Fixed-Switching-Frequency Background Capacitor-Current-Sensor Calibration for DC–DC Converters

Abstract

Background capacitor-current-sensor (CCS) calibration (CAL) is proposed for dc–dc converters to achieve fast load-transient response for small undershoot <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {US}}$ </tex-math></inline-formula> , overshoot <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {OS}}$ </tex-math></inline-formula> , and short settling time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm {S}}$ </tex-math></inline-formula> in the output voltage <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {O}}$ </tex-math></inline-formula> . The CCS’ impedance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z_{\mathrm {Cs}}$ </tex-math></inline-formula> is calibrated to a scaled replica of the output capacitor’s impedance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z_{\mathrm {Co}}$ </tex-math></inline-formula> , which varies with printed-circuit-board parasitics, process-voltage-temperature variations, and aging. Thus, the CCS shunts a current <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{\mathrm {Cs}}$ </tex-math></inline-formula> equal to a scaled output-capacitor current <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{\mathrm {Co}}$ </tex-math></inline-formula> , which instantly and accurately reflects load-current <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$I_{\mathrm {load}}$ </tex-math></inline-formula> transients. The CAL operates at a fixed switching frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {SW}}$ </tex-math></inline-formula> . At this <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {SW}}$ </tex-math></inline-formula> , although <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z_{\mathrm {Cs}}$ </tex-math></inline-formula> is dominated by its inductive part, this work can still calibrate its capacitive and resistive parts based on the time derivatives <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dV</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</sub> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dt</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dI</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cs</sub> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dt</i> , respectively. This fixed- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {SW}}$ </tex-math></inline-formula> CAL overcomes the bottleneck of the prior state-of-the-art CCS CAL, which must hop <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {SW}}$ </tex-math></inline-formula> to lower values to calibrate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z_{\mathrm {Cs}}$ </tex-math></inline-formula> capacitive and resistive parts, thereby enlarging <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {O}}$ </tex-math></inline-formula> steady-state ripples and transient fluctuations during CAL. Thus, only this fixed- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {SW}}$ </tex-math></inline-formula> CAL is suitable for background operation. Moreover, this CAL can be interrupted by a load-transient or dynamic-voltage-scaling event and be reactivated in quasi-steady state. The shortest CAL period is 8.8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{s}$ </tex-math></inline-formula> at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {SW}} = 30$ </tex-math></inline-formula> MHz without interruption. A buck converter with this CCS CAL is fabricated in 0.18- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> CMOS process and occupies 2.25 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Under a 2-A/4-ns step-up (step-down) load transient, the measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {US}}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {OS}}$ </tex-math></inline-formula> ) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t_{\mathrm {S}}$ </tex-math></inline-formula> are 36 mV (29 mV) and 56 ns (45 ns), respectively. Compared with prior state of the arts, this work achieves much smaller <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{\mathrm {O}}$ </tex-math></inline-formula> ripples and fluctuations during CAL, shorter CAL period, and faster load-transient response.