High frequency implications for switch-mode DC-DC converter design

High frequency content, it's not just the fundamental
The trend towards smaller DC-DC converter footprint is driving the industry to ever higher switching frequencies. To understand the impact of high switching frequency on DC-DC converter design, it will be useful to examine the spectral content of the switching waveform. Using the principle of superposition, the switching waveform (Figure 1 (a)) can be decomposed into three unique waveforms: a somewhat ideal square-wave (Figure 1 (b)), a triangular wave that represents the non-ideal rising edge of the pulse (Figure 1 (c)), and a triangle wave that represents the falling edge of the switching waveform (Figure 1 (d)). The rectangular waveform is the primary contributor of energy at the fundamental of the switching frequency with the familiar sin(x)/x , or sinc(x) envelope. The fast rising and falling edges contribute energy at 1/τ_R Hz and 1/τ_F Hz.

Figure 1. Switching waveform decomposition and associated frequency spectrum

As an example, the Enpirion, EN5335QI 3A-Integrated Inductor DC-DC converter, operates at a nominal 5 MHz. A 5 MHz switcher will have a 200ns switching period. Good efficiency requires that the rise and fall times be very small relative to the overall switching period. For this particular part, the rise time is 2ns and the fall time is ~3ns. The 2ns rise time corresponds to a frequency contribution at 500 MHz and the 3nS fall-time corresponds to frequency content at 330 MHz. Figure 1 (e) shows the power spectral density.

By considering the switching waveform and its corresponding frequency components, we can better understand the nature of the noise that must be controlled.

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