Parameter extraction for symmetric coupled-resonator filters.pdf
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1、IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 12, DECEMBER 20022971 Parameter Extraction for Symmetric Coupled-Resonator Filters Heng-Tung Hsu, Student Member, IEEE, Zhenyu Zhang, Student Member, IEEE, Kawthar A. Zaki, Fellow, IEEE, and Ali E. Atia, Fellow, IEEE AbstractA new pa
2、rameter-extraction procedure for sym- metriccoupled-resonatorfiltersispresented.Closed-form recursive formulas are derived for the synthesis of all the filter parameters (resonant frequencies of the individual resonators and couplings between resonators) from known measured or simulated zeros and po
3、les of input impedance functions of the singly terminated even- and odd-mode networks. Capable of accurately predicting the unavoidable spurious couplings between nearby resonators, this simple and straightforward procedure can eliminate complicated optimization routines and have extensive applicati
4、ons in design and tuning of filters. Index TermsCoupled resonator, filter. I. INTRODUCTION M ODERNmicrowavecommunicationsystems,especially satellite and mobile communication systems, require high-performance narrow-band bandpass filters having high selectivity and linear phase response consistent wi
5、th minimum weight and volume. To satisfy the stringent requirements, optimum filters must have the maximum possible number of transmission zeros placed at predetermined locations in the complex frequency plane from the synthesis point-of-view 1, 2, 1416. Among all the possible filter configurations,
6、 a coupled-resonator filter in a symmetric folded structure (the canonical form) is one of the preferable candidates 1. To further reduce the size, weight, and cost, there has been a growing interest in planar structures. Knowledge of the parameters of such high-performance fil- ters,fromtwo-portmea
7、surementsorsimulations,isveryimpor- tant since highly accurate couplings and resonant frequencies are required to ensure the desired responses. Parameter-extrac- tion methods have been extensively studied for the design and tuning of such filters. Thal 3 developed a method that incor- porated equiva
8、lent-circuit analysis programs with element op- timization routines. Accatino 4 utilized phase measurement of the input admittance of a short-circuited filter in conjunction withLCX(inductance,capacitance,andfrequency-independent reactance) synthesis and minimum pattern search optimization Manuscrip
9、t received April 5, 2002; revised August 20, 2002. H.-T. Hsu was with the Department of Electrical and Computer Engineering, University of Maryland at College Park, College Park, MD 20742, USA. He is nowwithAMCOMCommunicationsInc.,Clarksburg,MD20871USA(e-mail: becker ). Z. Zhang and K. A. Zaki are w
10、ith the Department of Electrical and Computer Engineering, University of Maryland at College Park, College Park, MD 20742 USA (e-mail: zakieng.umd.edu). A. E. Atia is with the Orbital Sciences Corporation, Dulles, VA 20166 USA (e-mail: ). Digital Object Identifier 10.1109/TMTT.2002.805283 techniques
11、 to extract the filter parameters. Various optimization routines have played important roles for traditional approaches in parameter extractions. The optimization variables are either network element values (for model-based approaches) 3, 5 or physical dimensions of the filters 7. Sensitivity analys
12、is of the optimization variables on the final responses has been per- formed and much effort has been devoted to improve the con- vergence of the optimization routines in all cases 58. While using optimization may be an attractive approach, it is usually inefficient, quite complicated, and tedious.
13、In addi- tion, the solutions may not be unique. Moreover, it depends strongly on the initial guess of the optimization variables and often results in nonoptimum (local minimum) solutions, espe- cially when the number of resonators is large. One major disad- vantage of using optimization for paramete
14、r extraction is that it may fail to predict accurately the spurious unwanted couplings betweennearbyresonators,whichcommonlyexistinsuchcom- pact-sized structures. Inthispaper,anewsimpleandstraightforwardparameter-ex- traction procedure for symmetric coupled-resonator filters is presented. This proce
15、dure is able to accurately predict the spu- rious unwanted couplings between nearby resonators directly. Closed-formrecursiveformulasarederivedwhichsynthesizeall the filter parameters from the zeros and poles of the even- and odd-mode input impedance functions of the symmetrically bi- sected singly
16、terminated networks. Equivalent-circuit represen- tation and circuit analysis of the symmetric coupled-resonator filters are included in Section II. Section III deals with the de- tailed derivation of the extraction procedure. Applications of this new approach to the design and measurement of filter
17、s pre- sented in Section IV shows the powerfulness of the proposed procedure. II. CIRCUITMODEL ANDANALYSIS Fig.1showstheequivalentcircuitofa canonicalcoupledres- onator filter. Each resonator is a seriescircuit with capac- itanceand total loop inductance . Couplings between resonatorsandare repre- s
18、ented by the frequency-independent reactance, andis theinput/output couplingresistance, respectively. For canonical filters, cascade (or series) couplings of the same sign are pro- vided between consecutively numbered cavities and shunt (or cross) couplings of arbitrary signs are provided between ca
19、vi- ties 1 and, 2, andetc. 1. In planar structures, spuriouscouplingsbetweencavities1and,2,and etc. always exist (as unwanted, but unavoidable) due to the very 0018-9480/02$17.00 2002 IEEE 2972IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 50, NO. 12, DECEMBER 2002 Fig. 1.Equivalent circ
20、uit of a canonical coupled resonator filters with the definitions of even- and odd-mode excitations. compact structure in this configuration. The following relations hold whenis the plane of symmetry (Fig. 1): (1a) (1b) Theloopequationsofthestructureinmatrixformcanbewritten as 2, 6 (2) In the above
21、expression,is the coupling matrix with the diagonal elements denoting the offset in resonant frequencies of each individual resonator, and the normalized frequencyis defined as (3) whereandare the center frequency and bandwidth of the filter, respectively. Analysis of the structure is most easily ac
22、complished using a bisection to obtain the singly terminated even- and odd-mode networks, as shown in Fig. 1. The input impedance at loopof the even- and odd-mode networks can readily be derived as 9 (4) The subscriptin (4) denotes the odd- and even-mode bi- section with the perfect electric conduct
23、or (PEC) perfect mag- netic conductor (PMC) placed at the plane of symmetry. The monic polynomialsandin (4) can be expressed as (5) (6) whereandare the normalized zeros of and, corresponding to the normalized zeros and poles of the input impedances of the bisected even- or odd-mode networks at loop
24、, respectively. The input reflection coefficient for the bisected networks can then be expressed as (7) Finally, the two-port scattering parameters of the whole struc- ture can be expressed in terms of the reflection coefficients of the bisected networks as (8a) (8b) The reflection coefficients of t
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