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. :)
Impedence curves of amps is not usually part of the spec's. But, when you read reviews where they have been measured you will usually find them referenced. One of the reasons is that SS amps generally have very low output impedence, well less than 1 ohm. The effect of this is that the speaker will see a very flat electrical signal.

Tube amps are notorious for having high output impedence 'curves' (one of mine has a rise to 3.5 ohms in the mid bass frequencies. The net effect of this is in the frequency where this rise occurs I will hear a corresponding rise in frequency response in the speaker. That's one reason some tube amps sound warmer/looser etc than others, and most warmer than SS. I'm unaware of a loudspeaker spec other than its impedence curve which would be meaningful. What I think (and I really mean think) would be helpful is if your speakers impedence curve dipped in the same frequency that the amps impedence rose they might produce a flatter tone than either would on its own.

Clear as mud? With any luck Sean will read this and sign in with a crystal clear explaination. As I said, FWIW.
I believe you can model the output impedance of an amplifier as an impedance in series with the impedance of the speaker cable and the impedance of the speaker. Thus, Z(total) = Z(amp) + Z(cable) + Z(speaker).

Within their design limits amplifiers are voltage sources, i.e., they will hold the voltage constant. So for a given output voltage the current drawn will be I = V / Z(total).

For Z(amp) << 1 ohm, Z(total) will be determined primarily by Z(speaker) and the voltage drop across R(amp) will be small. Thus, most of the output voltage reaches the speaker. This is the case for typical solid state designs.

For Z(amp) > 1 ohm, Z(total) will not be independent of Z(amp) and the voltage drop across R(amp) will not be negligible. Thus, a smaller fraction of the output voltage will be available to the speaker. This is the case for typical tube designs.

Z(amp) typically increases with frequency. Then for a nominal 8 ohm speaker load, a low Z(amp) will yield a relatively flat frequency response and a high Z(amp) will yield a rolled off high frequency response.

Z(speaker) is also determined by frequency. So, if Z(speaker) is relatively high across the audio band, then a Z(amp) of higher value could be tolerated and still yield a flat frequency response. On the other hand, if Z(speaker) is relatively low across the audio band, then a Z(amp) of low value would be required to yield a flat frequency response.

That's my reasoning. It may be completely wrong.
I'm not an expert on the subject but always heard that solid state amplifiers are low voltage, high current devices and work better with lower impedence speakers (8 ohms or lower), whereas tube amplifiers are high voltage, low current devices and work better with higher impedence speakers (8 ohms or higher; up to 16 ohms). Eventhough amplifiers put out more power into a 4 ohm load vs. an 8 ohm load, when the impedence of a speaker goes lower (4 ohms or less) it becomes an increasing difficult load for many amplifiers. Like Newbee pointed out, the impedence curve varies throughout the freqency range; some 4 ohm speakers, depending on their crossover design, may dip as far down as 2 ohms or even 1 ohm, which is a very difficult load for most amplifiers (except Krells which don't seem to mind). Hope this makes sense.
Output impedance is defined by the amplifiers Damping Factor. It is the ratio of the output impedance to the nominal speaker input impedance or load impedance.

In practice the higher the damping factor the better because cabling and the interaction of the amplifier and load will modify the response as amplifier input impedance rises and damping factor falls. A damping factor of around 100 is worth having if you seek accurate audio reproduction (above this there are still benefits but they may not be audible).

In short, an amplifier with high ouput impedance will be much less linear when coupled with a speaker than one with low output impedance. Warm one resonant bass response is also common with high output impedance amps as the natural low frequency resonance of the speaker drivers are not shunted/damped. (Some seek this warm bass response - in this case a high ouput impedance can be regarded as a tweak to get the desired sound. Some like to change cables to twak the soud an in this case too, a high output impedance amp and may be desirable as it magnifies the affects of cables.)
I agree with most of what Newbee said. Output impedance and speaker impedance together give the damping factor of the system, which is an indication of hte amp's ability to control the speaker. The higher the speaker impedance is over the amplifier output impedance, the higher the damping factor. It would be better, therefore, if your speaker and amplifier impedances dipped in the same spots. This is why many tube amplifiers (especially OTL, like AtmaSphere) like high impedance speakers, in the 8 - 16 ohm range. These are rare today, because solid state amplifiers have such low output impedances, the difference between 4 ohm and 8 ohm impedance has a vanishing differnece on the damping factor, but a solid state amp can put out more power into a 4 ohm speaker than an 8 ohm.
>>a solid state amp can put out more power into a 4 ohm speaker than an 8 ohm.<<

In some but not all solid state amplifiers.
Bob's explanation is a more accurate one than mine. The point is that impedance varies with frequency....therefore the response function of the combined system Amp-Cable-Speaker can vary greatly for amplifiers with high ouput impedance.....not necessaily a simple roll fact the speaker impedance variation with frequency will color the response when coupled with a high output imepdance amp. Newbee describes very well what this means in practice: tube amps often have higher ouput impedance and therefore tend to sound warmer (a non linear but desired coloration to the sound that can help tune a system towards audio nirvanna)

A low amplifier output impedance (very high damping factor) makes the effects of cable and speaker load impedance close to negligible....although an almost imperceptible roll off naturally exists due to skin effect in cabling (higher frequencies see every so slightly more impedance)
Thanks for all the replies.

In short, an amplifier with high output impedance will be much less linear when coupled with a speaker than one with low output impedance.
Shadorne (System | Reviews | Threads | Answers)

Tube amps are notorious for having high output impedance 'curves' (one of mine has a rise to 3.5 ohms in the mid bass frequencies. The net effect of this is in the frequency where this rise occurs I will hear a corresponding rise in frequency response in the speaker.
Newbee (System | Threads | Answers)

From the limited research I've done, these two statements sum up the effect the best.

According to this article, a high output impedance amplifier will contribute to a loudspeaker reproducing music that is out of balance across the frequency range. Frequencies in which the loudspeaker has high impedance will be proportionately louder than those frequencies in which the speaker has low impedance. Therefore, treble could be significantly louder than the midrange, etc, thus contributing to a situation where the speaker seems "bright".

Shadorne touched on the second effect of amplifier output impedance, the damping factor, which has the effect of controlling the motion of the drivers...and therefore "tighter" or "looser" bass.

The article to which I refer above states that:
The lower the amplifier output impedance, the lower the speaker produced voltage is. The lower the speaker produced voltage, the less effect it has on cone motion. A good rule to follow is that amplifier output impedance must be at least ten times lower than speaker impedance for good control of cone motion. This is called damping factor. Amplifier output impedance must be less than one ohm for best performance.

Therefore, if one agrees with the author, an amplifier's output impedance must be less than 1 ohm.

I suppose that answers my question, although I'd like to hear from an expert or two who might specifically state what output impedance measurement is considered too low (X ohm - low), too high (X ohm - high), and just right (X ohm - ideal). Let's call it the Goldilocks Output Impedance Rule.
The idea behind having a low output impedance is that the amp will behave more like a true voltage source. As the output impedance increases past 1 ohm, the amp begins to behave less like a voltage source and more like a current source.

You'll recall that Bob Carver places a 1 ohm power resistor in series with the binding posts labeled "current mode" in his Sunfire amps. He suggests using the voltage mode outputs for the woofer and the current mode outputs for the tweeter. He's trying to make the tube folks happy by purposely rolling off the treble.

You'll also recall that most solid state amps place an inductor in series with their outputs so that they will remain stable into capacitive speaker loads. This inductor causes the output impedance to increase with frequency and yes, the damping factor (defined against an 8 ohm load) will decrease.

From this discussion, we can see that either output impedance and more so damping factor are not very meaningful specs as manufacturers present them. Sometimes even the frequency isn't specified. It would give us more information if at least max and min was specified with their associated frequencies.

Regarding Bruce's article that Tvad referenced (thanks, by the way)... I don't know if his "Audio Reality" book is still available, but it's definitely worth picking up if you can find it.
I have spent most of the past few months designing a couple of loudspeakers specifically intended to work well with high output impedance tube amps. So hopefully what I learned (mostly the hard way) will add to the discussion.

I don't know enough about amplifier design to give a technical description of output impedance. From what I do understand, negative feedback is a means of significantly reducing the output impedance (raising the damping factor); unfortunately negative feedback often introduces audible problems. So, it's often an amplifier design trade-off.

Note that "damping factor" is calculated by dividing the input impedance of the loudspeaker (typically 8 ohms) by the output impedance of the amplifier. So discussions of damping factor are discussions of amplifier output impedance.

For ideal power transfer, the input impedance of the loudspeaker should be many times higher than the output impedance of the amplifier. Let's take Newbee's amplifier with the 3.5 ohm output impedance as an example of what happens with a high output impedance amplifier. We'll assume that the output impedance is 3.5 ohms across the spectrum (Newbee says it isn't, but I don't want to overly complicate this illustration).

Now let's say we pair up Newbee's amp with an "8 ohm" speaker whose impedance curve has a 40-ohm peak in the bass region, dips to 4 ohms in the midbass, rises to 20 ohms at the 2.5 kHz crossover, and gradually falls back to 8 ohms in the high treble. Assuming this speaker has a perfectly flat frequency response curve when driven by a low output impedance solid state amp, here's what will happen when it's driven by Newbee's amp:

The speaker/amp combination will have increased energy in the deep bass because the amp will deliver more than its 8-ohm rated power into the bass impedance peak, perhaps as much as 3 dB more. It will deliver only about half its rated power into the 4 ohm midbass dip, so we'll see a good 3 dB dip in that region. Into the high impedance in the crossover region we'll once again see increased output, maybe about 2 dB more. Since the impedance remains above 8 ohms across the treble region, the SPL will be remain slightly elevated in the top half of the spectrum. Overall, not a pretty sight. The increased deep bass energy might be beneficial, but above the bass region the net effect is clearly detrimental.

One solution would be to choose a loudspeaker that has frequency response dips in regions where the impedance curve has peaks, so that with a high output impedance amplifier the net effect will be a smoothing of the frequency response. Based on eyeballing frequency response and impedance curves, I think that Coincident and Silverline use this approach. Actually, I suspect that the designers used high output impedance tube amps in the design stage, but when SoundStage or Stereophile measures the frequency response they use a low output impedance solid state amp so we don't really see the frequency response that the designer intended.

Another solution is to keep the impedance curve as smooth as possible, so that the speaker's frequency response doesn't vary much with amplifier's output impedance. Obviously in the example above, if we'd used a "6 ohm" speaker whose impedance stayed between 4 and 8 ohms above the bass peaks, the result would be a much smoother frequency response than we got with our hypothetical "8 ohm speaker". The Reference 3a deCapo uses this approach, and according to SoundStage's measurements its impedance varies between about 5.5 and 11 ohms. Also, the 11 ohm maximum in the lower treble is in a region where the speaker normally has a frequency response dip. No wonder people with SET and OTL amps like it.

High amplifier output impedance certainly presents challenges in loudspeaker matching, but the reduced high order distortion (introduced by the high levels of negative feedback usually needed for ultralow output impedances) is in my opinion quite desirable. An in-depth study of distortion perception recently published in the Journal of the Audio Engineering Society points towards the same conclusion - namely, that high levels of low-order distortion are audibly insignificant while low levels of high order distortion tend to be quite audible and objectionable.

Bob and Duke, thanks for your great replies. Very helpful.

Still, no one has answered my basic question:

"What amplifier output impedance measurement is considered too low (X ohm - low), too high (X ohm - high), and just right (X ohm - ideal)?"

As an analogy, I know that a loudspeaker with an 8 ohm impedance is "just about right", given that a flatter impedance curve is more desirable than one that fluctuates wildly. Still, an 8 ohm nominal loudspeaker is a safe choice to be driven by a wide variety of amplifiers. On the other hand, a 4 ohm nominal loudspeaker starts to eliminate some amplifiers from contention, and a 12 ohm nominal loudspeaker opens up the possibility of mating with a wide variety of amplifiers.

So...what measurement of amplifier output impedance is analagous to these loudspeaker examples?

If you accept solid state amplifier technology and you do not desire to tweak the sound and wish for a tight controlled bass and wish to simplify it to a damping factor then I would say 80 is adequate and perhaps an ideal number.... i.e. for an 8 ohm load the amp should have an output impedance of of around 0.1 ohms. There is very little to be gained with even lower impedance and probably not audible anyway unless the speaker impedance drops very low.

BTW: This discussion applies to equipment input impedance too.....ideally you want a high input impedance (nominally around 10K Ohm) on all equipment prior to your speakers or headphones. This reduces the effect of interconnects and coupling of equipment in your system to almost negligible levels.
Duke, are you suggesting that amplifier impedence has a contstant value accross the spectrum, or were you only trying to simplify your explaination? You've confused the half of my brain I have still have left, I think! I thought amp output impedence was a varible over the frequency range.
Hi Tvad,

Sorry I completely overlooked your basic question.

I'm going to answer your question a little bit different from the way you asked it, and the numbers I'm pulling out of the air are somewhat arbitrary. I think whether or not an amp has "too low" and "too high" of an output impedance depends on the speakers as much as on the amplifier.

If the amplifier has an output impedance of .1 ohms or less (damping factor of 80 or more), I think it will have a flat frequency response into any speaker in production today. This may or may not be desirable! Many very high efficiency speakers have weak bass, but a relatively high impedance in the bass region, so they rely on an amplifier with a high output impedance to "warm up" the bass and restore proper tonal balance.

Between .1 and 1 ohms output impedance, the amplifier will work well with most speakers that do not rely upon high output impedance to warm up the bass.

Above 1 ohms output impedance, I think you better start looking at the speaker's impedance curve as well as its frequency response curve.

Above 4 ohms output impedance, the speaker's impedance curve is very important. Now as mentioned above, some speakers will definitely sound better when paired with an amplifier having a very high output impedance.

I think it's a good rule of thumb to avoid a speaker/amp combination where the speaker's impedance dips down to or below the amp's output impedance.

In practice, with most speakers the answer to your question is that there is no such thing as too high of an output impedance; only too low. With a few speakers, there's a "just right" range, but it varies from speaker to speaker.

I mentioned before that an amplifier may be trading off other sonic qualities to achieve a very low output impedance. Let me illustrate with a story involving the Wolcott monoblocks, which are push-pull tube amps with a variable output impedance control. On SoundLab electrostats at least, too low of an output impedance causes the sound to become dry and the soundstage depth to collapse. Unfortunately the variable output impedance control isn't marked so I don't know what value I'm choosing by ear. But at least in this case there are sonic tradeoffs to very low output impedance that I do not like.


I don't really know what amplifier output impedance curves really look like, and was just using an imaginary "flat" curve for my illustration. Capacitive or inductive behavior would of course change that.

Do you know what the output impedance curve on your amplifier looks like?

Thanks again Duke, that helps.

I have noticed the variable output impedance control on the Wolcott amplifiers. How cool is that?!
Tvad, I think the 10X rule of thumb for impedance matching between preamp and amp might be applied to the amp/speaker interface as well. I'm not sure how the larger current would affect things though.

Newbee, you are correct. Output impedance is a function of frequency. For solid state amps I think it is determined by the output inductor.
Duke, No I don't and I don't have the means to measure it.

Some years ago when it was reviewed in 'phile JA commented that its output impedence 'rose' to 3.5 ohms in the bass region. I noticed this particularily because I had some electrostats which had a impedence droop to 3.5 ohms in the bass region. In use I 'think' they complimented each other as I had a very flat in room response (except for a 32hz room node induced rise of 6db) with the combo and no other major frequency abberations.

Facinating stuff.... :-)
Damping factor has less effect on a speaker than most might imagine. Keep in mind that any waveform will cause an amplifier to produce power (and incidently, it is *power* that drives all speakers- voltage cannot be produced in the absence of current and current cannot be produced in the absence of voltage...). That power will cause a voice coil (or other motive mechanism) to obtain a particular location with respect to rest. As the power level changes, the VC will follow it- in effect power driven to excursion and back again. Damping factor only plays a minor role.

What is really happening is that we are able to hear what negative feedback does to sound. Too much (more "damping") and the sound dries up, too little and with *some* speakers you loose flat frequency response.

In general tube amps have less feedback and many have none. This is not because it is not somehow available (this is the 21st century after all and we *do* have the technology). The problem is that feedack is a failed concept and many designers recognize that.

IOW having a 'constant voltage' output characteristic is a thought model and does not have a basis in the real world where our ears exist. As humans we are often looking for ways to place things in neat cubbyholes but Life itself does not care what we think- it exists in spite of our thought. Feedback and constant voltage are examples of cubbyholes that are thus not actually real.
Atmasphere, "voltage cannot be produced in the absence of current". Are you sure about that?

The electrical potential (voltage) exists whether there is a load or not (whether current flows or not). Potential energy is real.

And actually it is the current flow that creates the magnetic field that causes the speaker driver to move. That motion will dissipate power.

And claiming that feedback is a failed concept seems ridiculous. Anyone that practices design knows that many aspects are double edged. Design/engineering is about balancing trade-offs as I'm sure you know.

And you'll have to explain "a 'constant voltage' output characteristic is a thought model and does not have a basis in the real world where our ears exist" cuz I'm not following it.

And yes humans compartmentalize knowledge. It's simply matter of efficiency.

Kind regards.
What is really happening is that we are able to hear what negative feedback does to sound

negative feedback just ensures linearity - it makes sure that the output matches the input. An electrical circuit operates at close to the speed of light...I doubt anyone can hear negative feedback in modern circuitry. Slew rates of good amps are typically 50 volts per micro second or enough to accurately reproduce a signal of well over 100 KHZ without distorting the signal. Since it is accepted that people rarely are able to hear anything above 20 KHZ then it is extremely doubtful that any slight anomalies of this kind of order are actually audible.

Speaker cones will try to keep moving because of inertia, the suspension pulls them back and as they move they induce current (EMF) in the coil which the amp will sense and will dampen by driving the output to match with the input. Provided the drivers have low mass, a high Xmax and a strong magnet then a powerful low output impedance amp should be able to control the driver well. If the driver is low quality, with a weak magnet and a low Xmax then it doesn't matter as much if the high powered amp has a high damping factor as the cones become harder to control as they travel well outside the linear range of the magnetic this case, ultimately, the suspension pulls them back in but unfortunately at this point you have large amounts of audible distortion).
Negative feedback in high levels is quite audible and it doesn't sound good. Most of it can be avoided to a great extent IF the circuit is properly designed and parts are very carefully matched. Most parts aren't matched all that precise and the attention to circuit lay-out ( nominal impedances ) aren't as widely used as one might think.

Voltage source output stages are available. As i've mentioned before, one should be looking at what the amps clip at as impedance varies, NOT the manufacturers rated power specs.

A high damping factor doesn't mean that the amplifier has more control over the speaker. What it does mean is that the variances in impedance that a typical loudspeaker produces as frequency is altered is less likely to modulate the output stage of the amplifier. There are quite a few other factors involved in this equation though, so don't always assume this to be true.

A high damping factor also means that the amp is more likely to act as a voltage source i.e. "double down" so long as the rest of the support circuitry ( primarily the power supply ) can deliver the goods. Many amps simply don't have enough power supply to get the job done as impedances are lowered. This is why i said that one should look at the power at clipping as impedance is varied, as clipping strains the entire amp quite thoroughly.

A very high damping factor is typically found in amps using GOBS of negative feedback and / or negating emitter resistors on the output devices. Gobs of negative feedback makes the amp sound hard and sterile. Think of late 1970's and early 1980's transistor gear that measured very good ( in terms of THD ) but sounded like hell.

The lack of emitter resistors makes the amp far more likely to blow up. When this type of output stage goes down, they typically do massive damage to the speakers. This is besides taking out the entire bank of output devices for that channel, making it more expensive to repair.

The original Phase Linear amplifiers are a prime example of this this type of design. They used quite a bit of negative feedback with no emitter resistors. Damping factor was rated in excess of 1000 into an 8 ohm load. In English, this means that the output impedance of the amp was less than .008 ohms according to the manufacturer.

When these amps "let loose" due to some type of malfunction in the output stage, they would quite typically light speakers on fire. This is how they got the nick-name of "Flame Linears". If using one of these amps, i would proceed with caution for the above reasons. Sean
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).

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.
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.
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.
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
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?
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.

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.
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.
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
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.

Atmasphere, not to belabor the point or insult you, but to be precise Ohms law does not apply because there is no load. Please review any college physics text for an explanation of electric potential. A practical example is a battery.

Kind regards,
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).
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 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!
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
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?
Benie, my question was not about low impedance speakers.

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.
Shadorne- Yes. This is a major reason why tubes continue to be popular- they create less loudness cues.
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

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: 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

* 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.
Thanks for that, Sean.
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 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
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
* 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.