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.

301322=4030\cdot {1\over 3}\cdot 2^2=40
Passive ratio scan rowThe checked bars separate passive and final budgets.passivefinal

A one-half passive ratio leaves sixty after gain

With the same input and gain, passive ratio 1/2 gives final budget 60.

301222=6030\cdot {1\over 2}\cdot 2^2=60
Passive ratio scan rowOnly the passive ratio changes.passivefinal

A two-thirds passive ratio leaves eighty after gain

Passive ratio 2/3 raises the passive output to 20 and final budget to 80.

302322=8030\cdot {2\over 3}\cdot 2^2=80
Passive ratio scan rowThree rows show the passive factor before gain.passivefinal