Filter Windows and Gain Budgets

Gain After Filter Scales Squared Budget

passive first, active second

Post-gain output budget is kept separate from passive transmission. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The passive filter output is separated first

The low-pass stage transmits 1/5 of the squared budget, so 20 becomes 4.

20⋅15=420\cdot {1\over 5}=4
Passive output firstPassive transmission is checked before gain.ffcratioinoutratioinoutlowpassgain

The active gain scales the squared budget afterward

A gain of 3 multiplies squared budget by 9, giving post-gain output 36.

4⋅32=364\cdot 3^2=36
Post-gain budgetThe gain stage is checked separately from the filter.ffcratioinoutratioinoutlowpassgain