Switching Interval Budgets

off-interval-removes-the-same-ripple

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.

If=Ii+VoffΔtLI_f=I_i+{V_{\text{off}}\Delta t\over L}
Switch-off interval setupThe off interval returns the current to its start value.L 3 HV -3 Vdt 3 sIi 3 AdI -3 AIf 0 A

Longer off-time removes more ripple

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

IiVoffΔtΔIIf3 A−3 V1 s−1 A2 A3 A−3 V2 s−2 A1 A3 A−3 V3 s−3 A0 A\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.

ΔIoff=−3 V⋅3 s/3 H=−3 A\Delta I_{\text{off}}=-3\ \text{V}\cdot3\ \text{s}/3\ \text{H}=-3\ \text{A}
Switch-off ripple intervalThe off interval returns the current to its start value.L 3 HV -3 Vdt 3 sIi 3 AdI -3 AIf 0 A