Faster Clock Tightens the Same Kind of Ledger - Electronic Circuits IV & XII: Digital Logic and Timing Closure Step by Step

A faster-clock-tightens-the-same-kind-of-ledger scan holds the selected edge index fixed and reduces the period across three rows, checking that the same edge time t_n = n * T moves earlier as the clock speeds up row by row. The arithmetic is exact only for the stated periods, edge indices, edge times, and rows in the ideal periodic-clock model. Real clocks add jitter, duty-cycle distortion, skew, finite rise time, threshold uncertainty, probe/calibration limits, finite precision, and measurement uncertainty.

Changing only the period changes the indexed edge times. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

With the longer period the third edge is later

For period 8 seconds, edge 3 is at 24 seconds.

3\cdot 8\ \text{s}=24\ \text{s}

Shorter periods tighten every indexed edge time

The selected index stays the same while the period is reduced row by row.

\begin{array}{c|c|c}T&n&t_n\\8\ \text{s}&3&24\ \text{s}\\4\ \text{s}&3&12\ \text{s}\\2\ \text{s}&3&6\ \text{s}\\\end{array}

With the shorter period the same edge is earlier

Changing only the period to 4 seconds moves edge 3 to 12 seconds.

3\cdot 4\ \text{s}=12\ \text{s}