PIERS ONLINE, VOL. 3, NO. 1, 27 77 CAD of Left-handed Transmission Line Bandpass Filters L. Zhu, V. K. Devabhaktuni, and C. Wang Department of ECE, Concordia University 14 de Maisonneuve West, Montreal H3G1M8, Canada Abstract Owing to the negative and nonlinear nature of phase constant (β) versus frequency, left-handed transmission lines (LH-TLs) can present higher values of β as compared to righthanded ones. As such, left-handed (LH) structures are promising in terms of size minimization of microwave circuits. In this paper, a simulation study leading to computer aided design (CAD) of LH-TL bandpass filters is presented. Motivated by a recent work, in which, a bandpass filter is realized by coupling several LH units, we propose a new structure consisting of a single unit with composite right/left-handed (CRLH) characteristics. The structure offers several advantages over traditional filters, e. g., compact dimensions and low loss. A new CAD algorithm for automated filter design, which can be valuable to designers, is demonstrated through an example. DOI: 1.29/PIERS69164931 1. INTRODUCTION Modern microwave circuits and systems require a large number of high-quality passive components. Multiple factors including cost and size can place stringent constraints on the choice of materials and on the complexity of technologies to be used in the fabrication of commercial products. Everincreasing demand for lower cost and higher performance has led to the constant exploration of new materials [1] and/or new structures [2]. In the microwave community, theoretical study of left-handed materials (LHM), which simultaneously exhibit negative permeability and permittivity, has been ongoing [3]. Hypothesis predicting the existence of left-handed (LH) mediums was experimentally verified in 21 [4] and several researchers have applied LH techniques to design RF/microwave circuits []. Among other innovative structures, LHM based bandpass filters have been studied [6, 7]. Typically, LH structures are promising both in terms of reduced size and wider bandwidth as compared to traditional right-handed RF/microwave structures. In this paper, a brief overview and simulation study of left-handed transmission line (LH-TL) bandpass filters is presented. Motivated by a recent work, we propose a compact bandpass filter structure exploiting composite right/left handed transmission line (CRLH-TL) concepts. As can be seen in Section 2, this structure offers considerable reduction of size and dramatic increase in bandwidth. Physical dimensions of the filter, i. e., design variables, can be adjusted to meet the given specifications. Based on simulations, a new CAD algorithm for fully-automated design of the filter is presented in Section 3. The algorithm begins with the initial physical dimensions. Enriched by the tuning knowledge base compiled as part of our study, the physical dimensions are then adjusted iteratively. At the end of each iteration, the algorithm checks if the specifications have been met, and continues or terminates accordingly. Finally, Section 4 contains concluding remarks. ω= β ( ) 1 LC ' ' ω ε ω=βc eff LH RH β Figure 1: Phase constant β of LH-TL and RH-TL as functions of ω for the lossless case. Here, the dashed line shows the linear nature of β of RH-TL and solid lines show the nonlinear nature of β of LH-TL for different values of L and C.
PIERS ONLINE, VOL. 3, NO. 1, 27 78 2. LH-TL BANDPASS FILTER STRUCTURES 2.1. Overview The electrical length of a transmission medium can be calculated as a product of its physical length and phase constant (β). For a given electrical length, if a high-β transmission medium can be used, the real-estate needs of the resulting component are bound to be smaller than traditional mediums. The wave number (γ) of a LH-TL in terms of per-unit-length impedance (Z ) and admittance (Y ) is given by γ(ω) = α(ω) + jβ(ω) = Z Y = (R + jωl ) 1 (G + jωc ) 1, (1) where R, L, C and G are per-unit-length quantities. For the lossless case, β(ω) = 1/ω L C. As can be seen in Fig. 1, higher values of β can be attained using LH-TL at certain frequencies and for certain L C values. Microwave components realized using LH-TL structures can hence lead to effective size minimization. 2.2. Coupling LH Bandpass Filter In this sub-section, a recent LH microstrip bandpass filter [8] is reviewed. Two inter-digital capacitors in series shown in Fig. 2 are considered as a single unit of LH-TL. The outer arms of these capacitors whose edges are grounded by vias act as inductors. The substrate height is.38 mm and ε r is 9.8. EM simulations performed using Zeland s IE3D and presented in Fig. 2(b) show a highpass behavior. A LH bandpass filter is then realized by coupling two afore-mentioned units as shown in Fig. 2(c). The simulation results are presented in Fig. 2(d). The filter has a centre frequency of 2.24 GHz and a 3 db bandwidth of 3 MHz. It has a flat pass-band and low return-loss. However, the structure is observed to have a limited bandwidth i. e., in the MHz range. If the bandwidth specification were to be in the GHz range, this structure would not be suitable. Width of fingers=.1mm Spacing between fingers=.1mm 1 1 2 3 3 4 1 1. 2 2. 3 3. 4 (b) Port 1 T D M S Port 2 L RH C LH C RH L LH RH LH CRLH l (b) Port 1 Port 2 1 1 2 1.8 2 2.2 2.4 2.6 2.8 3 1 1 2 3 3 4 6 7 8 9 1 LH Region RH Region (c) (d) (c) (d) Figure 2: Layout of a single unit of the LH-TL, (b) simulated S-parameters of the unit, (c) layout of the coupling LH filter, and (d) its simulated S- parameters. Figure 3: Layout of the CRLH-TL filter with D = 1.1 mm, T = 3.9 mm, M =.1 mm, N = 6 and S =.1 mm, (b) infinitesimal LC model of the lossless CRLH-TL, (c) simulated S-parameters of the CRLH filter, and (d) ω-β diagram resulting from ϕ(s 21 ). 2.3. CRLH Bandpass Filter Any LH-TL can be treated as a CRLH-TL, due to unavoidable parasitic series inductance and shunt capacitance that lead to a right-handed (RH) contribution, which increases with frequency ω []. Motivated by this idea, a compact section of Fig. 2 shown in Fig. 3 is considered. It
PIERS ONLINE, VOL. 3, NO. 1, 27 79 has been observed that by adjusting its physical dimensions, i. e., length (D) of outer arms, length (T ), width (M), number of fingers (N) and gap between fingers (S), this compact structure can be made to realize bandpass characteristics. The substrate height is.4 mm and ε r is 2.2. The EM simulation results of the structure in Fig. 3, whose lumped model is shown in Fig. 3(b), are presented in Fig. 3(c). These results show bandpass characteristics with wide bandwidth and low loss. Fig. 3(d) confirms that the structure is indeed a CRLH-TL. As can be inferred from Table 1 and Fig. 4, this simple yet interesting structure leads to considerable real-estate savings as compared to traditional ones. Table 1: Size comparison. Filter Size Traditional Microstrip Hairpin Filter Traditional Coupled Microstrip RH-TL Filter 1. 6. mm 2 28..61 mm 2 CRLH Bandpass Filter 4.23 1. mm 2 2 4 6 8 3 4 6 7 8 9 1 11 (b) Figure 4: Layout of the traditional coupled microstrip RH-TL filter and (b) its simulated S-parameters. 3. CAD METHODOLOGY FOR THE CRLH FILTER 3.1. Analysis of Simulation Results As it is the case with design of other modern RF/microwave circuits, CAD of CRLH filters is of potential interest to designers. As a first step toward developing a fully-automated CAD tool, a simulation study has been carried out. The design parameters have been varied (or swept) and their effect on various design specifications has been examined. Some of the results of the study are shown in Fig.. In Fig., each design parameter is varied, while keeping the other parameter values 1 2 3 4 D=.7mm D=.7mm D=.9mm D=.9mm D=1.1mm D=1.1mm D=1.3mm D=1.3mm 4 6 8 1 1 1 2 3 T=4.4mm T=4.9mm T=.4mm T=.9mm 4 6 8 1 1 2 3 4 M=.1mm M=.2mm M=.4mm 4 6 8 1 1 1 2 3 N=6 N=8 N=1 N=12 4 6 8 1 (b) (c) (d) Figure : (d) Simulated S-parameters of Fig. 3 with different values of D, T, M and N.
PIERS ONLINE, VOL. 3, NO. 1, 27 8 constant. Consequently, the overall effect of each design parameter on the filter s specifications is clearly brought out. Design/tuning of RF/microwave circuits is multi-dimensional and hence complex. Several strategies have been employed in the CAD area to address this challenge [9]. In this work, sensitivity information has been analyzed and compiled into a knowledge base shown in Table 2. Such knowledge identifies the design parameter(s), which highly influence each of the filters specifications. For instance, increasing N results in a negative shift in centre frequency. In Table 2, N C stands for negligible change. Tuning Action Change D Change T Change M Change N Table 2: Knowledge base for the CAD methodology. Centre Frequency. db Bandwidth Edge Frequencies NC NC NC NC / (slight change) NC / / / / NC / / (slight change) NC / / Note: Maximum pass-band attenuation and minimum stop-band attenuation are observed when impedance matching is satisfied. Figure 6: Flow-chart of the routine that forms a basis for the proposed CAD methodology.
PIERS ONLINE, VOL. 3, NO. 1, 27 81 3.2. Design Algorithm Based on the above knowledge base, a CAD algorithm shown in Fig. 6 has been developed for automated design of CRLH filers. 3.3. Design Example In this subsection, an example of filter design using the proposed CAD methodology is presented. Given user-specifications are A max =.1 db, A min = db, f c = 6 GHz and 3 db bandwidth BW = 2.GHz. Step 1: An initial IE3D simulation is performed with initial design parameter values. The width of the passband is almost zero as may be seen in Fig. 7. Step 2: Based on the flow-chart, the width of the passband can be increased by decreasing M, and this is a relatively simpler 1-dimensional design problem. Gradually decreasing M from.8 mm to.2 mm has resulted in a BW, which is closer to the given specification (see Fig. 7(b)). Step 3: The centre frequency (currently 7. GHz) can be improved, i. e., decreased, by increasing N. Changing N from 6 to 8 has resulted in f c = 6. GHz, which is closer to the given specification (see Fig. 7(c)). This change is categorized as a coarse adjustment. Step 4: A fine adjustment is performed by increasing T from 4 mm to 4.2 mm such that the specification f c = 6 GHz has been precisely met (see Fig. 7(d)). Step : In order to meet the desired values of attenuation, i. e., S 11 and S 21, D has been adjusted from 2 mm to.49 mm for impedance matching. As seen in Fig. 7(e), all the specifications have been met. 2 4 6 8 1 2 4 6 8 1 1 2 3 4 6 8 1 1 1 2 3 2 3 4 6 7 8 9 (b) (c) (d) (e) 1 1 2 3 2 3 4 6 7 8 9 1 1 2 3 3 4 4 2 3 4 6 7 8 9 Figure 7: Step 1 with D = 2 mm, T = 4 mm, M =.8 mm, N = 6, (b) Step 2 with D = 2 mm, T = 4 mm, M =.2 mm, N = 6, (c) Step 3 with D = 2 mm, T = 4 mm, M =.2 mm, N = 8, (d) Step 4 with D = 2mm, T = 4.2 mm, M =.2 mm, N = 8, and (e) Step with D =.49mm, T = 4.2 mm, M =.2 mm, N = 8. 4. CONCLUSIONS A simulation study of the recent LH-TL bandpass filters has been presented. Results of the study have been systematically incorporated into a CAD algorithm for automated design of CRLH filter starting from user-specifications. The proposed algorithm has been illustrated through a practical example. Future work will strive to develop a CAD tool and to study time-domain applications of the CRLH filter, e. g., LH delay-lines. REFERENCES 1. Gunasekaran, M., A simplified low-cost materials approach to shielding in EMC applications, Proc. Int. Conf. EM Compatibility, 8 61, Washington, DC, August 199. 2. Barnwell, P. and J. Wood, Fabrication of low cost microwave circuits and structures using an advanced thick film technology, Proc. IEMT/IMC Symp., 327 332, Tokyo, Japan, April 1998.
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