Behavior modelling for LC tank based oscillators

A design methodology for differential LC based oscillators is presented. The topology studied here makes use of an NMOS cross coupled pair, inversion mode PMOS varactors and a differential symmetrical inductor for the oscillator implementation. Simple test circuits are used to obtain the differential S-parameters for the individual building blocks. A mathematical empirical function is then assigned for each block to model its behavior as a function of the bias point and geometrical parameters. The results for the extracted models are in excellent agreement with simulation data for a typical 0.18 μm CMOS technology library. Finally, the models developed are manipulated together to provide an accurate graphical representation for the startup condition and design constraints lines where the interdependence of different design variables is taken into account. The approach is flexible in the sense that it enables designers to track and tune different design parameters during the optimization cycle. It can also be extended by analogy to other existing different topologies.