Sampled-data poles, zeros, and modeling for current-mode control

摘要

Exact and approximate sampled-data models in closed forms are derived for switching DC-DC converters under peak/valley current-mode control. The corresponding sampled-data poles and zeros in closed forms are also derived. The location and stability conditions of the poles and zeros, boundary conditions of subharmonic instability, and nulling of the audio-susceptibility are also derived. It is proved that the stable operating range of the source voltage is linearly proportional to the ramp slope. The sampled-data models agree with previous experiment results and accurately predict the subharmonic instability. The different view from the sampled-data model about the number and stability (minimum phase) of pole and zero does not necessarily invalidate the traditional continuous-time averaged model. However, this different view gives better prediction about converter dynamics and is useful for the analog or digital controller design for DC-DC converters.