Effect of Time Lag in Response to Switching Signal in Interrupted Electric Circuit

Abstract

In this study, we analyze the characteristics of an interrupted electric circuit. In particular, we focus on a special situation where the switching action of the circuit is delayed because of a time lag in the response to the switching signal. This situation is observed in switching circuits driven by a high-frequency switching signal. However, the fundamental characteristics of this type of circuit have not yet been clarified. To address this shortfall, we assume that a time lag of the response to the switching signal occurs in simple interrupted electric circuits, and investigate how this time lag affects circuit characteristics. First, we show the model of a circuit whose switching action is the same as that of a current-mode-controlled dc/dc converter. Here by using logic circuits, we impose an artificial time lag on the response to the switching signal. Next, we define a sampled data model (i.e., a return map) that we analyze in detail. Based on the return map, we derive one- and two-parameter bifurcation diagrams. Finally, we compare the bifurcation diagrams constructed with time lag to those constructed without time lag. The results clearly show that time lag is responsible for a new structure in the return map that does not occur in circuits with ideal switching. This new return map structure is a key to understanding the essential characteristics of circuits with time lag. Furthermore, the mathematical results are verified experimentally.