A high-resolution hybrid randomized modulation scheme for switched-mode DC-DC converters

Abstract

Summary form only given. Switched-mode dc-dc converters are routinely employed in the power supply section of low-power electronic systems, such as biomedical implants, to convert a supply voltage from one voltage level to another voltage level. The switched-mode dc-dc converter employs a modulator to modulate the output pulses. In Pulse Width Modulation (PWM)-based digital modulators, an N-bit counter is employed to generate 2<;sup>;N<;/sup>; possible pulse widths, where the value of N is relatively small (≤10). As a consequence of small N, the output has limited resolution that may cause steady-state limit cycles in closed loop converters. The limit cycles translate to harmonic distortion in the output power spectrum. The impetus is, therefore, to improve the output resolution without increasing N that would otherwise increase the clock frequency and power dissipation of the counter, and without causing harmonic distortion or limit cycles. To improve the output resolution, we propose to adopt the hybrid method that is often used in digital Class D amplifiers. We propose to combine our Randomized Wrapped Around Pulse Position Modulation scheme (RWAPPM) with a Q-bit (Q<;N) ΔΣ noise-shaper; the ΔΣ noise-shaper attenuates the quantization noise in lower frequencies. Fig. 1 depicts a switched-mode dc-dc buck converter whose digital modulator employs the proposed hybrid scheme. The hybrid scheme has three salient features. First, the output resolution is virtually unlimited since the average output from the ΔΣ noise-shaper is not limited into a fixed number of quantization levels. Second, since Q is smaller than N, the counter can use a lower clock frequency (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</sup> × f<;sub>;sw<;/sub>;, where f<;sub>;sw<;/sub>; is the sampling/switching frequency) and that potentially results in lower power dissipation. Third, the RWAPPM randomizes/dithers the pulse position to mitigate the harmonic distortion arising from steady-state limit cycles, including distortion from periodic output pulses, at a cost of a slight increase in ripple noise. Fig. 2 depicts the simulated output spectra (without low pass filtering) of the (conventional or non-randomized) PWM and hybrid schemes. Both are obtained at Q = 5 bits. The hybrid scheme employs a 2nd-order ΔΣ noise-shaper; the PWM has no ΔΣ noise-shaper. A down-conversion from 9 V to 1.5 V at f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sw</sub> = 100 kHz is simulated. The average V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">load</sub> is obtained at the desired 1.5 V for the hybrid scheme, whereas it is 1.4 V for the PWM due to its limited resolution. The ripple noise (after low-pass filtering) of the hybrid scheme is 2.8 mV and it is higher by 1.2 mV than that of the PWM. However, the output spectrum of the hybrid scheme is free from the harmonic distortion, unlike that of the PWM.