Cutoff Is Half Squared Response - Electronic Circuits VII: Frequency Response and Filters Step by Step

At cutoff the exact training claim is a squared ratio of one half. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A first-order low-pass is half squared at cutoff

At index 1, the low-pass squared ratio is 1/2.

|H_{\text{LP}}|^2 = {1\over 2}

A first-order high-pass is also half squared there

At the same index, the high-pass squared ratio is 1/2.

|H_{\text{HP}}|^2 = {1\over 2}