Abstract
In this paper, closed-form analytical equations for the time-domain amplitude of the MOS cross-coupled oscillators are derived. The procedure of the paper is based on estimating an accurate equation for describing the behavior of the cross-coupled MOS configurations and finding a reasonable solution for the nonlinear differential equation governing the circuit. The solution method is presented for a general equation and is valid for all possible second-order oscillators. Both of the long channel and short channel transistor topologies have been investigated. The resulted equations are in a good agreement with simulation results for a wide range of the circuit parameters and enable us to analyze and synthesize the oscillators with the desired transient behavior.
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