A Fast-transient Buck Converter with One-Cycle-Balancing Control for Single and Consecutive Load Steps

To power large-scale digital circuits such as FPGAs and microprocessors, fast transient buck converters are crucial for maintaining energy efficiency and load performance [1]–[6]. One-cycle charge balance (OCB), minimizing the undershoot/overshoot (US/OS) voltage <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{(Vus/Vos)}$</tex> and their recovery time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(t_{\mathrm{R}})$</tex>, is the optimal transient response of a buck converter. [7]–[9] utilized capacitor current sensor (CCS) and computational method to achieve OCB, but need complicated calibrations on 3 parameters, assisted by accurate inductor current <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(l_{\mathrm{L}})$</tex> sensors. [10] introduced an emulated-curve method that realizes a cost-effective computational OCB control. Fig. 1 explains its US OCB control: (1) After quickly detecting the transient event at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{o}$</tex>, the controller turns on the high-side power switch to raise <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{L}$</tex>. (2) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{L}$</tex> intersects the load current <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$/\mathrm{L}0$</tex> at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{1}$</tex>. [10] proved that for any <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$/\text{LD}$</tex> step, the emulated curve (EC, the expression for US given in eq. 1, starting from VREF) always intersects V<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>'s valley at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{1}. \Delta \mathrm{Q}=\mathrm{Q}_{1}$</tex> is the charge loss in the output capacitor C<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf>, represented by the valley value <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta V_0=Q_1 / C_0$</tex>. (3) Based on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Delta \mathrm{O}$</tex>, the OCB controller calculates the high-side switch turn-off time instant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{2}$</tex>, and the OCB control end time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t_{3}$</tex> for Co charge balance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Q}_{2}=\mathrm{Q}_{1}$</tex>. The OS OCB control is almost the same, except changing the EC expression for OS. This method is insensitive to the variations of Co's equivalent series inductance (ESL) and resistance (ESR), requiring only 1-parameter calibration (the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{Co}^{\mathrm{x}}L\mathrm{c}$</tex> term in eq. 1).