Analysis and Design of Dual-Mode CMOS LC-VCOs

We present a nonlinear analysis of the basic circuit of a dual-band voltage controlled oscillator (VCO), composed by an active one-port and by a double-tuned LC circuit. Both the frequencies and the amplitudes of the two modes of sinusoidal oscillation are calculated by closed-form expressions by which a detailed analysis of the steady-state and dynamical behavior of circuit is performed, including the stability analysis of the modes. We show the appearance of the phenomenon of the frequency hysteresis allowing us to explain the mechanism of the switching between modes and predict the VCOs performance over the whole operation range. The theoretical results, validated by Spice simulations of a VCO realized in 0.13 μm MOS technology and by measurements on a circuit prototype, provide useful design insights.