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Reducedorder Mapping and Designoriented Instability for Constant Ontime Currentmode Controlled Buck Converters with a PI Compensator
Xi Zhang, Jianping Xu, Jiahui Wu, Bocheng Bao, Guohua Zhou, and Kaitun Zhang 
Abstract 
The constant ontime currentmode controlled (COTCMC) switching dcdc converter is stable, with no subharmonic oscillation
in its current loop when a voltage ripple in its outer voltage loop is ignored. However, when its output capacitance is small or its
feedback gain is high, subharmonic oscillation may occur in a COTCMC buck converter with a proportionalintegral (PI)
compensator. To investigate the subharmonic instability of COTCMC buck converters with a PI compensator, an accurate
reducedorder asynchronousswitching map model of a COTCMC buck converter with a PI compensator is established. Based on
this, the instability behaviors caused by output capacitance and feedback gain are investigated. Furthermore, an approximate
instability condition is obtained and designoriented stability boundaries in different circuit parameter spaces are yielded. The
analysis results show that the instability of COTCMC buck converters with a PI compensator is mainly affected by the output
capacitance, output capacitor equivalent series resistance (ESR), feedback gain, currentsensing gain and constant ontime. The
study results of this paper are helpful for the circuit parameter design of COTCMC switching dcdc converters. Experimental results
are provided to verify the analysis results. 
Keyword 
Constant ontime currentmode control (COTCMC), Buck converter, Proportionalintegral (PI) compensator, Reducedorder mapping, instability 
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