At present time the problem of developing methods for numerical analysis of RF circuits in the time domain remains actual because the known Gear and trapezoidal methods used in SPICE simulators have a number of significant disadvantages. To evaluate the effectiveness of new numerical methods, special test problems are needed to determine the accuracy of methods in various operating modes. Numerical analysis of self-oscillating circuits in the time domain offers the most difficulties for circuit simulation programs (SPICE-simulators) since models of self-oscillating circuits can be both oscillatory and stiff simultaneously. The aim of this work is to create the model of a self-oscillating circuit that allows to quantify the accuracy of numerical methods. In accordance with the aim, the following problems are solved: the features of the numerical analysis of classical self-oscillators in SPICE-simulators are investigated; the generalized mathematical model of self-oscillating circuits is described; the universal circuit model of self-oscillating circuits for SPICE-simulators is presented; the quantitative accuracy assessment of numerical methods of transient analysis in SPICE-simulators was carried out. The model proposed in this paper makes it possible to determine the relative errors of numerical methods in the harmonic oscillations mode, in the relaxation oscillations mode, as well as in the «mixed» mode, when the circuit response contains both exponential components with different rates of change and quasiharmonic components. The obtained results confirm the high accuracy of the trapezoidal method in the mode of harmonic oscillations, and the Gear method in the mode of relaxation oscillations. The relative errors in determining the amplitude of oscillation using these methods for the corresponding operating modes do not exceed 3%. At the same time, in the «mixed» mode, the relative errors in determining the amplitude of oscillation for both methods can reach 100%, that confirms the need to use additional options or special methods of numerical analysis in SPICE-simulators.
