Here is a very recent article "cut and pasted" from the Audioholics website regarding this very matter.
Damping Factor: Effects On System Response
Monday, August 30 2004
Damping Factor: Effects On System Response
Analysis
Several things are apparent from this table. First and foremost, any notion of severe overhang or extended "time amplitude envelopes) resulting from low damping factors simple does not exist. We see, at most, a doubling of decay time (this doubling is true no matter what criteria is selected for decay time). The figure we see here of 70 milliseconds is well over an order of magnitude lower than that suggested by one person, and this represents what I think we all agree is an absolute worst-case scenario of a damping factor of 1.
Secondly, the effects of this loss of damping on system frequency response is non-existent in most cases, and minimal in all but the worst case scenario. Using the criteria that 0.1 dB is the smallest audible peak, the data in the table suggests that any damping factor over 10 is going to result in inaudible differences between that and one equal to infinity. It's highly doubtful that a response peak of 1/3 dB is going to be identifiable reliably, thus extending the limit another factor of two lower to a damping factor of 5.
All this is well and good, but the argument suggesting that these minute changes may be audible suffers from even more fatal flaws. The differences that we see in figures up to the point where the damping factor is less than 10 are far less than the variations seen in normal driver-to-driver parameters in single-lot productions. Even those manufacturers who deliberately sort and match drivers are not likely to match a figure to better than 5%, and those numbers will swamp any differences in damping factor greater than 20.
Further, the performance of drivers and systems is dependent upon temperature, humidity and barometric pressure, and those environmental variables will introduce performance changes on the order of those presented by damping factors of 20 or less. And we have completely ignored the effects presented by the crossover and lead resistances, which will be a constant in any of these figures, and further diminish the effects of non-zero source resistance.
Frequency-Dependent Attenuation
The analysis thus far deals with one very specific and narrow aspect of the effects of non-zero source resistance: damping or the dissipation and control of energy stored in the mechanical resonance of loudspeakers. This is not to suggest that there is no effect due to amplifier output resistance.
Another mechanism that most certainly can have measurable and audible effects are response errors due to the frequency dependent impedance load presented by the speaker. The higher the output resistance of the source, the greater the magnitude of the response deviations. The attenuation can be approximated given the source resistance and impedance vs. frequency:
where is the gain or loss due to attenuation, is the amplifier source resistance, and is the frequency dependent loudspeaker impedance.
As a means of comparison, lets reexamine the effects of non-zero source resistance on a typical speaker whose impedance varies from a low of 6W to a high of 40W .
Damping
factor
RG
GdB(MIN)
GdB(MAX)
GdB(ERROR)
¥
0 W
0 dB
0 dB
0 dB
2000
0.004
-0.006
-0.001
±0.003
1000
0.008
-0.012
-0.002
±0.005
500
0.016
-0.023
-0.003
±0.01
200
0.04
-0.058
-0.009
±0.025
100
0.08
-0.115
-0.017
±0.049
50
0.16
-0.229
-0.035
±0.098
20
0.4
-0.561
-0.086
±0.23
10
0.8
-1.087
-0.172
±0.46
5
1.6
-2.053
-0.341
±0.86
2
4
-4.437
-0.828
±1.8
1
8
-7.360
-1.584
±2.9
As before, the first column shows the nominal 8W damping factor, the second shows the corresponding output resistance of the amplifier. The second and third columns show the minimum and maximum attenuation due to the amplifiers source resistance, and the last column illustrates the resulting deviation in the frequency response caused by the output resistance.
What can be seen from this analysis is that the frequency dependent attenuation due to the amplifiers output resistance is more significant than the effects on system damping. More importantly, these effects should not be confused with damping effects, as they represent two different mechanisms.
However, these data do not support the assertion often made for the advantages of extremely high damping factors. Even given, again, the very conservative argument that ±0.1 dB deviation in frequency response is audible, that still suggests that damping factors in excess of 50 will not lead to audible improvements, all else being equal. And, as before, these deviations must be considered in the context of normal response variations due to manufacturing tolerances and environmental changes.
Conclusions
There may be audible differences that are caused by non-zero source resistance. However, this analysis and any mode of measurement and listening demonstrates conclusively that it is not due to the changes in damping the motion of the cone at the point where it's at it's most uncontrolled: system resonances. Even considering the substantially larger response variations resulting from the non-flat impedance vs. frequency function of most loudspeakers, the magnitude of the problem simply is not what is claimed.
End
As you can see from these calclulations, a damping factor of 5(1.6ohms/8ohm spkr) provides 0.86db variation in frequency response as a maximum. This falls well within a +/-1db spec. It is inside the +/- tolerance of any loudspeaker, and certainly far inside the tolerances of any listening room. Other factors in the listening system/room will far outweigh this factor, thus making it insignificant in magnitude, even in a low damping case such as 5.
How anyone can make a case that tube amps are "equalizers" from this performance data, is beyond me. I certainly hope that this puts this matter to rest.
Damping Factor: Effects On System Response
Monday, August 30 2004
Damping Factor: Effects On System Response
Analysis
Several things are apparent from this table. First and foremost, any notion of severe overhang or extended "time amplitude envelopes) resulting from low damping factors simple does not exist. We see, at most, a doubling of decay time (this doubling is true no matter what criteria is selected for decay time). The figure we see here of 70 milliseconds is well over an order of magnitude lower than that suggested by one person, and this represents what I think we all agree is an absolute worst-case scenario of a damping factor of 1.
Secondly, the effects of this loss of damping on system frequency response is non-existent in most cases, and minimal in all but the worst case scenario. Using the criteria that 0.1 dB is the smallest audible peak, the data in the table suggests that any damping factor over 10 is going to result in inaudible differences between that and one equal to infinity. It's highly doubtful that a response peak of 1/3 dB is going to be identifiable reliably, thus extending the limit another factor of two lower to a damping factor of 5.
All this is well and good, but the argument suggesting that these minute changes may be audible suffers from even more fatal flaws. The differences that we see in figures up to the point where the damping factor is less than 10 are far less than the variations seen in normal driver-to-driver parameters in single-lot productions. Even those manufacturers who deliberately sort and match drivers are not likely to match a figure to better than 5%, and those numbers will swamp any differences in damping factor greater than 20.
Further, the performance of drivers and systems is dependent upon temperature, humidity and barometric pressure, and those environmental variables will introduce performance changes on the order of those presented by damping factors of 20 or less. And we have completely ignored the effects presented by the crossover and lead resistances, which will be a constant in any of these figures, and further diminish the effects of non-zero source resistance.
Frequency-Dependent Attenuation
The analysis thus far deals with one very specific and narrow aspect of the effects of non-zero source resistance: damping or the dissipation and control of energy stored in the mechanical resonance of loudspeakers. This is not to suggest that there is no effect due to amplifier output resistance.
Another mechanism that most certainly can have measurable and audible effects are response errors due to the frequency dependent impedance load presented by the speaker. The higher the output resistance of the source, the greater the magnitude of the response deviations. The attenuation can be approximated given the source resistance and impedance vs. frequency:
where is the gain or loss due to attenuation, is the amplifier source resistance, and is the frequency dependent loudspeaker impedance.
As a means of comparison, lets reexamine the effects of non-zero source resistance on a typical speaker whose impedance varies from a low of 6W to a high of 40W .
Damping
factor
RG
GdB(MIN)
GdB(MAX)
GdB(ERROR)
¥
0 W
0 dB
0 dB
0 dB
2000
0.004
-0.006
-0.001
±0.003
1000
0.008
-0.012
-0.002
±0.005
500
0.016
-0.023
-0.003
±0.01
200
0.04
-0.058
-0.009
±0.025
100
0.08
-0.115
-0.017
±0.049
50
0.16
-0.229
-0.035
±0.098
20
0.4
-0.561
-0.086
±0.23
10
0.8
-1.087
-0.172
±0.46
5
1.6
-2.053
-0.341
±0.86
2
4
-4.437
-0.828
±1.8
1
8
-7.360
-1.584
±2.9
As before, the first column shows the nominal 8W damping factor, the second shows the corresponding output resistance of the amplifier. The second and third columns show the minimum and maximum attenuation due to the amplifiers source resistance, and the last column illustrates the resulting deviation in the frequency response caused by the output resistance.
What can be seen from this analysis is that the frequency dependent attenuation due to the amplifiers output resistance is more significant than the effects on system damping. More importantly, these effects should not be confused with damping effects, as they represent two different mechanisms.
However, these data do not support the assertion often made for the advantages of extremely high damping factors. Even given, again, the very conservative argument that ±0.1 dB deviation in frequency response is audible, that still suggests that damping factors in excess of 50 will not lead to audible improvements, all else being equal. And, as before, these deviations must be considered in the context of normal response variations due to manufacturing tolerances and environmental changes.
Conclusions
There may be audible differences that are caused by non-zero source resistance. However, this analysis and any mode of measurement and listening demonstrates conclusively that it is not due to the changes in damping the motion of the cone at the point where it's at it's most uncontrolled: system resonances. Even considering the substantially larger response variations resulting from the non-flat impedance vs. frequency function of most loudspeakers, the magnitude of the problem simply is not what is claimed.
End
As you can see from these calclulations, a damping factor of 5(1.6ohms/8ohm spkr) provides 0.86db variation in frequency response as a maximum. This falls well within a +/-1db spec. It is inside the +/- tolerance of any loudspeaker, and certainly far inside the tolerances of any listening room. Other factors in the listening system/room will far outweigh this factor, thus making it insignificant in magnitude, even in a low damping case such as 5.
How anyone can make a case that tube amps are "equalizers" from this performance data, is beyond me. I certainly hope that this puts this matter to rest.