Timing Denominator Factor Scan - Biophysical Instrumentation III: Control, Detectors, and Throughput Step by Step

Control duty needs a companion scan where active time stays fixed and program time moves. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The active numerator can stay fixed

Each row has the same checked active control time, but the full program time changes. That makes the duty denominator visible instead of hidden inside one example.

d=\frac{t_a}{t_p}

Three program lengths expose the duty denominator

The active-time column stays fixed while the total-time column changes. The repeated-time column still uses the whole program time, not only the active windows.

\begin{array}{c|c|c|c|c}t_{\text{program}}&t_{\text{active}}&\text{duty}&N_{\text{repeat}}&t_{\text{repeated}}\\8\ \text{s}&4\ \text{s}&\frac{1}{2}&2&16\ \text{s}\\10\ \text{s}&4\ \text{s}&\frac{2}{5}&2&20\ \text{s}\\12\ \text{s}&4\ \text{s}&\frac{1}{3}&2&24\ \text{s}\\\end{array}

Repeated time follows the program length

The long row repeats a 12 s program 2 times, so repeated time grows even though active time did not.

t_{\text{repeated}}=2\cdot12\ \text{s}=24\ \text{s}