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

This cutoff-is-half-squared-response lesson states the exact training contract at cutoff: both first-order low-pass and high-pass squared response ledgers read 1/2. The arithmetic is exact only for the stated normalized index and ideal filter model. Real cutoff measurements shift with component tolerances, loading, parasitic capacitance and inductance, finite bandwidth, calibration limits, finite precision, and measurement uncertainty.

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}