GAOptimized Compact Broadband CRLH BandPass Filter Using StubInserted Interdigital Coupled Lines
 Author: Jeon Jinsu, Kahng Sungtek, Kim Hyunsoo
 Publish: Journal of electromagnetic engineering and science Volume 15, Issue1, p31~36, 00 Jan 2015

ABSTRACT
The design of a new compact bandpass filter is proposed, which is based on the microstrip composite right and lefthanded transmissionline (CRLHTL) structure. Particularly, the interdigital coupled (IDC) lines of the CRLH geometry are proposed to be parted by inserting open stubs to meet the specifications on the passband. In addition, there is another pair of stubs to complete the design in a limited space. These are considered in the TLbased analysis and the design parameters are calculated by genetic algorithm optimization. The measurement is shown to be acceptable and agreeable with the circuit and electromagnetic field simulations. In addition, the zerothorder resonance (ZOR) phenomenon is verified.

KEYWORD
Broadband , CRLHMetamaterial , Interdigital Coupled Lines , Optimization , StubInserted

I. INTRODUCTION
In recent years, numerous studies have been conducted to exploit the benefits of broadband communication since LTE service began to enable carriers and terminals to transmit and receive hundreds of Mbps of data, as well as to step forward to realize a Gbps data transmission would lead to 5G services. As one of many such research activities, the methods of designing bandpass filters (BPFs) have been reported to keep abreast of evolving wireless communication systems equipped with multifunction antennas and circuitry as well [15].
Ishida and Araki [1] designed a very wideband BPF whose bandwidth is formed by adding zeros in the sections of the transmission line (TL). Its frequency response has notches only at the band edges and has an extremely narrow stopband. Wang et al. [2] presented the microstripandCPW BPF for broadband applications, which is based on the multimode resonator (MMR) in the form of multiples of a quarter wavelength to broaden the bandwidth and obtain an enlarged rejection region. The idea of the MMR of the half wavelength is also used in [3], where the coupled lines of a quarter wavelength are used as the inverter. This work demonstrates the extension of the lower and higher stopbands owing to increased coupling. A composite wideband filter was designed by Menzel et al. [4] by combining low and highpass filters as suspended stripline structures with different planes. Independently, Hsu et al. [5] presented composite microstrip filters for highspeed communication applications, where seven or eight TL sections of about a quarter wavelength are sequentially connected.
Recently, we suggested the design of a novel wideband filter based on the composite right and lefthanded transmission line (CRLHTL) metamaterial [6]. Contrary to the reference [6], we propose the use of one segment (smaller than one quarter wavelength) to make the component very compact. Besides, instead of mixing two types, for instance, as a hybrid of the microstrip and CPW, we use only the microstrip whose fabrication is inexpensive. Especially, in our proposed CRLH BPF geometry, we separate the interdigital coupled (IDC) lines by inserting open stubs between and grounded stubs to form a 1.7GHz bandwidth. Furthermore, out of the CRLH unit, we place another pair of open stubs to improve the passband performance. The proposed filter, whose size is less than 1 × 1 cm^{2}, is fabricated and measured to be proven acceptable for the specifications.
II. DESIGN OF THE CRLHTL TYPE UWB BPF
The conventional CRLHTL is a periodic structure with multicells, as shown in Fig. 1 [6]. The
i th cell consists of (C_{Li} ,L_{Li} ) for the lefthanded and (C_{Ri} ,L_{Ri} ) for the righthanded properties. However, Fig. 1 should be changed to 1 cell version for effective miniaturization in Fig. 2. As well, it is in the form of a Pisymmetric equivalent circuit.The lumped elements of the 1cell CRLHTL are obtained to generate a center frequency
f_{0} at 4 GHz and the band edgesf_{R} andf_{L} at 3.2 GHz and 4.8 GHz, respectively. Considering the balanced condition [6],f_{0} is equal to the zerothorder resonance (ZOR) point of the CRLH metamaterial line, the following formulas are used to obtain circuit elements.Although, we use the Fig. 2 circuit, as it will change in the physical implementation, and we propose a new and hybridphysical geometry, which will be explained later.
As it comprises the lumped elements and TL segments, it is called a hybridphysical circuit. The values of the CRLHTL BPF with open stubs are calculated as follows to achieve the objectives in Table 1A.
Fig. 2 is related to Fig. 3 through the pishaped IDC lines flanked with shorted stubs appearing in [7,8]. One block of the IDC lines is equally divided into the upper and lower blocks of the IDC lines (represented by
C_{s1} as part ofC_{Li} ) to make room for IDC open stubs as tuning elements.L_{Li} ,C_{Ri} , andL_{Ri} are embedded in TL segments as in [7,8]. As new elements, the IDC splitting open stubs are for removing the upperhalf range from the full ultrawideband (UWB), and the open stubs at the ports are for enhancing the attenuation level in the stopband and the impedance matching at the ports. Taking advantage of these elements and their genetic algorithm (GA)optimized values, the Fig. 3 circuit with 1 results in the frequency response in Fig. 4. The binary GA is used with a 0.5 crossover, a 0.1 mutation rate, 15 parameters, 5 bits per parameter and 80 individuals through 400 generations, and it converges to the solution after the 50th generation, as presented in Fig. 4(a). All the results in Fig. 4(b) are from the circuit simulation. The scattering parameters show that the passband transitions from 3.2 to 4.8 GHz, and the insertion and return loss appear ideally good (less than 1 dB and less than 15 dB, respectively). For the final realization, the lumped capacitorsC_{s1} in Fig. 3 are replaced by the IDC below.Even if the IDC line has been around for some time, as stated before, its geometric parameters will be explored to find the desired effective inductance
L_{Ri} as well asC_{Li} in our design, which differs from the others. The geometry of an nIDFfingered IDC line is described withW ,l , andS denoting the finger width, the finger length. and the spacing between the two adjacent fingers, respectively. The capacitance of Fig. 5 is given as follows:K (•) andK '(•) are the complete elliptic integral of the first kind and its complement. Along with the series IDC, the grounded stub as the shunt inductor plays an important role. This can be realized with the following structure.The expression as follows is commonly used for the inductance of Fig. 6 (
L_{Li} ) and each finger in Fig. 5 (L_{Ri} ). Though it is an approximate formula, it helps us quickly approach the initial size.where
h andt above mean the thickness of the substrate and metallization in use. The expressions for the other circuit elements are found in [9], as well as a conversion between the TL segment geometry and the corresponding circuit elements, and they are used to correct the electrical behaviors based on Eqs. (2) and (3). With all these values, the physical sizes are iteratively exploited until the acquisition of the desired performance.III. RESULT OF IMPLEMENTATION
First, the interdigital capacitor’s size is calculated to realize a capacitance of 0.35 pF. As a result, the finalized geometry and all its physical dimensions are shown in Fig. 7 and Table 2.
With the structure above, we use FR4 (
ε_{r} = 4.4) as the substrate and 4 GHz asf_{0} . Based on the input for the geometry, a 3D electromagnetic field simulation has been carried out to predict the real performance and to conduct a comparison with the measurement.Fig. 8 plots the circuit and 3D fieldsimulated scattering parameters
S _{11} andS _{21}, which are validated by the measurement. An excellent agreement is shown between the simulated and measuredS _{21} with almost the same shape of data curve, a bandwidth over 3.2 GHz through 4.8 GHz, and a insertion loss less than 1 dB (≈0.92). In addition, a good return loss lower than 15 dB is given, despite the small discrepancy due to the mechanical tolerance error. Next, from the analysis point of view regarding the design result above, we must verify the overall size as well as the ZOR of the CRLH property of this proposed geometry.As the basis of our proposed geometry is the CRLHTL, the metamateial property can be proven by watching the electric field and the dispersion diagram (or propagation constant vs. frequency diagram). Fig. 9(a) shows the ZOR phenomenon at
f_{0} (4 GHz) where the overall structure from port 1 to port 2 has almost the same electric field intensity (almost the same color means zero times the halfwavelength resonance or electric field of the same vector). Besides, seeing the dispersion curve as the relation of frequency vs. phase (= Beta × p), with respect to 4 GHz, lefthanded (or minus propagation constant) and righthanded (or plus propagation constant) regions are generated below and above the ZOR point at 4 GHz. Lastly, we show the photograph of our fabricated broadband BPF to verify how the proposed design has realized miniaturization (a lot less than a quarter wavelength).As in Figs. 7 and 10, our filter fits into the 1 × 1 cm^{2} area and is less than even a quarter wavelength in area (1.83 × 1.83 cm^{2}), which means 54% and greater than 70%size reductions from the conventional quarter wavelength and half wavelength, respectively. In addition, we compared our filter with other sizereduced broadband structures to present the differences, features, and advantages of the proposed method.
Based on the comparison in Table 3, our structure is the shortest due to the use of the ZOR effect, which helps our design to have an insertion loss below 1 dB. In addition, it is easier to fabricate our filter compared to the defected ground in [2] and the multilayers and metal housing in [4] now that ours is manufacturable as a printed 1layer planar geometry.
IV. CONCLUSION
A new compact UWB lowerhalf BPF has been proposed based upon the concept of the CRLHTL metamaterial. Only one unit of the CRLHTL is adopted and the two pairs of inner and outer open stubs are added to form the wanted passband. After a 3D electromagnetic field simulation and fabrication, the design is validated by the measurement to show an excellent performance of the frequency response with a 3.2–4.8 GHz band, a less than 1dB insertion loss and a less than 15dB return loss. Lastly, the proposed design makes the overall size of the filter less than 1 × 1 cm^{2} in area.

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[Fig. 1.] Circuit model of the periodic CRLHTL.

[Fig. 2.] Piequivalent circuit of the 1cell CRLHTL.

[Fig. 3.] Circuit model of ou r proposed filter geometry.

[Fig. 4.] Frequency responses of the prototype.

[Table 1A.] Design goal of this filter: lower half of the UWB

[Table 1B.] Initial values of the elements for the circuit above

[Fig. 5.] Microstrip interdigital coupled (IDC) lines.

[Fig. 6.] Grounded microstrip line stub for inductance.

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[Table 2.] Initial values of the elements of the proposed geometry

[Fig. 7.] Finalized version of our proposed geometry.

[Fig. 8.] S11 and S21 of the proposed bandpass filter. (a) Simulation and (b) measurement.

[Fig. 9.] Proof of the composite right and lefthanded zerothorder resonance (CRLH ZOR) property. (a) ZOR electric field and (b) dispersion diagram.

[Fig. 10.] Picture of the designed broadband bandpass filter.

[Table 3.] Comparison between our and other broadband filters