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We present a novel randomized wrapped-around pulse position modulation (RWAPPM) scheme for digital modulators of dc-dc converters. Unlike the reported modulation schemes that require a varying switching period (thereby resulting in high attenuation or complete elimination of discrete harmonics), the proposed RWAPPM conversely requires only a constant switching period (thereby advantageous in terms of easy realization in hardware), and yet, its discrete harmonics are negligible. We derive an expression for the spectrum of the RWAPPM scheme to analytically obtain the peak spectral power and ripple noise voltage of RWAPPM. This expression further provides insight to the parameters that influence the RWAPPM spectrum. We benchmark the RWAPPM scheme against the ubiquitous conventional pulsewidth modulation scheme and six reported (randomized and frequency modulation) schemes. The RWAPPM scheme features negligible discrete harmonics [≤ -158 dB relative to full scale (dBFS)], and among the modulation schemes, it features the lowest peak spectral power at -26.6 dBFS (before low-pass filtering) and relatively low ripple noise at 2 mVrms (after low-pass filtering) for a 3.6-2.5-V conversion and an effective switching frequency of 120 kHz. We verify the derived expression and attributes of the RWAPPM spectrum by computer simulations and on the basis of experimental measurements on a dc-dc converter.