Analysis of Millimeter-Wave LC Oscillators Based on Two-Port Network Theory

In this brief, a cross-coupled oscillator is analyzed based on the two-port network theory and the $Y$- parameter model for a transistor. Contrary to the previous works, the proposed analysis shows that LC cross-coupled oscillators have an additional and higher pure imaginary natural frequency at which the circuit cannot oscillate. The analysis investigates the sufficient condition at which the circuit is able to oscillate at this higher frequency. For the oscillation at the higher frequency mode, we propose adding an extra stage and making a three-stage ring oscillator. The equations obtained from this analysis indicate that the oscillation start-up condition depends on the oscillation frequency. Hence, increasing the speed of the oscillator does not satisfy the start-up condition of oscillators. Our analysis shows that the maximum frequency, in which the circuit stops oscillation in the ring oscillator, is higher than the cross-coupled oscillator and this maximum frequency is very close to the maximum frequency of the transistor.