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In this thesis the general Chebyshev filter synthesis procedure to generate transfer and reflection polynomials and coupling matrices were described. Key concepts such as coupled resonators, non-resonant nodes have been included. This is followed by microwave duplexer synthesis. Next, a technique to design dual band filter has been described including ways to achieve desired return loss and rejection levels at specific bands by manipulating the stopbands and transmission zeros. The concept of dual band filter synthesis has been applied on the synthesis of microwave duplexer to propose a method to synthesize dual band duplexers. Finally a numerical procedure using Cauchy method has been described to estimate the filter and duplexer polynomials from measured responses. The concepts in this thesis can be used to make microwave filters and duplexers more compact, efficient and cost effective.

Surface acoustic wave (SAW) technology has been in use for well over one century. In the last few decades, due to its low cost and high performance, this technology has been widely adopted in modern wireless communication systems, to build filtering devices at radio frequency (RF). SAW filters and duplexers can be virtually found inside every mobile handset. SAW devices are traditionally recognized as passive devices with high linear signal processing behavior. However, recent deployments of third generation (3G) and fourth generation (4G) mobile networks require the handsets to handle an increasing number of frequency bands with more complex modulation /demodulation schemes and higher data rate for more subscribers. These requirements directly demand more stringent linearity specifications on the front end devices, including the SAW duplexers. In the past, SAW duplexer design was based on empirically obtained design rules to meet the linearity specifications. Lack of predictability and an understanding of the root cause of the nonlinearity have limited the potential applications of SAW duplexers. Therefore, research on the nonlinearity characterization and an accurate modeling of SAW nonlinearity for mobile device applications are very much needed. The Ph.D. work presented here primarily focuses on developing a general nonlinear model for SAW resonators/duplexers. Their nonlinear characteristics were investigated by measuring the harmonic and intermodulation distortions of resonators. A nonlinear Mason model is developed and the characterization results are integrated into SAW duplexer design flows to help to simulate the nonlinear effects accurately and improve the linearity performance of the products. iv In this dissertation, first, a novel nonlinear Mason equivalent circuit model including a third order nonlinear coefficient in the wave propagation is presented. Next, the nonlinear distortions of SAW resonators are analyzed by measuring large-signal harmonic and intermodulation spurious emission on resonators using a wafer probe station. The influence of the setups on the measurement reliability and reproducibility is discussed. Further, the nonlinear Mason model is validated by comparing its simulation results with harmonic and intermodulation measurements on SAW resonators and a WCDMA Band 5 duplexer. The Mason model developed and presented here is the first and only nonlinear physical model for SAW devices based on the equivalent circuit approach. By using this new model, good simulation measurement agreements are obtained on both harmonic and intermodulation distortions for SAW resonators and duplexers. These outcomes demonstrate the validity of the research on both the characterization and modeling of SAW devices. The result obtained confirms that the assumption of the representation of the 3 rd order nonlinearity in the propagation by a single coefficient is valid