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L'espressivo 3.0, A High-End Autoformer Driver for Grado Headphones

Topics discussed in this article deal with high voltages that can and will kill you. Do not attempt to use this information unless you are qualified to work with high voltages. I am not responsible for your lack of knowledge or mistakes. Nor am I responsible for your utilization of my incorrect or misleading information. This is the internet, not an engineering text book.

This is still very much in the work in progress stage, so don't expect too much from it.

For a while now, I have been interested in the Espressivo headphone amplifier. There are things about it that I like a lot, such as the autoformer on the output, and the simplicity of the design. However, after playing with variations of the design (here, here and, here), I have been struck by what is an inherent paradox in the amplifier, and, frankly, in most heapdhone amplifiers.

Typically, source components like CD players output a signal that is approximately 2V rms. If you run that directly into a 32ohm headphones, assuming no limit to the current sourcing of your component, the headphones will draw about 63mA. In other words, about 125mW, or an eighth of a watt. This may not sound like much, but Grado headphones are extremely efficient, and in reality need only a fraction of this power to be loud. Indeed, I found that at listening levels that were just slightly too loud to be comfortable, I needed about 5mW. You might want higher power than 5mW at peaks, but not much higher.

What this means, then, is that for Grado 32 ohm headphones, headphone amplifiers are really better envisioned as being attenuators and current sources. Complicating this, though, is that practical experience suggests that an amplifier with the capability to give significantly more current than will be drawn tends to sound better. In other words, an amplifier with a low output impedance (Zout) and thus a high damping factor works best. One other thing is that Grado headphones have very benign impedance curves, almost a constant 32 ohms across the frequency range, which makes them near ideal loads for transformer coupled tubes.

Back to the Espressivo, it is interesting to note that it first attenuates the input signal with a resistor divider, it then uses a high gain tube to amplify that attenuated signal, and then uses an autoformer to once again attenuate the output signal and to lower the output impedance. The particular tube chosen has a low rp for the high mu, so the output power can be converted into a signal with a fair amount of current.

What is striking about this arrangement, however, is that two of the stages are partly, or for certain sources, entirely, unnecessary. That is, it is redundant to attenuate and then amplify the attenuated signal. This is particularly so as the amount the signal is reamplified is often less than it is attenuated, and, as low as the rp of the tube is, the tube's output impedance is often higher than that of the previous stage.

All this is to say that in some cases, the first two stages may be unnecessary. Instead, one can simply use an autoformer or transformer volume control as a variable output transformer that attenuates the signal and drops the output impedance at the same time. Indeed, if you get the driving stage right, there is no need for any other attenuator which will improve sound quality dramatically. The best amplifier, after all, is no amplifier.

None of this should be that new. People have been running their high output cd players into power amps for years using some sort of passive attenuation. Using transformers or autoformers for that attenuation is somewhat newer, but what seems to be novel here is using the autoformer on the output to accomplish both attenuation and impedance matching.

So, the L'espressivo++ is really two projects. One is an Espressivo so stripped down that it has no parts left other than the output autoformer. For many sources, this will be sufficient, indeed, more than sufficient, for spectacular sound. The other project, an active version, uses a low mu tube to add a slight amount of gain. This allows lower level sources or sources that do not have an enormous amount of output current, or the use of lower settings on the output for better damping. It does add more components to the signal path, so the design must be done carefully to minimize their influence.

Stripped Down Details
The primary difficulty in this project is sourcing the actual autoformers. The original uses the Peerless TL-404 autoformers, now made by Magnequest. As I've stated before, these are very expensive, but said to be very nice. Judging from the Espressivo page, the TL-404's have a 5K "primary", and secondaries at 500, 200, 50, 10, and 4 ohms. With the 1K rp tube used in the design, this equates to Zout of 100, 40, 10, 2, and less than 1 ohm. With a 2V input signal, this also equates to output signals of approximatly .63V, .4V, .2V, .09V, and .06V. These bottom two steps in the range are decent, if a little loud, for Grados, but they do not present a very fine grained volume selection and don't really allow for low volume listening.

What is really needed is something with more, and finer, attenuation options. To this end, Intact Audio offers a $200 Autoformer volume control. (They also offer a $400 version with more steps, but I don't think they are necessary.) This offers 14 steps in 3dB increments. It can take a maximum input signal of about 8V, which means that the active version below can use a higher mu tube for high Z phones.

The chart below shows, with a 32 ohm headphone load, what load the autoformers present to the source as well as the output voltage for each attenuation step, assuming a 2V signal.

dB Zload Z Ratio Turns Ratio Vout
0 32 1:1 1:1 2
-3 64 1:2 1:1.4 1.4
-6 125 1:4 1:2 1
-9 250 1:8 1:2.8 0.7
-12 500 1:16 1:4 0.5
-15 1000 1:32 1:5.6 0.36
-18 2000 1:64 1:8 0.25
-21 4000 1:125 1:11.3 0.18
-24 8000 1:250 1:16 0.125
-27 16000 1:500 1:22.6 0.09
-30 32000 1:1000 1:32 0.06
-33 64000 1:2000 1:45 0.04
-36 125000 1:4000 1:64 0.03
-39 250000 1:8000 1:90 0.02
-42 500000 1:16000 1:125 0.016

Those voltage ratings are a little generous as there will also be copper losses, etc. However, it is conceivabe that even at the lower end, this may be a little high for some. My main source, it turns out, puts out a bit less than 2V -- more like 1.5V -- which may be why this works so well for me. In that case, you may find you need the attenuator with more steps. Dave at Intact will also custom wind these for just a little more money to get the attenuation exactly where you need it. Or, you can find a way to reduce the gain in the source. This is often simply a case of resizing some feedback resistors on the inevitable I/V opamps, or using a smaller I/V resistor, or a lower mu tube.

Additionaly, the impedance load that the autoformer presents is also a little generous. In reality, the reflected load, which is shown, is in parallel with the inductance. And, this is one of the neatest things about these autoformers -- you can set the inductance by restacking the lams. When they ship, the laminations are butt stacked which leads to an inductance of about 20Hy. They can be restacked in various patterns yielding an inductance of up to about 172Hy. This is easy to do, and took me about 15 minutes to restack the pair. Directions for doing this are on the Intact Audio website.

Inductance presents a load of a certain impedance at a particular frequency, and what is ideal will depend on your source. The formula for doing this is on the Intact Audio web site in the AVC FAQ. The lower the inductance, the more linear the autoformers are. But, the higher the inductance, the higher the load. So, if you have a source with an opamp output with a very low Zout, then leaving them as is might be the most appropriate choice. On the other hand, a tube with a high rp (like a 6SN7 or 12AU7) might require a higher inductance. For what it's worth, I stacked mine with the highest possible inductance, and they sound great.

Active Details
The first active version is a simple solid state version. This is useful when you have sufficient voltage, but the source does not have the current to drive the phones, or the Source's Zout is too high to drive the transformers. Here, one can simply use a buffer to drive the autoformers.

A couple of things are worth noting. First, the resolution of these autoformers is extremely high so it is worth using a quality buffer circuit like the JISBOS buffer. However, because there is a DC blocking capacitor (more on this below) you can also use some of the single chip buffers like the BUF634 or HA5002 that when used outside of feedback loops tend to have some DC offset. Indeed, a MOS-FET follower may be the best option there is here.

Second, the DC blocking capacitor may not be necessary in all circumstances. The autoformers do not want much DC current as this will saturate the cores and destroy performance, but they can take a little. Because the Zout of the buffer is very low, the autoformers can be "butt stacked" which is where all the "E's" and the "I's" line up. This is how they are shipped, and where they are most linear. The inductance is also lower, but with the low Zout of the buffer, this is okay. The reason that butt stacking may be helpful here is that is creates a small natural air gap that can prevent the core from saturating with very small amounts of current. Probably something on the order of 5mA is fine. Since the DCR of these autoformers is about 50R, this means a DC offset of nearly 250mV should be fine. Thus, even a MOS-FET follower with a bipolar supply might be workable. The size of the cap is going to need to be found via experimentation, though it will get larger the lower the inductance.

The final thing to be addressed in the arrangement. Typically, these buffers go after a volume control as they are used to lower the Zout. So, the arrangement is a little counter intuitive. But, the function of the autoformers is to both lower volume and to lower Zout. Thus, by putting the autoformers after the buffer, Zout is actually lower. While this difference is likely incidental, it also assures that the autoformers are driven from a low impedance source, which is also beneficial.

Active Details -- Vacuum Tube Version
There are numerous ways to do the tube version, but in general, it looks like the above. The idea was to strip out the parts of the Espressivo that were both unnecessary, and which would degrade sound quality. This means not attenuating the signal and then re-amplifying it again. It also means biasing the tube in such a way as to eliminate the cathode bypass capacitor.

To this end, I first removed the volume pot on the input and used a low mu tube. The tube I chose is the 71a which is a directly heated triode. Rp is about 1700 ohms, and the filament is relatively easy to drive with a CCS (5V/250mA). For bias, since the 71a is happy around -18V, I simply used a pair of 9V batteries on the inside of an input transformer. There are lots of other ways to do this, with or without the transformer, but this worked well here. Additionally, because the filaments are both grounded and driven with constant current sources, the CCSes could be run off the same power supply, which generally does not work with DHTs. The power transformer I used only has a 6.3V winding, so I made a voltage doubler with a regulator and used this to feed ~9.5 clean volts to each CCS. This arrangement means that by simply adjusting the current supply, I can drop in other tubes such as the 6A3. Because the CCSes present a high impedance, this arangement also effectively keeps the filament supply isolated from the signal path.

click image for larger version

One need not go to quite these extremes, however. There are a number of indirectly heated triodes that have similarly low mu and low rp that will work well. The ubiquotous (in headphone circles) 6AS7/6080 is one, as is the 12B4A.

Additionally, if one does not mind the cathode bypass, then a much more conventional arrangement is possible with a small performance penalty.

A final technical consideration is how to size the parafeed capacitor. The general rule for doing this is to start with 1uF and keep paralleling more caps until the bass response is where it should be. There are also various simulators available to help in guessing. In this case, using the simulator, since the primary inductance of these autoformers is so high, a small cap is fine.

Indeed, the 1uf I used works quite well. There is, however, some tradeoff here. As noted earlier, I fully interleaved the autoformer cores which gives the maximum inductance, but which also degrades performance slightly. If one used a lower inductance, then the autoformers will sound slightly better, but a larger cap will be necessary. If your funds are unlinited, this might be a worthwhile tradeoff (though larger caps of the same type generally do not sound as good as their smaller versions) but for this project, keeping the cap small where a high quality cap could be afforded seemed like a reasonable tradeoff. Some experimentation is probably necessary to find the ideal relationship.

It is worth reiterating again that this is not really an amplifier as such. Instead, it is a current source and impedance matcher, and it is specifically for Grado headphones. Indeed, I only have the bottom 6 steps of the attenuator connected in mine, and I find that I really only use the last three. For some, an infinitly adjustable volume control will simply be too much to give up. But, for me, I have found that the three steps, which roughly correspond to quiet listening, normal listening, and a little loud, are all I ever need. And, the improvement in sound quality is so large that I am willing to give up a little volume convenience.

Last Update:Monday, 05-Jan-2009 15:49:07 EST