Sharp Rejection and Wide Stopband Microstrip Lowpass Filters using Complementary Split Ring Resonators

Chebyshev microstrip lowpass filters with improved performance, achieved by means of circular complementary split ring resonators (CSRR), are presented. CSRR particles exhibit frequency rejection bandwidths in the vicinity of their resonant frequencies that can be used to meliorate both selectivity and stopband in microstrip lowpass filters. Two configurations have been used: a stepped-impedance model and a configuration using open-circuited stubs. Microstrip filters having 5, 7 and 9 poles were designed and fabricated. Selectivity values up to 86 dB/GHz and suppression levels reaching 60 dB in the stopband were obtained. The filters have cutoff frequency around 2 GHz and rejection band up to 10 GHz. The insertion of the designed CSRR resonators in the ground plane of the filters removes all the transmission spurious observed in the analyzed frequency band. No considerable variation in the passband group delay is observed in the CSRRbased lowpass filters. A comparison is made among the filters designed in this and other referenced works, considering their number of poles and size. The measured results are in good agreement with the simulated ones. The presented filters can be candidates for applications using the VHF, UHF and L bands, being also very effective in the rejection of the S and C bands. Applications that demand the rejection of the first half of the X band can also use the filters detailed in this paper.


I. INTRODUCTION
Filters are important elements in many radiofrequency/microwave applications.Wireless Communications, for instance, continue to impose strict filter design requirements, demanding lightweight structures having high performance and reduced dimensions and cost [1].An alternative to planar structures is fabricating them using microstrip technology.Improvements in performance for microstrip lowpass filters can be obtained using higher degree structures [2].
The use of complementary split ring resonators (CSRR), first presented by Falcone et al. [3], is an configurations.

II. MICROSTRIP LOWPASS FILTERS: DESIGN AND ANALYSIS
In Fig. 1, the lowpass filter configurations used in this paper are shown.Two configurations have been chosen.The first one, known as stepped-impedance, uses high-impedance microstrip lines to approximate the inductors (L), whereas the capacitors (C) are built using low-impedance microstrip lines.The second configuration uses open-circuited stubs to fabricate the capacitors, maintaining the high-impedance lines to approximate the inductors [1], [2].
The formulations in [1] have been used to design the dimensions of the microstrip sections for each filter.The specifications for the structures are: cutoff frequency (f c = 2 GHz), filter order n (n = 5, 7 and 9), frequency response (Chebyshev, with passband ripple = 0.01 dB), and source/load impedance Z 0 (= 50 Ω).The relevant dimensions of the CSRRs used in this paper are organized in Table II, as well as their resonant frequencies.These values have been calculated using the model in [7].The fabricated modified ground planes are shown in Fig. 6.The CSRR resonators on the ground planes are aligned with the center of their respective microstrip lines, except for those in the extremities, which are 7 mm away from the input and output of the structures.III contains the values of the 3 dB cutoff frequency (f c ), stopband frequency (f s ) and selectivity (ξ) of the filters.The calculation of ξ follows the expression (1), defined in [8]: where α 2 and α 1 represent, respectively, the 20 dB and 3 dB attenuation points.The responses for the 7-pole CSRR-based filters are shown in Fig. 9. Filters F9 and F10 have cutoff frequencies of, respectively, 1.85 and 1.63 GHz.The rejection for these filters starts at 2.12 and 2.05 GHz, respectively.The values of insertion loss in the passband for F9 and F10 are around 1.2 dB.The selectivity values of these filters are presented in Table III.The responses for the 9-pole CSRR-based filters are depicted in Fig. 10.F11 and F12 have 3 dB cutoff frequencies equal to 1.92 and 1.58 GHz, respectively.The corresponding frequency values for the 20 dB attenuation points are 2.15 and 1.87 GHz.It is worth noticing that filter F11 presents an excellent rejection band between 2.42 and 5.23 GHz, with a very high rejection level (> 50 dB).It can be observed that the insertion loss in F11 and F12 is around 1.3 dB, considering the passband.
Different from the previous filters, these 9-pole CSRR-based filters present higher levels of ripple in the passband, which can be a drawback.Table IV presents a performance comparison among some of the designed lowpass filters and other referenced works.As it can be noticed, F8 has an excellent transition bandwidth of 200 MHz, and a stopband bandwidth of 4f c .This result is quite satisfactory, considering that the procedure to design this filter is considerably easier than the approaches described, for instance, to design the filters presented in [5] and [9]- [13].It is also shown a comparison among the sizes of the designed filters and some references.The parameter λ g , in Table IV, is the guided wavelength of a 50 Ω microstrip line at the cutoff frequency of the filter, as stated in [5].
Finally, simulated and measured group delay results are shown in Fig. 11.Considering the filters F11 and F8, which have the best performances (see Table IV), it can be seen that the experimental group delay in the passband (< 2GHz) for both filters has no considerable variation, maintaining its values up to 5 ns.The differences observed between the simulated and measured group delay curves can be interpreted, firstly, as an outcome of the welding losses, present only in the fabricated filters.
Secondly, other losses, as those present in the use of connectors and cables, are also part only of the experimental results.Some disturbances in the group delay curves are seen around the resonance frequencies of the added CSRR resonators.

Fig. 4 .
Fig. 4. Configuration and relevant dimensions of a circular CSRR.The metal parts are depicted in grey.

Fig. 5 .Fig. 6 .
Fig. 5. CSRR-based microstrip lowpass filters.The microstrip sections of the filters are depicted in black and the metallization of the ground plane is depicted in grey.TABLE II.CSRR DIMENSIONS FOR THE FILTERS DEPICTED IN FIG. 5. Filter CSRR radius (mm) c (mm) d (mm) f 0 (GHz) F7 (Fig. 5a)

Fig. 7 .Fig. 8 .
Fig. 7. Design procedure used to obtain the CSRR-based microstrip lowpass filters.IV.RESULTS Simulated and measured S 11 and S 21 results (in dB) of the designed CSRR-based lowpass filters are shown in Fig. 8, Fig. 9 and Fig. 10.A good agreement is observed between the simulated and experimental responses.The results were analyzed considering the experimental values.A comparison between the CSRR-based 5-pole microstrip lowpass filter results is shown in Fig. 8.

Fig. 10 .
Fig. 10.CSRR-based 9-pole microstrip filter S parameters, simulated and measured: (a) F11: stepped-impedance configuration and (b) F12: open-circuited stubs configuration.Comparing the results of the CSRR-based microstrip lowpass filters with the traditional ones (see TableIIIand Figs.[8][9][10], it can be affirmed that the CSRR-based filters having 5 poles presents a performance comparable (F7) or much more superior (F8) to the best result obtained by the traditional filters (F5 and F6), which are 9-pole structures.This leads to a filter with an area reduction of approximately 27%.The transmission spurious bands of the conventional microstrip lowpass filters (see Fig.3) were all removed due to the insertion of the designed CSRR resonators.

TABLE I .
DIMENSIONS (IN MM) OF THE MICROSTRIP SECTIONS OF THE FILTERS

F6 (9-pole)
Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 17 No. 1, March 2018 Fig.8(a), filter F7 has a 3 dB cutoff frequency of 1.95 GHz.The attenuation of this filter drops to 20 dB at 2.44 GHz.The 3dB cutoff frequency of filter F8, whose response is shown in Fig.8(b), is 1.97 GHz.The rejection of this filter occurs at 2.17 GHz.Consequently, F8 is a more selective filter than F7.Both filters have values of insertion loss in the passband around 1.1 dB.Table DOI: http://dx.doi.org/10.1590/2179-10742018v17i11101Brazilian Microwave and Optoelectronics Society-SBMO received 27 Nov 2017; for review 03 Dec 2017; accepted 08 Mar 2018 Brazilian Society of Electromagnetism-SBMag © 2018 SBMO/SBMag ISSN 2179-1074 140 According to

TABLE III .
CUTOFF FREQUENCY, STOPBAND FREQUENCY AND SELECTIVITY OF THE LOWPASS FILTERS.