duty-sets-ideal-average-output - Electronic Circuits XIV: Inductors and Switching Energy Step by Step

The average output claim is accepted only after interval balance. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A buck output is accepted after volt-second balance

The output is an average claim. It cites the same interval rows that first pass the inductor balance gate.

D={t_{\text{on}}\over t_{\text{on}}+t_{\text{off}}}\quad;\quad V_{\text{out}}=D V_{\text{in}}

Higher duty raises the ideal average output

Input voltage stays fixed. Each row has a balanced on/off pair, then duty sets the average output.

\begin{array}{c|c|c|c}D&V_{\text{in}}&V_{\text{out}}&\sum V_L\Delta t\\\frac{1}{4}&12\ \text{V}&3\ \text{V}&0\ \text{V}\cdot\text{s}\\\frac{1}{2}&12\ \text{V}&6\ \text{V}&0\ \text{V}\cdot\text{s}\\\frac{3}{4}&12\ \text{V}&9\ \text{V}&0\ \text{V}\cdot\text{s}\\\end{array}

Duty sets the ideal average output after balance is accepted

The duty fraction is derived from the same on/off rows that passed the volt-second balance check.

V_{\text{out}}=D V_{\text{in}}=\frac{1}{4}\cdot12\ \text{V}=3\ \text{V}