Comprehensive Analysis Of Generalized Chebyshev Bandpass Filter Coupling-Matrix

As the key device in a wireless communication system, microwave filter, the study ofits design theory has been accompanied by the development of microwave communications technology and communications systems. The development of wireless communications has been reacheda new levelsince we had been in the information age; the communication frequency is continuously improving, space electromagnetic environment is becoming more complex, the communication system and the communication equipment are confronted with a comprehensive test as the spread of the mobile communication terminal such as mobile phones and the promotion of Internet of Things technology. As that the performance ofthe microwave filters affects the signal transmission quality of the entire system usually, the requirements of microwave filter with thecharacteristics of smaller, higher frequency selectivity, insertion loss and smaller return loss tend to stringent, which is bring a great difficult to the design of filter. By using the method of coupling matrix synthesis, the filter can be constructed clearly, conveniently, fast and accurately as desired. In addition, the workload of design debugging later can be reduced significantly based on the pre-calculated mathematical analysis. The introduction of cross-couplingcan bring transmission zeros at a particular frequency which has been improved the filter’s performance greatly, and reduced the volume at the same time. In this paper,we analyzedthe whole design process of generalized Chebyshev filter mainly, and the works are following as below:First, we have introduced the basic theory and basic concepts of microwave filters, and analyzed the frequency response and parameters indices of the filter mathematical through introducing the two-ports network matrix, in addition, we also introduced a low-pass filter of Chebyshev prototypes and frequency conversion method that changed low pass prototype to a band-pass filter.Second, we introduced generalized Chebyshev filter synthesis theory and derivated the process of "N×N" and "N+2" coupling matrix synthesisdetailed which included the solve of characteristic polynomial; extracting of coupling matrix; and the selection and topology simplification of the coupling matrix, and programmed the entire design process overall by using the Matlab which realized the coupling matrix synthesis programmed, and simplified the design process of theory greatly.Third, we introducedthe comprehensive analysis and dual-band filter by using the coupling matrix based on the basic theory of the generalized Chebyshev filter. We also have derived the coupling matrixes ofthe traditional symmetrical dual-band-pass filter, plus zero symmetric dual-band filter and asymmetric dual-band-pass filter through the method of frequency conversion, which havebeen programmed to achieve.Fourth, by summarizing the theory above, we designed and analyzed two dual-band filters based on "N+2" coupling matrix, and wesimulated and optimized design by usingthe ADS (Advanced Design System) and Ansoft HFSS software. Finally, a filterhas been designed, and the results shown the correctness of the theory.