Please explain amplifier output impedance

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.

Duke

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.

Duke

Newbee,

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?

Duke

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

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

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