This chapter addresses the application of symbolic techniques on the
characterization of ring Voltage Controlled Oscillators (VCO). The symbolic
characterization of the VCOs comprises both the frequency-control voltage response and
a simplified formula for evaluating the phase-noise in the oscillator. Two methodologies
are shown for generating the frequency-control voltage response. The first one is based
on the evaluation of the delay introduced by each VCO delay cell. In the second an
approximate expression for the equivalent resistance of each VCO delay cell load is
considered, and used for deriving the VCO model. The adoption of the proposed
methodologies to submicron transistor sizes is illustrated. The application of the VCO
characterization into an optimization based design is described.
Keywords: Ring VCO, VCO model, symbolic characterization, optimization-based design, deepsubmicron
VCO characterization, semi-symbolic methodology, phase-noise characterization, Maneatis
delay cell, equivalent resistance, phase-noise minimization.
