John Broskie's Guide to Tube Circuit Analysis & Design

27 April 2006


A quick retrospection
After rereading the last blog entry, which I wrote while I was sick with the flu and my head hurt, I think I was a bit too pessimistic. I wanted to play by strict rules when designing an Aikido headphone amplifier, but tubes do not always play by those rules. Moreover, the vacuum tube’s rebel ways make our ears happier.

For example, it is much easier to increase a tube’s conduction than it is to turn its conduction off. This asymmetry works to the ear’s benefit in a single-ended amplifier, as negative-going voltage swings do not result in sharp square-wave edges, rather (because there is no feedback loop) they softly flatten, which the ear much prefers. In other words, the amplifier softly clips in the negative direction. And positive-going voltage swings are not limited to the textbook twice-the-idle-current formula, as the top triode in the Aikido output stage can conduct far beyond that mathematical limit.

So what we end up with is an amplifier that fools the ear into thinking it’s much more powerful than in fact it is, as the usual amplifier in-distress artifacts are missing. These grating artifacts are supremely important in judging how loud the reproduction is. The ear associates distortion with volume, so when some clown with the grossly-distorting boom box walks past, we cover our ears to protect them from the seeming high decibels, but, in fact, the sound pressure level is not that high at all, only the distortion is (maybe 70%). In the same vein, when you listen to extremely clean loudspeakers or headphones, you might not realize just how dangerously intense the sound pressure is, as the added distortion is so low. (I was once sitting three feet away from a friend, while listening to his gorgeous full-range electrostatic loudspeakers. After a few minutes, we tried to talk to each other, but we could not hear a word each other spoke, as the loudspeakers were playing so loud—they didn’t sound anywhere near as loud as they were in reality playing.)


A warning
Having just written the previous paragraph, I fell compelled to indulge my inner nanny and warn you that headphone listening is much more likely to damage your ears than working in a noisy factory, as OSHA has set limits at the factory; at home, it’s your responsibility. Furthermore, tube headphone amplifiers can sound so clean that you will want to dig deeper and deeper into a recording by upping the volume. Don’t. Always pause after about the first minute of playing and remove the headphones; if you hear any ringing, not mater how slight, turn down the volume. (I set my volume by adjusting it to what sounds right and, then, backing off a notch or two.)

My son, Adrian, at two, listening to his HD-650s

9-Pin Aikido headphone amplifiers
In an Aikido headphone amplifier, unlike our limited choice in octal-based dual triodes, many 9-pin options present themselves. The 5687 immediately comes to mind, but it won’t work in the Aikido 9-pin PCBs (or will that change? check back here often for new developments). The ECC99 looks interesting. (I have no experience with this hefty dual triode, so I ordered a pair to play with.) This triode can draw 38mA with zero grid bias with 100 volts across its cathode to its plate (the 6N1P only draws 7mA under the same conditions; the 6CG7, 11mA; the 12AU7, 12mA; the 12BH7, 24mA; the 6DJ8, 40mA; the 5687, 52mA; the 7119, 58mA; the 6H30, 111mA; the 12B4, 148mA; and just for comparison's sake, the 6BL7, 34mA; the 6BX7, 87mA; and the 6AS7, 567mA).

Well, since the ECC99 does not beat the 6DJ8 in terms of current conduction, and since its mu is only 22, compared to the 6DJ8’s 33, why bother with it? The answer is found in two specifications listed below: maximum plate voltage and maximum plate dissipation.

Typical characteristics:
Limiting values:
System I
System II


Most tube manuals state that the 6DJ8’s plate voltage limit is 130 volts, whereas the ECC99 is 400 volts. (To be honest, I don’t buy the unnaturally low maximum plate voltage for the 6DJ8, which I believe only refers to its use in a cascode circuit, wherein the top triode’s cathode would be 130 volts above ground; for example, I have tested 6DJ8s with 200 volts on the plate, while the triode was used in a grounded-cathode amplifier circuit with no problems. However, in the interest of not being sued: DO NOT USE MORE THAN 130 VOLTS on the plate.) In addition, the 6DJ8’s maximum plate dissipation is only 1.8 watts, whereas the ECC99 is 5 watts. These two important differences will allow for a much more robust output stage with an ECC99 than with 6DJ8.

The other clearly interesting triode is the 6H30/6N30. These Russian tubes are amazing. First of all, I like their hefty feel in my hand. Second, they can draw current: a maximum peak pulse current of 2-3A and 111mA with 100 volts on the plate and zero grid bias. Third, they are rated for 10,000 hours of use. This triode seems to be the right choice for a truly overbuilt headphone amplifier.


Input tubes
The input must perform two important tasks: provide voltage gain and contribute little noise. If the Aikido headphone amplifier is going to be feedback free, then this tube should not produce a voltage gain any higher than 15, with 8-10 being closer to the mark, so a 6CG7/6FQ7 or 12AU7 or 5963 would work nicely. On the other hand, if a global feedback loop wraps around the amplifier, the more gain the better, so a 12AX7 or 12AY7 or 5751 would be best. Of course, individual systems will have their own special gain requirements. And a 6N1P’s low noise might make its slightly too high gain worth accepting.


Aikido low-impedance headphone amplifier
The design goal here is to build an Aikido headphone amplifier that can drive Grado 32-ohm headphones (or the 55-ohm version of the AKG K 240M), without resorting to a global feedback loop. How much voltage and current does a 32-ohm headphone demand? Well, I remember reading that the iPod puts out a peak voltage of about 1 volt into a 32-ohm load, which equals 31mA of peak current. To comfortably match and, even, exceed this value, our tube-based output stage must draw something like 40mA at idle. No, the 6DJ8 will not work, as it only draws 40mA with its grid at the same voltage as its cathode and we need to draw twice this amount of current (80mA) at peaks. This is the point where I lose half the readers. I can almost hear all those heads being scratched.

(Now, if you and I were in the same room, with me looking you in the eye or over your shoulder, I would let you squirm for at least 30 seconds, maybe longer, as research has revealed that both a pause and a dose of unease actually helps the brain retain information. But since you are reading this, you will have to choose whether to pause here or continue blithely along.)

Basically, the bottom half of the Aikido output stage is something of a poor constant-current source, in that it conducts (roughly) the same amount of current no matter what the top triode current swings into the load are. Thus, if the top triode stops conducting altogether, then the bottom triode draws something close to its idle current through the load impedance. On the other hand, if the top triode doubles its conduction, half flows into the load impedance, while the other half, which equals the idle current, flows through the bottom triode. In other words, on positive peaks, the top triode must conduct twice the idle current and the bottom triode continues to conduct at its idle current value; at negative peaks, the top triode ceases to conduct and the bottom triode continues to conduct the idle current value. In the graph above, we the current relationships when a 1-volt sinwave is delivered into a 32-ohm load. Notice how all both top and bottom triodes conduct in phase. There is nothing push-pull about these plots.

(By the way, the Aikido does not use an SRPP as the first stage, in spite of what you might have read elsewhere; at no times do the top and bottom input triodes differ in current phase, besides the output is taken at the bottom triode's plate, not the top triode's cathode. A bit pedantic perhaps, but I prefer to err on the side of precise thinking—just to be different, if no other reason. So what topology is the first stage? A symmetrically grounded-cathode amplifier—pure single-ended operation.)

So, the 6DJ8 will not work, but the 6H30/6N30 can easily sustain the require 80mA of peak current flow, without entering positive grid bias or exceeding the plate’s dissipation limit. The penalty we pay is the high 0.825A heater draw and the higher cost of the tube. By the way, I recommend that you download the free Live Curves for the 6H30 program, as it will prove quite helpful in seeing the actual plate curves and the varying mu, rp, and gm that attends different plate voltage and plate currents. Yes, they are, in fact, inconstant constants. (I know that the Live Curves download hasn’t been working but I have fixed that problem by having my hosting company deleting executables.)

The above schematic reveals some interesting modifications to the stock Aikido amplifier. Note that the output stage holds no cathode resistors, that resistor R8 has been replaced by a piece of wire and R11 has been replaced by two signal diodes in series. Why? Two reasons: to offer the lowest possible output impedance to the headphones and to avoid using any cathode-resistor bypass capacitors. (I would still place a small bypass capacitor across the diode.) Also note how both coupling capacitors, C1 and C2, are wired in parallel.

This headphone amplifier presents about a 50-ohm output impedance, which isn’t all that great, but much, much better than many commercial tube-based headphone amplifiers. The (unloaded) gain is almost +20dB with the 6CG7/6FQ7 input tube, which is maybe a bit high, depending on the rest of your system. (The gain can be lowered by using a 12AU7 instead or by loading down the input tube with two 47k resistors, R6 and R5.)

The coupling capacitors are a mix of polypropylene and electrolytic. The addition of the electrolytic is unfortunate, but necessary, as the 32-ohm load requires a large-valued capacitor, which would be next to impossible to realize with just film capacitors. A 32-ohm load only requires a 250µF coupling capacitor to ensure a -3dB frequency of 20Hz. The 470µF coupling capacitor serves to extend further the low-frequency cutoff. The 4.7µF coupling capacitor bypasses the large electrolytic 470µF coupling capacitor. In place of a generic (or even obscenely expensive electrolytic), I would try a Rubycon photoflash capacitor, as these capacitors work quite well in this application. (Never use them in a power supply where they will suffer from excessive ripple current; nor ever use them too close a heat source; nor ever apply any voltage in excess of 85% their stated limit.)

The power supply is built on top of a 117Vac isolation transformer, which when (solid-state) rectified, yields about 170V. The 227-ohm resistor drops the B+ voltage down to 150 volts and filters away a good deal of power supply noise. A better choice would be an inductor with a DCR of 227 ohms.


Aikido headphone amplifier as an iPod buddy
Converting this Aikido headphone amplifier into an iPod companion requires changing the input tube, adding a feedback loop, and upping the power supply voltage-dropping resistor’s value, as shown below.

A small amount of PCB hacking is required, but not a lot, as no traces must be cut. Still, this is a project for the more advanced solder slinger.

What do these changes buy us? First, a much lower output impedance. Second, less total harmonic distortion and a more stable fixed gain. The downside lies in the harder clipping that the feedback loop introduces and the higher, although low level, harmonics in the distortion spectra. Moreover, relatively low input impedance makes using a normal volume potentiometer or stepped attenuator problematic.

And what about the sound? My guess is that hard-rock fans will prefer this sound, that classical-music fans will prefer the feedback free design, and that jazz fans will evenly divide in preference.


Next time
I don't know what we will cover next. Maybe unity-gain soilid-state buffers again, as I have come up with an interesting circuit that might make a big difference. (Or, I might have to cover this variation on the above circuit, depending on the swaying power of the e-mails I receive.)





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