This paper presents a novel synthesis method for asymmetric dual-passband microwave filters. The proposed method employs frequency transformation technique to determine the locations of poles and zeros of a desired filter. This method can be used to design dual-passband filters with prescribed passbands directly without any need of optimization process. Then an eight-pole asymmetric dualpassband filter is designed efficiently to validate the transformation technique. This universal method will be useful for the design of various high performance microwave dual-passband filters in the communication systems.

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Abstract. In this paper, a straightforward and accurate numerical modeling (a rational function called "tri-root bistable function") are proposed to represent the complete nonlinear bistable force-displacement characteristics. The rational function has a cubic polynomial numerator and quadratic polynomial denominator. With three different kinds of compliant bistable mechanisms, the tri-root bistable function is proved effective and accurate, and that it is capable of capturing the key features of a bistable kinetostatic curve accurately with fewer parameters. Then, for the classic fully-compliant bistable mechanism, six closed-form equations are presented and used to describe the relationships between the tri-root bistable function parameters and the mechanism's design parameters, which are achieved using a multi-variable nonlinear regression. The regression analysis is validated by nonlinear finite element analysis. Finally, a fully-compliant statically balanced mechanism consisting of three different classic fully-compliant bistable mechanisms is illustrated to show the capability of the proposed method in designing compliant multi-stable mechanisms.

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