the fabricated UWB filter in this work with other UWB filters. The design and fabrication of the proposed filter is simple compared with the references that have complicated configurations and elements that make them more difficult to fabricate. Although vias to ground are not drawback for PCB technologies, certainly is a technological step to avoid in certain applications like satellite devices. In addition, the UWB filter in this letter shows similar responses in insertion and return losses, and its size is comparable with the references devices. 4. CONCLUSION
An equivalent circuit model based on ABCD transmission matrices is proposed and implemented providing an analytical framework
DOI 10.1002/mop
for the design. Some parametric analyses are presented, about the operation limits of the design and, finally, a 3.1–10.7 GHz UWB bandpass filter device is proposed. Good agreement between theoretical predictions, electromagnetic simulations, and measurements are found. The proposed UWB bandpass EBG-based structure exhibits competitive performance at the same time that offers a useful design framework connecting analytically physical dimensions with the filter characteristics. REFERENCES 1. Revision of part 15 of the commission’s rules regarding ultrawideband transmission systems, In: First Note and Order Federal Communications Commission, Washington DC, ET-Docket 98–153, 2002. 2. L.S. Zhu, S. Sun, and W. Menzel, Ultra-wideband (UWB) bandpass filter using multiple-mode resonator, IEEE Microwave Wireless Compon Lett 15 (2005), 796–798. 3. J. Garcia-Garcia, J. Bonache, and F. Martin, Application of electromagnetic bandgaps to the design of ultra-wide bandpass filters with good out-of-band performance, IEEE Trans Microwave Theory Tech 54 (2006), 4136–4140. 4. T.B. Lim, S. Sun, and L. Zhu, Compact ultra-wideband bandpass filter using harmonic-suppressed multiple-mode resonator, Electron Lett 43 (2007), 1205–1206. 5. J. Xu, W. Wu, W. Kang, and C. Miao, Compact UWB bandpass filter with a notched band using radial stub loaded resonator, IEEE Microwave Wireless Compon Lett 22 (2012), 351–353. 6. S.W. Wong and L. Zhu, EBG-embedded multiple-mode resonator for UWB bandpass filter with improved upper-stopband performance, IEEE Microwave Wireless Compon Lett 17 (2007), 421–423. 7. A.M. Abbosh, Design method for ultra-wideband bandpass filter wide stopband using parallel-coupled microstrip lines, IEEE Trans Microwave Theory Tech 60 (2012), 31–38. 8. K.U. Ahmed and B.S. Virdee, Ultra-wideband bandpass filter based on composite right/left handed transmission-line unit-cell, IEEE Trans Microwave Theory Tech 61 (2013), 782–788. 9. X. Li and X. Ji, Nobel compact UWB bandpass filters design with cross-coupling between k/4 short-circuited stubs, IEEE Microwave Wireless Compon Lett 24 (2014), 23–25. 10. D.M. Pozar, Microwave engineering, Wiley, New York, NY, 1998. C 2015 Wiley Periodicals, Inc. V
PERFORATE-ARRAYS AS AN ALL-DIELECTRIC GRADIENT INDEX METAMATERIAL FOR HPM LENS Xue-Long Zhao, Cheng-Wei Yuan, Lie Liu, Sheng-Ren Peng, and Dan Cai College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha 410073, People’s Republic of China; Corresponding author:
[email protected] Received 4 May 2015 ABSTRACT: All-dielectric metamaterials have high potential for practical applications in high power microwave (HPM) area. In this article, a beam deflected flat lens made of all-dielectric metamaterial is
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