Design of Compact Uwb Bandpass Filter with Improved Out-of-band Performance Using Distributed Crlh Transmission Lines

This study presents an Ultra-Wideband (UWB) filter with improved out-of-band performance. The proposed filter adopts novel Composite Right/Left-Handed (CRLH) Transmission Lines (TLs), which are modeled with distributed elements instead of lumped elements. A unit cell of the CRLH TLs is theoretically analyzed to derive the design formulas. The analyzing results confirm that the proposed structures are CRLH TLs. A novel UWB bandpass filter with improved out-of-band performance is designed and fabricated using the induced formulas. The measurement results show that the fabricated UWB bandpass filter has an insertion loss of less than 2.8 dB, a bandwidth of 2.8-10.4 GHz and a rejection of more than 18 dB from 11.6 to 23.4 GHz.


INTRODUCTION
Since the Federal Communications Commission (FCC) released the frequency band of 3.1-10.6GHz for Ultra-Wideband (UWB) communications in 2002, UWB systems with high data rate, short-range and short-pulses have been rapidly developed for commercial purposes.Bandpass Filters (BPFs) are essential components of the UWB systems and thus have been studied extensively.Most of the UWB BPFs suffer from narrow upper stopbands and large overall sizes.Numerous filters have been designed using Multiple-Mode Resonators (MMRs) for improving upper-stopband performance.Some of these filters employed MMRs with lowpass structures structures (Wong el al., 2006;Wong and Zhu, 2007) and stub loaded MMRs, which are operated in quintuple or quadruple modes (Wong and Zhu, 2009;Deng et al., 2010;Wu et al., 2011).A Coplanar Waveguide (CPW) UWB BPF was proposed using MMR with steppedimpedance stubs (Honarvar and Sadeghzadeh, 2012).A radial stub loaded resonator with cross-shaped coupled lines was used to improve the out-of-band performance (Mohammadi et al., 2013).Defected Ground Structures (DGSs) were added to stub loaded or steppedimpedance stub loaded resonators (Yang et al., 2008;Tian and Chu, 2011;Gao et al., 2012).Moreover, UWB BPFs with improved out-of-band performance have been implemented using DGSs with a highpass filter or a BPF (Yang et al., 2007;Tang et al., 2008), BPFs with band stop filters (Li et al., 2008) and Composite Right/Left-Handed (CRLH) Transmission Lines (TLs) (Gong and Chu, 2008;Ahmed and Virdee, 2013).CRLH TLs can reduce the size and enhance the bandwidth of BPFs (Lai et al., 2004).
In this study, we present the design of a compact UWB BPF with improved out-of-band performance using novel distributed CRLH TLs.The dispersion characteristics of the distributed CRLH TLs are theoretically proved using even/odd-mode analysis method.The simulated and measured results of the proposed UWB BPF are in good agreement.

MATERIALS AND METHODS
The distributed CRLH TL unit cell shown in Fig. 1 is modeled with distributed elements instead of lumped elements.It cannot show explicitly which elements make Right-Handed (RH) TLs or Left-Handed (LH) TLs.The π equivalent circuit of the distributed CRLH TL unit cell can explain that the proposed unit cell is the CRLH TL unit cell.Because the circuit model is symmetrical, even/odd-mode analysis can be used to derive the π equivalent circuit and the transfer function.The even/odd-mode admittances of the unit cell of the distributed CRLH TLs are as follows: The series and shunt branch elements of the π equivalent circuit in Fig. 2a are as follows: where, Y 0 is the admittance of the input/output port.A transmission zero is created when S 21 = 0, i.e.: Therefore, a transmission zero is created when: where, θ 4,rej is the electrical length at the transmission zero frequency, ω rej , given by: (8) which is the resonant frequency of the series branch of the π equivalent circuit of the distributed CRLH TL unit cell and θ 4,0 is the electrical length at the center frequency of the filter, ω 0 .If θ 5 = 2θ 4 = 360°, the signals through paths 1 and 2 of the distributed CRLH TL unit cell shown in Fig. 1 are out of phase and cancel out to create another transmission zero.By using Bloch-Floquet theory, the dispersion relation and characteristic impedance of the unit cell can be expressed as (Pozar, 2012): where, Z B is the characteristic impedance normalized to the port impedance, Z 0 and: The dispersions and attenuations of the distributed CRLH TL unit cell are shown in Fig. 3, when θ 1 = θ 4 = 60°, θ 2 = θ 3 = 30° and θ 5 = 120° at ω 0 .The characteristic impedances of the stubs and TLs of the unit cell are determined using the method of the next paragraph.The calculated element values of the π equivalent circuit are as follows: from 3.1 to 7 GHz, Y a >0 and Y c <0 and from 7 to 10.6 GHz, Y a <0 and Y c >0.Therefore, in this CRLH TL unit cell, the RH and LH regions are 3.1-7.0and 7.0-10.6GHz, respectively.At the resonant frequencies, ω shi , of the shunt branch of Fig. 2a, γ = 0, thus indicating that the shunt branch is the parallel resonant circuit.The resonant frequency of the series branch is ω se = ω rej , namely, the series branch is the parallel resonant circuit.Therefore, the proposed unit cell is the CRLH TL unit cell.Figure 3 shows the wide passband characteristics between ω sh1 and ω sh2 and two attenuation poles at ω rej and 3ω 0 .Thus, the proposed distributed CRLH TL unit cell can be used to achieve wide out-of-band characteristics of a UWB BPF.
If the band edge frequencies, ω sh1 and ω sh2 , the transmission zero frequency, ω rej and Z B at ω 0 are given, we can calculate the characteristic impedances of each element of the unit cell using Eq. ( 5), ( 7), ( 9) and ( 10).One degree of freedom exists among the five characteristic impedances of the unit cell.Z 1 is a dominant parameter determining the slope parameter of the shunt resonator that creates the passband of the UWB BPF.Therefore, Z 1 is regarded as a free variable.The design specifications are as follows: the passband of the UWB BPF is 3.1-10.6GHz, the attenuation pole frequencies are 13.5 and 19.0 GHz and the characteristic impedance of the distributed CRLH TL unit cell is 50 Ω at the center frequency.When Z 1 is set to 100 Ω, the calculated impedances are as follows: Z 2 = 50 Ω, Z 3 = 86.1 Ω, Z 4 = 131.5 Ω and Z 5 = 107.9Ω.The frequency responses of the unit cell are shown in Fig. 4.

RESULTS AND DISCUSSION
The proposed UWB bandpass filter with improved out-of-band performance was implemented on a  1.00 0.51 0.3 0.50 0.44 *: fc is the maximum upper stopband frequency over an 18 dB rejection 0.6-mm thick FR-4 substrate with a dielectric constant of 4.4 and a loss tangent of less than 0.02.The fabricated UWB bandpass filter shown in Fig. 5 comprises two unit cells to ensure improved out-ofband performance.By using an Electromagnetic (EM) simulator, the dimensions of the structure were optimized to be as follows: w 1 = 1.17 mm, w 2 = 0.3 mm, w 3 = 0.55 mm, w 4 = 0.45 mm, w 5 = 0.2 mm, w 6 = 0.2 mm, l 1 = 6.5 mm, l 2 = 1.39 mm, l 3 = 2.35 mm, l 4 = 4.97 mm, l 5 = 2.48 mm, l 6 = 2.48 mm and l 7 = 4.57 mm.The size of the fabricated UWB BPF is 16.4×10.3mm 2 .The measurements were performed using an Anritsu 37347C vector network analyzer.Figure 6a shows the simulated and measured amplitude responses of the fabricated filter, which are in good agreement.The measured results show that the proposed UWB BPF has the insertion loss of less than 2.8 dB in the passband ranging from 2.8 to 10.4 GHz, the return loss over the passband is better than 11 dB and the rejection is more than 18 dB from 11.6 to 23.4 GHz.The simulated and measured group delays of the filter are drawn in Fig. 6b.The measured one varies between 0.29 and 0.44 nsec with a maximum variation of 0.15 nsec over the passband.The fabricated UWB BPF is more compact than those proposed by Gao et al. (2012) and Gong and Chu (2008) and has a simpler structure compared to Gao et al. (2012) and Tang et al. (2008), in which the UWB BPFs are implemented using DGSs.Its out-of-band performance is better than those of the previous works of Gong and Chu (2008) and Ahmed and Virdee (2013).The insertion losses of this study and Tang et al. (2008) are relatively large because they have been fabricated on FR-4 substrates, which have a relatively large loss tangent.Table 1 shows the performance comparison of this study and the previous works.

CONCLUSION
A UWB BPF with improved out-of-band performance that employs the distributed CRLH TLs is proposed in this study.The unit cell of the distributed CRLH TLs is theoretically analyzed to derive the dispersion characteristics and scattering parameters.The fabricated filter has a compact size, flat group delay and good out-of-band performance.The measured results are in good agreement with the simulation results.

Fig. 1 :
Fig. 1: Circuit model of the distributed CRLH TL unit cell 4) If Y a >0 and Y c <0, the distributed CRLH TL unit cell operates as a RH TL, as shown in Fig. 2b.If Y a <0 and Y c >0, it operates as an LH TL, as shown in Fig. 2c.The transfer function, S 21 , can be expressed as:

Fig. 3 :
Fig. 3: Dispersion and attenuation diagram of the distributed CRLH TL unit cell

Table 1 :
Comparison of UWB bandpass filters