Filter Ratio Cross Scans

Window Gain Budget Three-Row Scan

passive first, gain second

A filter window is multiplied before active gain squares the remaining budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Unity gain leaves the passive window budget unchanged

The passive window turns input budget 25 into 16. Gain 1 leaves final budget 16.

25⋅45⋅45⋅12=1625\cdot {4\over 5}\cdot {4\over 5}\cdot 1^2=16
Window plus gain scan rowThe passive output is separated before gain.ffcratioinoutffcratioinoutratioinouthighpasslowpassgain

A fractional voltage gain still squares exactly

The same passive output 16 is scaled by gain 3/2. Squared gain sends the final budget to 36.

16⋅(32)2=3616\cdot \left({3\over 2}\right)^2=36
Window plus gain scan rowThe fraction is pinned; no decimal gain is used.ffcratioinoutffcratioinoutratioinouthighpasslowpassgain

Doubling voltage gain quadruples the budget

The passive window still gives 16. Gain 2 makes gain-squared 4 and final budget 64.

16⋅22=6416\cdot 2^2=64
Window plus gain scan rowThree rows separate passive windowing from active gain.ffcratioinoutffcratioinoutratioinouthighpasslowpassgain