TIME-VARYING CIRCUIT ANALYSIS

Research Team: U. Reggiani, A. Massarini (Università di Modena e Reggio Emilia)

Objectives: Development of new computer-oriented methods for a large-signal time-domain analysis of switched networks. The switching elements, which can be either internally or externally controlled, are modelled as ideal switches.

Research topics

Development of a methodology for determining the unknown time-sequence of switched network circuit topologies

The method is based on the detection of possible discontinuities of capacitor voltages and inductor currents caused by ideal switch commutations. These discontinuities are associated to Dirac impulses of current and voltage, respectively. Using the state variable approach for the network solution allows the determination of the correct topology after each switching. The proposed representation of the Dirac impulse is innovative, as it is the technique for verifying internally controlled switch states through the proper examination of both the impulsive and nonimpulsive components of their controlling variables.

Development of an efficient and systematic procedure for the computer formulation of state and output equations of all circuit topologies of a time-varying linear active network, whenever they exist and make sense

State equations and output equations are obtained through the tableau matrix of the network. This matrix is built using a constraint matrix of a suitable n-port. The n-port results from the extraction from the network, as ports, of all the independent voltage and current sources, all the ideal switches, all capacitors and inductors, and the short circuit and open circuit elements introduced to account for output variables other than the previously mentioned port variables. Circuit topologies differing from one another because of the state of one or more switches are characterized by variable sequences that are different just for exchanges between current and voltage of the relevant switching ports. Therefore, the state equation of each single topology can be obtained very quickly from that of a previous one by means of a simple exchange of columns in the n-port matrix.

Main publications

1. A. Massarini, U. Reggiani “Computer-Aided Time-Domain Large-Signal Analysis of Switched Network,” in Proc. IEEE International Symposium on Industrial Electronics (ISIE’96), Warsaw (Poland), June 17-20, 1996, Vol. 2, pp. 567-572

2. A. Massarini, U. Reggiani, M. K. Kazimierczuck “Analysis of Networks with Ideal Switches by State Equations,” IEEE Trans. on Circuits and Systems - Part. I, Vol. 44, No. 8, pp. 692-697, Aug. 1997

3. A. Massarini, U. Reggiani “An Efficient Algorithm for the Formulation of State Equations and Output Equations for Networks with Ideal Switches,” The 2001 IEEE International Symposium on Circuits and Systems (ISCAS 2001), Sydney (Australia), May 6-9, 2001, Vol. III, pp. III521-III524