A passive-ratio scan separates the filter's kept budget from the later active gain, so attenuation is visible before amplification. The rows are exact only for the declared input budget, passive ratio, gain, and ideal linear transfer model; real filters add component tolerance, source and load impedance, parasitics, noise, temperature drift, finite amplifier headroom, and voltage/frequency measurement uncertainty.
The passive filter ratio changes the budget before active gain is applied. 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 one-third passive ratio leaves forty after gain
Input budget 30 times passive ratio 1/3 gives passive output 10, then gain 2 gives final 40.
30⋅31⋅22=40
A one-half passive ratio leaves sixty after gain
With the same input and gain, passive ratio 1/2 gives final budget 60.
30⋅21⋅22=60
A two-thirds passive ratio leaves eighty after gain
Passive ratio 2/3 raises the passive output to 20 and final budget to 80.