Reservoir Capacitors Bound Ripple

larger-capacitor-cuts-ripple

A capacitance contrast isolates the ripple denominator. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Capacitance sits in the ripple denominator

The same load current and recharge interval are kept. Only the capacitance is changed.

ΔV=IΔtC\Delta V={I\Delta t\over C}
Capacitance contrast setupThe denominator is the only moving part.Iload 2 Adt 3 sC 4 FdV 3/2 V

Larger capacitance lowers the same charge droop

The rows scan capacitance upward while the numerator stays fixed, so the voltage ripple steps downward.

IΔtCΔV2 A3 s1 F6 V2 A3 s2 F3 V2 A3 s4 F32 V\begin{array}{c|c|c|c}I&\Delta t&C&\Delta V\\2\ \text{A}&3\ \text{s}&1\ \text{F}&6\ \text{V}\\2\ \text{A}&3\ \text{s}&2\ \text{F}&3\ \text{V}\\2\ \text{A}&3\ \text{s}&4\ \text{F}&\tfrac{3}{2}\ \text{V}\\\end{array}

Doubling capacitance halves this ripple ledger

The load current and interval stay fixed. Only capacitance changes, so the checked ripple is smaller.

2 A⋅3 s/4 F=32 V2\ \text{A}\cdot3\ \text{s}/4\ \text{F}=\tfrac{3}{2}\ \text{V}
Larger capacitor contrastThe same charge draw spreads over a larger capacitance.Iload 2 Adt 3 sC 4 FdV 3/2 V