MODEL OF SELF-OSCILLATING CIRCUIT FOR TESTING NUMERICAL METHODS OF TRANSIENT ANALYSIS IN SPICE-SIMULATORS

Abstract

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.