Multistage matching networks and analytical frameworks for improving and/or optimizingthe networks is provided. In one example, a framework relaxes the resistive constraint on the input and load impedances of the stages of a multistage matching network and allows them to be complex. Based on this framework, the design of multistage matching networks can be improved or optimized, such as using a method of Lagrange multipliers. A design optimization approach, for example, can be used to predict an optimum distribution of gains and impedance characteristics among the stages of a multistage matching network. The efficiency of matching networks designed using this example approach is compared with a conventional design approach, and it is shown that significant efficiency improvements are possible.

In one implementation, an analytical approach to determining an improved and/or optimal design of a matching network in a capacitive or inductive WPT system is provided. In one implementation, for example, a framework is provided to enable stage(s) of the network to simultaneously provide gain and compensation. The multistage matching network efficiency can be improved and/or optimized, such as by using the method of Lagrange multipliers, resulting in the optimum distribution of gain and compensation among the L-section stages.

Methods to design band-pass acoustic wave microwave filters are disclosed. A performance metric related to an input impedance of a baseline filter design is calculated, the baseline filter design including a plurality of series surface acoustic wave resonators and a plurality of shunt surface acoustic wave resonators, each surface acoustic wave resonator having a respective resonant frequency. One or more alternative filter designs is established, each alternative filter design derived from the baseline filter design by reordering the resonant frequencies of two or more of the plurality of series surface acoustic wave resonators and/or two or more of the plurality of shunt surface acoustic wave resonators. A respective performance metric related to an input impedance of each alternative filter designs is calculated. A final filter design is selected from among the baseline filter design and the alternative filter designs based on the respective performance metrics.

Multistage matching networks and analytical frameworks for improving and/or optimizing the networks is provided. In one example, a framework relaxes the resistive constraint on the input and load impedances of the stages of a multistage matching network and allows them to be complex. Based on this framework, the design of multistage matching networks can be improved or optimized, such as using a method of Lagrange multipliers. A design optimization approach, for example, can be used to predict an optimum distribution of gains and impedance characteristics among the stages of a multistage matching network. The efficiency of matching networks designed using this example approach is compared with a conventional design approach, and it is shown that significant efficiency improvements are possible.

Methods to design band-pass acoustic wave microwave filters are disclosed. A performance metric related to an input impedance of a baseline filter design is calculated, the baseline filter design including a plurality of series surface acoustic wave resonators and a plurality of shunt surface acoustic wave resonators, each surface acoustic wave resonator having a respective resonant frequency. One or more alternative filter designs is established, each alternative filter design derived from the baseline filter design by reordering the resonant frequencies of two or more of the plurality of series surface acoustic wave resonators and/or two or more of the plurality of shunt surface acoustic wave resonators. A respective performance metric related to an input impedance of each alternative filter designs is calculated. A final filter design is selected from among the baseline filter design and the alternative filter designs based on the respective performance metrics.

Methods of designing band-pass filters are disclosed. A baseline filter design is established, the baseline filter design including a plurality of surface acoustic wave resonators having respective resonant frequencies, the surface acoustic wave resonators organized by resonant frequency into two or more groups. One or more alternative filter designs are established, each alternative filter design derived from the baseline filter design by reordering the resonant frequencies of two or more surface acoustic wave resonators within at least one of the two or more groups. A respective performance metric related to input impedance over a pass band is calculated for each of the baseline filter design and the alternative filter designs. A final filter design is selected from the baseline filter design and the alternative filter designs based on the respective performance metrics.

A filter design method isolates parasitic zeros in a modelled response by comparison with a representation of a target response, and computes an adjusted representation of the target response corresponding to an implementation of the adjusted target polynomial representation according to a desired filter type and incorporating the parasitic zeros thus isolated. The Parasitic zeros are then removed from this adjusted target polynomial representation, and also from the polynomial representation of the modelled response, and the two resulting representations used as the basis of an error function. This error function may then drive an iterative convergence minimising the error function, for example based on a stepwise convergence of parameters such as dimension values in a three dimensional model implementing each representation.

A method for optimizing impedance of a connecting element between a first component and a second component of a high-frequency apparatus. The first component and the second component have at least two level states, wherein the connecting element has an input impedance and an output impedance. The first component has respective impedances in each of the at least two level states, wherein the second component has respective impedances in each of the at least two level states. The method comprising the steps as follows: determining a respective magnitude of a difference of the first component between the complex conjugated input impedance and a respective impedance of the first component, determining a respective magnitude of a difference of the second component between the complex conjugated output impedance and a respective impedance of the second component, and simultaneously minimizing the respective magnitudes of the first component and second component relative to the in- and output impedances of the connecting element.

In one implementation, an analytical approach to determining an improved and/or optimal design of a matching network in a capacitive or inductive WPT system is provided. In one implementation, for example, a framework is provided to enable stage(s) of the network to simultaneously provide gain and compensation. The multistage matching network efficiency can be improved and/or optimized, such as by using the method of Lagrange multipliers, resulting in the optimum distribution of gain and compensation among the L-section stages.

Methods of designing band-pass filters are disclosed. A baseline filter design is established, the baseline filter design including a plurality of surface acoustic wave resonators having respective resonant frequencies, the surface acoustic wave resonators organized by resonant frequency into two or more groups. One or more alternative filter designs are established, each alternative filter design derived from the baseline filter design by reordering the resonant frequencies of two or more surface acoustic wave resonators within at least one of the two or more groups. A respective performance metric related to input impedance over a pass band is calculated for each of the baseline filter design and the alternative filter designs. A final filter design is selected from the baseline filter design and the alternative filter designs based on the respective performance metrics.