<font color='#000000'>Jon;
I appreciate your detailed and thorough analysis and the thought you put into your post. However, your conclusions are loaded with engineering fallacies.
First off, if you look at the RLC lumped parameters of 12AWG wire, say "Original Monstercable products, you will find that the DCR is about .002ohms/ft, Inductance is about .17uH/ft, Capacitance is about 22.2pF/ft. Take 100ft, which would be a worst case figure for someone who is running speaker wires to their surround sound speakers in their home theater room and multiply all of these metrics by a factor of 100, you will have:
DCR = .2ohms
L = 17uH
C = 2220pF
I recommend reading this link for a better understanding of cable metrics:
http://www.epanorama.net/documents/wiring/wire_resistance.html
If you model the L in series with the 4 ohm speaker load and the C in shunt with it, you will notice that the 3dB point is greater than 40kHz !!! I can live with that loss considering that the bandwidth of most normal humans hearing is about 1/2 half of that and almost no speaker on the planet in a typical living room can extend beyond 20kHz on/off axis.
As for Damping factor, your way off on that one. I cannot explain this concept any better than it already has been explained by a John Murphy (Physicist/Audio Engineer) as listed below:
http://www.trueaudio.com/post_013.htm
However, John basically explains that the DCR from the woofer is far greater than from the speaker cables for a resultantly lowered system damping factor, thus the cable DCR is a wash. In addition, almost all modern day solid state amplifiers have a high enough damping factor to handle a few hundred mohms of cable DCR.
Subject: Effect on Loudspeakers of Amplifier Damping Factor
(posted 2May01 to Bass List)
Chris asked:
> I realized after thinking about slew rate and damping factor that I
> wasn't sure what the damping factor in an amp really meant.
> Would somebody be kind enough to explain damping factor.
> Also, does damping factor relate to slew rate in any way?
The damping factor of an audio amplifier is unrelated to the slew rate of the amplifier.
An audio power amplifier's damping factor is defined as the ratio of the load impedance to the
output impedance of the amplifier.
Example 1:
Amp output impedance at 1k Hz is known to be: 0.25 Ohms
Impedance of the test load is 8 Ohms (at 1k Hz)
Damping Factor = (Load Impedance) / (Output Impedance) = 8 / 0.25 = 32 (dimensionless ratio)
Now, add a 0.25 Ohm speaker cable between the amp and the speaker and measure the
damping factor at the speaker terminals and you would get: Damping Factor = 16
(Note that damping factor varies with frequency)
Example 2:
What if you started with an amp with output impedance of 0.0025 Ohms?
DF = 8 / 0.0025 = 3200 WOW!, what a spec!
Now, add your .25 Ohm speaker cable and evaluate the damping factor at the speaker terminals:
New source impedance = 0.0025 + 0.25 = 0.2525 Ohms (at spkr terminals)
DF = 8 / .2525 = 31.7 Where did the DF=3000 go! I paid extra for that number!
Example 3:
Now determine the damping factor at the actual woofer terminals:
( Hint: Internally the speaker has a 0.5 Ohm inductor in series with the woofer)
Source Impedance = 0.0025 + 0.25 + 0.5 = 0.7525 Ohms (amp+cable+inductor)
DF = 8 / .7525 = 10.6
The point I'm trying to make is that the actual amplifier damping factor specification has little to do with the damping factor seen by a typical woofer...unless the woofer is welded directly to the output terminals of the amplifier ... there could be a patent here.
Many audio engineers are of the opinion that an amplifier damping factor of 10 or greater is
adequate. Those sky high damping factors seen on the spec sheets of some amps are frequently just inventions of the marketing department and are irrelevant to actual system performance. The effect of higher source impedances (lower damping factors) is the same as adding series resistance in the speaker cable. Ultimately, the effect is a micro equalization of the frequency response as the voltage drive to the speaker becomes non-flat due to the frequency dependant impedance of the speaker. (adding series resistance creates a small peak at the speaker's own impedance peak...often on the order of 0.25 dB or so) The effect of the series resistance of the "damping" of the speaker is difficult to see when the problem is viewed this way.
The Q(tc) of a closed box speaker is increased by the addition of a series resistance. Here is the formula for this increase in system Q:
Q(tc) = Q(tco) ( (Re + Rg)/ Re )
where:
Q(tc) is the final Q of the speaker system
Q(tco) is the Q of the speaker with zero Ohms source impedance
Re is the DC resistance of the speaker
Rg is the added series resistance
Example 4:
Say we have a speaker system with Q(tco) = 0.707 and DC resistance Re = 6.5 Ohms.
We add 0.25 Ohms of series resistance by way of our amp, speaker cable and crossover.
The net Q of the speaker then becomes:
Q(tc) = 0.707 ( (6.5 + .25) / 6.5 ) = .707 (6.75/6.5) = .734
So the effect of 0.25 Ohms series resistance is really to raise the Q of the speaker from .707 to
.734. We could calculate the damping factor...but who cares! We are really only concerned with
our net system response. Yes, you could say the "lower damping factor" has affected the transient response of the speaker for the worse. We've all heard the mysterious explanation that "the cone keeps moving after the signal has stopped". But I prefer to look at the problem in terms of the speaker's Q(tc). We can all relate to the speaker Q much better than "the cone keeps moving...".
So I prefer to move any discussion of amplifier damping factor away from the mysterious "cone
keeps moving..." and into the much better understood arena of speaker system Q.
As you can see there is much more to the issue of "speaker damping" than just the amplifier's damping factor. In many systems the amp's DF will be irrelevant to the final system response because of the series resistance added by the speaker cable and the passive crossover components (see Example 3 above). Speaker designers should always be aware of the source impedance from which their speakers will be driven so that they can compensate for the source impedance in their design. If in fact your goal is to design a speaker system that will have a net response Q(tc) = .707 then you will need to anticipate the Rg (source impedance) the driver will "see" and design the enclosure for some lower Q(tco) such that the Rg will raise the NET Q(tc) to the targeted 0.707.
Regards,
John
/////////////////////////////////////
John L. Murphy
Physicist/Audio Engineer
True Audio
http://www.trueaudio.com
Check out my recent book "Introduction to Loudspeaker Design" at Amazon.com
NP: Santana, Put Your Lights On
{Reprinted with permission from John L. Murphy 10/02/02)]
As for your theories about video cables, you posted far too many fallacies for me to address at this moment. I will come back when time permits.
In the meantime, I will allow your links to your website to remain in your original post for anecdotal reading purposes.</font>