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A more exact understanding of amplifier output impedance

MrPeabody

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It is a forgone conclusion that the great majority of modern amplifiers have output impedance below the threshold where it would affect the loudspeaker’s performance. But this is not likely true for all amplifiers currently in production, and even if it is true for all amplifiers currently in production, output impedance is still important because it will affect loudspeaker performance if it is too great. Note that I’m talking about the actual output impedance, not the damping factor. The damping factor is a related specification that uses a dummy value for the speaker impedance. Damping factor would be practically useless were it not for the fact that in effect it specifies the output impedance. To calculate the output impedance, divide the damping factor by whatever dummy value the manufacturer used for the speaker impedance.

There are two distinct means by which an amplifier’s output impedance can potentially affect the speaker’s frequency response. One of them is only remotely related to damping, but since it is the more important of the two, I’ll discuss it first. It has to do with the fact that the voltage split between the speaker impedance and the amplifier’s output impedance will be frequency-dependent if speaker impedance is frequency-dependent. Each impedance’s proportional share of the amplifier’s true output voltage is the same as its proportional share of the total series impedance. In the impedance curve for a typical speaker, the dips are not much lower than the nominal value, whereas the peaks are tall and skinny. At the peaks, the speaker’s share of the true amplifier output voltage can potentially be much greater than its nominal share, i.e., much greater than the mean value of its share over the full audio spectrum. We need to define a few variables:

OI : the amplifier Output Impedance
NI : the Nominal Impedance of the speaker (i.e., the mean value over the full audio spectrum)
PI : the Peak Impedance of the speaker

Note that if you are concerned with whether the resistance of the speaker wire is significant, you can calculate or measure this resistance and include it in the amplifier output impedance, or else subtract this resistance from the allowed output impedance after you’ve calculated it.

The speaker’s nominal share of the amplifier output voltage is given by this expression:
nominal voltage = true amplifier output voltage x NI / (NI + OI)

The speaker’s share of the amplifier output voltage at an impedance peak is:
peak voltage = true amplifier output voltage x PI / (PI + OI)

We want to express the ratio of these two voltages in decibels. Let’s call this “Peak_dB”.
Peak_dB = 20 Log [ peak voltage / nominal voltage ]
Peak_dB = 20 Log [ PI/(PI + OI) / NI/(NI + OI) ]
Peak_dB = 20 Log [ PI(NI + OI) / NI(PI + OI) ]

In general the goal is to insure that Peak_dB will be under some specific, chosen limit, most likely in the ballpark of .1 to 1, depending on the threshold at which a response peak is deemed audible. The variable Limit_dB is another decibel value. No one enjoys solving inequalities. It’s a dirty job, but since Mike Rowe isn’t gonna do it:

Peak_dB < Limit_dB =>
20 Log [ PI(NI + OI) / NI(PI + OI) ] < Limit_dB
Log [ PI(NI + OI) / NI(PI + OI) ] < Limit_dB/20
PI(NI + OI) / NI(PI + OI) < 10^(Limit_dB/20)

Note that the inequality immediately above was obtained by submitting both sides of the previous inequality to the exponential function ‘10^X’. The reason this is legit is that the exponential function increases continuously from -infinity to +infinity. As such, for any N and M, the inequality ‘10^N < 10^M’ is true if and only if the inequality ‘N < M’ is true. The values of N and M for which one of these inequalities is true are the very same values for which the other inequality is true. Now to work on that rational exponent:

PI(NI + OI) / NI(PI + OI) < (10^(1/20))^Limit_dB
PI(NI + OI) / NI(PI + OI) < (10^.05)^Limit_dB
PI(NI + OI) / NI(PI + OI) < 1.122^Limit_dB
PI(NI + OI) < 1.122^Limit_dB x (NI x PI + NI x OI)
PI x NI + PI x OI < 1.122^Limit_dB x NI x PI + 1.122^Limit_dB x NI x OI

Subtract ‘PI x NI’ from both sides and subtract ‘1.122^Limit_dB x NI x OI’ from both sides:
PI x OI - 1.122^Limit_dB x NI x OI < 1.122^Limit_dB x NI x PI - PI x NI
OI x (PI - 1.122^Limit_dB x NI) < PI x NI x (1.122^Limit_dB -1)

(I) OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit _dB x NI)

In the last step above, both sides of the inequality were divided by ‘(PI - 1.122^Limit_dB x NI)’. The direction of the inequality has to be reversed if this expression is < 0. In general when this situation occurs when solving an inequality it is necessary to pursue two solutions. However it is apparent that if this expression is < 0, the right side of (I) will be < 0, which means that after reversing the direction of the inequality we would only be requiring OI to be greater than some negative value, and doing so for PI values that are just barely greater than NI (i.e., for PI < NI x 1.122^Limit_dB). This other solution is thus a superfluous solution that we may simply ignore.

To do a sanity check on the solution, we need to choose values for NI, PI and Limit_dB, then evaluate the right-hand side of (I) to see how great OI can be such that the response peak will be within the limit we choose. Following this we need to choose values for OI just slightly below and slightly above the threshold, to confirm that Limit_dB will be exceeded for the larger value of OI but not for the smaller value. Let’s use some realistic values:

NI = 6 ohms; PI = 30 Ohms; Limit_dB = .5 dB

OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit_dB x NI)
OI < 30 x 6 x (1.122^.5 -1) / (30 - 1.122^.5 x 6)
OI < .451 ohms

This seems a reasonable result, so let’s calculate the response peak for two values of OI, one value slightly below .451 ohms and the other value slightly above .451 ohms. Let’s use .450 ohms and .452 ohms.
Peak = 20 Log [ PI/(PI + OI) / NI/(NI + OI) ]
Peak = 20 Log [ 30/(30 + .45) / 6/(6 + .45) ]
Peak = 20 Log [ 1.0591133 ] = .499 dB

When OI is slightly less than the threshold obtained via (I), the response peak is very slightly less than the chosen limit of .5 dB. Let’s see what happens when OI is equal to .452 ohms.

Peak = 20 Log [ 30/(30 + .452) / 6/(6 + .452) ]
Peak = 20 Log [ 1.0593721 ] = .501 dB

The inequality (I) thus appears to be correct.

How much lower will OI need to be if we use .1 dB for Limit_dB?
OI < 30 x 6 x (1.122^.1 -1) / (30 - 1.122^.1 x 6)
OI < .0871 ohms

It is interesting to observe that in both of these realistic cases, with Limit_dB assigned values of .5 dB and .1 dB, the calculated value for OI in ohms is approximately 90% of Limit_dB. This suggests a useful first-order approximation for estimating the maximum allowable amplifier output impedance in ohms. However the two cases are both specific to a speaker with 6 ohm nominal impedance. If we repeat the calculations for 4 ohm speakers and for 8 ohm speakers we would likely come up with different approximations, and the approximations would be different again for different values for PI, the impedance peak of the speaker.

How long is my 16 gauge speaker cable allowed to be if the amplifier output impedance is .15 ohms and I use .5 dB for Limit_db (with the same values for NI and PI)?
.451 ohms -.15 ohms = .301 ohms

The resistance of 16 gauge wire is about 4 ohms per thousand feet (at room temperature):
.301 ohms x 1000 ft / 4 ohms = 75 feet.

Since the true distance is double the length of the two-wire cable, you have to divide this in half. As long as each cable is no greater than 35 feet, it does not matter if they are not equal.

The same inequality works for the impedance dips, and allows us to get an accurate sense of the extent to which the impedance dips may pose tighter constraints for the speaker cable. If the nominal impedance is 6 ohms, the minimum impedance (this is the voice coil’s DC resistance) will be maybe 4.5 ohms. All we need to do is redo the calculation using 4.5 ohms for PI and with Limit_dB set to -.5 dB instead of +.5 dB.

OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit_dB x NI)
OI < 4.5 x 6 x (1.122^-.5 -1) / (4.5 - 1.122^-.5 x 6)
OI < 1.3 ohms

It may seem as though the impedance dips would impose tighter constraints on the speaker cable, in order that the cable resistance will be adequately small in relation to the speaker impedance. As concerns the affect on the speaker’s frequency response it is only the impedance peaks that matter, and the nominal speaker impedance suffices for consideration of the overall loss in the cable.

As for the other means (the means that actually does have something to do with damping), the best way to approach it is probably from the perspective of speaker Q. For both sealed enclosures and enclosures that use a port or a passive radiator, the overall shape of the response is largely determined by the system Q. System Q is linearly dependent on driver Q. If driver Q is increased by some specific percentage and this is not compensated by making the enclosure larger, the percentage increase in system Q will be the same as the percentage increase in driver Q.

The electrical damping of the driver makes up the major share of the driver’s damping and thus has a strong hand in determining the driver Q. The equations that tell us precisely how driver Q depends on the resistance in the voice coil circuit (primarily the coil itself) tell us that driver Q has a quasi-linear dependence on the total resistance in the circuit. Thus, when the amplifier’s output impedance is added to the voice coil resistance, the system Q increases by roughly the same percentage as the increase in the resistance in the voice coil circuit. This assumes that the enclosure volume is not increased to compensate; this is a good assumption given that it is not practical to accommodate differences in amplifiers by modifying the speaker enclosure. Also worth noting is that this relationship would be exact except for the fact that the driver Q is also influenced by mechanical damping, which is typically very small in comparison to the electrical damping. With the great majority of drivers, the total Q is not very different from the electrical Q, and the total Q of the driver has a sort of quasi-linear dependence on the total resistance in the voice coil circuit.

Thus, if we desire for the percentage increase in system Q to remain under some limit L, we need to insure that the amplifier’s output impedance (the real part of it) is no greater than L% of the voice coil’s DC resistance. For example, if the DC resistance of the coil is 4.5 ohms and we want to keep the increase in system Q to less than, say, 10%, this means that the amplifier’s output impedance will need to be less than (approximately) .45 ohms. Reportedly, most all modern speaker amplifiers meet this requirement with ample room to spare. Some of the economy class D amplifiers may be an exception, however the output impedance of even these amplifiers will likely be very low at the low frequency where driver damping is needed toward keeping the enclosure small. Some of the tube amplifiers may similarly be an exception.

All in all the reasonable conclusion seems to be that in a very small but uncertain percentage of cases, a speaker amplifier’s output impedance may be just barely great enough to produce a barely perceptible increase in speaker Q. If you use a tube amp or a class D amp, or if you use a class D headphone amplifier with a pair of highly sensitive headphones (they’ll likely have low impedance), or if you plug a typical pair of headphones into the headphone jack on most any receiver or integrated amplifier intended primarily for speakers, it is not out of the question that the frequency response of your speakers or headphones will be very slightly affected by the amplifier’s output impedance, via one or the other of the two means, possibly both of them acting in unison.
 
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MrPeabody

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I had to fix a couple of silly wrong-word mistakes, then changed the PDF.
 

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Head_Unit

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...which all reinforces my belief that once you get a decent quality big gauge cable, well, I just don't worry about speaker cables. ;) And the use cases with very long runs for me are situations where it's not critical listening (patio speakers or whatever). Still, it would be scientific to make some actual frequency response measurements with different cables, and see if anything changes. Someone did a multitone test and saw differences at the speaker terminals, but I don't remember where that was. Or how significant.
 

Blumlein 88

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Put your amps close to the speaker and feed them with XLR cable.

Oh and avoid ridiculous loads that drop below 1 ohm like my Soundlabs.
 

egellings

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I agree; put the amplifier near (or in) the speaker and send balanced signal over the distance to the amplifier.
 

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It is a forgone conclusion that the great majority of modern amplifiers have output impedance below the threshold where it would affect the loudspeaker’s performance. But this is not likely true for all amplifiers currently in production, and even if it is true for all amplifiers currently in production, output impedance is still important because it will affect loudspeaker performance if it is too great. Note that I’m talking about the actual output impedance, not the damping factor. The damping factor is a related specification that uses a dummy value for the speaker impedance. Damping factor would be practically useless were it not for the fact that in effect it specifies the output impedance. To calculate the output impedance, divide the damping factor by whatever dummy value the manufacturer used for the speaker impedance.

There are two distinct means by which an amplifier’s output impedance can potentially affect the speaker’s frequency response. One of them is only remotely related to damping, but since it is the more important of the two, I’ll discuss it first. It has to do with the fact that the voltage split between the speaker impedance and the amplifier’s output impedance will be frequency-dependent if speaker impedance is frequency-dependent. Each impedance’s proportional share of the amplifier’s true output voltage is the same as its proportional share of the total series impedance. In the impedance curve for a typical speaker, the dips are not much lower than the nominal value, whereas the peaks are tall and skinny. At the peaks, the speaker’s share of the true amplifier output voltage can potentially be much greater than its nominal share, i.e., much greater than the mean value of its share over the full audio spectrum. We need to define a few variables:

OI : the amplifier Output Impedance
NI : the Nominal Impedance of the speaker (i.e., the mean value over the full audio spectrum)
PI : the Peak Impedance of the speaker

Note that if you are concerned with whether the resistance of the speaker wire is significant, you can calculate or measure this resistance and include it in the amplifier output impedance, or else subtract this resistance from the allowed output impedance after you’ve calculated it.

The speaker’s nominal share of the amplifier output voltage is given by this expression:
nominal voltage = true amplifier output voltage x NI / (NI + OI)

The speaker’s share of the amplifier output voltage at an impedance peak is:
peak voltage = true amplifier output voltage x PI / (PI + OI)

We want to express the ratio of these two voltages in decibels. Let’s call this “Peak_dB”.
Peak_dB = 20 Log [ peak voltage / nominal voltage ]
Peak_dB = 20 Log [ PI/(PI + OI) / NI/(NI + OI) ]
Peak_dB = 20 Log [ PI(NI + OI) / NI(PI + OI) ]

In general the goal is to insure that Peak_dB will be under some specific, chosen limit, most likely in the ballpark of .1 to 1, depending on the threshold at which a response peak is deemed audible. The variable Limit_dB is another decibel value. No one enjoys solving inequalities. It’s a dirty job, but since Mike Rowe isn’t gonna do it:

Peak_dB < Limit_dB =>
20 Log [ PI(NI + OI) / NI(PI + OI) ] < Limit_dB
Log [ PI(NI + OI) / NI(PI + OI) ] < Limit_dB/20
PI(NI + OI) / NI(PI + OI) < 10^(Limit_dB/20)

Note that the inequality immediately above was obtained by submitting both sides of the previous inequality to the exponential function ‘10^X’. The reason this is legit is that the exponential function increases continuously from -infinity to +infinity. As such, for any N and M, the inequality ‘10^N < 10^M’ is true if and only if the inequality ‘N < M’ is true. The values of N and M for which one of these inequalities is true are the very same values for which the other inequality is true. Now to work on that rational exponent:

PI(NI + OI) / NI(PI + OI) < (10^(1/20))^Limit_dB
PI(NI + OI) / NI(PI + OI) < (10^.05)^Limit_dB
PI(NI + OI) / NI(PI + OI) < 1.122^Limit_dB
PI(NI + OI) < 1.122^Limit_dB x (NI x PI + NI x OI)
PI x NI + PI x OI < 1.122^Limit_dB x NI x PI + 1.122^Limit_dB x NI x OI

Subtract ‘PI x NI’ from both sides and subtract ‘1.122^Limit_dB x NI x OI’ from both sides:
PI x OI - 1.122^Limit_dB x NI x OI < 1.122^Limit_dB x NI x PI - PI x NI
OI x (PI - 1.122^Limit_dB x NI) < PI x NI x (1.122^Limit_dB -1)

(I) OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit _dB x NI)

In the last step above, both sides of the inequality were divided by ‘(PI - 1.122^Limit_dB x NI)’. The direction of the inequality has to be reversed if this expression is < 0. In general when this situation occurs when solving an inequality it is necessary to pursue two solutions. However it is apparent that if this expression is < 0, the right side of (I) will be < 0, which means that after reversing the direction of the inequality we would only be requiring OI to be greater than some negative value, and doing so for PI values that are just barely greater than NI (i.e., for PI < NI x 1.122^Limit_dB). This other solution is thus a superfluous solution that we may simply ignore.

To do a sanity check on the solution, we need to choose values for NI, PI and Limit_dB, then evaluate the right-hand side of (I) to see how great OI can be such that the response peak will be within the limit we choose. Following this we need to choose values for OI just slightly below and slightly above the threshold, to confirm that Limit_dB will be exceeded for the larger value of OI but not for the smaller value. Let’s use some realistic values:

NI = 6 ohms; PI = 30 Ohms; Limit_dB = .5 dB

OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit_dB x NI)
OI < 30 x 6 x (1.122^.5 -1) / (30 - 1.122^.5 x 6)
OI < .451 ohms

This seems a reasonable result, so let’s calculate the response peak for two values of OI, one value slightly below .451 ohms and the other value slightly above .451 ohms. Let’s use .450 ohms and .452 ohms.
Peak = 20 Log [ PI/(PI + OI) / NI/(NI + OI) ]
Peak = 20 Log [ 30/(30 + .45) / 6/(6 + .45) ]
Peak = 20 Log [ 1.0591133 ] = .499 dB

When OI is slightly less than the threshold obtained via (I), the response peak is very slightly less than the chosen limit of .5 dB. Let’s see what happens when OI is equal to .452 ohms.

Peak = 20 Log [ 30/(30 + .452) / 6/(6 + .452) ]
Peak = 20 Log [ 1.0593721 ] = .501 dB

The inequality (I) thus appears to be correct.

How much lower will OI need to be if we use .1 dB for Limit_dB?
OI < 30 x 6 x (1.122^.1 -1) / (30 - 1.122^.1 x 6)
OI < .0871 ohms

It is interesting to observe that in both of these realistic cases, with Limit_dB assigned values of .5 dB and .1 dB, the calculated value for OI in ohms is approximately 90% of Limit_dB. This suggests a useful first-order approximation for estimating the maximum allowable amplifier output impedance in ohms. However the two cases are both specific to a speaker with 6 ohm nominal impedance. If we repeat the calculations for 4 ohm speakers and for 8 ohm speakers we would likely come up with different approximations, and the approximations would be different again for different values for PI, the impedance peak of the speaker.

How long is my 16 gauge speaker cable allowed to be if the amplifier output impedance is .15 ohms and I use .5 dB for Limit_db (with the same values for NI and PI)?
.451 ohms -.15 ohms = .301 ohms

The resistance of 16 gauge wire is about 4 ohms per thousand feet (at room temperature):
.301 ohms x 1000 ft / 4 ohms = 75 feet.

Since the true distance is double the length of the two-wire cable, you have to divide this in half. As long as each cable is no greater than 35 feet, it does not matter if they are not equal.

The same inequality works for the impedance dips, and allows us to get an accurate sense of the extent to which the impedance dips may pose tighter constraints for the speaker cable. If the nominal impedance is 6 ohms, the minimum impedance (this is the voice coil’s DC resistance) will be maybe 4.5 ohms. All we need to do is redo the calculation using 4.5 ohms for PI and with Limit_dB set to -.5 dB instead of +.5 dB.

OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit_dB x NI)
OI < 4.5 x 6 x (1.122^-.5 -1) / (4.5 - 1.122^-.5 x 6)
OI < 1.3 ohms

It may seem as though the impedance dips would impose tighter constraints on the speaker cable, in order that the cable resistance will be adequately small in relation to the speaker impedance. As concerns the affect on the speaker’s frequency response it is only the impedance peaks that matter, and the nominal speaker impedance suffices for consideration of the overall loss in the cable.

As for the other means (the means that actually does have something to do with damping), the best way to approach it is probably from the perspective of speaker Q. For both sealed enclosures and enclosures that use a port or a passive radiator, the overall shape of the response is largely determined by the system Q. System Q is linearly dependent on driver Q. If driver Q is increased by some specific percentage and this is not compensated by making the enclosure larger, the percentage increase in system Q will be the same as the percentage increase in driver Q.

The electrical damping of the driver makes up the major share of the driver’s damping and thus has a strong hand in determining the driver Q. The equations that tell us precisely how driver Q depends on the resistance in the voice coil circuit (primarily the coil itself) tell us that driver Q has a quasi-linear dependence on the total resistance in the circuit. Thus, when the amplifier’s output impedance is added to the voice coil resistance, the system Q increases by roughly the same percentage as the increase in the resistance in the voice coil circuit. This assumes that the enclosure volume is not increased to compensate; this is a good assumption given that it is not practical to accommodate differences in amplifiers by modifying the speaker enclosure. Also worth noting is that this relationship would be exact except for the fact that the driver Q is also influenced by mechanical damping, which is typically very small in comparison to the electrical damping. With the great majority of drivers, the total Q is not very different from the electrical Q, and the total Q of the driver has a sort of quasi-linear dependence on the total resistance in the voice coil circuit.

Thus, if we desire for the percentage increase in system Q to remain under some limit L, we need to insure that the amplifier’s output impedance (the real part of it) is no greater than L% of the voice coil’s DC resistance. For example, if the DC resistance of the coil is 4.5 ohms and we want to keep the increase in system Q to less than, say, 10%, this means that the amplifier’s output impedance will need to be less than (approximately) .45 ohms. Reportedly, most all modern speaker amplifiers meet this requirement with ample room to spare. Some of the economy class D amplifiers may be an exception, however the output impedance of even these amplifiers will likely be very low at the low frequency where driver damping is needed toward keeping the enclosure small. Some of the tube amplifiers may similarly be an exception.

All in all the reasonable conclusion seems to be that in a very small but uncertain percentage of cases, a speaker amplifier’s output impedance may be just barely great enough to produce a barely perceptible increase in speaker Q. If you use a tube amp or a class D amp, or if you use a class D headphone amplifier with a pair of highly sensitive headphones (they’ll likely have low impedance), or if you plug a typical pair of headphones into the headphone jack on most any receiver or integrated amplifier intended primarily for speakers, it is not out of the question that the frequency response of your speakers or headphones will be very slightly affected by the amplifier’s output impedance, via one or the other of the two means, possibly both of them acting in unison.
Is there a simple relationship between amplifier damping factor and its' output impedance?

It looks to be an inverse relationship of some kind.
 

Blumlein 88

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Is there a simple relationship between amplifier damping factor and its' output impedance?

It looks to be an inverse relationship of some kind.
https://benchmarkmedia.com/blogs/application_notes/audio-myth-damping-factor-isnt-much-of-a-factor

You can read that article as well as the first post.

Damping factor is speaker impedance divided by amp output impedance. Simple if speakers were resistors, but they aren't. So damping factor varies with frequency due to the speaker impedance varying, and sometimes at higher frequencies amplifier output impedance rises. Rule of thumb was you wanted 10 to 100 depending upon whom you listened to.

So 8 ohm speaker and .8 ohm output impedance of big tube amp is about 10. Higher is better. Mostly is an issue only on the woofer end if at all.
 

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Ok, so "Damping Factor" is a ratio of impedances.

What is damping itself?
 
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https://benchmarkmedia.com/blogs/application_notes/audio-myth-damping-factor-isnt-much-of-a-factor

You can read that article as well as the first post.

Damping factor is speaker impedance divided by amp output impedance. Simple if speakers were resistors, but they aren't. So damping factor varies with frequency due to the speaker impedance varying, and sometimes at higher frequencies amplifier output impedance rises. Rule of thumb was you wanted 10 to 100 depending upon whom you listened to.

So 8 ohm speaker and .8 ohm output impedance of big tube amp is about 10. Higher is better. Mostly is an issue only on the woofer end if at all.
Ahh, that easy enough. My Emotivas state DF of 300 (assume re. 8ohms), so that's plenty.
 
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Is there a simple relationship between amplifier damping factor and its' output impedance?

It looks to be an inverse relationship of some kind.

Damping factor is the ratio of loudspeaker impedance to the amplifier's output impedance. Except that 8 ohms is used for the loudspeaker impedance. Since it is a figure of merit for amplifiers, it is necessary to use some standard, hypothetical value for the load (speaker) impedance. It is just a way to specify an amplifier's output impedance. I suppose that many people may not find it easy to assess the significance of the actual amplifier output impedance relative to the impedance of their speakers, so perhaps it is helpful to express amplifier output impedance in this sort of indirect way.
 

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Ok, so "Damping Factor" is a ratio of impedances.

What is damping itself?
I found this on KEF's website:


Here’s How Damping Factor Works

The voice coil of a speaker becomes a current generator that produces a flyback current that is sent to the amplifier (sort of a reverse answer to the current the amplifier sends the speaker). Every time the voice coil moves it creates this flyback current. If the load presented by the amplifier to this current is very low (high DF) this current is rapidly dissipated causing the force of the voice coil to diminish. The speaker diaphragm and surround assembly also make up a resonant system that will produce ringing (or unwanted resonances) within the operating range of the speaker, but rapid damping acts like a brake on the voice coil, therefore reducing the resonances. To complicate things further, voice coil impedance is complex, meaning it changes with frequency, temperature and power level.

This suggests that the woofer/amp system will present as highly damped for external excitation, with a very low Q and a high damping ratio, if the amp has a high DF.
 

Blumlein 88

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Ok, so "Damping Factor" is a ratio of impedances.

What is damping itself?
Good question. Well it was in the article I linked. It is damping of the motion of the loudspeaker cone (only when you use your JBLs or woofers Ray).
 

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Some selected quotes from an article titled "Damping, Damping Factor, and Damn Nonsense" written by Dr Toole over 45 years ago.
http://diyaudioprojects.com/Technic...ping-Factor-and-Damn-Nonsense-Floyd-Toole.pdf

The first, and perhaps the most important, observation to be made regarding damping factor in amplifiers is that it has really rather little to do with the damping of anything...
...
... Obviously, increasing amplifier DF beyond about 20 cannot significantly alter the electromagnetic damping of a conventional speaker.
...
Another way of saying all this is that tight, incisive, well-damped sound is the result of good speaker design not a high amplifier damping factor.
...
I think it is fair to say that, for most amplifier designs, damping factor is an almost incidental factor. The feedback necessary to achieve low distortion often leads directly to a low internal impedance, which in turn results in a high damping factor. So far as the damping of speaker transients is concerned, a DF of 20 or more will ensure that everything possible has been done -- the rest is up to the loudspeaker.
Choosing an amplifier on the basis of damping factor would be like choosing a high-performance car because it is red rather than black. It may result in the right choice, but for the wrong reason. It happens that many sports cars are red and many limousines black.
 
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MrPeabody

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https://benchmarkmedia.com/blogs/application_notes/audio-myth-damping-factor-isnt-much-of-a-factor

You can read that article as well as the first post.

Damping factor is speaker impedance divided by amp output impedance. Simple if speakers were resistors, but they aren't. So damping factor varies with frequency due to the speaker impedance varying, and sometimes at higher frequencies amplifier output impedance rises. Rule of thumb was you wanted 10 to 100 depending upon whom you listened to.

So 8 ohm speaker and .8 ohm output impedance of big tube amp is about 10. Higher is better. Mostly is an issue only on the woofer end if at all.

When I first read that article I was bothered by some of what the author (John Siau) wrote in the opening paragraphs. He sort of placed the blame on Dick Pierce and Andy Wehmeyer for what he considers a myth, that damping factor doesn't ever matter. Even if those two authors did what he said, I don't think it is a great "myth" that damping factor doesn't matter, because in the great majority of cases it doesn't. Not in 100% of cases, but the word "myth" seems too strong to fit the circumstance. Near the beginning, Siau wrote: "The mathematical analyses are correct, but the conclusions are incomplete and misleading!"

Here is the conclusion from Pierce's paper:

"There may be audible differences that are caused by non-zero source resistance. However, this analysis ... demonstrates conclusively that it is not due to the changes in damping the motion of the cone at the point where it's at its most uncontrolled: system resonances. We have not looked at the frequency-dependent attenuative effects of the source resistance, but that's not what the strident claims are about. ... people advocating the importance of high damping factors must look elsewhere for a culprit: motion control at resonance simply fails utterly to explain the claimed differences."

It does not seem to me that Pierce's conclusion is incorrect or misleading.

I looked again at Siau's article more recently. Overlooking the opening paragraphs, it is an informative, correct article. Like Siau, I treated the speaker as a resistive load in order to simplify the problem (for me as well as the audience). Siau wrote: "To keep the math simple, we will ignore the phase shifts that are produced by the inductive and capacitive characteristics of the speakers. In other words, we will ignore the phase angles shown by the dotted curve in Figure 1. This simplified analysis will give us the amplitude response of the amplifier-speaker interface."

I also like the calculator he included at the end of the article. Web-based calculators can be very handy.

By the way, I recently upload another article, explaining decibels, logarithms, sound pressure and sound power:

https://www.audiosciencereview.com/...s-sound-pressure-sound-power-explained.24484/
 
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As concerns the damping factor, it is pertinent to note, as did Dr. Toole and Dick Pierce and myself and others, that while this effect is the effect by which the term "damping factor" has obtained its name, it is not the effect by which excessively high amplifier output impedance would be likely to affect the sound, in the uncommon cases where sound quality is affected by excessively high amplifier output impedance. Should anyone desire to read more about the business of damping the cone motion, the reason should be to satisfy curiosity and to increase overall knowledge, which is a good enough reason. The article that Dick Pierce wrote back in the nineties does a very good job at explaining the business of damping cone motion. His article is linked from the previously mentioned Benchmark article. Here is a link to Pierce's article:

http://www.collinsaudio.com/Prosound_Workshop/Damping_Factor.pdf
 

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As concerns the damping factor, it is pertinent to note, as did Dr. Toole and Dick Pierce and myself and others, that while this effect is the effect by which the term "damping factor" has obtained its name, it is not the effect by which excessively high amplifier output impedance would be likely to affect the sound, in the uncommon cases where sound quality is affected by excessively high amplifier output impedance. Should anyone desire to read more about the business of damping the cone motion, the reason should be to satisfy curiosity and to increase overall knowledge, which is a good enough reason. The article that Dick Pierce wrote back in the nineties does a very good job at explaining the business of damping cone motion. His article is linked from the previously mentioned Benchmark article. Here is a link to Pierce's article:

http://www.collinsaudio.com/Prosound_Workshop/Damping_Factor.pdf
Excellent explanation. This isn't anything to worry about as long as the DF isn't very low.
 

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How should I interpret manufacturer's data sheets for amplifiers?

I have Powersoft D-Cell 504 and Digimod amp modules. For both the data sheets state "Damping factor @ 8 Ohm: > 500 @ 100 Hz". They do state the input impedance (10 kOhm balanced), but not the output impedance.

Can I just take 8/500 = 0,016 Ohm and assume that this is the (maximum) output impedance of these amps? Or is that not applicable?
 

DonH56

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How should I interpret manufacturer's data sheets for amplifiers?

I have Powersoft D-Cell 504 and Digimod amp modules. For both the data sheets state "Damping factor @ 8 Ohm: > 500 @ 100 Hz". They do state the input impedance (10 kOhm balanced), but not the output impedance.

Can I just take 8/500 = 0,016 Ohm and assume that this is the (maximum) output impedance of these amps? Or is that not applicable?
You can assume that at 100 Hz, but strike "(maximum)". The damping factor falls (output impedance goes up) as frequency increases. I would not be surprised if it is below 50 at 10 kHz. See e.g. https://www.audiosciencereview.com/...amping-factor-and-speakers.23968/#post-807327

HTH - Don
 
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