Active Filter Contracts

Active Filter Separates Ratio and Gain

An active filter budget has a passive ratio and a separate gain stage. 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 ratio is applied first

Input budget 25 times passive ratio 4/5 gives passive output 20.

25⋅45=2025\cdot {4\over 5}=20
Passive stage firstThe passive output bar is checked.passivefinal

Gain is a separate squared multiplier

Gain 2 gives gain-squared 4 and final budget 80.

20⋅22=8020\cdot 2^2=80
Active filter outputThe final bar is checked after gain.passivefinal