Using Large Signal S-parameters to Design Low Power Class-b and Class-c Cmos Cross-coupled Voltage Controlled Oscillators

This article presents a method for design of cross-coupled LC oscillators using open-loop technique and large signal scattering matrix parameters (S-parameters) in place of well known and established negative resistance approach. Thanks to the open-loop methodology, the main circuit parameters such as loaded quality factor, steady-state oscillation amplitude and signal frequency under large signal regime can be extracted without, often tedious and time consuming, transient simulations. The most important aspect of the proposed method is its ability to provide relatively simple and intuitive representation of a cross-coupled oscillator under changing bias conditions, with 10% accuracy in comparison to analysis in time domain. The presented methodology is not technology specific, however CMOS was chosen due to its availability, relative low cost and popularity of circuit implementation. The article shows two low power, sub-1 V voltage controlled oscillator prototypes, one operating in class-B, the other one in class-C, designed using the described method and operating under the reduced power supply requirements yet retaining a state of the art Figure of Merit (FoM) of various VCO reported in the literature.