Active Filter Contracts

Phase Filter Audit Closes the Chain

The capstone closes phase timing, impedance current, and active-filter 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

The timing and current claims are checked first

Phase is 1/8 cycle, and 10 volts over 5 ohms gives 2 amperes.

ϕ=18,I=105=2\phi={1\over 8},\quad I={10\over 5}=2
Phase and current auditThe phase and impedance checks both close.periodlagphasephaseRXZ

The active filter budget closes last

Budget 25 times 4/5 times gain-squared 4 gives 80.

25⋅45⋅22=8025\cdot {4\over 5}\cdot 2^2=80
Filter budget auditPassive ratio and gain-squared are checked separately.passivefinal