An improved sampled-data current-mode-control model which explains the effects of control delay

A new sampled-data model for the current-mode controlled buck converter includes for the first time the effects of delay in the pulse-width-modulator (PWM), Modified z-transforms are used in this new model for constant frequency trailing-edge modulation, Realistic amounts of delay are found to be particularly significant when the buck converter is operating in the continuous conduction mode near the discontinuous conduction mode boundary. The new model is used to predict the Loop gain measurements obtained with the "digital modulator" and with conventional measurement techniques. It is shown that conventional loop gain measurement techniques are insufficient to measure the loop gain in this region of operation. It is also shown that the digital modulator can add a significant amount of delay, thereby altering the loop gain of the circuit being measured. Unlike the case of a continuous system, PWM delay is found to significantly alter the low-frequency loop gain magnitude of this sampled-data system, The new model predicts the boundary condition for sub-harmonic instability, and reduces to Ridley's current-mode control model for the case of zero delay. Experimental corroboration is presented.