Quadrature VCOs based on direct second harmonic locking: Theoretical analysis and experimental validation

Abstract

We propose a theoretical analysis of the class of quadrature VCOs (QVCOs) based on two LC-oscillators directly coupled by means of the second harmonic. The analysis provides the conditions for the existence and stability of steady-state quadrature oscillations and a simplified model for the phase noise (PN) transfer function with respect to a noise source in parallel to the tank. We show that the figure of merit defined as the product between PN and current equals that of the single VCO, confirming that quadrature generation is achieved by this class of QVCO without degrading that figure of merit. An analytical model for the phase quadrature error due to tank mismatches is also proposed. The validity of all analytical models is discussed against numerical simulations. A practical implementation at 3.26 GHz with ±20% tuning range in a 0.13 μm CMOS technology is also presented, confirming the main theoretical findings. Copyright © 2009 John Wiley & Sons, Ltd.