Please explain amplifier output impedance


I have recently read a few loudspeaker reviews which mention that the speakers would likely work best with low output impedance (or high output impedance) amplifiers.

So, what measurement defines low output impedance (or high output impedance) on an amplifier? What's the numerical value of low and high output impedance, and what is "average"?

Also, what specification of a loudspeaker provides info that would indicate using an amplifier with particular output impedance?

Thanks in advance for explaining this in laymen’s terms. :)
tvad
No worries Sean! I agree with much of your comments regarding the ideal amplifier also. The issue for me personally when I set forth on the designs I did was how to get around the ill effets of negative feedback. Some of our early designs used it, and we pressed the limits of the tubes to produce super wide open loop bandwidth, in an attempt to put the propogation delay effects out beyond 20KHz. The result was full power bandwidth to nearly 30 MHz!

It didn't solve the feedback issues though (which I have previously discussed). We had set the feedback up so that we could switch it. In the end we chose zero feedback, and in the process discovered that a different set of design rules emerges.

I've had some discussion of these rules and the competing (more accepted, Voltage Paradigm) rules in the past. Both have challenges to overcome- the Power Paradigm has to find ways to make amplifiers more universal as you say and the Voltage Paradigm has to find a way to get loop feedback to arrive at the input of the amplifier in time to make the correct adjustment, not an approximate one (in order to create a musical presentation). Both are serious challenges!
David@davidberning.com: I understand that electrical damping, mechanical damping, amplitude linearity, transient response, loading characteristics, etc... are all different yet inter-related subjects. Achieving excellent results in one area may end up compromising performance to some extent in another area. This is where design variables come into play and the engineer / designer must do some juggling in order to achieve what they think will result in the best balance.

As far as your comments go about an amp with a negative output impedance, you are right, this is not that difficult to do. The end result would typically be a design that was highly stable into various loads, but not very linear in terms of transient response, dynamics and desirable sonics. Once again, there's a design trade-off involved due to the ( limited ) technology available to mankind as we know it today.

Having said that, i think that far too many concentrate on certain areas while neglecting others, resulting in equipment that might measure well under certain test conditions, but perform FAR less accurately / musically in the real world. That's because the product is not well rounded, but instead, concentrates on measuring / performing certain measurable tasks better than others.

If you would be so kind, can you refer me to what issue Stereophile reviewed the ZH-270 in? I know i have this issue, but haven't been able to locate exactly which one it is.

Atmasphere: There are no "perfect" amplifiers, so of course, NOTHING is "universal" by design. Having said that, some amps are FAR less sensitive to loading characteristics while providing more consistent performance from speaker to speaker and system to system.

Unless one is interested in working with "chameleon" components that change both electrical and audible measurements at the drop of a hat, selecting gear that is of a more "universal" nature makes building a reasonably decent sounding and consistent performing system a little easier. Otherwise, one runs into problems with crediting certain changes to one specific component ( or cable ) change, when in reality, that one change triggered other changes in the chain. This results in a cumulative effect, making it harder to both recognise and disect exactly what is going on and why.

When something like this happens, stability is compromised, resulting in a wider tolerance of potential results. There is also less potential to transfer said results into another system by following similar approaches with slightly different componentry. This is why so many "recommendations" here are NOT universal by nature, but extremely system and personal preference dependent.

An ideal amplifier would have an output stage that would mimic the load impedance that it sees on a real time basis, adjusting as dynamic conditions and frequency are altered. Such a design would require unlimited voltage and current potential with phenomenal transient response. We don't have anything anywhere near this, so all one can do is to choose the lesser of evils and shoot for some form of electrical consistency with pleasant sonic results.

As far as my belief / stated comments regarding your preference of speakers, i based my comments on the speakers that i've seen you set your gear up with at various shows. I had assumed that you would have selected support componentry that you not only find sonically desirable, but also brings out the best qualities of your gear. From what i can recall, what i have seen you working with under those conditions were all vented designs. Granted, show installations may not always be what a manufacturer would recommend under optimum installation conditions, but one would think that they would at least strive to deliver something close. Forgive me for making any assumptions in that area if i am mistaken. Sean
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I repeat, a low output amplifier impedance does not guarantee proper speaker damping. It often actually overdamps the speaker. The subject of overdamping, critical damping and underdamping is a well-studied topic in engineering

I agree that damping is well studied in engineering, however, in engineering "damping" is NOT the same thing as the audio "damping factor" term used to describe an amplifier. Actually "damping factor" is simply a reflection on the amp output impedance relative to to the speaker load. This is an "indication" of how well an amplifier can be expected to handle a reactive load. It should not taken as gospel ...there is a lot more to an amplifier than damping factor.

Once the output impedance is low relative to the load then the "damping" of the driver (suspension/magnet/coil)and box will dominate the response...The amplifier simply puts the correct voltage over the speaker terminals which always pushes the driver towards the proper position (as determined by the audio signal) by supplying the appropriate current.

In theory more current can be supplied for a given amplifier voltage if the output impedance is lower...i.e more "push" in the right direction.

Apologies if I have oversimplified things but I don't see how amplifier damping factor can be regarded in quite the same way as the critical damped response that is often saught in most speaker designs.
Hi Sean, I can't think of an amplifier that that qualifies as 'universal use'. For any example you can think of I can think of a speaker it does not work with. On that account your argument seems to fall apart. It is also not true that I 'prefer vented speakers', in fact what I prefer is speakers that sound right regardless of their technology. I use headphones (Stax, Grado) and master tapes for reference to avoid the pitfalls that you (?might?) have assumed that I have fallen prey to.

We've used a variety of speakers over the years including acoustic suspension ('sealed'), horns, bass reflex, magnetic and ES planars. On all of these speakers it was easy to demonstrate that our amps were making correct bass against the typical power house transistor amps which do not.

I should also point out that I do use a set of design rules based on reality and easily proven. Nor do we lack in the measurement department for them (see our website for details). IOW we respect the human ear and the rules that *it* uses, rather than made up rules that it does not use.
Thank you, Duke.
The 27 ohm maximum was at about 3 kHz, which is not a good place to have a response anomaly
Indeed, although rather benign compared to a (expensive) branded speaker I onced measured with a friend...! And you had few components in the signal path messing things up, which is a bonus. After all, a push-pull (or an OTL?) amp may work wonderfully with that... who knows...
Mr Berning sez
By the way, (Sean,) what (..you..) would think of an amplifier with negative output impedance
Not to hi-jack the conversation -- but hasn't Mr Pass tried/experimented with something like that?
By the way, Sean, what would think of an amplifier with negative output impedance? After all, the output impedance of the amplifier must be added to the dc resistance of the speaker cable and speaker voice coil resistance in the damping equation. An amplifier with negative output impedance would increase the true damping factor further. Building such an amplifier is not difficult, I once modified an old Heathkit tube amp by applying some current feedback to do this. I can't remember what it sounded like, as I did this over 30 years ago, but never pursued it further.
Apparently my point was missed about the subject of speaker damping. The point that I was making concerned the subject of optimum damping in response to a transient waveform. Music is made up mostly of transients whereby many frequencies are present at once and transient attacks are part of the normal program source. Stereophile frequency flatness measurements represent a different type of measurement and do not address the transient properties of the speaker-amplifier. I repeat, a low output amplifier impedance does not guarantee proper speaker damping. It often actually overdamps the speaker. The subject of overdamping, critical damping and underdamping is a well-studied topic in engineering. No one interested in this subject would ever assume that the most is the best without verifying with measurements. I have done this and I described the apparatus that I developed for these measurements in my previous post.

Oh by the way, Berning amplifiers have a nominal output impedance of less than two ohms, but the user can increase this in the ZH270 by setting the feedback switch to MED or LOW to best optimize system transient response and user preference.

10-15-06: Audiofeil
Well let's see how long this thread lasts. I'm betting on late Sunday afternoon and I have no dog in this fight.
If so, it'll be too bad. This thread has more useful discussion and debate than any in a long time, IMO.
Sean & Dave,

Thanks for talking this discussion even further.

There are quite different design philosophies behind the conflicting views on output impedance;

One philosophy is that the amplifier and cables should have a minimum affect on the speaker response - i.e. the speaker is designed for SS amps of many types and the speaker impedance variation with frequency is NOT intended to affect system frequency response. (provided the amp has enough power to drive the load this philosophy leads to consistent results => the flat speaker response will be maintained provided it is coupled with a low output impedance SS amp.)

The other philosophy is that amplifier and cables should be chosen in order to augment/adjust speaker response by behaving as a kind of "equalizer" or a tuned system; in this case, system response will vary as a function of speaker impedance. (amp ouput impedance - cable - speaker load act together as a filter/equalizer on the sound => this leads to a system which can be tuned to taste, according to the preferences of the user and the selected high output impedance amp)

It is the differing philosophy that leads to different views on amplifier output impedance. There are advantages to both. One is consistent and accurate; but you get what you get. The other approach offers greater flexibility for tweaking to taste.

This is why I qualified my earlier comments in this thread by saying they were generalizations for SS amps an not for tubes. Tubes seem to be desirable to those that like a certain flavor to the sound...a certain warmth or punch to the bass. (and there is nothing wrong with that. Doug Sax, one of the industry leading professional Mastering Engineers, uses tubes for mastering for this very reason. Indeed, most people seem to prefer an equalization curve with a boosted bass and a rolled off treble.
One more thing. Sometimes i'm simply debating something based on the technical merits of the subject at hand. I do this from an educational standpoint, and to be honest, because i like to debate. There's nothing wrong with discussing opposing points of view, having some fun and possibly learning something along the way. : )

As i've said many times in the past, i only know what i do because others have taken the time to share their knowledge and try to educate me. I'm trying to do the same thing. Sometimes, my methods may not be the best or most "friendly", but then again, i've never claimed to be "PC" or a "teacher" by trade. I'm simply a big-mouth sharing my point of view, so take it for what it's worth : )

Having said that, my pointing out what "I" consider to be technical flaws in a product does not mean that one can't like / listen to / enjoy a product that i have attributed these specific "negative" connotations too. As i've said before, one should buy / use / listen to / enjoy what brings them closer to the music and their system goals. The owner of the system is the only one that has to be pleased with the end result, negating most any other comment that i or anyone else could ever make about a given product or installation.

As a case in point, i typically tend to like the sound of Cary tubed amps, even though i don't own any of them. I know that they are quite coloured and less than linear into most loudspeaker loads, primarily due to their high output impedances and some other factors. Like some of the products mentioned above, these items fall into the "specialty" products category and i treat them as such. They can require very careful attention to detail in terms of selection of mating components to say the least.

Having said that, the end result of installing one of these amps ( or something similar ) into a system can be a very luxurious and smooth sound with great spatial characteristics. While i know that i'm NOT listening to strictly what was on the record and am hearing quite a bit of "system artifacts", it doesn't make it any less enjoyable.

I just wanted to put things into perspective, as i know that some will be upset with my post above for various reasons. If it upsets you, blow it off and consider the source : ) Sean
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Well let's see how long this thread lasts. I'm betting on late Sunday afternoon and I have no dog in this fight.
It should be noted that Mr Berning is a manufacturer of audio gear. As far as i know, all of his tubed amplifier designs are of a VERY high output impedance, hence his propensity to defend this type of product.

Those that are interested in such subjects may want to look at some "reasonably unbiased" test results as conducted and published by Stereophile on this very subject. The article titled "Questions of impedance interaction" has several different graphs documenting the linearity of four different amplifiers driving three very different speakers.

Remember, these graphs are of the actual amplitude linearity / loading characteristics / frequency response of the amp going into the speaker, NOT the measured response AFTER the speaker output. In effect, you are seeing how various amps deal with various loads, not the actual output of the speakers as driven by those specific amps.

Given the phenomenally distorted / non-linear frequency response / loading characteristics of some of these amps, the output response of the speakers would be even more distorted / non-linear. After all, the speaker can only try to reproduce what is fed into it, and if the amplifier is feeding a phenomenally non-linear signal into the speaker, one can only expect further distortions after the speaker.

As can be seen in the test results, the two low output impedance solid state amps ( Hafler & Aragon ) remain extremely consistent in amplitude output ( linearity of frequency response ), regardless of the load they are presented with. While these would commonly be referred to as a high damping factor design, one can see the benefits of using a very low source output impedance as compared to a higher ( speaker ) load impedance. That's because the difference in impedance between the source and the loudspeaker load acts as an "impedance buffer".

This "impedance buffer" (or "higher damping factor") reduces the potential for the varying impedance that the speaker presents to "load down" or "modulate" the output of the amplifier. This can be seen as output remains quite consistent, regardless of frequency or the impedance that these amps are presented with.

The Melos tubed amp results are kind of tricky. In the text of the article, Mr Norton states the following: "Since the Melos 400 also had a relatively low output impedance for a tube amplifier (at 0.43 ohms at low and mid frequencies, rising to 1.2 ohms at 20kHz, from its 8 ohm tap), I took that opportunity to run some frequency-response measurements using an actual loudspeaker as the load for the amplifier".

While this would seem to be a pretty stable design as far as tubed amps are concerned, and the results somewhat confirm that other than a sloping high frequency response, the results are somewhat misleading. That is, the Melos might have an output impedance ranging from .43 ohms up to 1.2 ohms as frequency varies, but this is on the 8 ohm tap. If you re-read the text pertaining to the actual testing on this amp, the results that Norton chose to publish were based on the 4 ohm tap of this amp.

This is somewhat deceiving and most people aren't technically sharp enough to catch something like this. One has to question why the tests and wording were published in the manner that they were. This is why i said that the test results were "reasonably unbiased". I don't know the reasons of why Mr Norton did or worded things the way that he did, but the text and test results were not consistent pertaining to this one specific brand of product.

Using the approach that Norton did i.e. choosing a lower impedance tap on the output transformer, the transformer itself and the tubed output stage sees less stress. In doing so, there's more of an " impedance buffer" built into this approach, hence the pretty decent output linearity / loading characteristics presented by this amp under this set of test conditions. As a side note, distortion was probably also drastically reduced due to the reduction in output stage modulation by using the tap that he did.

Now, take a look at the results of the tubed Sonic Frontiers amp. This amp has an output impedance of above 3 ohms, resulting in a damping factor of less than 2.7 into an 8 ohm load. As can clearly be seen, the lack of "impedance buffer" or "damping factor" is extremely evident. The amplitude linearity / frequency response into any of these loads is quite poor, especially when compared to the low output impedance SS designs.

As can be seen, the varying impedance of the speaker directly coincides with the varying loading characteristics of the amp. In some cases, the linearity of this amp is inferior to the frequency response of what many would consider even a "decently flat" loudspeaker. Driving the Martin-Logan's, the actual frequency response of the amp looks more like a scenic shot of hills and valleys than a piece of "reference grade audiophile approved" electronics.

With this set of speakers, the Sonic Frontiers amps is down well over -5 dB's by 20 KHz with a massive depression in the warmth, lower midrange and midrange frequencies. All of this with an amplifier that has an output impedance of slightly over 3 ohms. Obviously, this type of situation is an extreme example of why "system synergy" becomes SO important in certain installations.

Obviously, this type of performance puts the Sonic Frontiers ( and other amps like it ) into the "specialty category". That is, they are FAR from being universal in application. This is due to the inability to drive various loads with any reasonable form of amplitude linearity. As a side note, it should be noted that a lack of amplitude linearity is NOT measured as a part of THD, IMD, etc..., but is a measure of "frequency response tolerance". In effect, it is a distortion all to itself.

For sake of reference and comparison, the test results that i've seen for one of Mr Berning's products showed the amp as having an output impedance of appr 5 - 10 ohms or so ( can't remember the specifics ). This could be why he included the following in his response: "In practice, the system frequency response flatness will likely have the similar degrees of deviation for all amplifiers from zero to 10 ohms output impedance".

All i can say to that is "HA HA HA". If such were the case, all amps would sound pretty similar on any given set of speakers because the SYSTEM frequency response would all be equally flat. As was verified in the Stereophile test results, this is obviously NOT true. If such were the case, there would be very little reason to buy one amp over another, as the only difference would be power ratings and potential spl's. As most all of us frequenting this forum know, such is simply not the case.

On top of that, Mr Berning also stated the following: "Yes, if the output impedance of the amplifier was 50 ohms, and a very underdamped speaker reached a 50 ohm impedance, there would be a sharp peak in the system response". While MANY speakers do have a 50 ohm peak in the low frequency region, especially vented designs with large woofers, most amps do not come anywhere close to having a 50 ohm output impedance. That makes this analogy useless in the real world.

Getting back to the real world and applying a high level of logic to what Mr Berning did state, let's refer back to the Stereophile article i previously referenced. As was seen in that articles test results, we could definitely see that as the output impedance of the amp was brought closer to the input impedance of the speaker i.e. reducing the "damping factor", the response became more peaky / less linear. That's because of the lack of "impedance buffer" that i previously mentioned. In an audio amplifier, the response would get even more ragged looking / non-linear if the output impedance of the amp actually matched the input impedance of the speaker. This would be due to having a near zero damping factor / impedance buffer.

As such, Mr Berning was not exagerating in his 50 ohm - 50 ohm example and Stereophile's test results tend to confirm this. Applying further logic to what Mr Berning stated, he is basically telling us that the response of his own amp, with a measured output impedance of 5 - 10 ohms, will produce very peaky, non-linear response when driving a speaker with a nominal impedance of 5 - 10 ohms. As poor as the Sonic Frontiers amp performed with a "damping factor" of 2.7 into an 8 ohm load, the Berning amp would have a "damping factor" of near ZERO at 8 ohms over part of the audible bandwidth. How linear do you think that would be?

Obviously, we are talking about another "specialty" product here, which i don't have a problem with. People buying such a product should be familiar with what they are buying, so long as the manufacturer and sales people are honest and ethical about the performance potential of the product and what it takes to make it work as they planned.

In that respect, Mr Berning has been honest and forthright about at least one of his products, and we should thank him for contributing to this thread. His contributions allowed us to dig deeper into this subject and actually make some real world comparisons in an apples to apples format, courtesy of the Stereophile test results. Sean
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There is no universal correct amplifier output impedance. This is why we and others offer a means to adjust output impedance/damping on some models. Many system designers have known this for years, and damping adjustment controls were found on some amplifiers going back to the 1950s or before. The reason that there is no one correct output impedance is because the speaker is a mechanical system with inertia and its transient response is very much determined by the source impedance driving it. Each speaker design behaves differently, and it is usually desirable to achieve what's called "critical damping". If the mechanical system (speaker) is under damped, the cone will overshoot and ring in response to a step transient. If it is overdamped, it will undershoot and be slow to reach its proper position. Underdamping happens when the output impedance of the amplifier is too high, where as overdamping occurs when the output impedance is too low. In terms of the bass reproduction, underdamping results in an overly warm resonant reproduction, and overdamping results in a overly dry and heavy presentation. Neither of these are correct. When the amplifier output impedance is optimum, the bass will have its most natural reproduction. A damping/feedback control on the amplifier lets the user best tune the speaker, and yes, the room acoustics enter into it as well.

I made a gadget for observing the optimum damping of a speaker cone in response to a step transient driven from various impedances. The device uses a lightweight conductive foil that can be taped to the cone of the driver, and a matching RF based capacitance probe is used to detect cone movement and display it on an oscilloscope. I can confirm various degrees of over and under damping, and have tested speakers that range from wanting to see as high as a 7.5 ohm amplifier output impedance (this was a large driver and quite unexpected) to speakers that are still underdamped with zero output impedance. I find that most high-end speakers fall in the range of working best with 2-4 ohms amplifier output impedance.

Of course, this is the bass driver movement and is easiest to measure. The higher frequency drivers in a particular speaker may want to see something different, and it seems still impossible to be completely scientific in determining what is really best when the whole frequency spectrum is taken into account. This is why it is really best to simply listen with an open mind, and not assume that there is a spec that will really tell you how good or accurate a speaker-amplifier combination is going to be.

Over an over again people get hung up on worrying about the issue of a high output impedance amplifier impedance affecting the frequency response. It is very easy to try to explain the sonic differences by making the argument that the frequency response of the system wobbles all over the place because the amplifier output voltage goes up at frequencies where the speaker impedance rises. Yes, this does happen, but how flat do these people think the frequency response in the listening room is if this were not to happen. Yes, if the output impedance of the amplifier was 50 ohms, and a very underdamped speaker reached a 50 ohm impedance, there would be a sharp peak in the system response. Whereas some speaker drivers can reach 50 ohms, an amplifier with an output impedance of as high as 5-10 ohms will largely tame it (but perhaps not properly damp it). In practice, the system frequency response flatness will likely have the similar degrees of deviation for all amplifiers from zero to 10 ohms output impedance. The particular frequency points of maximum and minimum response can be expected to shift around slightly, but this alone would not account for a significant enhancement or degradation of the sound. They will sound very different though, but because of the damping.
Tvad: Unfortunately, there is no "Big Dummy's Guide To Assembling A High Fidelity Music Reproduction System". It's NOT that easy. But then again, if it were that easy, you would have to find some other frustrating and equally expensive hobby to spend your time on : )

Personally, i have always thought that a "good" product was a "universal" product. Anything that requires very specific mating of componentry is strictly a "specialty" item. If one is getting involved with that type of product, they should be prepared to deal with the specifics that come with it. This is why i tend to "knock" certain products, as they are very specific in what they do. This makes them less than ideal for the average user that wants to maintain some semblance of balance.

Having said that, there's nothing wrong with a manufacturer targeting a certain market. So long as they are forthright in their product descriptions and are willing to make specific recommendations as to how to achieve optimum performance with their product(s) and others that will mate well with them, more power to them.

Atmasphere / Ralph: Your comments pertaining to damping factor are evidenced in how you design and impliment your products, which is good. This shows a form a consistency in both thought and action. This makes it easier for the consumer to understand what they are getting and what to expect from a given manufacturer / product line.

Having said that, i don't think that your amps are a "universal" product as described above. This moves them over into the "specialty" category ( in my opinion ). Given that you are willing to work with your customers and offer specific recommendations with reasoned explanations, your company is a great example of the "specialty" market.

The fact that you are willing to contribute to these threads and in other forums, share your opinion in a forthright manner without soft shoe dancing or pulling punches, etc... lets the customer know where you stand, what they can expect from you and your products and what will work best. Kudo's to you, as i wish more manufacturers were like this.

With all of that in mind, we obviously have differences of opinion on certain aspects of sound reproduction. You typically prefer vented speakers, whereas i typically prefer sealed speakers. You typically prefer a lower damping factor, i typically prefer a moderate to reasonably high damping factor. The sonic differences between each approach are typically easily identifiable when listening.

This does not make one approach "better" than the other sonically, as that all boils down to personal preference. Obviously, the differences could easily be debated electrically and acoustically. In that respect, i "know" that i'm right, and you "know" that you're right, so where does that leave us???

Suffice it to say that, it all still boils down to what one likes as an individual and system synergy. The only way that one would know for certain whether a product would be right for them would be to use & listen to that product for themselves. Knowing how things work and being able to decipher standardized test results can point us in a given direction, but they can't give you all of the answers. There's just too many variables involved and that's why the "Big Dummy's Guide" hasn't been written as of yet. Laura Dearborn, Robert Harley, etc... have tried, but the results are still pretty variable : )

As such, all one can do is to learn, listen and compare for themselves. When you find something that you like, sit back and enjoy both the music AND your new toy. After all, that's what it's all about, isn't it? Sean
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I think there is no real good rule of thumb. Everyone has to just listen to the amp/speaker combo and decide for themselves.
Tboooe (System | Reviews | Threads | Answers)
Not to necessarily critique Tboooe's comment, but it prompted a thought.

It seems to me that if considerable discussion is had by several contributors to this thread, all of whom appear to know what they're talking about (at least to this non-technical layman), specifically identifying output impedance and/or damping factor as it relates to speaker impedance and how they affect sound. And, if mathematical relationships are developed that correlate and explain amp/speaker performance, which is what I gather has been discussed in these posts...then, to toss it all away by saying that there is no good rule of thumb and everyone simply has to listen to amp/speaker combinations and decide for themselves, is to disregard science and engineering and instead throw up our hands at any attempt to use specifications to narrow down choices for the best potential amp/loudspeaker matches.

I come away from these discussions believing the audiophile hobby is overcomplicated. This is undoubtedly due to the large numbers of boutique specialists who build their products in a semi-vacuum choosing to place ease-of-use and ease-of-matching at the bottom of the priority list. I understand this can be a benefit insofar as it allows almost infinite possibilities to tailor a system's sound, but it can also work to a cross purpose by keeping the goal elusive.

Please accept this as a comment from a music loving end-user who is not an electrical engineer, technophile, or DIY'er.

Someone could make a fortune by simplifying. I suppose Linn has been the most successful at this concept...and perhaps NAIM to a lesser extent, but these two manufacturers still haven't cornered enough of the market for me to believe there isn't room for others on a smaller scale and budget.

Thank you. Please remember to tip your waiter or waitress... and try the veal.
I have been following this thread with interest and doing my own novice research on this topic and it seems that there is no right answer here in terms of whether or not damping factor is a relevant spec. Here are some of the tidbits I have picked up:

1. The mechanical damping of the speaker plays the largest role in terms of how the cone movement is damped

2. The effect of any damping factor above 10 is impossible for humans to hear

3. A static damping factor number does tell the entire story since both amp and speaker impedance changes with frequency.

4. A high damping factor is misleading as it could mean the use of a lot of negative feedback which could have adversely affect the sound

These are just some bits of info I have picked up from reading about dampiing factor so please refrain from blasting me with flames. I am by no means an expert in this area.

I think there is no real good rule of thumb. Everyone has to just listen to the amp/speaker combo and decide for themselves.
Success. I think we all agree if you accept that my persepctive is "old school" (from electronics text books, linearity, accuracy etc.)

Furthermore, I fully agree with Atmasphere that a low frequency ambience or bass definition is what a tube amp or an amp with a lower damping factor does to the sound.
Hi Gregm,

No problem, that's a fair question. I won't give a highly specific answer, but hopefully the generalities will be useful.

You can design a crossover with the values optimized to produce the desired transfer function with a minimum number of parts. Or, you can design a more complex crossover that uses what looks like redundant circuitry, such as parallel resistor legs at different places within the circuit. The more complex crossover gives you more options when you start trying to juggle the impedance without spilling the frequency response.

I worked within the minimum-parts-count topology to smooth the impedance, but at best was only able to keep it between 7 and 27 ohms above the bass peaks (a nearly 4-to-1 spread). The 27 ohm maximum was at about 3 kHz, which is not a good place to have a response anomaly.

Switching to a what-the-heck-high-parts-count topology, I got the impedance down to between 8 and 13 ohms above the bass peaks, and the 13 ohm maximum is at 400 Hz where an extra dB or so helps offset the baffle step a bit.

The topology and combination of values that produced a good impedance curve without spoiling the frequency response was largely the result of trial and error. My modelling program did not do a very good job of predicting what the impedance curve would be, perhaps due to non-ideal behavior of the components. So I spent a lot of time changing crossover parts, measuring frequency response, and measuring impedance. I'm sure there's a better way.

Duke
Success? I would consider damping over 20:1 to be excessive. I use master tapes for reference and one thing has become clear over the years: high damping factor equates to not getting the bass right; retentive (not in a good way) IOW punch without real definition and the first thing to go is always low frequency ambience.

Some speakers are intentionally designed for amps of higher output impedance (new paradigm, BTW) in order to take advantage of the benefits such amps offer. IOW there is no *ideal* value for output impedance- it all depends on the speaker...

The lesson here is that you have to pay attention to the speaker/amplifier interface regardless of the amplifier or speaker that you have chosen. To ignore this means you could flush thousands of dollars away to no good effect.
* For those that can't do the math, an output impedance of .2 ohm would produce a damping factor of 40 as referenced to an 8 ohm speaker. This would be an acceptable starting point for someone trying to drive a larger woofer with a decent sized motor structure. Smaller diameter woofers with smaller motors and / or limited excursion might get away with a slightly lower DF ( damping factor ) without any really noticeable problems.

Much earlier in this thread I suggested 80 as an "ideal" damping factor or 0.1 Ohm output impedance as a good number to seek for a nominal 8 Ohm speaker load (not too much negative feedback and not too lacking in linearity/control when coupled with a speaker).

I can also live with Sean's very close suggestion above. I think, at least for once, we are reaching a consensus on your question Tvad; you have your "Goldilock's" answer as to what may be considered too low, too high and "just right" for amplifier output impedance in relation to load.

Of course, I hope everyone understands that this is a huge generalization that applies to SS amps and I would never recommend choosing one component over another based on this criteria alone.
Duke: I don't need to tell you or anyone else that has truly dug deeply into designing / building a great speaker that the amount of work / R & D ( research & development ) that one can put into such a project can be mind-boggling. The things that make an audible difference are too high to count, let alone factoring in how to manipulate exactly which "mods" or "tweaks" to use in conjunction with others. Obviously, there are a LOT of design variables and personal decisions to be made when arriving at the final product. Even then, with most DIY speakers, that final product is typically NOT "final" by any means.

Having said that, it amazes me at what some of these manufacturers produce, market and settle for at the prices that they charge. Same thing goes for Pro Sound reinforcement and guitar / bass cabinets. These are typically low to medium grade drivers stuffed into a poorly built and designed box using whatever low grade wiring and hardware that they can find. Sean
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Duke notes:
It took me a very long time to get the impedance curves smooth enough that there wasn't a significant tonal balance difference depending on which amp I used. Easy to smooth the impedance curves, but hard to do so without screwing something else up
Indeed it is! How did you go about it --if I'm not asking a sensitive question? Cheers
Sean, I recently spent several weeks designing two loudspeakers specifically to work well with high output impedance tube amps. I wanted them to also work well with low output impedance solid state amps, though that was a secondary priority.

Getting the speakers to work well with a high output impedance amp was not difficult as long as I kept the speaker's input impedance about 15% higher than the amplifier's output impedance. Now granted a higher impedance speaker would have theoretically worked better, but the 16-ohm drivers I tried didn't sound as good. So I opted for what sounded better to me.

A much greater challenge was meeting my secondary priority - that the speakers still sound good with a solid state amp. It took me a very long time to get the impedance curves smooth enough that there wasn't a significant tonal balance difference depending on which amp I used. Easy to smooth the impedance curves, but hard to do so without screwing something else up. And in the end I'd still say that optimium bass tuning with the solid state amp is a few Hz higher than with the high output impedance tube amp because I left the bass impedance peaks intact (didn't try to smooth them by overstuffing the cabinet). To accomodate both amp types (as well as variations in room boundary reinforcement) I went with a port system that is somewhat user-adjustable.

Tvad, PHY and Lowther both make full-range drivers that have a nominal impedance of 16 ohms, and I don't think they dip below 12 ohms.

Let me mention two other speaker lines with models that work well with SET and OTL amps: Silverline and Reference 3a.

The Silverline Sonatina III, Bolero and Panatina II don't have particularly smooth impedance curves, but with a solid state amp their frequency response curves dip where their impedance curves peak. So with a high output impedance tube amp, their frequency response will be smoother than with a solid state amp.

The Reference 3a DeCapo has a very smooth impedance curve, varying between about 6 and 11 ohms above the bass region. And, the 11 ohm maximum is in the region where there's a frequency response dip with a solid state amp, once again helping to smooth the frequency response with an OTL or SET tube amp.

Duke
Tvad: The speakers that came to mind right away were the Coincident's that you mentioned. I don't know of others that i can rattle off though, as i really don't pay attention to / go out of my way looking for such designs. Most all of my gear / installations revolve around lower impedance designs, hence my lack of familiarity. Having said that, my preferences in loudspeakers also tends to dictate my preferences for higher powered SS amps that run in a very rich Class AB or Class A mode.

As to output impedance on an amp, my personal opinion ( and that is all that it is ) would be to "draw the line" at about .2 of an ohm or so*. Obviously, there's a bit of a "fudge factor" involved here and what i would consider to be "acceptable" would somewhat depend on the load that it would be driving. Obviously, i would like to see it lower than this, but with some designs, that would require the use of massive amounts of feedback. At that point, it becomes a balancing act as far as which evil you want to subdue the worst.

With that in mind, most tubed amps are noticeably above this level, hence the looser low frequency response and greater variations in performance from speaker to speaker. I have seen some tubed amps that exhibited output impedances that were quite high i.e. above 8 ohms on certain taps. These amps would tend to be extreme sonic chameleons i.e. drastically changing their bandwidth, transient response and tonal balance as the load that they saw was varied. It would be a situation like this where some speaker cables can DRASTICALLY make very audible differences. Sean
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* For those that can't do the math, an output impedance of .2 ohm would produce a damping factor of 40 as referenced to an 8 ohm speaker. This would be an acceptable starting point for someone trying to drive a larger woofer with a decent sized motor structure. Smaller diameter woofers with smaller motors and / or limited excursion might get away with a slightly lower DF ( damping factor ) without any really noticeable problems.

In some cases, a lower damping factor might actually be desirable, as it might lend a fuller tonal balance to an otherwise thin sounding system. Only problem is, that loss of DF would typically come at the expense of transient response, so once again, system synergy comes into play.

10-12-06: Sean
...lower output impedance is typically considered to be a more desirable trait in most cases.
In your view, what measurement is considered to be a lower output impedance?

BTW, I recently did an extensive search for loudspeakers. I'd say the list included 20 loudspeakers from 20 manufacturers. They were all dynamic designs. Only one model had a nominal impedance above 10 ohms (Coincident Super Eclipse III). I don't believe a 10+ nominal impedance is a realistic goal when shopping for loudspeakers...even on esoteric horn loaded loudspeakers.

Perhaps you could offer three loudspeakers that have 10+ ohm nominal impedance?
Tvad: There isn't a specific point where an amp is either considered to be high or low output impedance as it is a relative thing. Having said that, a lower output impedance is typicall considered to be a more desirable trait in most cases. As previously mentioned, this sole criteria should not be used to judge whether one amp is "better" than another, but looked at as part of the total package when considering system synergy / component compatability.

If one wants to avoid potential problems in this area, look for speakers that maintain a relatively higher nominal impedances. Some speakers are specifically designed to stay above 10+ ohms. As you probably know, these are designed to be more compatible with tubed amps that typically demonstrate higher output impedances. Sean
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Shadorne- Yes. This is a major reason why tubes continue to be popular- they create less loudness cues.
Atmasphere,

Interesting. Perceived loudness clearly can be different from actual loudness. I have experienced this too. My speakers go well over 100 db continuous SPL levels at the listening position and yet the perceived sound is less loud than when my daughter plays iTunes at maximum distorted levels from the mini 10W speakers connected to our PC in the study.

In fact I have to ask her to turn it down even though the SPL levels are miniscule in the kitchen which is about 20 feet from the study; distortion is tiring, distracting and it seems we are very sensitive to low levels of it.

This may also explain why compression and limiting applied to modern pop CD's makes them sound very loud and unpleasant, especially at higher listening levels (when perceived loudness due to distortion and real loudness become most unpleasant). The CD "loudness wars" are a way to intentionally manufacture distortion in order to get a unpleasant & louder sounding music that gets everyones attention.

I read somewhere that IMD distortion occurs in the ear and this is how we perceive loudness, therefore, distortion that is added before the sound reaches our ears is interpreted as loud.
Tvad: "To bring this discussion back around to my original question, when a reviewer states that a particular loudspeaker would likely work best with a low output impedance amplifier"
When looking for an Amp, look for one that gives you a 4 ohm rating in the specs. Alot of amps give you the spes. for 8 ohms only. What you need is an Amp that will give you a 4 ohm rating and then you will be in the Ballpark to drive most low impedence speakers!!

PS. Did you have a certain speaker in mind or was it just a general question on low inpedence Speakers?
This is one of the reasons why i strive to build GOBS of dynamic headroom into my systems and believe in multiple amplifiers that are actively limited to covering only a small portion of the audible range. By reducing the stress on any given part of the system, and limiting the electrical interaction between various parts of the system, THD and IMD are drastically reduced. This is not to mention that dynamics are increased and signal purity remains quite high, regardless of drive levels.

On another note and as i've stated before, "clean" signals can be played at mugh higher spl's and they don't sound as loud as they really are. You also don't suffer nearly the amount of listening fatigue that one experiences on a "dirtier" system at lower spl's. Sean
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Hi Shadorne, if you look at the quote you will see that it is in fact *harmonic distortion*, not IMD. Several studies now have shown the same thing: the human ear/brain system uses odd-order harmonics beyond the 7th harmonic or so as loudness cues. In nature these harmonics are quite low- and even very slight enhancement of them is easily detected by the human ear.

I learned this years ago while servicing an amplifier on the bench. The output of the amplifier was connected to a loudspeaker and a VU meter. The amp had a sine wave at the input. While malfunctioning and making less than 20db of its normal output, it still sounded louder than the normal undistorted output. Once you experience this you will not forget it!
His study found that very high levels of low order distortion (30% second harmonic) were inaudible, but very low levels of the type of high order distortion produced by large amounts of negative feedback were quite audible and highly objectionable

I assume you are refering to Intermodulation Distortion or IMD distortion in an amp that is oscillating from large amounts of negative feedback. I agree that this is far more detrimental to the sound and something our ears seem quite sensitive to. Harmonic distortion is often indistingushable from the real sound of the instrument because the pitch of the note does not change (the note becomes fuller or leaner sounding). Even harmonic distortion is particularly hard to discern as your physicist friend points out. My understanding is that odd harmonics are more easily discerned, although still not nearly as easy to discern as IMD.

Hearing Harmonics

IMD distortion is one of the best arguments for promoting active speakers. Separate amplification for each driver over a limited bandwidth can only help to reduce IMD distortion significantly. Compare this to passive full range speakers where the amplifier must control the woofer at 40HZ and the tweeter at up to 20 Khz....hardly suprising that such a broadband system introduces audible IMD due to the combined interaction of all the drivers, the crossover and the amplifier fighting to control them.
Hi Bob, in the case you mention, no work would be done. IOW this has no bearing on driving a speaker.

Shadorne, in fact we operate in a world of paradigms. If this was glossed over in school, paradigms are a set of rules that are accepted as fact until the flaws in the rules are perceived. Then a new paradigm emerges; the old paradigm comes to an end. We are living in an era of transistion (which has been going on for the last 10?-15? years) now: some of the stuff that you (and me, and thousands of others) were taught is now being found to be not so truthful. Take a look at Duke's post above- it points directly to the problem that negative feedback causes- in fact negative feedback is a failed concept (old paradigm) in audio. Astrology too was taught in the world's major universities as fact less than 400 years ago :)

What the theory of negative feedback overlooks is that propagation delay exists. Since propagation delay is a fact of the real world we are now witnessing the emergence of a new paradigm.

The alternative paradigm has a different set of rules. It too looks for low distortion, but achieved in a way that does not offend the human ear (i.e. no feedback).
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I'm friends with a physicist who specializes in audio, and a couple of years ago he presented two papers on distortion perception at the Audio Engineering Society Convention. His study found that very high levels of low order distortion (30% second harmonic) were inaudible, but very low levels of the type of high order distortion produced by large amounts of negative feedback were quite audible and highly objectionable. Also, the type of distortion produced by amplifier crossover distortion and hard clipping were highly objectionable.

"Auditory Perception of Nonlinear Distortion", Earl Geddes and Lidia Lee, AES Preprint numbers 5890 and 5891. Earl and Lidia demonstrate that standard distortion metrics, THD and IMD, correlate poorly with distortion perception. In fact, THD actually has a slightly negative correlation to distortion perception! (Meaning that a signal with high THD is likely to be perceived as lower in distortion than a signal with low THD). They proposed an alternative distortion metric that correlates very well with distortion perception, but it has not caught on.

Earl has since made some very interesting discoveries about linear distortion too, but that hasn't been published yet.

Anyway, my point is that the type of distortion introduced by large amounts of negative feedback has been demonstrated to be both audible and objectionable.

Duke
I've specifically mentioned the Td ( Time delay ) of a circuit that Ralph makes mention of several times in the past. Shorter signal paths with a consistent impedance will have a lower Td, which is a good thing. I only know of one manufacturer that has ever published this spec as standard procedure.

Speed and time delays are one of the reasons why local feedback works "better" than global feedback. That is, local feedback isn't as slow to respond and the correction factor is smaller in amplitude. On the other hand, global feedback is both slower with greater correction factors involved, making it less desirable. No matter how fast the error correction rate is, it is NOT "instantaneous". As such, it has the potential to introduce other distortions into the equation. Kinda funny how circuitry that is designed to cancel distortion can actually introduce distortion, isn't it???

As far as having maximum voltage with minimal current flow, this is definitely a reality. If such were not the case, we wouldn't have to worry about such things as arcing or corona. Yes, there is current flow involved, but it is minimal compared to the amount of voltage involved.

Try to measure the resistance of air by holding two test leads a few inches apart. With that high of a resistance ( next to infinity ), the current flow involved in arcing across that gap would be quite low even though the voltage required would be quite high. Kind of an extreme example, but i used this as i thought it would be easier to understand than trying to explain antenna theory : ) Sean
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Negative Feedback is a failed concept

I humbly beg to disagree. Done properly, negative feedback produces excellent accuracy, stability and linearity in electronic operational amplifiers. If this is not the case, then much of my first year electrical engineering and the techniques employed by hundreds of thousands of engineers is deluded. I doubt that the entire electrical engineering industry suffers such monumental delusions as to use failed concepts for most analog circuitry.
10-10-06: Atmasphere
The reason Negative Feedback does not work is two-fold. Propagation delays inside all audio amplifiers insure that negative feedback arrives with a delay with respect to the input signal its supposed to provide correction for. At bass frequencies this problem is not profound, but at treble frequencies it is responsible for added odd-ordered harmonic content which (although in small levels) is something that the human ear uses as loudness cues- in effect a source of unnatural harshness to the human ear.
I believe it is this issue that Dakiom Feedback Stabilizers claim to correct. I have no idea if they work as advertised on amplifiers.
There is no hard and fast threshold but IMO, anything over 1 ohm is definately high output impedance. Many SS amps will be about 10x lower and tube amps are up to 10x higher so 1 ohm threshold seems to a decent rule of thumb.

Sean - My comment about amp impedance rising above 50kHz was based on at least a 3dB rise so it would visibly start to deviate around 20kHz. And you are definately correct in saying that many amps can't even do that well. I read all the Stereophile measurements several times each, no matter the piece of equipment. I am happy they are still around to do the good old fashioned measurements, even if I realize they aren't very applicable to musical reality. Nonetheless, I feel there is a lot to be said for an amplifer with an elegant set of curves.

Arthur
To bring this discussion back around to my original question, when a reviewer states that a particular loudspeaker would likely work best with a low output impedance amplifier, should one assume (based on comments made earlier in this thread), that a low output impedance measurement is .1 ohm? At what measurement (expressed in ohms) does the threshold cross from low output impedance to marginally high output impedance...1 ohm?
Arthur: Those are very good points and well worth clarifying. Thanks for taking the time to point them out AND explain them.

I have often said that it is the sum of manufacturer spec's that count more than any individual spec by itself. Even then, most manufacturers don't provide the quantity of spec's that one needs to make such information truly useful.

As to your comment about most amps having a linear output impedance up to appr 50 KHz, that is kind of generous in my experience. Many amps exhibit a noticeable increase in output impedance at or slightly above 10 KHz. How severe this is will depend on the design of the amp. By 50 KHz - 80 KHz or so, performance is starting to suffer quite noticeably. This is why many amps round the leading edge of a 10 KHz square wave. That is, the higher output impedance is part of a bigger problem i.e. limited bandwidth due to the amp being too slow to properly respond. Combine the limited bandwidth / lack of speed with the rising output impedance and you end up with that slightly rounded square wave that you see so often in Stereophile test measurements.

If you think that this sounds "bad", there are REALLY slow / limited bandwidth / higher output impedance amps fail the 1 KHz square wave test. When this type of amp encounters a very fast high energy high frequency transient, most of the attack, definition and duration is lost. This translates into a soft sounding blur, which some people like. This is probably more true with digital recordings and playback, which tends to sound hard, bright and glaring in many systems.

Other than that, this thread could go on and on contrasting various designs and goals. Suffice it to say that there are a LOT of variations that come into play with any / every design. When all is said and done though, the end result is a summary of what the designer / engineer thought was most important. Whether or not you like that product will depend on your own personal preferences and how well that specific component blends with the other gear in your system. As far as i know, there are no spec's to quantify personal preference. Sean
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Yes, it is impossible to make voltage without current. Power=Voltage X Current. Even in a preamp the voltage is there because current is there also. This fact is inescapable and is the result of Ohm's Law, the basic law of all electricity.

The reason Negative Feedback does not work is two-fold. Propagation delays inside all audio amplifiers insure that negative feedback arrives with a delay with respect to the input signal its supposed to provide correction for. At bass frequencies this problem is not profound, but at treble frequencies it is responsible for added odd-ordered harmonic content which (although in small levels) is something that the human ear uses as loudness cues- in effect a source of unnatural harshness to the human ear.

Negative feedback runs counter to the rules our ears use and we're stuck with the ears we have. If we could eliminate the propagation delays inside audio amplifiers and gain stages, NF would work, but until then Negative Feedback is a failed concept.
High damping factor is allways desirable. Since speakers are a reactive load they respond to the amplifier signal with a counter eletromotiv force that the amp must deal with, and with a low damping factor the amp will have more intermodulation distortion because of this fact. Low damping factor will cause the amp to have more problems in controlling the speakers drivers properlly.
Negative feedback in high levels is quite audible and it doesn't sound good.

Agreed. A badly designed circuit will sound terrible. Most manufacturers try to avoid building unstable circuitry. However, in the pursuit of ridiculously high damping factor specifications (for marketing purposes), it is certainly possible to build a dangerously unstable circuit. Extremely high amplifier gain will lead to instability and oscillations. This occurs when feedback times open loop gain approaches negative one. In this case, the closed loop gain will approach infinity...which is of course not possible and everything becomes oscillatory, distorted and clipped.

In general, typical SS amplifier circuitry (with negative feedback loops), although very linear when operated within tolerance, are not at all forgiving when they are over-driven; typically when over-driven they sound harsh and then damage speakers fairly quickly. Certainly, high levels of negative feedback are likely to lead more quickly to catastrophic behavior.

Since music is very dynamic, it is relatively easy to over-drive equipment. Some SS gear has built in protection circuitry that is designed to detect and protect equipment from damage.
Sean's post above is right on but I would like to add a couple important technicalities.

First and most importantly, amplifiers are tested by STATIC means. This means two things: The test signal is continuous and repetitve, e.g., a sine wave or square wave. Secondly, the load is a resistance and not an IMPEDANCE. The difference between the two gets butchered all the time but basically, impedance takes capacitive and inductive effects into account whereas resistance does not. Many times, people use the word "impedance" but if you take a close look, they are actually using an "averaged resistance" at best. This is incorrect use of terminology but it runs rampant, especially here. :)

The sum total is that music is a very dynamic signal that is constantly changing. The speaker's impedance, in most cases, is a ridiculous mess of ups and downs. Combine the two and you get drastically different damping factors, reflected waves and varying slew rates at different points in time AND for different frequencies. None of this information is faithfully represented by the manufacturer's specs.

But as we already know, you have to listen to get a feel for how an amp/speaker combo works - and that some who measure great, fall short in reality due to poor handling of dynamics. Listening is the best feedback on performance you can get because only then are all the real variables taken into account.

The issue of negative global feedback is different than that of negative local feedback. The two are, again, not to be confused. Global feedback puts the entire amp in the loop whereas local feedback is only for the active devices. This latter one is always required for very good stability but the former is optional, depending on the quality of component matching, parasitic inductances, capacitive coupling, type of active devices and layout quality.

I have looked at the output impedance curves of a few amplifiers using an impedance analyzer. In the frequency domain, most of them are very flat but have an inductive rise at high frequencies (>50kHz or so).

Arthur