Pull-up Current Margin Scan - Electronic Circuits II Step by Step

A pull-up input has an ideal high state and a closed-state current that follows source voltage and pull-up resistance. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Open pull-up has high voltage and no current

When the switch is open, the output node rises to the source voltage and the ideal pull-up branch carries no current.

\text{open switch}\Rightarrow V_{\text{out}}=12\ \text{V},\quad I=0\ \text{A}

Closed current scales with source voltage

Hold the pull-up resistance fixed and close the switch. The current rises one row at a time because the same resistance sees more source voltage.

\begin{array}{c|c|c}V_s&R_{\text{pull}}&I_{\text{closed}}\\6\ \text{V}&3\ \text{ohm}&2\ \text{A}\\9\ \text{V}&3\ \text{ohm}&3\ \text{A}\\12\ \text{V}&3\ \text{ohm}&4\ \text{A}\\\end{array}

Closed current falls as pull-up resistance grows

Now hold the source voltage fixed and change only the pull-up resistance. The current column moves the other way.

\begin{array}{c|c|c}V_s&R_{\text{pull}}&I_{\text{closed}}\\12\ \text{V}&3\ \text{ohm}&4\ \text{A}\\12\ \text{V}&4\ \text{ohm}&3\ \text{A}\\12\ \text{V}&6\ \text{ohm}&2\ \text{A}\\\end{array}

The rendered closed case is just Ohm's law

For the resistance-scan middle row, the source is 12 volts and the pull-up is 4 ohm, so the closed current is 3 amperes.

12\ \text{V}/4\ \text{ohm}=3\ \text{A}

The pull-up model has two trusted states

The helper deliberately keeps this model ideal: open means high with no current, and closed means a current set by source voltage and pull-up resistance. Real leakage and transistor details stay out of this chapter.

\text{open}: I=0,\quad \text{closed}: I=V_s/R_{\text{pull}}