Abstract
In this paper, a compact ellipticresponse microstrip low pass filter (LPF) is presented with a wide stopband using stepped impedance resonators. With high attenuation in the stopband, the overall size reduction of the proposed filter is achieved using a novel defected ground structure technique using an interdigital capacitor and complementary split ring resonator (CSRR). A 4.2 GHz LPF is designed and simulated on FR4 substrate and a stop band of 8.8 GHz is obtained by utilizing interdigital and complementary split ring resonator. Results further show that the use of Ushaped high impedance line on the top layer of filter enhances the stopband bandwidth by 2.2 GHz. In the final design, the passband insertion loss is found below 0.5 dB, and –10 dB is obtained over a band from 5.06 GHz to 17.06 GHz between input and output ports. The normalized circuit size of the filter is 0.417× 0.202 and the figure of merit is calculated about 55 at the cutoff frequency. These proposed LPFs have promised significant advantages in the stopband characteristics with an acceptable rolloff rate for spuriousfree communications.
Index Terms
Complementary Split Ring Resonator (CSRR); Defected Ground Structure (DGS); High impedance line; Microstrip filter; Mitering; Size reduction
I. INTRODUCTION
Microwave filter is designed to filter out undesired signals like outside band frequencies, harmonics, and spurious mixing products to reduce the system noise. Filters generally have frequency responses like lowpass, highpass, bandpass and bandstop. Practically, it is difficult to obtain ideal characteristics of the filter such as zero insertion loss in the passband, infinite attenuation in stopband with sharp transition region from passband to stopband [^{1}[1] D.M. Pozar: “Microwave Engineering,” John Wiley & Sons Inc; 2012.]. A stepped impedance or highlow (hilo) microstrip lowpass filter (LPF) is usually preferred due to properties like low insertion loss, easier design and fabrication. However, such microstrip filters have some disadvantages like gradual cutoff frequency (f_{C}) response, larger size due to inductance realization, harmonics of higher order and poor stopband characteristics [^{1}[1] D.M. Pozar: “Microwave Engineering,” John Wiley & Sons Inc; 2012.][^{3}[3] Y. Yang, X. Zhu and N. C. Karmakar, “A Novel Microstrip Lowpass Filter Using Compact Microstrip Resonant Cells and Uniquely Shaped Defected Bottom Structures,” Microwave Opt Technol Lett, vol. 54, pp. 2462–2464. 2010.]. To eliminate such disadvantages, many novel types of microstrip LPFs have been explored for improved stopband performance. These LPFs involve modifications like folding the high impedance line into meandered line [^{4}[4] M. A. Zhewang, K. Nomiyama and Y. Kobayashi, “Microstrip Lowpass Filters with Reduced Size and Improved Stopband Characteristics,” IEICE Trans Electron, vol. E88–C, pp. 6267, 2005.], Ushaped line [^{5}[5] A. Rajput, K. Patel and A. Birwal, “Compact Microstrip Lowpass Filter Design Using UShaped Folded HighImpedance Line,” Microw Opt Technol Lett, vol. 60, pp. 1812–1815, 2018.], Ushaped resonator for gradual transition [^{6}[6] M. Hayati, F. Shama, “Compact Microstrip LowPass Filter with Wide Stopband Using Symmetrical UShaped Resonator,” IEICE Electronics Express, vol. 9, no. 3, pp. 127–132, 2012.], spiral loaded tapered compact microstrip resonator cell [^{7}[7] M. R. Khezeli, M. Hayati and A. Lotfi, “Compact Wide Stopband Lowpass Filter Using Spiral Loaded Tapered Compact Microstrip Resonator Cell,” International Journal of Electronics, vol. 101, no. 3, pp. 335–382, 2014.], steppedimpedance hairpin resonator [^{8}[8] L. H. Hsieh and K. Chang, “Compact EllipticFunction LowPass Filters Using Microstrip SteppedImpedance Hairpin Resonators,” IEEE Trans on Microwave Theory and Techniques, vol. 51, no. 1, pp. 193–199, 2003.], novel patch resonator [^{9}[9] J. L. Li, S. W. Qu and Q. Xue,”Compact Microstrip Lowpass Filter With Sharp RollOff And Wide StopBand,” Electronics Letters, vol. 45, no.2, pp. 110–111, 2009.], the composition of a circular hairpin resonator and a pair of coupled parallel stepped impedance resonators (SIRs) [^{10}[10] M. Yang, J. Xu and Q. Zhao et al, “Compact Broad Stopband Lowpass Filters Using SIRsLoaded Circular Hairpin Resonators,” Progress in Electromagnetics Research, vol. 102, pp. 95–106, 2010.], the stubloaded coupledline hairpin unit [^{11}[11] V. K. Velid and S. Sanyal, “Sharp RollOff Lowpass Filter with Wide Stopband Using StubLoaded CoupledLine Hairpin Unit,” Microwave and Wireless Components Letters, vol. 21, no.6, pp. 301–303, 2011.], tapered resonator [^{12}[12] M. Hayati, F. Shama and H. Abbasi, “Compact Microstrip Lowpass Filter with Wide Stopband and Sharp RollOff Using Tapered Resonator,” International Journal of Electronics, vol. 100, no. 12, pp. 1751–1759, 2013.] etc.
Most of these designs either suffer with low attenuation (<20 dB) range in the stopband or have larger size. In addition, for better rolloff rate as well as compactness, an ellipticalfunction response is used in many LPFs which are based on several structures, such as steppedimpedance hairpin resonator [^{8}[8] L. H. Hsieh and K. Chang, “Compact EllipticFunction LowPass Filters Using Microstrip SteppedImpedance Hairpin Resonators,” IEEE Trans on Microwave Theory and Techniques, vol. 51, no. 1, pp. 193–199, 2003.], tapered resonator [^{12}[12] M. Hayati, F. Shama and H. Abbasi, “Compact Microstrip Lowpass Filter with Wide Stopband and Sharp RollOff Using Tapered Resonator,” International Journal of Electronics, vol. 100, no. 12, pp. 1751–1759, 2013.], slitloaded tapered compact microstrip resonator cell [^{13}[13] M. Hayati and A. Lotfi, “EllipticFunction Lowpass Filter with Sharp Cutoff Frequency Using SlitLoaded Tapered Compact Microstrip Resonator Cell,” Electronics Letters,vol.46, no. 2, pp. 143–144, 2010.], symmetrically loaded radialshape patches and meandered transmission line [^{14}[14] J. Wang, L. J. Xu, S. Zhao, Y. X. Guo et al, “Compact QuasiElliptic Microstrip Lowpass Filter With Wide Stopband,” Electronics Letters, vol. 46, no. 20, pp. 1384–1385, 2010.], triangular patch resonators and radial patch resonators [^{15}[15] J. Wang, H. Cui and G. Zhang, “Design of Compact Microstrip Lowpass Filter with UltraWide Stopband,” Electronics Letters, vol. 48, no. 14, pp. 854–856, 2012.], symmetrically loaded triangular and high–low impedance resonators [^{16}[16] J. P. Wang,L. Ge, Y. X. Guo and W. Wu, “Miniaturised Microstrip Lowpass Filter With Broad Stopband And Sharp RollOff,” Electronics Letters, vol. 46, no. 8, pp. 573–575, 2010.], Pshaped resonators [^{17}[17] M. Hayati, M. Validi, F. Shama et al,”Compact Microstrip Lowpass Filter with Wide Stopband Using P Shaped Resonator,”Journal of Microwaves, Optoelectronics and Electromagnetic Applications,vol.15, no. 4, pp. 309318, 2016.], novel asymmetric structures for resonator and suppressor [^{18}[18] M. Hayati, F. Shama, “A Compact Lowpass Filter with Ultra Wide Stopband Using Stepped Impedance Resonator,” Radioengineering, vol. 26, no. 1, pp. 269274, 2017.], wide stopband using trisection stepped impedance resonator [^{19}[19] D. Packiaraja, K. J. Vinoy, M. Ramesh et al, “Design of Compact Lowpass Filter with Wide Stopband Using TriSection Stepped Impedance Resonator,” Int. J. Electron. Commun. (AEÜ),vol. 65, pp. 1012– 1014, 2011.] etc.
Recently, a microstrip lowpass filter made using a rectangular resonator and high impedance elements is reported with a wide stopband bandwidth of 18.7f_{C} for f_{C} = 1.01 GHz [^{20}[20] S. H. Kazemi and M. A. Hayati “Compact Microstrip Lowpass Filter with Wide Stopband,” International Journal of Microwave and Wireless Technologies, vol. 11, no. 9, pp. 885893, 2019.]. To increase the compactness of designed filter with better harmonic control, sometime a slot is made on the ground (bottom) conductor to create extra parasitic elements. Such structure is known as a defected ground structure (DGS) [^{21}[21] A. O. Ertay and S. Simsek, “Design of EllipticFunction Microstrip Filters with Defected Bottom Structures,” In: PIERs Proceedings, Stockholm, Sweden, pp. 18381842, 2013.]. Various kinds of DGS designs are proposed for different filter types and explored the desired properties like compactness [^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.],[^{22}[22] J. X. Chen, J. L. Li, K. C. Wan et al, “Compact QuasiElliptic Function Filter Based On Defected Bottom Structure,” In: IEE Proceedings: Microwaves, Antennas and Propagation, vol. 153, no. 4, pp. 320324, Aug. 2006.], [^{23}[23] A. B. AbdelRahman, A. K. Verma, A. Boutejdar et al, “Compact Stub Type Microstrip Bandpass Filter Using Defected Bottom Plane,”IEEE Microwave and Wireless Components Letters, vol. 14, no. 4, pp. 136 – 138, 2014.], sharp rejection [^{24}[24] W. H. Tu and K. Chang, “Compact Microstrip LowPass Filter with Sharp Rejection,” IEEE Microwave and Wireless Components Letters,vol. 15, no. 6, pp. 404406, 2005.], wide stopband [^{25}[25] M. Al Sharkawy, A. Boutejdar and E. G. Mahmoud,”Design of UltraWide StopBand DGS LowPass Filter Using Meander and Multilayer Techniques,” Microwave and Optical Technology Letters, vol. 55, no. 6, pp. 12761281, 2013.], multiband response [^{26}[26] C. Chang, W. Chen and Z. Zhang, “A Novel DualMode DualBand Bandpass Fllter with DGS,” In: PIERS Proceedings. Marrakesh, Morocco, pp. 17231726, Mar. 2011.]. In some applications, sharp transition region plays a vital role for rejection of intermodulation products and so that the rolloff rate should be analyzed for these applications [^{27}[27] A. B. AbdelRahman, A. K. Verma, A. Boutejdar et al, “Control Of Bandstop Response Of HiLo Microstrip LowPass Fllter Using Slot In Bottom Plane,” IEEE Transactions on Microwave Theory and Techniques, vol. 52, no. 3, pp. 10081013, 2004.], [^{28}[28] A. Kumar, A. Sawant and M. V. Kartikeyan, “Investigation of Fractal DGS Microwave Fllters,” In: Proceedings of 2013 National Conference On Communications (NCC), pp.14, Feb. 2013.]. Also, the resonant frequency of the slot can be varied by changing the number of metal fingers which are incorporated in the slot instead of changing the size of slot [^{29}[29] S. V. Makki AlDin, A. Ahmadi, S. Majidifar et al, “Sharp Response Microstrip LPF Using Folded Stepped Impedance Open Stubs,” Radio Engineering, vol. 22, no. 1, pp. 328332,2013.][^{32}[32] D. Gadvi and U. Shah, “Microstrip Lowpass Filter Designs Using Defected Bottom Structure,” International J of Research in Engg Tech, vol. 4, no. 10, pp. 4348, 2015.]. Also, a squareshaped complementary split ring resonator (CSRR) filtering can be used for isolation improvement [^{33}[33] R. Selvaraju, M. H. Jamaluddin, M. R. Kamarudin et al,”Complementary Split Ring Resonator for Isolation Enhancement in 5G Communication Antenna Array,” Progress in Electromagnetics Research C, vol. 83, pp. 217228, 2018.]. Such CSRR offers high filtering (bandrejection) capability which is generally required for coupling suppression along with compact size and ease of fabrication.In this way the search for compact filter design structure with smooth curve of group delay and wide stopband can over to use in the extensively spread microwave and millimeterwave systems. To achieve such ideal response, approach of combining the interdigital capacitor and CSRR DGS are used.
In the presented work, the interdigital capacitor is placed as a DGS at the bottom layer to increase the stopband region for a fifth order elliptical lowpass filter accompanied with CSRR and a wide stop band is achieved. With optimization of interdigital/CSRR DGS on the bottom layer and Ushaped high impedance line on the top layer using in CST microwave studio, we obtained the maximum stopband of about 12 GHz (relative to – 10 dB) on a physical size of only 22.22 mm × 9.5 mm including 50 Ω feed lines.
II. 5^{th} ORDER HIGH LOW ELLIPTICAL LPF (HLELPF)
Design of a 5^{th} order HLELPF is accomplished using two capacitive lowimpedance elements and three inductive highimpedance elements. Filter specifications are chosen as a cutoff frequency (f_{C}) of 4 GHz, maximum stopband insertion loss of 30 dB, 100 Ω and 20 Ω as high and low impedances, respectively and a FR4 material is taken as a substrate which has a dielectric constant (ε_{r}) of 4.5 and thickness of 1.5 mm along with copper layer thickness of 35 μm.
For the 5^{th} order LPF design, the values of inductance (L_{i}) and capacitor (C_{i}) can be obtained from the immittance (g_{i}) values using the following equations [^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.], [^{21}[21] A. O. Ertay and S. Simsek, “Design of EllipticFunction Microstrip Filters with Defected Bottom Structures,” In: PIERs Proceedings, Stockholm, Sweden, pp. 18381842, 2013.].
and
where
and, Z_{o} = filter impedance (50 Ω)
These lumped elements are realized by high (Z_{h}) and low (Z_{l}) impedance lines, whose electrical lengths can be obtained by equations (3) & (4) [^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.], [^{21}[21] A. O. Ertay and S. Simsek, “Design of EllipticFunction Microstrip Filters with Defected Bottom Structures,” In: PIERs Proceedings, Stockholm, Sweden, pp. 18381842, 2013.].
For highimpedance line,
For lowimpedance line,
So, the physical lengths of these lines are obtained as follows [^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.], [^{21}[21] A. O. Ertay and S. Simsek, “Design of EllipticFunction Microstrip Filters with Defected Bottom Structures,” In: PIERs Proceedings, Stockholm, Sweden, pp. 18381842, 2013.],
For highimpedance transmission line length,
For lowimpedance transmission line length,
The schematic of the HLELPF is shown in Figure 1 and details with dimensions are given in Table I for filter designed using FR4 substrate, where g_{0} and g_{6} represent the source and load sections included for matching purpose.
As we can see from Table I, a combination of high and lowimpedance lines can be used to realized L_{2}/C_{1} and L_{4}/C_{2} resonators [^{1}[1] D.M. Pozar: “Microwave Engineering,” John Wiley & Sons Inc; 2012.],[^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.], which offers high reflections due to unwanted reactance and susceptance at their junctions, respectively. In addition, these combinations will have a large size [^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.]. To realize the shunt connected series LC for a threepole symmetric stepped impedance LPF with the elliptic reponse, the low impedance lines (C’s) are connected in series with high impedance CPW line (L’s) as DGS to ground plane [^{34}[34] M. C. VelazquezAhumada, J. Martel, and F. Medina, “Lowpass Elliptic Filters Using Mixed MicrostripCPW Technologies,” PIERS Online, vol. 3, no. 7, pp. 997999, 2007.].In order to make a symmetrical structure, initially the following approximation formula is used to estimate a single transmission line for L_{2}/C_{1} and L_{4}/C_{2} resonators [^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.].
where B_{2}(f) represents a “compensated” susceptance formed by the line elements L_{2} and C_{1}, and ΔB_{123}(f) represents an unwanted total equivalent susceptance due to the first three inductive line elements (L_{1}, L_{2} and L_{3}) [^{2}[2] H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.].
We estimated the dimensions of low impedance lines (C’s) to represent the shunt connected series LC using equation (7) Similar approach has been applied for the line elements L_{4} and C_{2} to be realized with a single transmission line. The approximate lengths of all sections are given in Table I. An HLELPF with these dimensions is designed on Computer Simulation Technology (CST) software as shown in Figure 2(a) where top layer is synthesized for the symmetrical filter. The optimized dimensions (width W’s and length L’s) are given in Table I. This complete LPF design has dimensions of 25.59 mm × 11.6 mm.
As can be seen in Figure 2(b), the cutoff frequency (f_{C}) is obtained as 4.22 GHz and in the passband centered at 2 GHz, the maximum return loss (RL) is 18 dB and the insertion loss (IL) is 0.41 dB. The bandwidth of stopband is obtained from 5.1 to 11.2 GHz i.e. 6.1 GHz corresponding to 10 dB attenuation.
III. HLELPF WITH DEFECTED GROUND STRUCTURE
A. Simulation of HLELPF with slot and interdigital capacitor DGS
For an improvement in the stopband, we introduced a simple rectangular shape slot as a defected ground structure (DGS) just below the three highimpedance lines of top layer [^{3}[3] Y. Yang, X. Zhu and N. C. Karmakar, “A Novel Microstrip Lowpass Filter Using Compact Microstrip Resonant Cells and Uniquely Shaped Defected Bottom Structures,” Microwave Opt Technol Lett, vol. 54, pp. 2462–2464. 2010.]. On the bottom layer, the two side slots are made of size of 4.90 mm width × 3.70 mm length whereas the center slot has the size of 4.90 mm width × 5.60 mm as illustrated in Figure 3(b) [^{32}[32] D. Gadvi and U. Shah, “Microstrip Lowpass Filter Designs Using Defected Bottom Structure,” International J of Research in Engg Tech, vol. 4, no. 10, pp. 4348, 2015.]. The etched rectangular slots individually act as a shunt LC resonator, in which the etched area size is controlling the inductance and capacitance is controlled by the distance between the edges. On increment of the etched area series inductance is enhanced with corresponding decrease in the shunt capacitance due to increment in between the edges. Due to the introduction of slots, additional shunt LC resonators are developed shown in Figure 3(c), which alters the current distribution on the bottom layer and so the frequency response also varied with slightly change in the attenuation poles.
(a) Top and (b) bottom layers of HLELPF (Design 2) and (c) equivalent lumped prototype of bottom layer.
In respect to the equivalent circuit shown in Figure 3(c), the input impedance Z_{in} of the bottom layer is modeled using the lumped elements [^{35}[35] M. M. Rehaman, M. S. Islam, H. Y. Yong, T. Alam, M. T. Islam, “Performance Analysis of a Defected GroundStructured Antenna Loaded with StubSlot for 5G Communication,” Multidisciplinary Digital Publishing Institute, vol. 19, no. 11, 2634, Sept. 2019., ^{36}[36] M. K. Khandelwal, B. K. Kanaujia, S. Kumar, “Defected Ground Structure: Fundamentals, Analysis, and Applications in Modern Wireless Trends,” International Journal of Antennas and Propagation, vol. 2017, Article ID 2018527, 22, 2017.] as given in the equation (8),
The values of equivalent lumped elements are obtained as: L_{1}=L_{2}=L_{4}=L_{5}= 6.12 nH, L_{3}=9.26 nH, C_{1}=C_{3}= 0.0297 pF, C_{2}=0.0196 pF. These lumped values provide the resonant frequencies of 11.8 GHz and 11.814 GHz, respectively due to first (and third) and second resonators. So, as the slot dimensions generated the resonant frequencies of about 11.8 GHz, the reflections are found to increase at 11.2 GHz and beyond. So, in 11.8 to 14.25 GHz range, the S_{21} response is flattened to about 7dB. Consequently, stopband BW increases to 6.8 GHz, as shown in Figure 4. In addition, a maximum insertion loss (IL) of 0.53 dB is found in passband. At f_{C} = 4.25 GHz, the phase delay and group delay are obtained as 0.107 ns and 0.179 ns, respectively. In such slot DGS, changing the slot dimensions can shift the frequency however further reduction in transmission loss is less expected. To further improve the stopband BW, the DGS can be modified with incorporation of a band stop filter with sufficient bandwidth at the bottom layer.
In the next modification, an interdigital capacitor (IDC) is used as a DGS in place of the rectangular slot resonator as shown in Figure 5(a) and (b) [^{32}[32] D. Gadvi and U. Shah, “Microstrip Lowpass Filter Designs Using Defected Bottom Structure,” International J of Research in Engg Tech, vol. 4, no. 10, pp. 4348, 2015.]. Here, the metal finger has a dimension of 0.49 mm × 3.2 mm for targeting high reflection near 12.5 GHz and beyond. First, we placed IDC at the center i.e. in place of the second slot of Design 2 whereas in the second modification on the bottom layer as in Figure 5(b), IDC of same dimensions is placed on two side slots by 90° rotation and center rectangular slot is kept same [^{32}[32] D. Gadvi and U. Shah, “Microstrip Lowpass Filter Designs Using Defected Bottom Structure,” International J of Research in Engg Tech, vol. 4, no. 10, pp. 4348, 2015.]. The equivalent circuits of bottom layer with such modifications are shown in Figure 5(c) and (d), respectively. Here, IDC is presented by a series RLC resonator with two shunt capacitor.
Interdigital capacitor on the bottom layer of filter (a) first modification (Design 3), (b) second modification (Design 4), (c) equivalent circuit of bottom layer (Design 3), (d) equivalent lumped prototype of bottom layer (Design 4).
As the width of the metal finger is directly related to the capacitance of the IDC so, the increment of width of the capacitor leads to decrease in the equivalent capacitance. If the number of fingers is increased with keeping width of the fingers and space between fingers constant, then capacitance of IDC increases with corresponding decrease in the quality factor. With increasing space between the fingers, then the capacitive effect of the IDC is increased. The similar effect can also be observed on the equivalent inductance of the bottom layer. Equivalent circuit of IDC suggested the extension of stopband by higher capacitance or reduced inductance as IDC is a multiconductor structure with passband and stopbands [^{37}[37] F. P. CasaresMiranda, P. Otero, E. MárquezSegura et al, “Wire Bonded Interdigital Capacitor,” IEEE Microwave and Wireless Components Letters, vol. 15, no. 10, pp. 700702, 2005.]. With the equivalent circuit model as shown in Figure 5(c) [^{35}[35] M. M. Rehaman, M. S. Islam, H. Y. Yong, T. Alam, M. T. Islam, “Performance Analysis of a Defected GroundStructured Antenna Loaded with StubSlot for 5G Communication,” Multidisciplinary Digital Publishing Institute, vol. 19, no. 11, 2634, Sept. 2019., ^{36}[36] M. K. Khandelwal, B. K. Kanaujia, S. Kumar, “Defected Ground Structure: Fundamentals, Analysis, and Applications in Modern Wireless Trends,” International Journal of Antennas and Propagation, vol. 2017, Article ID 2018527, 22, 2017., ^{38}[38] R. S. Beeresha, A. M. Khan, M. Reddy H V, “Design And Optimization Of Interdigital Capacitor,” International Journal of Research in Engineering and Technology, vol. 5, no. 21, pp. 7378, Nov. 2016.], the input impedance formula as shown in equation (9) is obtained as,
The values of equivalent lumped elements of bottom layer (Design 3) are found as: L_{1}=L_{2}= 6.122 nH, C_{1}=C_{2}= 0.0297 pF, R_{s}=0.7003 Ω, L_{s}=0.8796 nH, C_{s}= 28.9821 pF, C_{p1}=C_{p2}= 0.17593 pF. From these lumped element values, the resonant frequencies are obtained as 11.8 GHz (passed) and 9.1 GHz (stopped) for the shunt and series/shunt LC resonators, respectively due to the end slots and IDC, with the given dimensions on the bottom layer (Figure 5a).
For the equivalent circuit with 90° rotation in the side slots shown in Figure 5(d), Z_{in} is written as [^{35}[35] M. M. Rehaman, M. S. Islam, H. Y. Yong, T. Alam, M. T. Islam, “Performance Analysis of a Defected GroundStructured Antenna Loaded with StubSlot for 5G Communication,” Multidisciplinary Digital Publishing Institute, vol. 19, no. 11, 2634, Sept. 2019., ^{36}[36] M. K. Khandelwal, B. K. Kanaujia, S. Kumar, “Defected Ground Structure: Fundamentals, Analysis, and Applications in Modern Wireless Trends,” International Journal of Antennas and Propagation, vol. 2017, Article ID 2018527, 22, 2017., ^{38}[38] R. S. Beeresha, A. M. Khan, M. Reddy H V, “Design And Optimization Of Interdigital Capacitor,” International Journal of Research in Engineering and Technology, vol. 5, no. 21, pp. 7378, Nov. 2016.],
The lumped element values are obtained for the bottom layer as: L_{1}= 9.348 nH, C_{1}= 0.0194 pF, R_{s1}=R_{s2}=1.7429 Ω, L_{s1}=L_{s2}= 1.117 nH, C_{s1}=C_{s2}= 13.546 pF, C_{p1}=C_{p2}= C_{p3}= C_{p4}= 0.17593 pF. With these values the small transmission at 11.8 GHz is possible due to the center (second) slot and beyond it, the side IDCs support the nontransmission of higher frequency. The simulated responses of Design 3 and Design 4 are given in Figure 6(a) and (b), respectively.
As the values of inductance and capacitance generated in the side slots have offered a passband around 11.8 GHz and afterwards the stopband with minor change in f_{C} (4.255 GHz), IL and RL in pass band as can be seen in Figure 6(a). This modification has slightly decreased the BW of stopband to 6.5 GHz due to a transmission peak of 7 dB at 11.8 GHz due to first and third slots. For the second modification on the bottom layer as in Figure 5(b), the stopband BW is further reduced to 6.1 GHz with a resonance peak at 11.5 GHz (shown in Figure 6b). However, the reflections are higher beyond this frequency due to two side IDCs till the negative reflection peak at 13.9 GHz. Miniaturization of IDC beyond above mentioned dimensions is difficult, which restricts shifting of passband and stopband towards higher frequency. So, if the peak at 11.8 GHz can be addressed by other means, the increase in stopband BW is possible.
B. Simulation of HLELPF with IDC/CSRR
To achieve stop frequency as 11.8 GHz, we have incorporated a complementary split ring resonator (CSRR) arranged in a mirror orientation and IDC, respectively on the place of the side slots and on the centre slot with slight change in dimensions. The physical dimensions of CSRR are taken as follows: width and length of fingers are 0.49 mm and 4.9 mm, respectively with a gap of 0.4 mm. The top layer, bottom layer and equivalent circuit of bottom layer are shown in Figure 7.
(a) Top layer, (b) bottom layer of HLELPF with IDC/CSRR (Design 5), and (c) equivalent lumped prototype of bottom layer.
After the insertion of CSRR, the lumped element values of inductor and capacitor decrease significantly in order to increase the stop band frequency from previous designs where only IDC and rectangular slot DGS have been placed. Thus, the characteristic impedance of the bottom layer for such filter structure is increased. From Figure 7(b), an equivalent lumped element circuit of the bottom layer can be designed as shown in Figure 7(c) [^{33}[33] R. Selvaraju, M. H. Jamaluddin, M. R. Kamarudin et al,”Complementary Split Ring Resonator for Isolation Enhancement in 5G Communication Antenna Array,” Progress in Electromagnetics Research C, vol. 83, pp. 217228, 2018., ^{38}[38] R. S. Beeresha, A. M. Khan, M. Reddy H V, “Design And Optimization Of Interdigital Capacitor,” International Journal of Research in Engineering and Technology, vol. 5, no. 21, pp. 7378, Nov. 2016.], where IDC is presented by a series RLC resonator with two shunt capacitors and mirrored CSRR is by two shunt LC resonators. The equivalent input impedance formula as shown in equation (11).
The values of lumped elements are obtained as: L_{1}=L_{2}=L_{3}=L_{4}= 1.13nH, C_{1}=C_{2}=C_{3}=C_{4}= 1.33pF, C_{p1}=C_{p2}= 0.22pF, L_{s}= 1.114nH, C_{s}= 13.546 pF, R_{s}= 0.34Ω. These values suggested 4.4 GHz as a resonant stop frequency due to CSRR/IDC and so, its harmonics are stopped which will lead to the wide stop band.
In the simulation response of this design shown in Figure 8, the maximum RL of 16 dB and IL of 0.42 dB are obtained at 2.9 GHz i.e. ripples in passband are shifted. Although f_{C} increases to 4.34 GHz due to CSRR, significant increase in stopband BW is also noticed from 6.5 GHz to 8.8 GHz (i.e. 5.2  14 GHz). This happened due to increment of characteristic impedance by insertion of CSRR which slightly changes the resonant frequency of the overall filter structure as discussed above and the quality factor is also observed to reduce. The further rejection of band from 11.8 GHz to 14 GHz is observed due to CSRRs on the both side slots, which resulted in the wide stopband.
IV. SIMULATION OF HLELPF WITH USHAPED LINE AND IDC/CSRR
In order to address the compactness of filter, top layer is modified by inserting a U shaped highimpedance line in place of the straight line as reported in [^{5}[5] A. Rajput, K. Patel and A. Birwal, “Compact Microstrip Lowpass Filter Design Using UShaped Folded HighImpedance Line,” Microw Opt Technol Lett, vol. 60, pp. 1812–1815, 2018.]. On top layer of this filter, dimensions of lowimpedance line are kept unchanged and on the bottom layer, IDC/CSRR DGS of Figure 7(b) is placed as shown in Figure 9(a). Also to mitigate the problems of parasitic capacitance due to reflections and accumulation of charges at the corners of Ushaped lines, a 50% mittering is performed with the dimension of 0.42 mm at the corners in all three Ushaped lines, which is shown in Figure 9(b) keeping the same bottom layer (as in Figure 7b). Lumped equivalent model of its bottom layer is same as mentioned in Figure 7(c), there is no significant change is expected in lumped element values due to Ushaped line in the top layer of the structure. However, the physical length of the filter is reduced. The initial simulated responses of such two designs showed a 3dB f_{C} close to 4 GHz, but with harmonics at the stopband. Harmonics at the stopband occurred due to the different L values (sizes), so such modifications on top layer deteriorate the flatness of stop band, although the BW of stopband increased beyond frequency of 16 GHz as reason is mentioned in previous design description. Harmonic reduction achieved by increasing IDC capacitance and shifting the CSRR resonance, which regained flatness in stopband. Thus, the final optimized bottom layer with dimensions is shown in Figure 9(c).
(a) Top layer of HLELPF with Ushaped line (Design 6) and (b) top layer with mitered Ushaped line (Design 7), and (c) optimized bottom layer with IDC/CSRR DGS.
In the simulation response of HLELPF with Ushaped line and optimized IDC/CSRR (Figure 10a), the values are obtained as follows: minimum RL in the pass band as 15 dB @ 2 GHz with IL of 0.54 dB, phase delay and group delay as 0.161 ns and 0.244 ns, respectively at f_{C} = 4.07 GHz and bandwidth of stopband as 11.01 GHz (5.07 – 16.98 GHz). Increment in insertion loss is observed due to conductor loss of metal and dielectric loss of dielectric material used in CSRR instead of a slot, which basically depends on loss tangent of the material. Rolloff factor of the filter is also found to be increased upto 6.145 dB/GHz due to insertion of DGS elements as more number of elements increases the order of the overall filter i. e. sharpness as noticed after simulation. Here two attenuation poles are obtained at 8.484 GHz and 12.51 GHz due to variation of inductance lengths. Also, one resonance peak of 7.85 dB in S_{11} is observed at 14.82 GHz. The overall dimension of the filter is reduced to 22.22 mm × 9.5 mm i.e. by 28.89% compared to the original design of Figure 2(a). Similar response is observed for HLELPF with mitered Ushaped line, which is shown in Figure 10(b) except a peak of 8.35 dB in S_{11} at 14.88 GHz. However, the advantage of this Design 7 is BW of 12.0 GHz for stopband corresponding to 10 dB attenuation.
Simulated Sparameter response of (a) HLELPF with Ushaped line and (b) HLELPF with mitered Ushaped line.
The characteristics of lowpass filter designs reported in this work are summarized in Table II as discussed in this section and previous section. The LPF performance parameters like, rolloff rate (β), relative stopband (RSB) bandwidth for 20 dB return loss, normalized circuit size (NCS), and figureofmerit (FOM) are calculated from the known relations [^{9}[9] J. L. Li, S. W. Qu and Q. Xue,”Compact Microstrip Lowpass Filter With Sharp RollOff And Wide StopBand,” Electronics Letters, vol. 45, no.2, pp. 110–111, 2009., ^{18}[18] M. Hayati, F. Shama, “A Compact Lowpass Filter with Ultra Wide Stopband Using Stepped Impedance Resonator,” Radioengineering, vol. 26, no. 1, pp. 269274, 2017.] and comparison of last three designs is given in Table III.As given in Table III, the performances of Design 6 and Design 7 are comparable to the earlier reported filters [^{8}[8] L. H. Hsieh and K. Chang, “Compact EllipticFunction LowPass Filters Using Microstrip SteppedImpedance Hairpin Resonators,” IEEE Trans on Microwave Theory and Techniques, vol. 51, no. 1, pp. 193–199, 2003., ^{19}[19] D. Packiaraja, K. J. Vinoy, M. Ramesh et al, “Design of Compact Lowpass Filter with Wide Stopband Using TriSection Stepped Impedance Resonator,” Int. J. Electron. Commun. (AEÜ),vol. 65, pp. 1012– 1014, 2011., ^{21}[21] A. O. Ertay and S. Simsek, “Design of EllipticFunction Microstrip Filters with Defected Bottom Structures,” In: PIERs Proceedings, Stockholm, Sweden, pp. 18381842, 2013., ^{31}[31] A. TiradoMendez, H. JardonAguilar, R. FloresLeal et al.”Improving Frequency Response Of Microstrip Filters Using Defected Bottom and Defected Microstrip Structures,” Progress in Electromagnetic Research C, vol. 13, pp. 7790, 2010.]. In addition, the proposed filters in this work achieved wide stopband of 8.15 GHz with high attenuation (> 20 dB) in the stopband with the compact circuit size.
V. CONCLUSION
A fifth order hilo elliptic LPF was simulated for the cutoff frequency of 4.2 GHz on FR4 substrate for a wide band stop response. The results showed that the insertion loss in the low frequency passband is less than 0.5 dB from DC to 4 GHz and the stopband of 6.1 GHz BW is obtained corresponding to the 10 dB attenuation for the initial filter design. On improvisation using various DGSs like slot, interdigital capacitor and CSRR, the stopband BW increases to 8.8 GHz without affecting other parameters of this filter. Further replacing high impedance line on top layer by Ushaped line with mitering leads to compactness of filter by about 29% and offered the wide stopband BW of 12 GHz with attenuation level higher than 10 dBas well, which equals to 3fc. The final compact proposed filter has the dimensions of 22.22 mm × 9.5 mm, in which RL, IL, rolloff rate and stop band BW are improved by about 9.7%, 26.5%, 42% and 80%, respectively. In future, modifications on the top layer like use of “S” or “C” shaped line for compact filter can be applied and to improve the stopband response, slot on capacitive line of top layer or different shapes of slots in bottom plane such as elliptic, semicircular, triangular, pishaped can be incorporated.
ACKNOWLEDGMENT
The work was supported by the Research & Development Scheme 201516 of the University of Delhi (RC/2015/9677 dated 15/10/2015).
REFERENCES

^{[1]}D.M. Pozar: “Microwave Engineering,” John Wiley & Sons Inc; 2012.

^{[2]}H. J. Sheng, M. J. Lancaster, “Microstrip Filters For RF/Microwave Applications,” John Wiley And Sons Inc, pp 2975, pp. 117121, 2001.

^{[3]}Y. Yang, X. Zhu and N. C. Karmakar, “A Novel Microstrip Lowpass Filter Using Compact Microstrip Resonant Cells and Uniquely Shaped Defected Bottom Structures,” Microwave Opt Technol Lett, vol. 54, pp. 2462–2464. 2010.

^{[4]}M. A. Zhewang, K. Nomiyama and Y. Kobayashi, “Microstrip Lowpass Filters with Reduced Size and Improved Stopband Characteristics,” IEICE Trans Electron, vol. E88–C, pp. 6267, 2005.

^{[5]}A. Rajput, K. Patel and A. Birwal, “Compact Microstrip Lowpass Filter Design Using UShaped Folded HighImpedance Line,” Microw Opt Technol Lett, vol. 60, pp. 1812–1815, 2018.

^{[6]}M. Hayati, F. Shama, “Compact Microstrip LowPass Filter with Wide Stopband Using Symmetrical UShaped Resonator,” IEICE Electronics Express, vol. 9, no. 3, pp. 127–132, 2012.

^{[7]}M. R. Khezeli, M. Hayati and A. Lotfi, “Compact Wide Stopband Lowpass Filter Using Spiral Loaded Tapered Compact Microstrip Resonator Cell,” International Journal of Electronics, vol. 101, no. 3, pp. 335–382, 2014.

^{[8]}L. H. Hsieh and K. Chang, “Compact EllipticFunction LowPass Filters Using Microstrip SteppedImpedance Hairpin Resonators,” IEEE Trans on Microwave Theory and Techniques, vol. 51, no. 1, pp. 193–199, 2003.

^{[9]}J. L. Li, S. W. Qu and Q. Xue,”Compact Microstrip Lowpass Filter With Sharp RollOff And Wide StopBand,” Electronics Letters, vol. 45, no.2, pp. 110–111, 2009.

^{[10]}M. Yang, J. Xu and Q. Zhao et al, “Compact Broad Stopband Lowpass Filters Using SIRsLoaded Circular Hairpin Resonators,” Progress in Electromagnetics Research, vol. 102, pp. 95–106, 2010.

^{[11]}V. K. Velid and S. Sanyal, “Sharp RollOff Lowpass Filter with Wide Stopband Using StubLoaded CoupledLine Hairpin Unit,” Microwave and Wireless Components Letters, vol. 21, no.6, pp. 301–303, 2011.

^{[12]}M. Hayati, F. Shama and H. Abbasi, “Compact Microstrip Lowpass Filter with Wide Stopband and Sharp RollOff Using Tapered Resonator,” International Journal of Electronics, vol. 100, no. 12, pp. 1751–1759, 2013.

^{[13]}M. Hayati and A. Lotfi, “EllipticFunction Lowpass Filter with Sharp Cutoff Frequency Using SlitLoaded Tapered Compact Microstrip Resonator Cell,” Electronics Letters,vol.46, no. 2, pp. 143–144, 2010.

^{[14]}J. Wang, L. J. Xu, S. Zhao, Y. X. Guo et al, “Compact QuasiElliptic Microstrip Lowpass Filter With Wide Stopband,” Electronics Letters, vol. 46, no. 20, pp. 1384–1385, 2010.

^{[15]}J. Wang, H. Cui and G. Zhang, “Design of Compact Microstrip Lowpass Filter with UltraWide Stopband,” Electronics Letters, vol. 48, no. 14, pp. 854–856, 2012.

^{[16]}J. P. Wang,L. Ge, Y. X. Guo and W. Wu, “Miniaturised Microstrip Lowpass Filter With Broad Stopband And Sharp RollOff,” Electronics Letters, vol. 46, no. 8, pp. 573–575, 2010.

^{[17]}M. Hayati, M. Validi, F. Shama et al,”Compact Microstrip Lowpass Filter with Wide Stopband Using P Shaped Resonator,”Journal of Microwaves, Optoelectronics and Electromagnetic Applications,vol.15, no. 4, pp. 309318, 2016.

^{[18]}M. Hayati, F. Shama, “A Compact Lowpass Filter with Ultra Wide Stopband Using Stepped Impedance Resonator,” Radioengineering, vol. 26, no. 1, pp. 269274, 2017.

^{[19]}D. Packiaraja, K. J. Vinoy, M. Ramesh et al, “Design of Compact Lowpass Filter with Wide Stopband Using TriSection Stepped Impedance Resonator,” Int. J. Electron. Commun. (AEÜ),vol. 65, pp. 1012– 1014, 2011.

^{[20]}S. H. Kazemi and M. A. Hayati “Compact Microstrip Lowpass Filter with Wide Stopband,” International Journal of Microwave and Wireless Technologies, vol. 11, no. 9, pp. 885893, 2019.

^{[21]}A. O. Ertay and S. Simsek, “Design of EllipticFunction Microstrip Filters with Defected Bottom Structures,” In: PIERs Proceedings, Stockholm, Sweden, pp. 18381842, 2013.

^{[22]}J. X. Chen, J. L. Li, K. C. Wan et al, “Compact QuasiElliptic Function Filter Based On Defected Bottom Structure,” In: IEE Proceedings: Microwaves, Antennas and Propagation, vol. 153, no. 4, pp. 320324, Aug. 2006.

^{[23]}A. B. AbdelRahman, A. K. Verma, A. Boutejdar et al, “Compact Stub Type Microstrip Bandpass Filter Using Defected Bottom Plane,”IEEE Microwave and Wireless Components Letters, vol. 14, no. 4, pp. 136 – 138, 2014.

^{[24]}W. H. Tu and K. Chang, “Compact Microstrip LowPass Filter with Sharp Rejection,” IEEE Microwave and Wireless Components Letters,vol. 15, no. 6, pp. 404406, 2005.

^{[25]}M. Al Sharkawy, A. Boutejdar and E. G. Mahmoud,”Design of UltraWide StopBand DGS LowPass Filter Using Meander and Multilayer Techniques,” Microwave and Optical Technology Letters, vol. 55, no. 6, pp. 12761281, 2013.

^{[26]}C. Chang, W. Chen and Z. Zhang, “A Novel DualMode DualBand Bandpass Fllter with DGS,” In: PIERS Proceedings. Marrakesh, Morocco, pp. 17231726, Mar. 2011.

^{[27]}A. B. AbdelRahman, A. K. Verma, A. Boutejdar et al, “Control Of Bandstop Response Of HiLo Microstrip LowPass Fllter Using Slot In Bottom Plane,” IEEE Transactions on Microwave Theory and Techniques, vol. 52, no. 3, pp. 10081013, 2004.

^{[28]}A. Kumar, A. Sawant and M. V. Kartikeyan, “Investigation of Fractal DGS Microwave Fllters,” In: Proceedings of 2013 National Conference On Communications (NCC), pp.14, Feb. 2013.

^{[29]}S. V. Makki AlDin, A. Ahmadi, S. Majidifar et al, “Sharp Response Microstrip LPF Using Folded Stepped Impedance Open Stubs,” Radio Engineering, vol. 22, no. 1, pp. 328332,2013.

^{[30]}R. Y. Yang,Y. L. Lin,C. Y. Hung et al, “Design of A Compact And SharpRejection LowPass Filter With a Wide Stop Band,” Journal of Electromagnetic Waves and Applications, vol. 26, no. 1718, pp.2284–2290. 2012.

^{[31]}A. TiradoMendez, H. JardonAguilar, R. FloresLeal et al.”Improving Frequency Response Of Microstrip Filters Using Defected Bottom and Defected Microstrip Structures,” Progress in Electromagnetic Research C, vol. 13, pp. 7790, 2010.

^{[32]}D. Gadvi and U. Shah, “Microstrip Lowpass Filter Designs Using Defected Bottom Structure,” International J of Research in Engg Tech, vol. 4, no. 10, pp. 4348, 2015.

^{[33]}R. Selvaraju, M. H. Jamaluddin, M. R. Kamarudin et al,”Complementary Split Ring Resonator for Isolation Enhancement in 5G Communication Antenna Array,” Progress in Electromagnetics Research C, vol. 83, pp. 217228, 2018.

^{[34]}M. C. VelazquezAhumada, J. Martel, and F. Medina, “Lowpass Elliptic Filters Using Mixed MicrostripCPW Technologies,” PIERS Online, vol. 3, no. 7, pp. 997999, 2007.

^{[35]}M. M. Rehaman, M. S. Islam, H. Y. Yong, T. Alam, M. T. Islam, “Performance Analysis of a Defected GroundStructured Antenna Loaded with StubSlot for 5G Communication,” Multidisciplinary Digital Publishing Institute, vol. 19, no. 11, 2634, Sept. 2019.

^{[36]}M. K. Khandelwal, B. K. Kanaujia, S. Kumar, “Defected Ground Structure: Fundamentals, Analysis, and Applications in Modern Wireless Trends,” International Journal of Antennas and Propagation, vol. 2017, Article ID 2018527, 22, 2017.

^{[37]}F. P. CasaresMiranda, P. Otero, E. MárquezSegura et al, “Wire Bonded Interdigital Capacitor,” IEEE Microwave and Wireless Components Letters, vol. 15, no. 10, pp. 700702, 2005.

^{[38]}R. S. Beeresha, A. M. Khan, M. Reddy H V, “Design And Optimization Of Interdigital Capacitor,” International Journal of Research in Engineering and Technology, vol. 5, no. 21, pp. 7378, Nov. 2016.
Publication Dates

Publication in this collection
11 Nov 2020 
Date of issue
Dec 2020
History

Received
07 July 2020 
Reviewed
09 July 2020 
Accepted
13 Oct 2020