Abstract: A method using a computer program for numerically simulating an electrical circuit, in a computer system, having a plurality of nodes and a plurality of circuit elements. A circuit description of the electrical circuit together with tstart and tstop times of a time interval are read into the computer system with at least one input value of the electrical circuit for at least one specific time in the time interval. Voltage values and/or current values at the nodes of the electrical circuit are calculated in the selected time interval using table-based models for the circuit elements. From these voltage values and/or current values, a simulation time tn in the time interval [tstart; tstop] under consideration is selected at which system equations are determined describing the circuit elements by physical formulas and dynamic effects of the elements are described by differential equations.

Abstract: A system relationship function is defined which describes the “external response” of a set of coupled linear components in an electrical circuit. A differential equation system is defined for the set of coupled linear components, and a predetermined number of eigenvalues are determined for the homogeneous differential equation system. An error is indicated for the eigenvalues which is caused by ignoring those eigenvalues which have not been determined within the homogeneous differential equation system. If the error is less than a given setpoint error, then the system relationship function is produced from the differential equations which are described by the determined eigenvalues. If the error is greater than the limit, then further eigenvalues are determined, for which an error is in turn determined. This method is continued iteratively until the error is less than the limit.

Abstract: In the method, following an operating point determination of the quartz resonator circuit, a substitution of the equivalent circuit diagram of the quartz resonator by an independent current source is implemented with the initial, previously determined amplitude of the current of the dynamic arm of the quartz resonator. The dynamic equilibrium state is determined for this circuit arrangement with firing methods or methods of harmonic balance. After a resubstitution of the current source by the equivalent circuit diagram of the quartz resonator, a transient analysis is implemented for the dynamic equilibrium state. This method is iteratively implemented as long as the identified growth rate lies above a prescribable barrier.