Multiphase Buck Input RMS Current

\( D = \frac{V_{out}}{V_{in}} = \) 0%

Ideal Phase Shift = 0° per phase

Average Input Current = 0 A

Total Input RMS Current = 0 A (full heating value, includes DC + AC)

Input Capacitor Ripple Current (AC RMS) = ≈ 0 A

\( \Delta I_{L(pp)} \) per phase = 0 A (0% of avg per phase)

Why Use RMS (not Average) for Input Capacitor Stress?

Multiphase interleaving reduces input RMS current by staggering the pulses drawn from the source. This lowers stress on the input capacitors.

RMS is always ≥ average because squaring emphasizes peaks. Capacitor heating (and most conduction losses) scales with I²R, so peaks matter far more than valleys or average value.

• • Average current → sets overall power flow and DC losses
• • RMS current → determines ripple heating in capacitors (ESR, ripple current rating)
• • Spiky waveforms → much higher heating than smooth ones with the same average

Total RMS vs. AC Ripple RMS

• • Total RMS — entire waveform (DC + AC) → used for total I²R losses in source path, wiring, MOSFETs
• • AC Ripple RMS — only the pulsating part → what capacitors actually experience
  \[ I_{\text{ripple RMS}} = \sqrt{I_{\text{total RMS}}^2 - I_{\text{avg}}^2} \]
  This is the value listed in capacitor datasheets under "ripple current".

In a good multiphase buck design (especially near 50% duty with low inductor ripple), interleaving can make AC ripple RMS very small — that's the real benefit you're seeing in the chart.