Holding passive output fixed makes active gain a separate squared factor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Gain one keeps the passive budget

The passive output is fixed at 20. Gain 1 gives final budget 20.

2012=2020\cdot 1^2=20
Active gain scan rowGain is a separate squared factor.passivefinal

Gain two makes four times the passive budget

The same passive output with gain 2 gives gain-squared 4 and final budget 80.

2022=8020\cdot 2^2=80
Active gain scan rowThe final bar grows after the passive ratio.passivefinal

Gain three makes nine times the passive budget

With gain 3, gain-squared is 9 and final budget is 180.

2032=18020\cdot 3^2=180
Active gain scan rowThe source factor is the gain, not the filter ratio.passivefinal