A low-pass cutoff scan holds the signal budget fixed while the cutoff moves the squared transfer ratio. The halving and other row outputs are exact only for the declared frequencies, cutoff values, and ideal first-order low-pass model; real filters add component tolerance, source and load impedance, parasitics, finite op-amp bandwidth and headroom, noise, temperature drift, and frequency/voltage measurement uncertainty.
Holding signal frequency fixed shows how the low-pass squared ratio moves with cutoff. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
At cutoff the low-pass keeps one half
The signal and cutoff are both 6 hertz, so index 1 gives low-pass ratio 1/2. The output budget is 10.
20⋅21=10
A higher cutoff keeps more of the same signal
The cutoff rises to 12 hertz while the signal stays 6 hertz. The ratio is 4/5, so output budget is 16.
20⋅54=16
A lower cutoff rejects more of the same signal
The cutoff drops to 3 hertz, making index 2. The ratio is 1/5, so output budget is 4.