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A constant on-time current-mode (COTCM) control features inherent phase-current balancing, good stability margin and improved light-load efficiency which is a new mandate for many CPU power applications nowadays. For a delicate application such as adaptive voltage positioning (AVP) application, however, the output voltage regulation of a COTCM converter is often inadequate when constant converter output impedance feature is also required. In this paper, a modified converter with a DC-offset correction circuit is presented. A small-signal model is also developed based on describing-function approach which is complicated but necessary to uncover the inherent nature of this control scheme. Experimental results will be shown. A comparison with a ripple-based constant on-time (RBCOT) control scheme will also be given.