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

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?

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.

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