Design of CRLH‑TL BPF with controllable attenuation poles

the attenuation poles near the passband are proposed.

the circuit parameters so that the input susceptance of the tap-coupled stub diverges.However, BPFs using only right-handed (RH) circuits still increase the size inversely proportional to the resonant frequency, and there is a limit to miniaturization even for filters with a small number of stages.Therefore, the research on filters and antennas using composite right/left-handed (CRLH)-TL, which enable circuit miniaturization, has been actively studied in recent years [5][6][7].The CRLH-TL BPFs of [8,9] are realized in sizes 0.51 g × 0.37 g and 0.20 g × 0.22 g , which are smaller than conventional BPFs consist- ing of only RH circuits.By applying the tap-coupling to a CRLH-TL, it is possible to realize compact BPFs with controllable attenuation poles [10].However, to the best of the authors' knowledge, there have been few studies on the control of attenuation poles in a CRLH-TL BPF applied tap-coupling.
In this study, the resonators in which the distributed constant line is applied a tapcoupling and loaded with the left-handed (LH) circuit are designed.The attenuation pole is located by the tap-coupled stub loaded with the LH circuit at the lower or higher frequency region than negative-first resonance.Next, the BPF composed of the tap-coupled CRLH-TL resonators is designed based on the classical design theory of filters [11].The parallel resonant circuit in the two-stage BPF including the J-inverter is replaced with a tap-coupled CRLH-TL resonator under a narrow-band approximation [12].The designed BPF is fabricated, and the S-parameters of the BPF are analyzed and measured by a circuit simulator software and a vector network analyzer (VNA), respectively.This study aims to realize the compact CRLH-TL BPF which can control multiple attenuation poles.When a TL is lossless, the DD is generally defined as where φ and Ṡij (i, j = 1, 2) are the phase delay and S-parameters in the 2-port circuit [13].If the 2-port circuit is symmetrical and impedance-matched, Ṡ12 = Ṡ21 = e −jθ and Ṡ11 ≈ Ṡ22 ≈ 0 and DD is conveniently expressed by instead of Eq. ( 1), where theta is the phase of Ṡ21 .Figure 2a and b shows a distributed constant line (RH-TL) and a 2-cell T-type LH circuit, where l in Fig. 2a is stub length.The DDs θ RH and θ LH , i.e., the phase of Ṡ21 in Fig. 2a and b can be calculated as Note that β is the phase constant, R is the terminal resistance (50 ), and ω is the angular frequency.A(= D), B , and C in Eqs. ( 4)- (7) indicate the ABCD parameters of the 1-cell T-type LH circuit.However, the proper DD of the circuit which only consists stubs such as Fig. 1 cannot be derived by Eq. ( 2) because φ is constant.According to reference [14], the DD can be equivalently defined by the phase of the reflection characteristics when C in and C out are excluded and Port "Output" is opened to make it a 1-port circuit.S ′ 11 is represented as where B in1 is the input susceptance of the openstub, B in2 is the input susceptance of the stub loaded with LH circuits, and X in is the input reactance of the LH circuit.From Eqs. ( 8)-( 12), the equivalent DD is the phase of S ′ 11 divided by two and depends on the product of the whole input susceptance and the terminal resistance.

Dispersion diagram of each circuit
Figure 3 shows the DD for each of the three circuits shown in Figs. 1 and 2. Note that the DDs of Figs. 1, 2a, and b are calculated by Eqs. ( 9), (3), and (4), respectively, where the circuit parameters are written in the title of Fig. 3.It is confirmed that the DD of the RH-TL is always positive in phase and varies linearly from 0 degrees, while the DD of the LH circuit is always negative in phase and varies nonlinearly.Therefore, the DD of (8) 3 The DDs of the circuits shown in Figs. 1 and 2 the CRLH-TL has the respective characteristics of the RH-TL and the LH circuit, and the phase changes from the negative region to the positive region.Focusing on the DD in Fig. 1, we can see from Fig. 3 that the phase is in the negative region at 0-3.597 GHz and in the positive region from 3.597 GHz and beyond.Therefore, from Fig. 3, it can be verified that the tap-coupled resonator loaded with LH circuit in Fig. 1 is a CRLH-TL.However, the resonator in Fig. 1 is regarded as RH-TL when C L equals 0 pF because the resonator is constructed by only openstubs.

Tap-coupled resonators loaded with LH circuit
Next, the tap-coupled CRLH-TL resonators in Fig. 1 are designed.Note that C in , C out are inserted into the I/O section to facilitate confirming resonance by under-coupling.In this study, the resonators are designed according to the specifications shown in Table 1, where f −1 is a negative-first-order frequency and f att is an attenuation pole.As for the control of f att , it is located at the distributed constant line loaded with the LH circuit in Fig. 1.The advantage of controlling f att in the stub is that there is the possibility to shorten the stub length when f att is a low frequency.If f att is controlled by the open- stub, the stub length increases as f att decreases.On the other hand, depending on the values of such as L L and C L , the stub length may be shorter than in the case of an open- stub.Therefore, f att is located using the stub loaded with the LH circuit in this study.The circuit parameters for each type of resonator can be obtained from Eqs. ( 10)-( 12) expressed by If Eq. ( 13) (the resonance condition) and Eq. ( 14) (the condition of realizing an attenuation pole) are satisfied simultaneously, Z 0 , l 1 , l 2 , C L , and L L are determined in Table 2. Also, C in and C out of Type 1-6 resonators are 0.10 pF to make f −1 sharp.We simulate the transmission characteristic | Ṡ21 | and B in2 of the resonators using a circuit simulator.and 6 show that each f −1 is generated during 1.96 − 1.98 GHz and each f att is confirmed at desired frequency.The error in f −1 should be caused due to C in and C out which are not taken into account when designing the resonators.Moreover, each B in2 in Figs. 5  and 7 diverges at each f att in Figs. 4 and 6, which means f att can be controlled by the (13) Table 1 The design specifications of the resonators tap-coupled distributed constant line loaded with LH circuit.Thus, the tap-coupled CRLH-TL resonators are capable of controlling f att at either lower or higher region fre- quencies than f -1 .

Design and fabrication of tap-coupled CRLH-TL BPF
Figure 8 and Table 3 show the CRLH-TL BPF using the tap-coupled resonators shown in Fig. 1 and the specifications of the BPF, respectively.Note that N, C r1 and C r2 , f −1 , ∆f , and f attx (x=1, 2) are the number of stages, the capacitances of the parallel resonators, the negative-first-order frequency, the bandwidth, and the attenuation poles, respectively.We design the CRLH-TL BPF in accordance with the steps as follows; 1.The lumped-element BPF including J-inverters is designed based on a classical design method [11].2. The parallel resonators in the lumped-element BPF are replaced with the tap-coupled CRLH-TL resonators using a narrow-band approximation [12].Figure 9 shows a lumped-element BPF including J-inverters.Firstly, the BPF in Fig. 9 meeting with the specifications shown in Table 3 is designed.The circuit parameters such as C in and C out and the gap capacitor C g are obtained according to [11].Secondly, the parallel  resonators are replaced with the tap-coupled CRLH-TL resonators shown in Fig. 10.We note that the capacitance C e in , C e out , and C g in Fig. 10 are connected in parallel due to cance- ling the negative elements in Fig. 9.The replacement of the resonators is executed based on a narrow-band approximation [12], where the following equations (15) Fig. 9 The BPF schematic including J-inverter Fig. 10 Replacement of the parallel resonant circuits to the CRLH-TL resonators are used.Note that B inx_all is the input susceptance of the CRLH-TL resonator, B inx1 and B inx2 are the input susceptances of the openstub and the distributed constant line loaded with LH circuit, respectively.Also, X inx is the input reactance of the LH circuit and b x is the relational expression between the susceptance slope parameters of the parallel resonators and the tap-coupled CRLH-TL resonators.The attenuation poles are located by the distributed constant line loaded with LH circuit as well as the design of the CRLH-TL resonators.The conditions that Eqs. ( 15), (17), and (19) (the condition of realizing a bandwidth) should be satisfied when replacing the resonators as in Fig. 10.Finally, the circuit parameters such as the characteristic impedance Z 0x , the stub length l x1 and l x2 , and LH inductance/capacitance L Lx and C Lx are obtained.The flow of replacing the resonators and calculating each cir- cuit parameter is performed according to the flowchart shown in Fig. 11.Calculating Z 0x , l x2 , L Lx , C Lx , and l x1 simultaneously would take a great deal of time.However, Fig. 11 shows that Z 0x , l x2 , L Lx , and C Lx can be calculated prior to l x1 .This is because l x1 is inde- pendent of the condition of Eq. ( 17) so that it takes less time than the method of calculating five circuit parameters at the same time.After obtaining four circuit parameters, l x1 is calculated by Eqs. ( 15) and ( 19), and each circuit parameter is shown in Table 4. Figure 12 shows the S-parameters simulated by a circuit simulator.The simulated results show that f −1 , f att1 , and f att2 are generated at 2.00 GHz, 1.55 GHz, and 2.70 GHz, respectively.Also, ∆f is 154 MHz which means the error rate of ∆f is 2.67 %.The error in ∆f should be caused when replacing the resonators under the condition of a narrow-band approximation, which is inevitable.However, the characteristics of the CRLH-TL BPF are approximately satisfied and the attenuation poles are confirmed at the desired low/high region frequency than f −1 .In addition, the total length of Resonators 1 and 2 in Fig. 8 is 13.85 mm and 18.75 mm.The length of a conventional half-wavelength ( /2 ) resonator is 74.95 mm when the resonant frequency is 2.00 GHz, i.e., Resonators 1 and Resonator 2 are 81.5 % and 75.0 % shorter than /2 reso- nator.The significant miniaturization of the resonator length should be the effect on the LH circuit.Therefore, we can design the compact CRLH-TL BPF with two controllable attenuation poles.
Next, we fabricate the BPF using a substrate with MEGTRON6 R-5775 (dielectric constant ε r : 3.7, substrate thickness h: 0.63 mm, and metal thickness t: 18 µ m) and Mits Electronics Seven Mini based on the parameters shown in Table 4. Figure 13a and b shows the structure and top view of the BPF with a flat ground plane, where the CRLH-TL resonators are bent to suppress the stray coupling between the resonators.Note that l p1 , l p2 , l f , w w1 , w 2 , w f , s, and s t in Fig. 13a indicate the pad length, the feed line length, the width of Resonator 1 and Resonator 2, the feed line width, the gap to place capacitors, and the gap to ground inductors, respectively.In this study, the inductors and the capacitors are realized by chip capacitors and a wire inductor (0.20 mm dia.) adjusted the length.
The reason for using the chip elements is to easily confirm the usefulness of the design.Also, the stub lengths written in Fig. 13 are varied from the values of Table 4 due to a wavelength-shortening effect.The pads present at the tip of the resonator are for soldering C Lx and L Lx .The thru holes are drilled to make L Lx conductive to the ground.C in and C out are mounted between the input/output and Resonator x, and C g is mounted  between Resonator 1 and Resonator 2, respectively.After soldering these components on the substrate, the S-parameters of the BPF are measured using Agilent (now Keysight Technologies) E5071C-2D5 ENA Series Network Analyzer shown in Fig. 14 and compared with the simulated results.A short-open-load-thru calibration is mechanically conducted to remove the effect of the measurement equipment and cables by using Keysight Technologies 85052D 3.5mm economy calibration kit.The range of frequency is between 300 kHz and 6 GHz, and the number of plots is 1601.Also, the IF bandwidth and the input power of VNA are 70 kHz and -5 dBm in this study.The S-parameters of the CRLH-TL BPF are shown in Fig. 15, where the dotted lines are the simulated results and the solid lines are the measured results, respectively.From the measured results, the attenuation poles of the lower region unite and it is confirmed that f −1 , ∆f , and f att2 are 2.00 130 MHz, and 2.66 GHz, which mean ∆f is 15.6 % narrower than simulated results and f att2 is slightly shifted toward the lower region.The major reason for the errors in the transmission characteristics should be caused by the tolerance of the chip capacitors and the wire inductors, stray capacitors, and edge effects.Also, the insertion loss and return loss at f −1 are 2.47 dB and 30.9 dB, respectively.It is believed that the resistance components of the chip elements should make the S-parameters worse and the improvement is prospected by using quasi-lumped elements such as interdigital capacitors and spiral inductors with less loss instead of chip elements [15].However, most parts of the S-parameters are good agreement with the theoretical and measured results.Moreover, the size of the CRLH-TL BPF is 16.21 mm × 15.01 mm or 0.18 g × 0.17 g , where g = 88.38 mm corresponds to the guided wavelength using MEGTRON6 at the frequency of 2.00 GHz.The performance comparison with previously published BPFs is listed in Table 5.From Table 5, it is confirmed that the size of the fabricated filter is smaller than that of the present filters.The BPF in this study is similar to [16,17] in having attenuation poles; however, notably, this work can freely control attenuation poles both near and far from the passband.
Therefore, a compact BPF with two controllable attenuation poles is realized by using the tap-coupled CRLH-TL resonators.

Conclusion
Resonators and BPFs using tap-coupled CRLH-TL were studied in this work.In the CRLH-TL resonators, an attenuation pole can be controlled to the desired frequency in either the lower or higher region than a negative-first-order frequency.We designed, simulated, and fabricated a prototype BPF composed of the CRLH-TL resonators.The simulation results show that the attenuation poles can be controlled at the designated low and high frequency regions.The S-parameters measured by the VNA agreed well with that of the simulation software analysis.Also, the insertion loss and the return loss at the negative-first-order frequency were 2.47 dB and 30.9 dB, which would be improved by replacing chip capacitors and wire inductors to low loss quasi-lumped elements.Moreover, the total lengths of the CRLH-TL resonators in the BPF were significantly shortened by 81.5 % and 75.0 % compared with a conventional /2 openstub resonator and the size of the fabricated BPF is 0.18 g × 0.17 g .Therefore, a compact and highly selective resonator and BPF were realized by the tap-coupled CRLH-TL.This study contributes to realizing a compact filter with

Figure 1
Figure1shows a tap-coupled resonator loaded with LH circuit, where L L and C L are LH inductor and capacitor, l 1 and l 2 are stub length, Z 0 is characteristic impedance, and C in and C out are input/output (I/O) capacitors, respectively.Before designing the resonators, we investigate that the resonator in Fig.1is a CRLH-TL by using a dispersion diagram (DD).

Fig. 1
Fig.1The schematic of the tap-coupled resonator loaded with LH circuits

Fig. 2
Fig. 2 The schematics of a distributed constant line and b 2-cell T-type LH circuit.Note that a is one of RH-TL Figures 4, 5, 6, 7 are the simulated | Ṡ21 | and B in2 of the resonator of Type 1-6.Figures 4

Fig. 12 Fig. 13 a
Fig.12 The simulated S-parameters of the CRLH-TL BPF

Table 2
The obtained circuit parameters of the CRLH-TL resonators

Table 3
The design specifications of the tap-coupled CRLH-TL BPF

Table 4
The circuit parameters of the BPF

Table 5
The comparison between the present workNote that CF, FBW, IL, and PB mean center frequency, fractional bandwidth, insertion loss, and passband, respectively good characteristics in which attenuation poles can be freely controlled by a simple method, and the CRLH-TL BPF is a promising candidate for the applications of 5G technology such as satellites and mobile communications.