A Space-Mapping Based CAD Methodology for Modeling Temperature Characteristics of Combline Resonators

Transcription

1 PIERS ONLINE, VOL. 3, NO. 7, A Space-Mapping Based CAD Methodology for Modeling Temperature Characteristics of Combline Resonators A. Kashi 1, P. Kumar 2, M. Caron 2, and V. K. Devabhaktuni 1 1 Department of ECE, Concordia University S-EV5.139, 1455 de Maisonneuve W., Montreal, H3G 1M8, Canada 2 Mitec Telecom Inc., 9000 Trans-Canada Highway, Montreal, H9R 5Z8, Canada Abstract In this paper, we propose a new space-mapping based CAD modeling methodology for modeling temperature characteristics of combline resonators. With the aid of two commercial simulation tools, namely Ansoft HFSS and Agilent ADS, this methodology generates accurate temperature models of combline resonators. The method is generic i. e., it is capable of generating corresponding models for a variety of resonator structures including the mushroom and straight, using only one frequency sweep in HFSS. Fine EM simulations from HFSS are used to create an ultra-fast model in ADS, which is extremely useful to RF/microwave designers. DOI: /PIERS INTRODUCTION Frequency drift due to temperature changes is a key concern in RF/microwave filter design. This aspect is particularly critical in the case of combline resonators used in a wide variety of RF/microwave systems. Several conventional temperature compensation techniques have been employed. For instance, special materials with low thermal coefficients of expansion, e. g., invar, have been used. However, such materials could result in other problems such as low thermal conductivity and high cost. Alternatively, it was shown that for a combline resonator with given dimensions of housing and resonator rod, perfect temperature compensation can be achieved at two resonant frequencies via appropriate selection of materials for the housing and the rod [1 4]. Another recent temperature compensation method [5] advocated use of a shape memory alloy (SMA) actuator. In order to integrate temperature compensation solutions such as the above into RF/microwave filter design, an accurate and fast temperature drift model of a combline resonator is essential. A simple relationship between the resonant frequency of a combline resonator and the temperature exists [5]. However, this traditional model is not accurate enough and fails to cover different rod structures (see Fig. 1). As such, there is a demand for a reasonably accurate model, which takes into account all the physical dimensions of a combline resonator. A direct approach to address this problem is to use detailed theoretical models such as the full-wave EM solvers. In practice, full-wave EM simulations tend to be CPU-expensive and hence unsuitable for design/optimization tasks. This scenario leads to research on novel EM based CAD models, which is the subject of this paper. In this paper, a CAD methodology based on space-mapping is proposed for the development of accurate/fast temperature models of combline resonators. The methodology is implemented using appropriate coarse model (Agilent ADS) and fine model (Ansoft HFSS) as in any space-mapping framework. All the steps involved in the proposed methodology are illustrated through a practical example. 2. REVIEW OF SPACE-MAPPING FRAMEWORK Space-mapping tool [6 9] effectively connects fast coarse models to align with accurate/cpuintensive fine models in the design parameter space. For instance, the response-residual spacemapping (RRSM) surrogate is matched with the fine model response through a parameter-extraction process [10]. As shown in [10], SM-optimization/modeling algorithms involve four essential steps as shown in Fig. 2. Initially, suitable coarse and fine models are selected. In comparison with the fine model, the coarse model should possess acceptable accuracy and relatively high computationspeed. In the second step, a suitable mapping function is selected. Commonly used mathematical functions include simple linear, polynomial, or rational functions and complex Artificial Neural Network (ANN) functions. In the third step, the fine model is simulated, e. g., simulation of an EM

2 PIERS ONLINE, VOL. 3, NO. 7, : R c * _ P ( x) = argmin R( x) R ( x) n n A R n B R c f : R s : R f R _ s R f < ε ( A= 1, B= 0) P ( x) = A x+ B (a) (b) Figure 1: (a) Mushroom rod and (b) straight rod resonator structures. Capacitors shown by dotted and solid lines contribute to equivalent gap capacitor (C gap ) and equivalent screw capacitor (C screw ) respectively. Figure 2: Flowchart of the space-mapping algorithm [10] used in this work for temperature modeling of combline resonators. structure in HFSS workspace. The final step is parameter extraction, which is an iterative process leading to computation of mapping parameters. At the end of the fourth step, the mapping is updated and the surrogate model is derived. Subsequently, the response of the surrogate model is verified to see whether or not it matches the fine model s response over the entire frequency range of interest. If the two models do not match, the algorithm repeats steps two through four Coarse Model Agilent ADS has a vast library of circuit models that can be used as coarse models. As shown in Fig. 3, the idealized coarse model for a combline resonator is a coaxial transmission line, which is loaded by two types of capacitors. The effective capacitance between the rod and the cavity, shown in Fig. 1, can be calculated using parallel plate capacitor equation C gap = ε 0A d where ε 0, A and d represent permittivity of the free space, area of the parallel plates, and separation between the plates respectively. Another type of capacitance, which is caused by the penetration of the tuning screw into the rod, can be calculated using the cylindrical capacitance equation C screw = 2πkε 0 L, (2) ln (b/a) where ε 0, k, L, b and a denote permittivity of the free space, relative permittivity, length of screw penetration, diameter of the rod hole, and diameter of the screw respectively. Based on the above calculations, the input impedance of the coarse model is given by Z in = jz 0 tan ω c l + 1 j (C gap + C screw ) ω Z 0 = (1) µ ln b/a ε 2π, (3) where Z 0, l, and c represent characteristic impedance, length of the rod, and speed of the light respectively. In practice, the geometry of a combline resonator changes with temperature. As such, all the lengths such as cavity height and rod diameter change with respect to three factors: temperature drift, initial length and the material s coefficient of thermal expansion. In a case, where the rod is made up of two materials and has a different housing, the equivalent thermal expansion coefficient γ can be calculated as a γ = (a + b) α + b β, (4) (a + b)

3 PIERS ONLINE, VOL. 3, NO. 7, Geometry at 25ºC Coarse Model Thermal Expansion Coefficient Geometry as a function of temperature Figure 3: Representation of the coarse model as a function of temperature and γ in ADS. where α and β are the coefficients of thermal expansion of the two materials. In (4), a and b are the initial lengths of the two materials. In an attempt to take into account the effects of temperature, we replaced the absolute geometrical values by temperature-dependent symbolic expressions as shown in Fig Fine Model In this work, EM simulations of combline resonator based on Ansoft HFSS are considered as the fine model. EM data from HFSS consisting of S-parameters versus frequency is in touchstone format. An S-parameter file, namely SnP in ADS, can import such data. In SnP, n stands for the number of ports. For example, Fig. 4 depicts a one-port S-parameter file component (S1P). It is to be noted that S-parameters can then be converted into Z-parameters by library functions of ADS. Capacitors after mapping Initial identical mapping Figure 4: S1P representation in ADS. Figure 5: Implementation of the proposed linear mapping in ADS taking into account the fringing effects Linear Mapping The capacitance values calculated using Equations (1) and (2) do not account for certain phenomena, e. g., fringing that depends on the geometry of the rod. As such, it is necessary to adjust these approximate values to accurate ones. The fringing effects are accounted for using the linear mapping C gap+fringing = ratio gap C gap + offset gap C screw+fringing = ratio screw C screw + offset screw, (5) where ratios and offsets are mapping parameters. Implementation details are shown in Fig Parameter Extraction Responses of coarse and fine models are matched through a parameter-extraction process. More specifically, ratio gap, ratio screw, offset gap and offset screw (5) are iteratively adjusted based on fullwave EM simulations from the fine model i.e., Ansoft HFSS. To implement this step, an optimization framework shown in Fig. 6 has been setup in ADS. The goal for such optimization process is to accurately match both magnitude and phase of Z in computed using coarse and fine models. Hybrid optimization option in ADS is employed. 3. NUMERICAL RESULTS For the purpose of illustration, a combline resonator with mushroom structure is considered. EM simulations have been performed using HFSS and resulting S-parameter data is loaded into ADS

4 PIERS ONLINE, VOL. 3, NO. 7, Frequency Sweep Optimization Goals Mean Equations Optimization Setting Figure 6: Implementation of the optimization procedure is ADS leading to parameter extraction. i Geometry mm Cavity Dia. (a) 61 Cavity Height (b) 65 f a Resonator Mushroom Height (c ) 3 Resonator Mushroom Dia. (d) 34 Resonator Base Height (e) 52.5 Resonator Base Dia. (f ) Resonator Hole Dia. (g) 13.8 Screw Dia. (h) 5 Screw Length (i) 15 Figure 7: Geometry of the combline resonator modeled in this work. (a) (b) Figure 8: (a) Magnitude of the input impedance computed using the coarse (zin11) and the fine (zin22) models, (b) phase of the input impedance computed using the coarse (zin11) and the fine (zin22) models. Table 1: Comparison of numerical results from simulations and measurements. CTE Cavity Aluminum 6061 (23.6 ppm/ C) CTE Screw Brass (20.3 ppm/ C) Case #1 Case #2 CTE Resonator SS (9.9 ppm/ C) Temp. Drift (Simulated) ppm/ C Temp. Drift (Measured) ppm/ C CTE Resonator Invar (1.3 ppm/ C) Temp. Drift (Simulated) ppm/ C Temp. Drift (Measured) ppm/ C

5 PIERS ONLINE, VOL. 3, NO. 7, via an S1P file. Fig. 8 shows the matching of Z in from the coarse model (after parameter extraction and coarse model update) and the fine model. The combline resonator is simulated for two different rod materials: stainless steel and invar. The results show a ±2ppm/ C error, which is satisfactory in terms of model accuracy. Table 1 shows a comparison of the results from both simulations and measurements. 4. CONCLUSIONS A new CAD modeling algorithm based on space-mapping has been proposed. Using the systematic steps of this methodology, temperature behavior of a variety of combline resonator structures can be modeled. The resulting models are accurate and fast and hence can be of practical significance in RF/microwave filter design/optimization. ACKNOWLEDGMENT The authors wish to gratefully acknowledge the support from the Canada Research Chairs (CRC) program, the Natural Sciences and Engineering Council of Canada (NSERC) and FQRNT/NATEQ. Mr. Iwan Jemczyk (Vice-President, Engineering) of Mitec Telecom is thanked for creating opportunities for collaboration. REFERENCES 1. Wang, C. and K. A. Zaki, Temperature compensation of combline resonators and filters, IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, CA, , June Yao, H.-W. and A. E. Atia, Temperature characteristics of combline resonators and filters, IEEE MTT-S Int. Microwave Symp. Dig., Phoenix, AZ, , May Alford, N. M., J. Breeze, S. J. Penn, and M. Poole, Tunable, temperature-compensated high Q and high thermal conductivity dielectrics for Ku and Ka band communications, IEE Microwave Filters and Multi-plexers Colloquium, Ref. 2000/117, 6/1 6/4, November Chen, S. W., K. A. Zaki, and R. F. West, Tunable, temperature compensated dielectric resonators and filters, IEEE Trans. Microwave Theory Tech., Vol. 38, , Keats, B. F., R. B. Gorbet, and R. R. Mansour, Design and testing of SMA temperaturecompensated cavity resonator, IEEE Trans. Microwave Theory Tech., Vol. 51, , Bandler, J. W., R. M. Biernacki, S. H. Chen, P. A. Grobelny, and R. H. Hemmers, Space mapping technique for electromagnetic optimization, IEEE Trans. Microwave Theory Tech., Vol. 42, , Bandler, J. W., R. M. Biernacki, and S. H. Chen, Fully automated space mapping optimization of 3D structures, IEEE MTT-S Int. Microwave Symp. Dig., San Francisco, CA, , June Bakr, M. H., J. W. Bandler, R. M. Biernacki, S. H. Chen, and K. Madsen, A trust region aggressive space mapping algorithm for EM optimization, IEEE Trans. Microwave Theory Tech., Vol. 46, , Bandler, J. W., R. M. Biernacki, S. H. Chen, R. H. Hemmers, and K. Madsen, Electromagnetic optimization exploiting aggressive space mapping, IEEE Trans. Microwave Theory Tech., Vol. 43, , Bandler, J. W., A space-mapping design framework, IEEE Trans. Microwave Theory Tech., Vol. 52, , 2004.