The issue is that the output impedance (hence DF) of an amplifier is not constant. It is frequency dependent which is the minor issue. The major issue is that it is level dependent. Think about a PP Class AB1 tube amplifier. At low level where both tubes conduct, the output impedance is low(ish). But when one tube goes in cutoff, the output impedance is that of the other (conducting) tube, that is about double of the low level case where both tubes were conducting. GNFB will help a bit, but still...
Yes, very important point. Linearity od the output imedance is more important than high DF figure. And standard measurements are opaque to it.
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That's why the DF is not a very good figure of merit for an amplifier.
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Here are links to three articles (by Tomcik, Augspurger and Preisman) that might be of interest:
http://dissident-audio.com/Loudspeakers/CriticalLSDamping.pdf
http://diyaudioprojects.com/Technical/Papers/The-Damping-Factor-Debate-by-George-Augspurger.pdf
https://www.pearl-hifi.com/06_Lit_Archive/02_PEARL_Arch/Vol_05/Sec_23/1386_Loudspeaker_Damping.pdf
The Rp of the output tubes tends to be higher (flatter plate curves) near the quiescent point than it is up near the knee where only one tube conducts and load goes Ra-a/4. This tends to flatten out the output impedance vs. drive - in much the same way as composite gm curves of a push pull tend to flatten versus a single tube. Push pull isn’t just about efficiency, it’s also about imperfections cancelling one another.
I suppose the term “damping factor” made a lot more sense when numbers were low and it could be approximated by dividing the nominal OPT primary impedance by the Rp of the output tube. And then multiply by the amount of feedback, if any. Since 40 to 60 dB of feedback was unlikely, you wouldn’t get those super high numbers that they get to claim today for a very small change in Zout.
Consider amplifier output stages that do not have negative feedback, locally or globally.
(There are many good amplifiers that do not have any negative feedback).
If the output impedance is not linear versus signal amplitude . . .
Then there will be one or another order of harmonic distortion caused by the changing output impedance.
1. A different way to look at a single ended output stage (that has no negative feedback):
A single ended output has lower output impedance when the output tube is near maximum current (rp is lower).
A single ended output has higher output impedance when the output tube is near cutoff (rp is higher).
The amplifier gain increases when rp is lower.
The amplifier gain is lower when rp is higher.
More gain for one polarity of the signal, and less gain for the opposite polarity of the signal.
Well . . . that sounds just like 2nd Harmonic distortion. A single ended stage has dominant 2nd harmonic distortion.
(The gain is Asymmetrical).
2. A push pull output stage impedance is not linear versus signal amplitude.
But the change in output impedance is symmetrical.
So the gain of one signal polarity versus the gain of the opposite polarity changes, but it is symmetrical from one polarity to the other.
Well . . . that sounds like 3rd Harmonic distortion. A push pull output stage has dominant 3rd harmonic distortion.
3. Do you think this only applies to vacuum tubes?
How about solid state amplifiers?
4. Consider a woofer that is driven by an amplifier that has Asymmetrical impedance versus signal (single ended amplifier).
Then consider the same woofer that is driven by an amplifier that has Symmetrical impedance versus signal (push pull amplifier).
Food for thought?
(There are many good amplifiers that do not have any negative feedback).
If the output impedance is not linear versus signal amplitude . . .
Then there will be one or another order of harmonic distortion caused by the changing output impedance.
1. A different way to look at a single ended output stage (that has no negative feedback):
A single ended output has lower output impedance when the output tube is near maximum current (rp is lower).
A single ended output has higher output impedance when the output tube is near cutoff (rp is higher).
The amplifier gain increases when rp is lower.
The amplifier gain is lower when rp is higher.
More gain for one polarity of the signal, and less gain for the opposite polarity of the signal.
Well . . . that sounds just like 2nd Harmonic distortion. A single ended stage has dominant 2nd harmonic distortion.
(The gain is Asymmetrical).
2. A push pull output stage impedance is not linear versus signal amplitude.
But the change in output impedance is symmetrical.
So the gain of one signal polarity versus the gain of the opposite polarity changes, but it is symmetrical from one polarity to the other.
Well . . . that sounds like 3rd Harmonic distortion. A push pull output stage has dominant 3rd harmonic distortion.
3. Do you think this only applies to vacuum tubes?
How about solid state amplifiers?
4. Consider a woofer that is driven by an amplifier that has Asymmetrical impedance versus signal (single ended amplifier).
Then consider the same woofer that is driven by an amplifier that has Symmetrical impedance versus signal (push pull amplifier).
Food for thought?
There's a big variety of SS output stage topologies. Each has specifics in regard to linearity of the output resistance. Most common is push-pull complementary emitter follower in AB class. Depending on the quiescent current, output impedance of a single arm is higher at low amplitudes. As amplitude rises, impedance decreases until it becomes dominated by emitter resistors Re. Combined impedance of the positive and negative arm has a shape of gull wings. See chapter 9 in Douglas Self's book "Audio Amplifier Design".
Well matched mosfets in the same configuration operated in A class without source resistors can in theory provide linear output impedance.
It should be mentioned, SE output stages are free of high order nonlinearity in the crossover region. Ro may or may not be linear by itself but is free of discontinuity.
Check this fantastic thread by Peufeu to learn about real life SS output stages.
I think that this is where small-signal analysis stops being insightful. Instead of non-linear output impedance, look at the effect as distortion caused by the exponential relationship between current and voltage.
Ed
Ed
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chp_mk,
Thanks for the information.
There are lots of topologies.
Many solid state push pull output stages are essentially 'totem pole', and are without any output transformer; and are instead direct coupled or cap coupled.
Totem pole outputs can be emitter + emitter, collector + collector or collector + emitter; or N + N channel, or N + P channel.
Complementary Symmetry, Pseudo Complimentary Symmetry, etc.
Many solid state single ended do not use an output transformer, some use a choke as a current source or choke current sink, etc.
The very late 50s and very early 60s had 6 transistor AM pocket radios, they had PNP output transistors that drove a small push pull output transformer. And one model I had, used two 1.5V batteries for + 1.5V and - 1.5V, and a totem pole output to the high impedance speaker.
Thanks for the information.
There are lots of topologies.
Many solid state push pull output stages are essentially 'totem pole', and are without any output transformer; and are instead direct coupled or cap coupled.
Totem pole outputs can be emitter + emitter, collector + collector or collector + emitter; or N + N channel, or N + P channel.
Complementary Symmetry, Pseudo Complimentary Symmetry, etc.
Many solid state single ended do not use an output transformer, some use a choke as a current source or choke current sink, etc.
The very late 50s and very early 60s had 6 transistor AM pocket radios, they had PNP output transistors that drove a small push pull output transformer. And one model I had, used two 1.5V batteries for + 1.5V and - 1.5V, and a totem pole output to the high impedance speaker.
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As Chris Hornbeck was implying, most discussions of damping factor completely overlook the "elephant in the room," which is that the DC resistance of the speaker coil needs to be added in to output impedance of the amplifier, plus the impedance of the leads from the amplifier to the speaker. It barely matters whether the output impedance of the amplifier is 0.05 ohms or 1.0 ohms, when you add in the 6 ohms or so of DC resistance of the speaker coil.
He is talking about the voice coil not the R of a series inductor.
dave
dave
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Normally the test of DF on lab of Audioreview in Italy is done at three frequencies, 100 Hz, 1kHz, 10kHz to see the differences. The test is done exactly at the binding post of the amp.
Sometimes there is a short tech description when the results are variable
For tube amp is not normally to measure it because the value are very low, as usual
Walter
Sometimes there is a short tech description when the results are variable
For tube amp is not normally to measure it because the value are very low, as usual
Walter
That’s when it is important to measure it - when the DF values are low. Whether the output Z is half an ohm (high feedback, pentode output with two gain stages), a couple ohms (single ended triode, ultralinear) or tens of ohms (no feedback pentode) actually makes a difference in loudspeaker tuning. Doesn’t make a hill of beans difference below tenths of ohms.
And in fact, not only should the DC resistance of the speaker coil be added into the amplifier output impedance that appears in the denominator in the damping factor calculation, it should also be subtracted out from the "loudspeaker imedance" in the numerator.
If we take a rough and ready model where we think of a loudspeaker as an ideal (zero DC resistance) inductor with reactance Z0, in series with its actual DC resistance R0, then the nominal "impedance of the loudspeaker" is very roughly Z= Z0 + R0. (Not really, of course, since we should not just add reactances and resistances, because of the different phase angles. But just as a rough and ready indication of the way things will look, it will do for now.)
If the output impedance of the amplifier is R1, then the standard calculation of the "damping factor" would say it is Z/R1, i.e. (Z0 + R0)/R1. This can of course be very big, if R1 is very small and Z is, say, 8 ohms.
But the actual resistive damping of the voice coil is essentially characterised by the ratio Z0/(R0 + R1). Compared with the "standard" calculation, where R0 is added in the numerator, in fact R0 should instead be added in the denominator.
In an example such as an 8 ohm speaker with Z0= 2 ohms and R0= 6 ohms (again, the same caveat abou the rough and ready approximations here!), the true damping factor will never be better than about 0.33, no matter how low the output impedance of the amplifier.
Wait a minute, are you all saying that the new Accuphase E-4000 (DF-800), isn't better than my "old" E-480 (DF-600)? Phew, that's a relief! 😀
Certainly not because of the DF itself. Design “features” that result in crazy high “damping factors” may result in improved ability to handle difficult loads or to tolerate overloads with less audible “consequences”.
Modern semi-con (linear, but not class-D) amplifier folk think about the issues of push-pull amplifiers in terms that they call "transconductance doubling", by which they mean the difference in output stage transconductance between the small central region where both (paralleled banks of) output devices are contributing (still conducting) to output signal and the larger nether reaches of signal where output devices take turns. Output devices are, Nelson Pass exotics excluded, always followers, so output impedance is reciprocal to transconductance.
Vacuum valves have terrible and expensive limitations trying to drive coupla-Ohm loudspeakers. They just can't be made in the scale of impedance needed, so must be impedance matched over a ridiculously wide bandwidth (1000:1 ! Yikes) with transformers. But, they do have the unique spidey-sense superhero ability to safely operate HOT. Vacuum valves can easily operate at high enough temperatures to operate an amplifier in class-A, meaning with no transconductance doubling and no crossover distortion, completely monotonic. This can be done with semi-cons but isn't trivial; only exotics even try.
For us DIYers, designing a speaker electrical damping and crossover function around a finite (non-zero), but fixed, source resistance is easily do-able, giving us an advantage over commercial designs, whose only universally applicable choice is zero Ohms.
All good fortune,
Chris
Vacuum valves have terrible and expensive limitations trying to drive coupla-Ohm loudspeakers. They just can't be made in the scale of impedance needed, so must be impedance matched over a ridiculously wide bandwidth (1000:1 ! Yikes) with transformers. But, they do have the unique spidey-sense superhero ability to safely operate HOT. Vacuum valves can easily operate at high enough temperatures to operate an amplifier in class-A, meaning with no transconductance doubling and no crossover distortion, completely monotonic. This can be done with semi-cons but isn't trivial; only exotics even try.
For us DIYers, designing a speaker electrical damping and crossover function around a finite (non-zero), but fixed, source resistance is easily do-able, giving us an advantage over commercial designs, whose only universally applicable choice is zero Ohms.
All good fortune,
Chris
It was a tongue in cheek post, but a good answer anyway. The rest of the published specs appear identical, BTW. But the control buttons are a different shape! 😀
Good job of scaring away the OP guys! I mean, we're not here to help, right, we're here to show off our expertise.
That worked well.
Jan
That worked well.
Jan