An active-gain scan holds the passive output fixed so the gain-squared factor can be checked as its own source of final budget. The exact final budgets assume declared gain values and an ideal linear active stage; real active filters have finite op-amp bandwidth, slew rate, rail headroom, noise, component tolerance, source/load interaction, temperature drift, and voltage/frequency measurement uncertainty.
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.
20⋅12=20
Gain two makes four times the passive budget
The same passive output with gain 2 gives gain-squared 4 and final budget 80.
20⋅22=80
Gain three makes nine times the passive budget
With gain 3, gain-squared is 9 and final budget is 180.