Fig. 4. Comparison of two different carriers of a triangle wave and a sawtooth wave.

a A triangle wave sequence is adopted to generate the PWM sequence. The top waveforms, v_C and V_ref, are the triangle wave and the dc reference signal, respectively. The middle waveform, v_g, is the generated PWM sequence, i.e., the gate signal. The bottom waveforms, i_L and i_o, are the inductor and output currents, respectively. At the moment of the frequency shift at the peak of the triangle wave, the output current remains stable (Δi_o = 0). b A sawtooth wave sequence is adopted to generate the PWM sequence. The top waveforms, v_C and V_ref, are the sawtooth wave and the dc reference signal, respectively. The middle waveform, v_g, is the generated PWM sequence, i.e. the gate signal. The bottom waveforms, i_L and i_o, are the inductor and output currents, respectively. At the moment of the frequency shift, the output current remains stable (Δi_o = 0). The frequency shift occurs on the upward ramp of the sawtooth wave, where the high level of v_g lasts for ½T_on1. c A triangle wave sequence is adopted to generate the PWM sequence. The top waveforms, v_C and V_ref, are the triangle wave and the dc reference signal, respectively. The middle waveform, v_g, is the generated PWM sequence, i.e. the gate signal. The bottom waveform, v_{g_1}, is the fundamental component of the gate signal. When the duty cycle of the gate signal changes, the phase of v_{g_1} remains constant. d A sawtooth wave sequence is adopted to generate the PWM sequence. The top waveforms, v_C and V_ref, are the sawtooth wave and the dc reference signal, respectively. The middle waveform, v_g, is the generated PWM sequence, i.e. the gate signal. The bottom waveform, v_{g_1}, is the fundamental component of the gate signal. Φ₀ and Φ₁ refer to the phase of before and after the duty cycle changes. The phase of v_{g_1} varies with a change in the duty cycle.