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Analysis of Novel Approach to Design of Ultra-wide Stopband Microstrip Low-Pass Filter Using Modified U-Shaped Resonator
Analysis of Novel Approach to Design of Ultra-wide Stopband Microstrip Low-Pass Filter Using Modified U-Shaped Resonator
ETRI Journal. 2015. Oct, 37(5): 945-950
Copyright © 2015, Electronics and Telecommunications Research Institute (ETRI)
  • Received : February 13, 2014
  • Accepted : May 20, 2015
  • Published : October 01, 2015
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About the Authors
Gholamreza Karimi
Ali Lalbakhsh
Khatereh Dehghani
Hesam Siahkamari

Abstract
A novel microstrip low-pass filter is presented to achieve an ultra-wide stopband with 11 harmonic suppression and very sharp skirt characteristics. The filter is composed of a modified U-shaped resonator (which creates two fully adjustable transmission zeroes), a T-shaped resonator (which determines a cut-off frequency), and four radial stubs (which provide a wider stopband). The operating mechanism of the filter is investigated based on a proposed equivalent-circuit model, and the role of each section of the proposed filter in creating null points is theoretically discussed in detail. The presented filter with 3 dB cut-off frequency ( f c = 2.35 GHz) has been fabricated and measured. Results show that a relative stopband bandwidth of 164% (referred to as a 22 dB suppression) is obtained while achieving a high figure-of-merit of 15,221.
Keywords
I. Introduction
A microstrip low-pass filter (LPF) with compact size and high performance is one of the most important components in microwave circuits. This component is characteristically low-cost and easy to fabricate, as well as being easy to combine with other microwave circuit components [1] . There are a lot of techniques to simultaneously achieve compact size and high performance in relation to microstrip LPFs. Employing planar resonators [2] [6] is one such technique. Another such technique is to use modified stepped-impedance hairpin resonators [2] . Although the authors of [2] [3] could achieve a filter with ultra-wide stopband by employing radial stubs and shunt open stubs at the feed points of a center-fed coupled-line hairpin resonator, it provided a gradual roll-off.
To construct a microstrip LPF of compact design that can achieve an ultra-wide stopband, loaded radial-shaped patches were used in [4] [5] . However, the proposed microstrip LPFs of [4] [5] introduced a low insertion loss in the stopband. Adding a pair of stepped-impedance open stubs loaded on both ends of a high-impedance microstrip line was a proposed solution by [6] to improve the stopband characteristic in this kind of structure. In a similar procedure, both triangular patch resonators and polygonal patch resonators were introduced in [7] ; however, the roll-off was not sharp enough. The authors of [8] employed properly arranged rat-race directional couplers to operate as bandstop transversal filtering sections to extend a stopband. Although this approach is new, it increases the circuit size. In [9] , a single T-shaped resonator in combination with a novel suppressing cell was utilized to realize an LPF with 5 harmonic suppression. In [10] , a broadside-coupled microstrip-coplanar waveguide was utilized to design an LPF with extremely wide stopband. In spite of this extremely wide stopband, the filter failed to provide a sharp roll-off. The presented filter in [11] , which employed a resonator with slotted ground plane, suffered from the same problem. In terms of investigating the operating mechanisms of microstrip filters, several theoretically-based approaches have been explained in some recently published papers [12] [14] .
In this paper, a novel approach to designing an LPF is presented. Unlike the majority of the literature related to the design of microstrip filters, here we focus on the theoretical aspects of resonator design; by doing so, the presented analysis can be generalized to other microwave components. For instance, by employing the presented modified U-shaped resonator and making an appropriate use of extracted equations, transmission zeroes can be adjusted to suppress harmonics in different microwave components such as power dividers or diplexers [15] .
Firstly, in this paper, a modified harmonic-suppressing U-shaped resonator and its equivalent LC circuit are presented and analyzed. Secondly, a T-shaped resonator is adopted in the aforementioned resonator, and finally, bandstop filters in the form of radial stubs are implemented. Thus, an ultra-wide stopband, from 2.35 GHz up to 26 GHz, with an attenuation of more than 22 dB is achieved.
II. Design of Harmonic-Suppressing Resonator
- 1. Equivalent Circuit and LC Parameters Extraction
The geometric structure of the novel U-shaped resonator and its LC circuit are depicted in Fig. 1 . Since the modified U-shaped resonator is both vertically and horizontally symmetrical, the proposed LC circuit is also symmetrical. In Fig. 1(b) , L 1 and L 2 represent the inductance of the high impedance transmission line; L 3 is the resultant inductance of each open stub; C 1 is the sum of the capacitances of the junction discontinuities between the main feed line and two upper and lower high-impedance lines; C 2 is the series coupling capacitance between the two identical stubs; and C 3 is the sum of metal–insulator–metal capacitances and shunt capacitance associated with the gap (“ S ” in Fig. 1(a) ). The resonator’s dimensions in Fig. 1(a) are as follows: l 1 = 2.05, l 2 = 1.69, l 3 = 5.4, l 4 = 2.6, l 5 = 8.24, w 1 = 0.13, w 2 = 0.3, w 3 = 2.0, w 4 = 2.23, w 5 = 0.4, and S = 0.89 (all in millimeters). The values of the lumped elements ( L 1 , L 2 , L 3 , C 1 , C 2 , and C 3 ) can be extracted by use of the methods discussed in [1] , and then they are optimized slightly to achieve a very similar response to electromagnetic (EM) simulation. The yielded values are L 1 = 0.61 nH, L 2 = 3.5 nH, L 3 = 0.6 nH and C 1 = 1.22 pF, C 2 = 0.003 pF, C 3 = 1.2 pF. Figure 2(a) shows the EM and LC results.
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(a) Layout of proposed U-shaped resonator and (b) LC equivalent circuit.
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(a) EM and circuit simulation results of proposed U-shaped resonator on substrate with relative dielectric constant of 3.38 and thickness of 0.508 mm and (b) effect of gap capacitance on location of multiple zeroes.
- 2. Characteristics of Novel U-Shaped Resonator
The proposed modified U-shaped resonator introduces two adjustable transmission nulls at 5.5 GHz and 6.5 GHz. It is clear that C 1 and L 1 do not contribute to make these resonance frequencies, whereas C 2 , C 3 , L 2 , and L 3 do; L 3 and C 3 create a deep transmission null at around 6 GHz, while the presence of the gap capacitor ( C 2 ) turns this transmission zero into two separate zeroes with equal distance from 6 GHz. Figure 2(b) shows the positions at where multiple zeroes occur for three different values of C 2 . As it is demonstrated in Fig. 2(b) , for smaller values of C 2 , the two shunt-connected series LC resonators ( L 3 , C 3 ) will be isolated having no connection to each other; therefore, the resonance frequency of the two resonators will be equal to around 6 GHz, which results in a deep transmission zero with around 140 dB attenuation. By contrast, for larger values of C 2 , the two resonators are correlated and introduce two different zeroes with around 70 dB attenuation, as shown in Fig. 2(b) . Thus, to alter the position of the center of multiple zeroes, L 3 and C 3 must be modified, and to alter the distance of the two separate zeroes from their center, C 2 should be modified. So, two completely adjustable transmission zeroes are realized.
To demonstrate the dominant effects of C 2 , C 3 , and L 3 on the locations of transmission nulls, the extracted LC circuit will be analyzed in detail as follows. By exploiting the symmetry of the LC equivalent circuit shown in Fig. 1(b) and owing to the fact that C 1 and L 1 do not have any effect on the locations of transmission zeroes, the LC circuit in Fig. 1(b) is redrawn in Fig. 3 . Based on the concept of a transmission zero, in which there is no signal at the output of the circuit, a fourth-order polynomial equation is yielded (see (1)). The roots of (1) are the transmission zeroes of the proposed novel U-shaped resonator. Since L 2 does not appear in α and the value of the second term in β , 2 L 2 C 2 , is considerably smaller than the first term, 2 L 3 ( C 2 + C 3 ), it can be concluded that L 2 has an insignificant effect on the location of transmission zeroes. In other words, C 2 , C 3 , and L 3 control the location of transmission zeroes.
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Simplified LC equivalent circuit of proposed U-shaped resonator.
( S 2 α +1) 2 + S 2 (2 α +β)=0,
α= L 3 2   C 3 ( 2 C 2 + C 3 ),  β=2 L 3 ( C 2 + C 3 )+2 L 2 C 2 , f 1 , f 2(GHz) = 25 π × 0.1(2 α +β) ± 0.1(2 α +β ) α
One of the features of the proposed U-shaped resonator is that the introduced transmission zeroes can be modified for different applications. Accordingly, the widths of w 2 and w 5 determine the location of the center frequency of the multiple zeroes, while the separation of S determines the distance of the multiple zeroes from the center frequency, by increasing w 2 and decreasing w 5 , both the inductance of L 3 and the capacitance of C 3 decrease. This causes the center frequency of the multiple zeroes to shift to a higher frequency, as shown in Fig 4(a) . In this case, the effect of variation of S on the center frequency is negligible in comparison with the effects of w 5 and w 2 . On the other hand, a decrease in S results in an increase in the value of the coupling capacitor ( C 2 ), which causes the near and far band transmission zeroes to shift to lower and higher frequencies, respectively, as shown in Fig. 4(b) . In this case, the effects of altering w 5 and w 2 are insignificant.
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Adjustability of U-shaped resonator: (a) tuning center frequency and (b) tuning distance between two separate zeroes (delta).
III. LPF Design
To sharpen the frequency response of the proposed fully adjustable suppressing cell, a T-shaped resonator is connected to the main high impedance line, which acts as a shunt connected series L-C resonator (as named L 4 and C 4 in Fig. 5(b) ). This resonator introduces a transmission zero at around 2.7 GHz, which can be easily calculated by (2). C 4 and L 4 can be obtained from (3) and (4) as 4.29 nH and 0.63 pF, respectively. In these equations, Z OC , λ gC and Z OL , λ gL correspond to low- and high-impedance lines, respectively. It should be noted that due to some disregarded discontinuity effects, there is an insignificant 10% discrepancy between the calculated resonance frequency by (4) and the obtained value by the EM simulation in Fig. 5(d) .
f r = 1 2π C 4 L 4 ,
L 4 = 1 ω c Z OL sin( 2π λ gL l L )+ 1 ω c Z OC tan( π λ gC l C ),
C 4 =  l C Z OC v p + 1 ω c 1 Z OL tan( π l L λ gL ),
where
v p = c εeff 2 .
The presence of this T-shaped resonator not only causes the coupling capacitor ( C 2 ) to turn into two coupling capacitors ( C 2 ′), but it also divides L 2 into two equal inductors ( L 2 /2) as shown in Fig. 5(b) . Finally, since the inductance line in the T-shaped resonator is really thin, the final equivalent circuit is yielded in Fig. 5(c) . As it can be seen from Fig. 5(c) , this circuit has maintained the same topology as that of the LC circuit in Fig. 1(b) . Indeed, adding the T-shaped resonator makes the coupling distance narrower, and as a result, the value of the coupling capacitor increases from C 2 = 0.003 in Fig. 1(b) to C 2 = 0.0042 in Fig. 5(c) . Thus, by increasing the distance between the edge of the U-shaped resonator and the vertical part of the T-shaped resonator ( S ′), the coupling distance is extended. Consequently, this leads to a reduction in the value of C 2 , resulting in a smaller delta (which means a closer distance between transmission zeros). So, the roles of the coupling distance ( S and S ′) and C 2 have remained unchanged after connecting the T-shaped resonator. All values pertaining to the lumped elements are tabulated in Table 1 .
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(a) U-shaped resonator after adding T-shaped resonator (l6 = 1.6 mm, l7 = 6.37 mm, w6 = 4.5 mm, w7 = 0.13 mm); (b) and (c) equivalent circuits of Fig. 5(a); and (d) EM and circuit simulation results.
Values of lumped elements (units:C, pF;L, nH).
Fig. C1 C2 C3 C4 C2 L1 L2 L3 L4
1(b) 1.22 0.0030 1.20 0.61 3.5 0.60
5(b) 1.72 1.01 0.64 0.057 0.61 3.5 0.66 4.50
5(c) 1.72 0.0042 1.01 0.72 0.61 3.5 0.66 5.24
To expand the stopband to 26 GHz, four open radial stubs are used. Figure 6 shows the layout and insertion loss of the proposed radial stubs. The dimensions of the four stubs are calculated to create four transmission zeros to suppress four transmission poles located at 9.35 GHz, 12.37 GHz, 17.4 GHz, and 19.27 GHz. The dimensions for the first to forth stub are w = 0.2 mm, 2.3 mm, 4.2 mm, and 3.1 mm, respectively. It is also possible to modify the proposed filter to suit different applications, since the cut-off frequency is controlled mostly by l 6 , w 6 , and w 7 . As is shown in Fig. 7 , by increasing both l 6 and w 6 and decreasing w 7 , the near-band transmission zero moves to a lower frequency and the passband becomes narrower. This is because by increasing both l 6 and w 6 , the capacitance of C 4 increases; and by decreasing w 7 the inductance of L 4 increases. These changes result in a smaller cut-off frequency.
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(a) Proposed radial stubs and (b) frequency response of four radial stubs.
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Cut-off frequency as function of scaling factor.
IV. Simulation and Experimental Results
The proposed LPF has been implemented on a substrate with a relative dielectric constant εr = 3.38, thickness h = 0.508 mm, and loss tangent tan δ = 0.002. Simulations are done by an EM-simulator (ADS Momentum). The S-parameter is measured by an Agilent network analyzer N5230 A. Figure 8 shows a final layout and a photograph of the fabricated prototype. It can be seen from Fig. 9 that the filter has a 3 dB cut-off frequency equal to 2.35 GHz, an insertion loss of less than 0.6 dB in the passband from DC to 2 GHz, a return loss better than 10.6 dB, and a suppression level higher than 22 dB from 2.53 GHz up to 26 GHz. Thus, the proposed filter has the property of 11 harmonic suppression. Although some spurs exist in the stopband due to the inherent presence of harmonics in the microstrip line, all spurs have been kept below −22 dB by a proper design. The relative stopband bandwidth of the LPF is about 164%. Furthermore, the size of the proposed filter is only 12.9 × 16.1 mm 2 , which corresponds to 0.16 λ g × 0.20 λ g . The return loss in the stopband region is very small, indicating negligibly small radiation loss. The transition band from 2.35 GHz to 2.53 GHz with −3 dB and −20 dB, respectively, is 0.18 GHz, showing that the filter has excellent skirt performance. For comparison, Table 2 compares the performance of the proposed filter with that of some of the latest filters based on several specifications explained in [4] . According to Table 2 , the presented filter exhibits a high figure-of-merit (15,221) among the quoted filters.
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(a) Layout of proposed filter and (b) photograph of fabricated filter.
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Simulated and measured S-parameters of proposed low-pass filter.
Performance comparisons among previous filters and proposed one.
Ref. RO (ζ) RSB SF NCS AF FOM
[2] 30 1.25 1.5 0.08×0.08 1 8,789
[3] 95 1.40 2.0 0.21×0.10 1 11,951
[4] 36 1.32 1.5 0.07×0.07 1 11,534
[5] 37 1.65 1.5 0.11×0.09 1 9,065
[6] 22 1.55 1.5 0.09×0.08 1 7,095
[8] 200 1.41 2.0 0.60×0.30 1 2,805
[9] 46 1.37 2.0 0.25×0.15 1 3,279
[10] 74 1.70 1.7 0.13×0.31 1 5,306
[11] 82 1.28 2.5 0.11×0.22 1 10,842
[12] 62 1.72 3.0 0.310×0.24 1 4,430
This work 135 1.64 2.2 0.16×0.20 1 15,221
Note: RO means roll-off rate according to 3 dB and 40 dB attenuation points, RSB means relative stopband bandwidth, SF means suppression factor, NCS means normalized circuit size, and AF means the architecture factor. FOM= ζ×RSB×SF NCS×AF
V. Conclusion
A compact LPF with sharp roll-off and wide stopband bandwidth is proposed and implemented. The filter is composed of a U-shaped fully adjustable resonator, four radial stubs, and a T-shaped resonator. The first two sections contribute to the creation of an ultra-wide stopband, while the T-shaped resonator provides a fully adjustable cut-off frequency with a very sharp roll-off. The results indicate that the demonstrated filter achieves very high figure-of-merit in comparison to the latest fabricated filters. With the above desirable features, the proposed filter could be employed for microwave communication applications.
BIO
Corresponding Author ghkarimi@razi.ac.ir
Gholamreza Karimi received his BS, MS, and PhD degrees in electrical engineering from Iran University of Science and Technology, Tehran, Iran, in 1999, 2001, and 2006, respectively. Since 2007, he has been with the Electrical Department, Razi University, Kermanshah, Iran, where he is now an associate professor. His main research interests are low power analog and digital IC design; RF IC design; and modeling and simulation of RF/mixed signal IC. He is also interested in microwave devices and artificial intelligence systems.
ali.lalbakhsh@yahoo.com
Ali Lalbakhsh received his BS degree in communication engineering from Islamic Azad University, Boroujerd, Iran, in 2008 and his MS degree in communication engineering from Islamic Azad University, Science and Research Branch, Tehran, Iran, in 2011. From 2010, he has been lecturing at Islamic Azad University, Kermanshah, Iran. His research interests are microwave passive and active components; antenna design; periodic and electromagnetic band gap structures; and evolutionary algorithms. He has been a member of both the Institute of Electrical and Electronics Engineers and the Institute of Electronics, Information and Communication Engineers since 2011. He has also served as a reviewer for several journals.
khatere_dehghan@yahoo.com
Khatereh Dehghani received her BS degree in electrical engineering from Islamic Azad University, Science and Research Branch, Tehran, Iran, in 1996 and her MS degree in electrical engineering, from Islamic Azad University, Science and Research Branch, Kermanshah, Iran, in 2013. Her research interest is RF/microwave circuit design.
hesamsiahkamary@yahoo.com
Hesam Siahkamari received his BS degree in electrical engineering from Islamic Azad University, Kermanshah, Iran, in 2010 and his MS degree in electrical engineering from Razi University, Kermanshah, Iran, in 2013. His current research interest is RF/microwave circuit design.
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