High damping without feedback: how and when…

The previous articles I published on this topic have sparked the curiosity of several readers who privately asked me for more information on this thorny subject. The articles I am referring to (which I recommend reading) are these:

To summarize, the point is that although the hi-fi press and various tube audio gurus keep stubbornly spreading the myth of the zero-feedback amplifier as the only way to achieve good sound, the reality I see is that many people are dissatisfied with the sound of their equipment or the gear they sell. These gurus and the hi-fi press have demonized everything that uses feedback, pushing manufacturers to follow the trend, but in doing so they have narrowed the range of available choices to the point where many people abandon this world entirely or move to solid state because they are no longer willing to spend money on equipment they find disappointing. This has restricted the market to hyper-expensive gear, often of questionable merit, and the clientele to a niche of people who are too often extremist and fanatical. And it doesn’t end there because this madness is starting to affect the solid-state world too, as zero-feedback transistor/FET amplifiers are popping up here and there. Manufacturers are blinded by the prices extremist customers are willing to pay, losing sight of the far larger numbers of the general public.

I have already shown, in my own small way, that using very high-quality transformers together with moderate and well-designed feedback can lead to amplifiers with unique sonic qualities that are highly appreciated even by those who have been listening to music for decades and who until now have dismissed certain technical solutions because they were demonized everywhere in tube audio circles, only to be surprised by what can be achieved when things are done properly, reaching results once considered impossible or long sought after in zero-feedback tube amplifiers by endlessly swapping valves without ever achieving the desired outcome. But the gurus continue their mad rush towards the abyss, losing customers after bleeding them dry, ruining equipment, ruining the market and the credibility of an entire sector.

The question that a site visitor asked me was:

With a high budget, would it be possible to design and build, for example, a single-ended triode amplifier with no feedback at all, neither global nor local, that still sounds good? To be paired with high-sensitivity speakers that are easy to drive?

I want to point this out because the question once again proves the proselytism of the gurus who say that if you want something to sound good you must spend a lot and the project must be done “properly”. Yet no one explains how a project needs to be done to be considered “proper”, and above all, I have more than once seen equipment sold for several thousand euros (not necessarily Chinese) with so many functional flaws that I had to tell the customer that to make it sound good, it would have to be rebuilt from scratch, throwing everything away including the transformers… Because I am honest. Other “technicians” they visited before me simply took their money selling them valves that were supposed to fix everything but fixed nothing, because if the circuit is wrong no valve can solve the malfunction. The others made money selling a bag of valves, while I told the truth and earned nothing, but in the long run these people will pay for their dishonesty, or at least one hopes so, because there is still a large group of users who love to constantly change equipment and valves.

So, going back to the question above, my answer is that you just need to make a properly designed circuit with a correct use of feedback to achieve excellent results. As I explained in the articles linked above, the biggest problem of the absence of feedback in an amplifier is the very low damping factor and all the sonic issues it causes, especially when the amplifier is paired with speakers that have high inertia (large-diameter cones) and/or reflex ports.

The real question is therefore:

Is it possible to have a decently high damping factor in a tube power amplifier without using feedback?

As I have already mentioned in other articles, the “natural” damping factor, that is, the damping that the output stage shows even without feedback, depends 50 percent on the output transformer and 50 percent on the output tube, or more precisely on the internal resistance of that tube. The characteristics of the output transformer are in turn largely linked to those of the tube, so in the end one could say that, if the transformer is almost a compulsory choice, the responsibility for the final result in terms of damping depends mostly on the tube, and driver circuitry has nothing to do with it. Everything therefore depends solely and exclusively on the internal resistance of the output tube, on its operating class (class A or AB), and on the transformer turns ratio.

As already stated in other articles, the Damping Factor is simply a way to assign a “score” to the output resistance of a circuit, or Rout. In fact, the DF value is obtained from the Rout previously calculated using the formula: DF = L/Rout, where L is the value of the load. Feedback is nothing more than a way to lower the Rout of a circuit.

In the case of a tube amplifier, theory states that if one wants to increase damping without using feedback, it is necessary to use a tube that inherently has a very low internal resistance. But which tubes are suitable and which are not? Generally speaking, for the no-feedback damping approach to work, you need tubes with internal resistances lower than 200ohm, or you need to put tubes in parallel to reach a combined Ri low enough. Parallel single-ended is discouraged because the transformer suffers from DC and has higher losses, while a push-pull configuration in class A turns out to be the best solution.

Therefore the tubes must be triodes or pseudo-triodes, and the range of suitable choices is limited to 6080 / 6AS7 / 6336 / 6C33 and their equivalents… (anyone who knows other tubes with similar characteristics is invited to mention them in the comments).

All the other tubes, even the well-known and beloved ones praised by audiophiles, including the much-loved 2A3 / 300B / 845 / 211, have Ri values that are too high and, when used with zero feedback, end up with extremely low damping factors, never higher than 2 or 3 (and anyone claiming high damping factors with these tubes, zero feedback, is simply lying).

Theoretical Zero-Feedback Damping Calculation

Given this theoretical circuit:

We have a transformer with a turns ratio “n” made of a primary and a secondary winding; both windings have a parasitic resistance RDC1 and RDC2. The RDC1 must be considered in series with the Ri of the triode, while RDC2 must be considered in series with the loudspeaker. Rout is calculated with this formula:

((Ri+RDC1)/(n*n))+RDC2

How do we calculate the turns ratio?

Square root of Imp.Pri/Imp.Sec

Where both primary and secondary impedances are expressed in ohm.

Let us assume the triode is one section of the 6336A with an internal resistance of 330ohm, the transformer RDC1 is 80ohm, RDC2 is 0.3ohm, primary impedance is 3k and secondary 8ohm, thus the turns ratio is: 19.365:1

((330+80)/(19.365*19.365)) + 0.3 = 1.39ohm
Equivalent to a damping factor DF of “L/Rout”, that is 8/1.39 = 5.7 (just acceptable)

What happens if we modify the transformer to have a 4ohm secondary instead of 8? The turns ratio becomes 27.386:1, while RDC2, which was about 0.3ohm, becomes about 0.2 (not 0.15… be careful, the windings do not double from 4 to 8ohm!) so the formula becomes:

((330+80)/(27.386*27.386)) + 0.2 = 0.746 (rounding decimals)
Equivalent to a damping factor DF of 4/0.746 = 5.36

So the damping does not change when switching between the various transformer taps; the slight difference between the two calculations comes from rounding, which disproves the claim of some nonsense-spewing individuals that damping is different if you use an 8ohm speaker on the 8ohm tap rather than a 4ohm speaker on the 4ohm tap.

What happens if we use a very famous and fashionable 300B with an Ri of 740, with a classic 3k transformer, ratio 19.365, RDC1 of 64ohm and RDC2 of 0.09ohm…

((740+64)/(19.365*19.365)) + 0.09 = 2.234
DF 8/2.234 = 3.58 (insufficient)

Let us continue to have fun: someone who cannot calculate or measure claims to have PSE amplifiers with 845 tubes and damping factors allegedly in the three digits. The Ri of the 845 is 1700ohm, divided by 2 because there are 2 tubes in parallel: 850ohm. Same 3k transformer but much larger than the one used with a 300B because of the higher power, thus with higher RDC… I do not even need to calculate it, it is obvious that the damping will be much lower than 3.5…

Now that I have demonstrated that with the fancy famous tubes you go nowhere in terms of zero-feedback damping, let us return to our 6336A. What happens if I use a transformer with 5k primary instead of 3k? The turns ratio is 25:1 and let us assume an RDC1 of 100ohm (hypothetical value).

((330+100)/(25*25)) + 0.3 = 0.988ohm
Equivalent to a damping factor DF of “L/Rout”, that is 8/0.988 = 8.09 (absolutely excellent damping factor)

It may look like we have found the Holy Grail, but unfortunately these were all theoretical calculations assuming an ideal transformer with zero losses, thus with an energy transfer of 1 between primary and secondary. Unfortunately, in real transformers energy transfer is always less than 1, so there is an additional “phantom” resistance in series with our circuit that you can imagine inserted between primary and secondary, in the magnetic domain. The electrical energy passing through the primary is converted into magnetic energy that is transferred to the secondary and then again into electrical energy; in this triple conversion process (electrical/magnetic/electrical), there are unavoidable losses that can be imagined as an additional resistance in series with the circuit.

The second problem is that by increasing the primary impedance of the transformer, the load line seen by the tube becomes much flatter, so there is a drastic decrease in the power transferred to the load. One could compensate for this problem by shifting the operating point to a much higher voltage, but by their nature tubes like the 6080/6336 etc. cannot withstand very high plate voltages. The 6336A datasheet indicates a maximum plate voltage of 400volt, but this is under “absolute values”, which means it is not advisable to operate it this high… it must be the upper dead point where the load line ends; the idle point must therefore be much lower. Some more chances could be had with TV line-output tubes connected as triodes, which can handle much higher voltages and therefore higher impedances, but they also have much higher Ri, so in the end you probably still end up stuck and unable to go much further without feedback… Let us try to calculate what happens with a single-ended 845 on a transformer with 12k primary, ratio 38.73, RDC1 217ohm, RDC2 0.22

((1700+217)/(38.73*38.73)) + 0.22 = 1.498
DF 8/1.498 = 5.3

As it clearly appears, we are always around the same values, and trust me, no one can break the laws of physics, except maybe God… and the scam artists who write such things, but those are just a bunch of lies. I would also like to point out that RDC2 is very important for the final result: it is therefore a good thing that the secondary winding has the lowest possible DC resistance, otherwise it compromises the damping factor. Therefore, it is good practice that all sections of the secondary are connected in parallel when possible, which goes against what some individuals claim, saying that secondary sections must be connected in series because the voltages would not be equal between the various sections and they would fight each other and distort blabla… if you wind them poorly with different numbers of turns you will surely have problems, if not, it is just paranoia, like many other pointless things one reads from these people.

The push-pull dilemma

And how is the damping calculated in push-pull? This topic has sparked a war among gurus… In push-pull, should the 2 tubes be considered in series or in parallel? The gurus say in parallel, but unfortunately they are wrong. In push-pull the calculation remains the same, but the internal resistance of the 2 tubes is added. Ignoring the transformer winding resistances, the equivalent circuit can be imagined like this:

To measure the output impedance you must short the two equivalent generators that simulate the two tubes (in practice you null the audio signal at the amplifier input). The output impedance is what you see from the amplifier output looking into the secondary, and it is equal to the series of the two internal tube resistances referred to the secondary. And this is not because the tubes operate in opposite phase, but because the primary is physically connected in series with the tubes.

Someone might think that the circuit to be considered should actually be this:

It may seem that the capacitor in the schematic could change things, but it does not: in a class A push-pull amplifier, the signal currents in the two halves are equal and opposite, so no signal current flows through the power supply. It is well known that in a class A push-pull amplifier the power drawn from the power supply is constant and does not depend on the audio signal amplitude, precisely because the audio signal current does not flow through the power supply capacitor.

Let us look at a practical application

A customer asked me to wind a 6kAA transformer to use with the two sections of a 6336A in push-pull class A, precisely to experiment on this theory that I had been thinking about for some time and which eventually led me to write this article. The transformer has a primary RDC of 196ohm, and the secondary is about 0.7ohm.

((660+196)/(27.386*27.386)) + 0.7 = 1.84
DF 8/1.84 = 4.34

Once the test circuit is built on the bench, it delivers more than 10 watts with an effective DF of 4.0, obviously due to transformer losses not considered in the theoretical calculation. In this setup the 6336 is biased at 90mA per section, for a total dissipation of 40 watts out of a possible 60; by slightly increasing the bias current the tube Ri decreases and damping increases a bit more. The customer who ordered these 6k transformers then compared the results with other transformers made by other suppliers and with a pair of 7k:6ohm transformers (turns ratio 34.157:1) mismatched by connecting an 8ohm load to the 6ohm tap, resulting in distortion at low frequencies because the primary inductance was insufficient in that mismatched condition, but only to measure the resulting DF. In that situation, the transformer reflected an impedance of about 9k to the tube and the measured DF was about 8, but with a drastic power drop, reduced to 6 watts.

To verify the scenario he simulated, I connected a 12ohm load to my 6k:8ohm transformer (ratio 27.386), reflecting an impedance of 9k to the primary, and I also obtained a DF of 8 despite the turns ratio of my transformer being lower than that of the other 7k:6ohm transformer (ratio 34.157). This indicates that, in all likelihood, if I had built a 9k:8ohm transformer (ratio 33.541), I would have had essentially the same results (or better) but without compromising low frequencies.

My conclusion is that it is basically not worthwhile to chase high damping factors with zero-feedback tube circuits, because you end up with very low efficiency in terms of power. Just think that the 6336A dissipates 60 watts, getting as hot as the sun, to deliver barely 6 watts to the speaker, slightly less than what a common EL34 can give you, which reaches 7 in single ended. And the quality of those 6 watts with a damping factor of 8 does not differ from the quality of another 6 watts with the same damping obtained through well-designed feedback. Then you must take into account that in a lightly biased class AB it could already deliver 15 and, with a bit of NFB, easily have a damping factor of 8 or 10.

I know that many people want to keep denying reality and believe that no-feedback sounds better. However, it is undeniable that with these tubes you can achieve decent damping using lower amounts of feedback than what would be necessary with other tubes and for this reason they should be considered “interesting” by DIY builders.