Improving the accuracy for amplitude and frequency of analytical equation of single-ended ring oscillators based on circuit and transistor parameters

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Abstract
This paper aims to find a closed-form expression for the frequency and amplitude of single-ended ring oscillators when transistors experience all regions. In this paper, the analytical relationships presented for ring oscillator amplitude and frequency are approximately derived due to the nonlinear nature of this oscillator, taking into account the differential equation that governs the ring oscillator and its output waveform. 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. The relationship is presented for the frequency, 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 0.18 µm technology.

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