Stable Equilibrium State Analysis of the Differential Ring Oscillator with Even Number of Stages

The start-up conditions for differential oscillator with an even number of stages are analyzed in this paper. Compared with those that have an odd number of stages, such oscillators may have two stable equilibrium states besides an astable equilibrium state in which the circuits can start to oscillate. To avoid the risk of possible latching up into the stable states, an additional start-up circuit technique is proposed. The proposed circuit should also reduce the start-up time. The theory is further confirmed with the design and fabrication of three kinds of differential ring Voltage-Controlled Oscillator (VCO), a 3-stage one, 4-stage ones with and without the start-up circuit based on a 0.13 m standard CMOS process. The measurement results show that the 3-stage one and the 4-stage one with the start-up circuit have the correct output oscillation signals, but the 4-stage without the start-up circuit has nothing to output.