Circuit Function Characterizing Tunability of Resonators

In this paper we study a sensitivity function of resonance frequencies to capacitance change in resonators with capacitive tuning, which characterizes the local tunability. This function is a circuit function, similar to the input and transmission functions. The features of the sensitivity function, leading to tunability increasing, are defined. The founded features are used to construct resonators from segments of transmission lines with an extended tuning range. The tunability limitations of resonators tunable by one or several capacitors are determined. Synthesized transmission line resonators can be used in tunable bandpass filters. They allow the filter to be tuned over a wider frequency range for a given capacitance change Cmax/Cmin. If the tuning range is specified, the filter will perform the adjustment at a lower ratio Cmax/Cmin. This leads to a smaller change in the insertion loss of the filter in a given frequency range.