Bifurcationanalysis of an LC-tank VCO including the variable capacitance

An alternative approach for designing fully integrated LC oscillators based on the Andronov-Hopf bifurcation analysis including a nonlinear overall-model for MOS transistors (EKV model) is introduced. In the presented procedure the capacitance of the VCO is described in terms of geometric transistor dimensions. This leads to an extended bifurcation analysis which considers only the widths and lengths of the used transistors. For the description of the MOS capacitance a basic-charge-model, as it was introduced in the work by Enz and Vittoz, was used in combination of an explicit analytic approximation of the surface potential. Our procedure enables the consideration of the oscillator amplitude as an additional design parameter in the VCO design process. Furthermore it allows the designer to receive a more exact estimation of the varactor dimensions in advance. The procedure has been implemented in a software toolbox in Matlab which employs a graphical optimization process that facilitates the analytical determination of the required design parameters.