duty-sets-ideal-average-output - Electronic Circuits XIII & XIV: Power Supplies and Switching Energy Step by Step

A duty-sets-ideal-average-output scan accepts the buck output only after the inductor volt-second balance ledger has closed. With a 12 V input, duty rows of 1/4, 1/2, and 3/4 give ideal average outputs of 3 V, 6 V, and 9 V only for the stated balanced-switching model. Real converters add ripple, switch and diode drops, ESR, control delay, thermal limits, calibration limits, finite precision, and measurement uncertainty.

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}