What the equation means is that when voltage is reduced to half it's original value, power is reduced to one quarter it's original value.Yes, of course. I stated that in my post here.
Hold on, this goes to my previous comment: you can't just cite equations without understanding what the equations mean. first, the equation 20log(v2/v1) is a dB relationship in *power* not in voltage; a relationship which is true under certain conditions (which, btw, are articulated in the previously cited henry ort reference as well as in my previous comments).Paperw8, the fundamental misconception you have, which ultimately leads you to incorrectly assert that first order filters roll off at 3db/octave, is the notion that the numerical db value describing the ratio of two signals applied to a given resistive load will be different depending on whether voltage or power is being considered.
I'll mention, btw, that early in my career as an electrical design engineer, a great many years ago, I had the exact same misconception, until my boss enlightened me.
The value of that number is one and same, whether voltage or power is being considered. For a given resistive load, reducing the applied voltage by a factor of 2 reduces power by a factor of 4 (as you agree), and the change in signal level is 6db. Period.
The db change in that situation if voltage is being considered is 6db; the db change if power is being considered is 6db; the db change is 6db, period. That is why the formula for db as computed from voltage levels includes the constant "20," while the formula for db as computed from power levels includes the constant "10." Otherwise the two numerical values wouldn't work out to be the same, as you'll agree.
Kijanki's post provides an elegant mathematical proof of the equivalency of the two formulas, 10log(P1/P2) and 20log(V1/V2), as does the Ott paper, in a different way. But until you recognize that a db is a db, regardless of whether power or voltage is being considered, the other differences in our positions, including the issue of filter rolloff which started the discussion, will remain unreconcilable.
Regards,
-- Al