Study On Synthesis And Diagnosis Techniques Of Microwave Passive Components

Microwave resonators filters and diplexers are important components in moderncommunication systems (such as wireless base stations and communication satellites).Starting from given specifications, it is often a long journey for a designer to obtain thefinal physical realization of a typical filter or diplexer. This long journey usuallyinclude the determination of transmission zeros and filter order, coupling matrixsynthesis, diagnosis and tuning in the stage of EM (electromagnetic) design forphysical dimensions, fabrication and measurement, and/or diagnosis and tuning in thestage of the production. This paper focuses on the study of the synthesis and diagnosisof resonators filters and diplexers. The detailed studies are given as follow:First, a method to determine the filter order and the optimum locations oftransmission zeros of resonators bandpass filters (including self-equalized filters) ispresented using genetic algorithm (GA). This method is based on constructing anobjective error function according to given amplitude and/or group delay specifications,and then the filter order and transmission zeros (TZs) can be obtained by minimizingthe proposed error function using GA. The method has solved the first problem ofcoupling matrix synthesis of general Chebsyshev coupled-resonator filters. In addition,a single optimization algorithm based on single SolvOpt that synthesizes couplingmatrices for coupled-resonator filters is presented. The rules for setting initial values ofSolvOpt are proposed to find global minimum of the cost function.Second, for the diagnosis of the resonators filters without source-load coupling,two diagnosis methods, including a three-parameter optimization method and afive-parameter optimization method, are presented. The methods can be applied forextracting the coupling matrix and the unloaded Q (also called filter diagnosis) fromthe measured or electromagnetic simulated S-parameters of a narrow bandcross-coupled resonator bandpass filter. In the methods, the Cauchy method is appliedfor determining the characteristic polynomials of the S-parameters of a filter in thenormalized low-pass frequency domain, the phase-shift effects of the measured (orelectromagnetic simulated) S-parameters are removed for the first time by optimization,and the unloaded Q (assuming all the resonators with the same unloaded Q) is also obtained simultaneously by optimization.Third, a two-stage optimization method is proposed for accurately extracting thecoupling matrix (CM) and the unloaded quality factor (unloaded Q) of each resonatorfrom the measured (or simulated) S-parameters of lossy cross-coupled resonatorbandpass filters. The method is based on the proposed five-parameter optimizationmethod with proper extension to handle the presence of source-load coupling andnon-uniform unloaded Q for each resonator.Fourth, a novel approach using admittance parameters (also know as Y-parameters)is proposed to extract the coupling matrix of a lossy cross-coupled resonator bandpassfilter with source–load (S-L) coupling. The Y-parameters are calculated bycharacteristic polynomials corresponding to the measured S-parameters, and then theunloaded Q of resonators and the coupling matrix can be extracted from theY-parameters. The method allows one to diagnose a filter with S-L coupling withoutnecessity of dealing with the degenerate poles problem of the Y-parameters and themeasurement noise.Last, two methods for synthesizing coupled resonator diplexers composed of TXand RX filters (two types of junctions connecting the TX and RX filters areconsidered). One method is that the coupling matrices of the TX and RX filters (MTXand MRX) are synthesized independently, and then the coupling matrix of the diplexerscan be obtained from MTXand MRX. Another method is that the"N+3" couplingmatrix of overall diplexer can be obtained based on the proposed linear frequencytransformation and hybrid optimization methods. The proposed filter diagnosismethods can also be applied to guide the tuning of each channel in the diplexer.The synthesized coupling matrix of a filter or diplexer can be used for analyzingthe amplitude and group delay responses of this filter or diplexer and obtaining theirinitial physical dimensions. The proposed diagnosis methods can guide the tuning inthe stages of the EM design and/or production of a cross-coupled resonator filter ordiplexer, and thus accelerate the design and the physical realization of this filter ordiplexer, which can reduce production costs and scheduling.