Compact Band-Pass Filter Using Modified Ω-shaped Resonator and Source Load Coupling for Transmission Zero Improvement

This article investigates a compact band-pass filter using modified Ω-shaped resonator and source load coupling for transmission zero improvement. In this article, source load coupling has been used to improve the insertion loss response and a number of transmission zeros in the upper stop-band, so that the chance of interference from adjacent wireless bands can be reduced. In order to determine the metamaterial characteristics for the designed filter structure dispersion diagram and vectored electric-field with no phase variation has been illustrated. The simulated and measured 3dB fractional bandwidth for the designed filter structure is 26.05% and 26.12% at the center frequency of 2.38 and 2.33 GHz respectively. It offers compactness with an electrical footprint area of 0.245λg × 0.201λg, where λg is the guided wavelength at the center frequency of 2.33 GHz. The presented filter structure seems a potential candidate for different wireless applications such as Bluetooth (2.4–2.48 GHz), WLAN/WiFi (2.4–2.49 GHz) and Wi-MAX (2.5–2.69 GHz).


Introduction
The recent development in wireless communication system requires compact band-pass filter with improved insertion loss performance [1]. In early years, several attempts have been utilized to reduce the filter size. For this purpose, in the year of 1998, Yu et al. [2] utilized open loop resonators coupled with crossing lines. Further, in the year of 2004, Allison filed a U.S. patent on compact edge coupled filter. In this approach the parallel edge coupled filter has been modified into multiple coupled resonators [3]. Size of the resonator of these filters is nearly half of the guided wavelength which restricts the compactness. In order to overcome the above mentioned problem, a new approach of MTMs (metamaterials) came into existence.
MTMs are artificially designed materials with unique properties of negative permittivity and permeability [4]. Several efforts have been made which utilizes the concept of MTMs to improve the response of compact filters [5][6][7][8][9][10]. In [5] Luo et al. utilized a complimentary split ring based resonator to design a bandpass filter with wideband and improved selectivity. A CPW fed compact bandpass filter with controllable transmission zeros (TZs) by separated electric and magnetic coupling has been discussed in [6]. In [7], Tang et al. utilized meandered loop hexagon line to reduce the size of the filter. Further, in literature [9], a compact dual band bandpass filter has been designed and investigated. Among both the filtering bands one band is claimed with the modified complementary split ring resonator and another with interdigital capacitor. In the year of 2019, Choudhary et al. [10] utilized folded coupled line and open-circuited L-shaped strip to design a compact dual band bandpass filter. Another approach to design a bandpass filter with substrate integrated waveguide has been reported in [11].
In this article, a compact bandpass filter using modified Ω shaped resonator and source load coupling for TZ improvement has been designed and discussed. In order to design this filter structure the concept of CRLH-TL has been utilized. Designed filter structure is configured with series gap and shunted via to offer left handed capacitance and left handed inductance. Further source load coupling improves insertion loss performance and introduces additional TZ in the upper stopband.

Design and Analysis for Designed Bandpass Filter
Design procedure of the proposed filter structure starts from the concept of CRLH-TL. It is a well-known factor that the perfect right-handed transmission line has low-pass nature and the perfect left-handed transmission line has high-pass nature. The CRLH-TL is the combination of perfect right-handed and perfect left-handed transmission line. From the above discussion it can be concluded that the CRLH-TL has bandpass nature. The selection of modified Ω-shaped resonator has been done to achieve more compactness [4]. Initially, with the use of via and series gap simplified CRLH-TL based structure has been created, shown in Fig. 1(a).
To improve the response, patches are introduced which modify the associated series inductance and capacitance and offer two resonance peaks with negligible bandwidth, as shown in Fig. 1(b). Further the ground plane has been modified to improve the matching and allows a wideband response, Fig. 1(c). In order to achieve a desired response, filter dimensions have been optimized. For this purpose Ansys HFSS 13.0 three dimensional electromagnetic full wave simulator have been used. After that the source to load coupling has been done to improve the insertion loss response, depicted in Fig. 1(d).
The geometrical configuration of the designed filter structure with its proportions has been mentioned in Fig. 2. The equivalent circuit diagram for the designed filter structure, Fig. 3(a), have left-handed capacitance (C L ) which is modelled by the separation between patches (G 1 ). The feed line and patches represent right-handed inductance L R1 and L R2 respectively. Further the separation between source and load feed lines (G) originates one coupling capacitance (C C ) in series. Left-handed inductance (L L ) is associated with via and bottom ground plane structure and the separation between top and bottom structure separated by substrate creates right-handed capacitance (C R ). In order to investigate the MTM property of the designed filter structure Bloch-Floquet theorem has been exploited. According to this the dispersion relation can be expressed in terms of immittances of equivalent circuit diagram Here d, Z s (ω), Y p (ω) and β(ω) are the physical length of the unit cell, series impedance, shunt admittance and propagation constant respectively.
Condition for the occurrence of resonance is given in (4) Equations (1) and (4) can be utilized to calculate the dispersion relation and zeroth order resonance (ZOR). Dispersion relation can also be expressed in terms of S-parameters [12].
Simulated dispersion graph has been plotted and shown in Fig. 3(b). Since the ZOR is the point at which βd become zero means ZOR supports infinite wave propagation at a non-zero frequency. So it is evident from the graph that the ZOR occurred at the frequency of 2.21 GHz. Additionally, the graph has two sections those are separated by ZOR, i.e. LH-region and RH-region. LH region extended from 2 to 2.21 GHz while RH-region lies from 2.21 to 2.72 GHz. In order to validate the equivalent circuit  Further, ZOR has been also confirmed by the no phase variation graph of vectored E (electric) field, shown in Fig. 4. It can be clearly observed that the vectored Efield has almost no phase variation on the patches and feed lines, hence confirms ZOR [13].  Figure 5(a) shows the transmission coefficient graph at various values of G (gap between source and load feedlines). Decrement in G corresponds to stronger coupling between source and load treated as port-1 and port-2, which results into an additional transmission zero in the upper stopband of the filter response. It can be explained by the phase difference between the RF signal propagates from Ω shaped path and source load coupling path at the port-2 [14]. Figure 5(b) depicts the input reflection coefficient plot at distinct values of G 1 . It is evident that by increasing G 1 (separation between patches) both the resonance frequencies are shifted towards higher frequencies.

Result and Discussion
The top and bottom view of the fabricated proto-type of the designed filter structure has been shown in Fig. 6. It is printed on the Roger RT-Duroid 5880 substrate (ε r = 2.2) of thickness 1.58 mm. The simulated and measured S-parameters for the designed filter structure have been depicted in Fig. 7. It is observed that the simulation and measured S-parameters follow approximately same pattern. The deviation in simulated and measured S-parameters may be because of the substrate non-uniformity, soldering losses, fabrication tolerance. It may be also because of the uncertainty of the relative dielectric constant and the height of the substrate [ The designed filter structure offers 3dB simulated and measured fractional bandwidth of 26.05% and 26.12% centered at 2.38 and 2.33 GHz respectively. It offers compactness with electrical footprint area of 0.245λ g × 0.201λ g , where λ g (ε eff = 1.6, λ g = 101.78 mm) is the guided wavelength at the center frequency of 2.33 GHz. In order to calculate the effective permittivity (ε eff ) and guided wavelength (λ g ) equations (5) and (6) where, H and W stand for thickness of substrate and width of the microstrip-line respectively [15]. On the basis of above two equations the calculated value of effective dielectric constant and guided wavelength are 1.6 and 101.78 mm respectively.
Additionally, it offers maximum simulated and measured transmission coefficient of -0.03 dB and -0.54 dB along with simulated and measured input reflection coefficient better than -15 dB and -14.90 dB in the complete working band. Figure 8 shows the simulated and measured group delay plot for the designed structure which is almost flat throughout the band. Flat response indicates transmission with least distortion. Average simulated and measured group delay for the designed filter structure is 0.91 and 1.71 nsec respectively. Table 1 presents a comparison chart of this work with previously published works.

Conclusion
In this article, a compact band-pass filter using modified Ω-shaped resonator and source load coupling for transmission zero improvement has been illustrated. Designed filter structure provides compactness with overall electrical size of 0.245λ g × 0.201λ g , where λ g is the guided wavelength at the center frequency of 2.33 GHz. In this filter design source to load coupling has been done to improve transmission coefficient and generate two TZs in the upper stop-band. Further, the dispersion analysis has been performed to investigate the MTM property of the designed filter structure.