Analysis of frequency and amplitude in CMOS differential ring oscillators

• A new analytical approach is proposed for differential ring oscillators.
• The exact equations on the amplitude and frequency is derived in the proposed method.
• It provides the condition which the oscillator passes from being linear to nonlinear.
• Analytical results confirm the simulation results in 0.5 to 10 GHz frequencies.

In this paper, a new method for computing the amplitude and frequency of differential ring oscillators (ROs) is proposed. The analysis is performed in two separate parts. In the first of these, equations are derived with the assumption of a sinusoidal waveform of outputs, while in the other, the outputs are assumed to be exponential. It is shown that the derived equations for frequency and amplitude are sufficiently exact. In addition, conditions in which sinusoidal and exponential output occur are thoroughly discussed. In the instances in which the results did not satisfy the necessary conditions for sinusoidal output, the output is assumed to be exponential. Moreover, the related analytical equations are written, and the new expressions for frequency and amplitude of ROs are derived. Analytical results are confirmed by simulation results, using the Taiwan Semiconductor Manufacturing Company 0.18 µm technology model. The simulation results indicate the high level of accuracy of the proposed model.