buck-duty-output-three-row-scan - Electronic Circuits XIII & XIV: Power Supplies and Switching Energy Step by Step

An ideal buck converter uses duty fraction times input voltage as the average output only after the inductor balance closes. The duty rows are exact lossless training ledgers; real outputs move with diode or switch drops, resistance, ripple, load transients, control timing, and voltage measurement uncertainty.

Accepted duty rows map the same input voltage to three average outputs. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Duty becomes output voltage after balance passes

Every row first balances the inductor. Only then is the duty fraction allowed to set an ideal average output.

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

Three duty rows scan the same input voltage

The input voltage stays at twelve volts. Duty moves from one quarter to one half to three quarters, and output follows.

\begin{array}{c|c|c|c}D&V_{\text{in}}&V_{\text{out}}&\sum Vt\\\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}

The output row is accepted after the balance row

The displayed output voltage cites the accepted interval balance instead of standing alone as a caption.

V_{\text{out}}=\frac{1}{2}\cdot12\ \text{V}=6\ \text{V}