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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 mV rms (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.

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This paper proposes a novel method for extracting Finite State Machines (FSMs) from flattened gate-level netlist. The proposed method which employs a potential state register elimination technique and a two-level FSM separation strategy is highly applicable to control-intensive circuits. The potential state register elimination technique is based on control signal identification whereas the two-level FSM separation strategy is based on enable tree identification and the strongly connected components algorithm. To demonstrate the efficacy and to illustrate the unique features of the proposed FSM extraction method, the Synopsys DesignWare DW8051 microcontroller is used as the benchmark circuit for comparison and simulations. Results show that the proposed method reduces the complexity of the extracted FSMs in terms of number of state registers in an FSM by more than 90% as compared to the reported technique.