transformers/output impedance

I'm confused, or is it a question accepted that the use of output transformers for tube amplifiers, aims to lower the output impedance of the same, to match with the impedance of the speakers? However, how can a passive device (transformer) influence the output impedance of an active amplifier unit? I say that the output impedance is a characteristic of the amplifying machine, and transformers only optimize the ratio of its ability to deliver current, with the current requirements of the speaker, easily translated by its impedance
Transformer is basically an impedance converter. To set proper conversion ratio we need to know speaker's impedance and recommended tube "plate load impedance". If we don't know speaker's impedance we can measure DC resistance and multiply it by about 1.25 (impedance is mostly resistive). Plate loading we can find in tube's datasheet (or plate-to-plate loading impedance in Push-Pull configuration).
We need our transformer to reflect speaker impedance (secondary side) to plate loading impedance (primary side). Transformer impedance ratio is a square of turns ratio.

Example: Plate load impedance is 10,000 ohms and speaker impedance is 4 ohms. Necessary transformer impedance ratio will be 2,500. Turns ratio will be square root of 2500 = 50. Voltage and current ratios will follow turns ratio. Secondary voltage change will be 50 times smaller than primary but secondary (speaker's) load current will be 50 times smaller on primary side.

As you can see it would require very big voltage changes on primary to get decent output voltage, hence power delivered to speaker. We can lower this ratio by finding tubes operating at lower plate loading impedance or to put tubes in parallel.
Thank YOU,
In your example, we say this
is a transformer 1-50? The final voltage, after transformer will decrease 50 times, but amperage will increase 50 times. The power (watts) will remain the same.
The same power, but with an lower output impedance?
160562 .... you are wandering in the same technical mind (pun intended) field that I found myself. What Kijanki said is spot on. You may find it helpful to retrace the steps I have taken to avoid the land "minds" I stepped on by pulling some of my posts.

One interesting post in particular dealt with "back impedance matching." IOW, output trannies work both ways. The output tranny steps down output tube voltage and impedance characteristics to the match speaker load. At the same time, a speaker's impedance characteristics, which vary as a function of frequency, are stepped up on the primary side of the tranny. This is the load the output tube "see."

As Ralph (Atmasphere) and Al (Almarg) have explained, output tubes operate best (i.e., low distortion and power delivery) if presented with a load (impedance) that falls within the tubes "sweet spot." Since speaker loads vary as a function of frequency, the output tubes may operate outside their sweet spot. If so, power delivery and distortion may suffer to some degree.

The optimum solution: if using a tube amp, (i) select speakers with a ruler flat impedance curve that corresponds to the output taps (e.g., 4, 8 or 16 ohms; preferably 4 or 8), (ii) )zero phase angle characteristics and (iii) high sensitivity. Good luck with finding a speaker possessing all of these characteristics at the same time ... and that sounds good.

Bottom line: life is about compromise and trade-offs. Ce la vie.
That's right, except for the losses in transformer. This impedance cannot be simply measured with ohmmeter because transformer does not operate at DC but behaves according to ohm laws for the CHANGES in voltage. It is called reflected impedance. Transformer has to be large enough to carry desired power. Cross section of the center of the core is proportional to square root of power and is roughly 1 square inch for 50W (for 200W it will be 2 sq inch etc.). We want as few turns as possible to avoid losses in copper but we have to provide minimum number of turns per volt. This number is inversely proportional to square area of the core and is smaller for large transformers. Knowing maximum voltage and turns per volt we can establish absolute number of turns. We select core material, size and number of turns to prevent core saturation, when magnetic flux is higher than max flux density rated for given core.

All this is also related to frequency. It is easier to saturate transformer at lower frequencies and it has to be taken into account for size of core and number of turns per volt.
Absolutely right Bifwynne. That's why audio is more of the art than science. We can calculate but have to match and listen.
Thanks Kijanki. As I have come to appreciate, there are so many design considerations and trade-offs going on, at some point, amp design is about acoustic philosphy and art. Ergo why Ralph (Atmasphere) opted for the OTL amp topology.

As a consumer, though difficult, IMO, it is incumbent on me to at least understand enough of the theory so I can make as an informed a choice as possible when matching components. Admittedly, it has been a verticle learning curve, marked with many missteps and dead-ends.

Bifwynne, some people believe that transformers and capacitors have no place in signal path. Eliminating output transformer is nice but requires some descent output impedance to drive speakers and it is usually achieved by placing a lot of large tubes in parallel. Unfortunately heaters take a lot of power. 6AS7G that Atmasphere was using takes 2.5A at 6.3V =15.75W per tube. 20 tubes will dissipate 315W. If you prefer stereo listening it will be 630W. Adding main circuit will result in more than 1kW - a space heater (nice in the winter). On the other hand we audiophiles are eager to sacrifice for great sound, and I've heard it is great.
Gotcha Kinjanki. I'd love to hear one of Ralph's OTL amps, but part of my verticle learning curve of bad choices is that I bought speakers that were designed and voiced to be driven by a low output impedance, high power, high current SS amp. I'm dumb-arsed lucky that my ARC Ref 150 has a low'ish output impedance, especially off the 4 ohm tap, and has a large power supply (1040 joules), so it can deliver some serious juice when needed.

Unfortunately, I am dubious (albeit not certain) that one of Ralph's amp would be a good match for my speakers. If Ralph thinks differently, he should of course chime in and correct my misconception.

You also need to consider the negative feedback if any around the amp, it too will lower the the output impedance and speed up it's precieved HF bandwidth.

Feedback can make a very average quality output transformer look reasonable, at the expense of less gain and some stablity, also some believe that the lush tube midrange can suffer as well, but maybe it's just the tighter bass because of the lower output impedance that takes away a bit of that midrange bloom.

A good test for an output transformer is to see it's bandwidth and damping factor (output impedance) with the feedback removed, this btw also increases the gain and can also make the amp more stable.
Really well made output transformers don't need feedback unless they have to drive harder speaker loads.

Cheers George
I agree with George's point in regard to output transformers. The really good ones can avoid the need for introducing NFB, if one choses to use easy to drive speakers. While I appreciate the sound reasoning and theory of eschewing the output transformer, the very best sounding tube amplifiers I've heard all utilize them! So definitely "art" plays a large role in designing audio components.
Thank you all,
Is nice that when I start this thread I was thinking in preamplifiers, even if I did not say, because it was easyer to introduce the subject talking about amplifiers.
Now I can say, The more we learn, the long we know the way is
To clarify a few points made immediately above:

Negative feedback has only a minor effect on high frequency bandwidth. This is because HF bandwidth is a function of the risetime (or slew rate) of the circuit, which will not be affected by bandwidth. However, there is a *perception* that it has this effect, because feedback will add trace amounts of odd ordered harmonic distortion, which is perceived as brightness by the human ear.

Transformers do indeed transform impedance, and in *both* directions. So if for example a 16 ohm tap is loaded with a 4 ohm load, the power tubes will see a load that is considerably lower than they will be able to drive properly. Distortion will be higher and output power will be lower. This is why its important to select the right tap.

The use of feedback has little to do with the transformer, and everything to do with the linearity of the amplifier circuit that precedes it. Usually the driver sections are fairly linear, but output sections may not be if tetrodes or pentodes are used. It is this reason that feedback is used rather than the choice of output transformer.

Almost any transformer currently in use in a hifi amp is capable of operating in a design without feedback. Again, feedback will not have a large effect on improving bandwidth of the transformer due to the demands that would be made on the preceding circuitry.

IOW, the reason you see zero feedback tube designs is not because a transformer is particularly suited for it, more so it has everything to do with the linearity of the circuitry preceding. In Charles1dad's case, his amps have triode power tubes which are inherently linear- no need for feedback.

To be clear, the use of a transformer can indeed reduce the output impedance, but there is a myth that adding loop negative feedback will too. It doesn't. I'll explain that further if anyone asks.
To be clear, the use of a transformer can indeed reduce the output impedance, but there is a myth that adding loop negative feedback will too. It doesn't. I'll explain that further if anyone asks.

That is what I always felt and have taken a lot of flack for it. I think a little further explanation would help a lot of us Ralph.
Ok Ralph .. you offered. Please do. :)

Perhaps you might also touch on the what is meant in plain English when ARC says its amp's "[o]utput stage coupling is a combination of “ultralinear” and Audio Research’s patented 'partially cathode-coupled' topology ...." From what little I can glean from the description, it looks like some variant of local feedback. That's just a guess.
Gentlemen, what Ralph appears to be referring to regarding the relation between feedback and output impedance was discussed extensively in this thread, beginning with the post that the link opens at.

Best regards,
-- Al
P.S. to my last post. Was thinking to myself that if zero negative feedback is so disadvantageous, why would top flight companies like ARC use it???

This is just a guess ... so here goes. Perhaps simply stated ... NF is used to reduce the output impedance and increase DF for **marketing** purposes.

As Ralph and Al have explained many times already, the world of tube friendly, true Power Paradigm speakers is not as large as Voltage Paradigm friendly speakers. So .. using NF to reduce output impedance and increase DF increases the playing field of speakers that may be compatible. That's my thesis.

Perhaps a good case in point is the match with my amp and speakers. Technically speaking, my speakers are poster-child "SS-amp" friendly speakers because they have rough impedance and negative phase angle functions. Yet my ARC amp manages to muscle its way through the tough spots with a modicum of aplomb.

I am somewhat dubious that a true Power Paradigm amp having a "high'ish" output impedance would do as good a job. Not because of design, build or sonic deficiencies. But just because of the "high'ish" output impedance. At the very minimum, all other factors being equal, there will be a tipping point where acoustic coloration will outweigh reduced NF induced distortion (e.g., TIM and odd-ordered harmonics).

I don't know how most Power Paradigm amps address power supply issues. I suspect that access to lots of joules can only be a good thing when the amp is being tasked to deliver current when called upon.

This post is just a bunch of guesses. So please don't come down hard on poor little me. Perhaps Ralph who is in the business can speak to the bona fides of my surmises.

Hi Bifwynne, first you are correct that the cathode cross-coupling thing you see in ARC amplifiers is a form of negative feedback. I've used this a lot when modifying Dyna ST-70s. I think the oldest amp I have seen with that was employed in a Leslie organ speaker made in the 1950s.

To your second point- the highish output impedance of a Power Paradigm amplifier (SETs being a good example) may or may not be a problem, based entirely on what speaker you are using. You may recall in that article I wrote on the subject that I mentioned that the two design approaches can't be mixed or else you wind up with tonal anomalies (due to the voltage response of the amp on the speaker).

This is why horns had such a bad reputation for so long- their crossovers were designed for amps with a higher output impedance, and so the older ones in particular can sound 'honky' as drivers in the system can be trying to operate outside of the passband the designer had in mind.

Conversely, a choke in series with a woofer is supposed to cause the woofer response to fall off at a certain frequency, but if the amplifier output impedance is high, the amplifier power will not drop off in the way that it is supposed to, causing the woofer to play higher frequencies than the designer had in mind (this would be an example of a Power Paradigm amp being used with a Voltage Paradigm speaker).

Regarding the output impedance (for those that did not follow the link Al dropped), its pretty simple. Amps with a lower output impedance can drive lower impedance loads with greater ease than amps with a higher output impedance. I think we all understand that simple fact.

So if we add feedback, will that cause the amplifier to make more power into lower impedances? The answer is 'no'. You get more power into lower impedances by having larger heatsinks, larger power transformers, larger output transformers, more tubes, etc. You can't get more power out of an amp by adding feedback- that would violate a fundamental rule of electronics known as Kirchoff's Law.

IOW, the term 'output impedance' as we generally understand it in audio is a 'charged term' in that it has a meaning that only works inside the Voltage Paradigm in audio. Anywhere else the term refers to the internal impedance of the output circuit, whatever that might be.
Al and Ralph, I reread Ralph's explanations in the other thread. I understand a little bit better why using the term "output impedance" is a bit of a misnomer. Maybe the industry could sex-it-up by referring to the attribute as "synthetic" or "apparent" or "hypothetical" output impedance.

I think the point that Ralph was trying to make is that using a meter to measure an amp's impedance/resistance at the output taps is **not** what the term "output impedance" is speaking to. Instead, it's referring to the amp's operational behavior in delivering current/power to a speaker load **as though** it's output impedance was a specified number.

Where an amp's "apparent" output impedance is close to zero, one could expect that the amp would double down current/power if speaker load is halved, but only if it is acting like a true constant voltage source, and **only if the amp is performing within its operational limits.**

And ... as Ralph said, using NF only permits the amp to perform in such a fashion. Ergo why the use of the term "output impedance" without an additional adjective is a bit of a misnomer, almost misleading.

I guess in a goofy kind of way, if a designer kept adding NF to the circuit, at some point, the NF could be greater than the current/power being delivered by the main output circuit. This may be what Ralph meant when he said that NF could also be viewed as a voltage source.

Well, maybe I still don't get all of it, but maybe a little bit more than I did before. This still makes amp/speaker matching a tricky business.
Output impedance and ability to drive low impedance are two different things. My amplifier has DF=4000 at low frequencies but cannot drive speakers below 3 ohms.

I cannot speak of tube amps but in SS amp feedback always reduces output impedance. I made this small example a while ago as a proof:

Let’s take amplifier that has gain of 30 (31.6dB). When input voltage is 1V output voltage is 30V. Output voltage drops (for whatever reason) 1V under 1A load to 29V. That's 1ohm output impedance (DF=8).

Now, let's build this amp with gain of 300 but feed 3% of the output voltage back to the input in opposite phase. As a result amplifier’s output is the same 30V as before but input is the difference between 1V and 3% of 30V = 0.1V Let’s verify (1V-0.03*30V)*300=30V

Let’s load this amplifier with 1A. Our voltage drop inside is still 1V under 1A load, but output voltage will be higher than 29V because we subtract less from the input. Output voltage will be 29.9V and output impedance will be 0.1V/1A=0.1ohm (DF=80). Let’s verify. (1V-0.03*29.9V)*300-1Vdrop=29.9V.

Output impedance dropped 10 times. Expression 1+B*Aol is known as “Improvement Factor”. In our case B (“Feedback Factor”) = 0.03 (3%), Aol (“Open Loop Gain”) = 300 thus Improvement Factor = 1+0.03*300=10

Adding NFB WILL add more power to lower load impedance because output impedance is lower. I'm sure Ralph has maximum power in mind.

It is important to realize that it doesn't matter in above example why voltage initially dropped by 1V at 1A load. It could be output impedance or bandwidth limit (or anything else). NFB will reduce output impedance, increase bandwidth, improve linearity - hence THD and IMD.

I think the point that Ralph was trying to make is that using a meter to measure an amp's impedance/resistance at the output taps is **not** what the term "output impedance" is speaking to. Instead, it's referring to the amp's operational behavior in delivering current/power to a speaker load **as though** it's output impedance was a specified number.


I'm sure Ralph has maximum power in mind.

Correct. The maximum output power will be a function of the internal impedance of the output stage. Its Ohm's Law after all :)