This is how I see it:
- The power in the speakers is a GIVEN in your experiment and determined solely by the CURRENT going through them. The current is the same in all the cases you presented hence the power is the same AT ANY INSTANT IN TIME.
Actually, no.
Examine the case of both speakers being driven by the SAME amplifier. That is the initial condition I had set, in order to eliminate the variable of the amp.
Both speaker sets (at the amp terminals) START with the same voltage. But yet, the monowire set receives power that is modulated by the addition of the 2AB component (recall this is what I first stated, Jim agreed, and you agree with Jim)
- The power output by the amplifier is the same.
Umm, again, no. This is your assumption. The fact that one wireset is dissipating more power (or less) at any instant, means that one speaker set is not receiving identical power (in time) as the other one (my assertion).
- The power dissipated in the wires is different (instantaneously speaking). True. Ergo someplace else in the circuit is compensating for this. We both got this part wrong (I blamed the amp, which is wrong) but Jim got it right in his analysis:
He did? Where? How does an orthogonal (reactive) component compensate instant to instant, that of a dissipative element?? Remember, since the amp can only look at the speaker through the wires, and both wires are dissipating DIFFERENTLY, how can the speaker terminals be exactly the same??
- The only things left in the circuit that can compensate are the filters. Weird you say? Not really as the filters are required to set up the conditions you specify. They are constrained on one side by the speakers (who's power dissipation is a given and fixed) and the wire dissipation on the other hand. They do not miraculously do the right thing, their behavior is imposed on them and simply a consequence of the circuit topology.
Who said the speakers do the same thing???? Not I...that would be an assumption. Since the wires dissipate energy differently, and the reactive components do not dissipate at all, the balance is up to the speakers. Time shifted energy is THE CRUX OF THE ISSUE. Not average power. All heck breaks loose once we leave steady state..(hint)..
- There is no violation of energy anywhere in this. At any instant:
Pamp = Pwire + Pfilters + Pspeaker
Since the amp voltage is equal in both cases, there is a difference because the wires dissipate differently.. The assumption that the speakers act exactly the same in time violates conservation of energy..
Note however that Pfilters can be negative and must average out to 0 since they are reactive elements. This quite elegantly also provides us with an explanation as to why the 2AB component has to average out to 0 as well (as you have pointed out it does).
Umm...there is no such thing as negative power..I assume you meant storage vs release..and they both act 90 degrees out..
The 2AB power envelope, which does indeed has a negative component, is an anomoly, a construct that cannot exist standalone..it can only exist as a modulation of the A squared plus B squared entities...they always are equal to or greater than the 2AB component. Otherwise the system would cool down...
The 2AB component has a net zero integral. Hence my concern that it cannot be seen by a math package that looks for integrated power (that would be an FFT).
Nice try though....very well thought..
It's been a pleasure reading and responding to you..do not quit..
Cheers, John
ps..I'm glad I gave you the link to Jims webpage..it allows a commonality of discussion..