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This paper addresses the spectral characteristics of a dual randomised pulse width modulation scheme (RCFM-RPPM) for reducing conducted EMI in the basic DC-DC converters (buck, boost, and buck-boost) operating in discontinuous conduction mode (DCM). It combines two simple schemes, random carrier frequency modulation (RCFM), and a random pulse position (RPPM). First, the modulating principle of the dual randomised PWM is presented. Then, a mathematical model of power spectral density (PSD) that characterises the switch voltage of the three basic DC-DC converters is derived. The mathematical model is validated by simulation of a buck converter operating in DCM. Analytical and simulation results show the effectiveness of PSD spreading of the dual randomised scheme compare to the simple randomised schemes. Moreover, the PSD analysis is confirmed by FFT (Fast Fourier Transform) analysis of the switch voltage. Finally, the effect of randomness levels on the PSD spreading is studied.

Spectral analysis of switch voltage for dual randomized PWM DC-DC converters operating in DCM