Improving the Accuracy for Amplitude and Frequency of Analytical Equation of Single-ended Ring Oscillators Based on Circuit and Transistor Parameters

The analytical relationships presented for amplitude and frequency of the ring oscillator are derived approximately due to the nonlinear nature of this oscillator. In the case where the transistors experience the cut-off region, the relationships presented so far have no connection between the frequency and the dimensions of the transistor, which is not valid in practice. In this paper, considering the circuit’s governing equation and the ring oscillator’s output waveform, a relation for the frequency is presented, including the dimensions of the transistor. Also, a simple and approximately accurate relationship for the oscillator amplitude is provided in this case. The validity of these relationships has been investigated by analyzing and simulating a single-ended oscillator in 0.18μm technology.