An analytical equation for the oscillation frequency of high-frequency ring oscillators

An analytical equation for the oscillation frequency of a ring oscillator is derived. The derivation is done using a novel method which does not need to find an expression for the delay of each stage. The resulting equation includes the effect of time-varying parasitics. It also includes the effect of the gate resistance, which has a large effect on the oscillation frequency at high frequencies. Measurement results of ring oscillators fabricated in a 0.18-μm CMOS process show that the resulting equation has an average error of 8% over a large range of parameter variations.