off-interval-removes-the-same-ripple - Electronic Circuits XIII & XIV: Power Supplies and Switching Energy Step by Step

An off-interval-removes-the-same-ripple scan holds the inductance and negative freewheel voltage fixed and varies the off interval across three rows, checking that delta-I_off = V_off * delta-t / L removes the current gained during on-time row by row. The arithmetic is exact only for the stated inductances, off-voltages, intervals, current changes, final currents, and rows in the ideal inductor and ideal switching model. Real converters add winding resistance, switch loss, diode drop, core saturation, ripple approximation, current-sense/probe calibration limits, finite precision, and measurement uncertainty.

The freewheel interval must remove the current gained during on-time. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Off-time uses negative inductor voltage

The current begins above zero. The negative freewheel voltage removes current for a measured interval.

I_f=I_i+{V_{\text{off}}\Delta t\over L}

Longer off-time removes more ripple

The negative voltage and inductance stay fixed while the interval grows.

\begin{array}{c|c|c|c|c}I_i&V_{\text{off}}&\Delta t&\Delta I&I_f\\3\ \text{A}&-3\ \text{V}&1\ \text{s}&-1\ \text{A}&2\ \text{A}\\3\ \text{A}&-3\ \text{V}&2\ \text{s}&-2\ \text{A}&1\ \text{A}\\3\ \text{A}&-3\ \text{V}&3\ \text{s}&-3\ \text{A}&0\ \text{A}\\\end{array}

The off interval removes the same ripple

The freewheel interval uses a fixed negative training voltage, so the checked current change is negative.

\Delta I_{\text{off}}=-3\ \text{V}\cdot3\ \text{s}/3\ \text{H}=-3\ \text{A}