General closed-form equations for amplitude of parallel coupled quadrature oscillator

In this paper, for the first time, a new method with closed-form analytical equations is presented to calculate the oscillation amplitude of fourth-order oscillators, such as quadrature oscillators. This method is actually based on the general form of the differential equations describing the structure of the fourth-order oscillators and finding a solution for the nonlinear differential equations governing this type of oscillator. The introduced method is a general method that is valid for all fourth-order oscillators and is also independent of the oscillation frequency. Using the proposed method, complex and time-consuming simulation tools will no longer be needed to calculate the oscillation amplitude in a steady state. Moreover, the presented closed-form equations help the designers to understand the design compromises and design the oscillator for their specific and desired conditions. In addition, to evaluate the correctness of the presented equations, a comprehensive analysis of the oscillation amplitude of the quadrature oscillator in the steady state is performed, and a closed-form equation is presented for the oscillation amplitude of the oscillator in the steady state, which is proposed for the first time in this paper. A comparison between the simulation results and theoretical computations confirms the validity of the proposed method. In this paper, for the first time, a new method was presented to calculate the oscillation amplitude of fourth-order oscillators, such as quadrature oscillators. This method was based on solving nonlinear differential equations with a good approximation. In fact, a new easy-to-understand manual calculation technique was introduced to calculate the oscillation amplitude.image