Billy K. H. Wong

Computation of the cycle state-variable sensitivity matrix of PWM DC/DC converters and its applications

This paper presents a generalized technique for computation of cycle state-variable sensitivity matrix of pulse-width-modulated (PWM) dc/dc converters. It determines the sensitivity of the state variable variation, with the inclusion of the effects of changing the topology duration on the sensitivity matrix. A basic sensitivity graph for each circuit topology is derived. By cascading corresponding graphs, a sensitivity matrix of multiple topologies is formulated. The correctness of the proposed method is compared with other methods in the performance of the steady-state determination and stability analysis.

Dual-loop iteration algorithm for steady-state determination of current-programmed dc/dc switching converters

The methodology starts with separating the gate signal from the feedback circuit to the power stage in order to convert a closed-loop configuration into an open-loop one. The first iteration loop applies the Newtons method together with a time-domain simulation technique to find the steady-state state variables when the transformed configuration is operating at a constant duty cycle. The second iteration loop is to find the steady-state duty cycle using the secant method. The algorithm includes all of the advantages of a previously developed time-domain simulation technique and solves the nonconvergence problem in the single-loop iteration method, due to the amplifying effect of poor guess values of the state variables on the duty cycle in the feedback path during the iteration. A current-programmed boost converter is illustrated. The performances of the single-loop and the proposed methods are compared. The theoretical results are verified with the experimental measurements.

A systematic graphing technique for small-signal low-frequency characterization of PWM DC/DC converters

This paper presents a systematic graphing technique for the small-signal low-frequency characterization of pulsewidth-modulated (PWM) DC/DC power converters. The methodology starts with using a discrete-time state-space description to formulate a small-signal sensitivity graph for each circuit topology. Each graph correlates state-variable sensitivities with the topology duration, input source and state vector at the beginning of the topology. The overall converter sensitivities in one switching cycle are obtained by cascading the respective graphs in accordance with the sequence of the topologies. As the proposed method integrates with original algorithms for obtaining the time-domain responses and the steady-state operating point of converters, it is unnecessary to have a priori understanding of the converter operation and is possible to obtain actual circuit waveforms within one switching cycle. The proposed method is exemplified by analyzing a PWM boost converter operating in continuous conduction mode and discontinuous conduction mode under open-loop and closed-loop control, respectively. Theoretical predictions are verified with experimental measurements.

Time-domain simulation of power electronics circuits using state variable quadratic extrapolations

A new stepwise time-domain analysis technique for power electronics circuits is presented. At each simulation step the rate of change of each state variable is determined by the corresponding reactive element parasitic resistance and state value obtained after performing a modified nodal analysis (MNA). A quadratic state trajectory description for each reactive element is formulated. To ensure the correct topological operation of the power stage, the algorithm monitors the position and checks the validity of all switches, requiring no a priori knowledge of their switching relationships. All computations require simple algebraic manipulations of resistive networks only. An example of simulating the response of a zero-voltage-transition PWM buck converter is illustrated. The results are favorably compared to the previous method using constant nodal voltage approximation, experimental measurements, and the commercial software PSpice.

Computation of state variable sensitivities of PWM DC/DC regulators and its application

A generalized technique for computation of state variable sensitivities of PWM DC/DC regulators is presented. The methodology not only considers the sensitivities of the state variable variations, but also takes their effects on varying the topology duration into account. A basic sensitivity graph for single topology is firstly derived. It is then propagated to determine the sensitivities of regulators with multiple topologies. Simple mathematical computation and network transformation are required only. The state variable sensitivity matrix is applied to determine the steady-state operating point, using a newly developed dual-loop iteration algorithm and to examine the stability of operation. The algorithm is illustrated with an example of boost regulator. The theoretical predictions are verified with the results obtained from available literature.

Modular graphing technique for small-signal low-frequency characterizations of PWM DC/DC regulators

This paper addresses the development of a modular graphing technique for small-signal low-frequency characterizations of pulse-width-modulation (PWM) DC/DC regulators. The methodology starts with the derivation of a unified input sensitivity graph for a single circuit topology to correlate the state-variable sensitivities with the topology duration and the input source. By integrating with previously developed state-variable sensitivity graphing technique, the overall regulator sensitivities in one switching cycle, and hence the small-signal transfer characteristics are obtained by cascading the respective graphs in accordance with the sequence of the topologies. The proposed method is exemplified by analyzing a PWM boost regulator.