Closed-Form Analytical Equations for Amplitude and Frequency of High-Frequency CMOS Ring Oscillators

New closed-form equations are proposed for frequency and amplitude of a ring oscillator. The method is general enough to be used for all types of delay stages. Using exact large-signal circuit analysis, closed-form equations for estimating the frequency and amplitude of a ring oscillator are derived as an example. The method takes into account the effect of various parasitic capacitors to have better accuracy. The validity of the resulted equations is verified through simulations using TSMC 0.18 ¿m CMOS process. Simulation results show the better accuracy of the proposed method compared with others.