A new family of semi-analytical recursive convolution algorithms (SARC) suitable for efficient numerical analysis of linear systems in the time domain is presented. Consecutive output samples in the SARC algorithms are calculated with higher accuracy than in other recursive convolution algorithms. The main idea and outline of an error analysis are presented and some areas of the SARC algorithm's application are considered. The application of SARC algorithms to the synthesis of discrete-time filters is pointed out as a method of filter design.

A new method of large-signal time domain simulation of switch-mode power circuits is presented. The method is based on a family of semianalytical recursive algorithms (SARA) of convolution. A general simulation method and examples of simulation results for buck and boost DC-DC converters are given. Because of absolute stability, high accuracy, low numerical complexity, and high speed, SARA algorithms seem to be a very convenient tool for simulation of switch-mode circuits.

The averaged models of switch-mode DC-DC power converters are discussed. Two methods of averaged model derivation are considered - the first, based on statespace averaging and the second, on the switch averaging approach. The simplest converters: BUCK, BOOST and BUCK-BOOST working in CCM (continuous conduction mode) or DCM are taken as examples in detailed considerations. Apart from the ideal converters, the more realistic case of converters with parasitic resistances is analyzed. The switch averaging approach is used more frequently than the other and is believed to be more convenient in practical applications. It is shown however, that in the deriving the averaged models based on the switch-averaging approach, some informalities have been made, which may be the source of errors in the case of converters with parasitic resistances, or working in DCM mode.

The separation of variables approach to formulate the averaged models of DC-DC switch-mode power converters is presented in the paper. The proposed method is applied to basic converters such as BUCK, BOOST and BUCK-BOOST. The ideal converters or converters with parasitic resistances, working in CCM and in DCM mode are considered. The models are presented in the form of equation systems for large signal, steady-state and small-signal case. It is shown, that the models obtained by separation of variables approach differ in some situations from standard models based on switch averaging method.

Large-signal and small-signal averaged models of basic switch-mode DC-DC power converters: BUCK (step-down) and BOOST (step-up) are presented. Models are derived with the separation of variables approach and have the form of equivalent circuits, suitable for a circuit simulation. Apart from equivalent circuits, small-signal transmittances of converters for CCM and DCM modes are discussed. Parasitic resistances of all components of converters are taken into account. A few examples of simulations and measurement results of selected converter characteristics are also presented. It is shown, that neglecting parasitic resistances (often met in works of other authors) may lead to serious errors in an averaged description of converters.