buck-duty-output-three-row-scan - Electronic Circuits XIV: Inductors and Switching Energy Step by Step

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}