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John
Broskie's Guide to Tube Circuit Analysis & Design

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21 April 2006

Aikido PCBs and tube sockets
available at the GlassWare Yahoo Store

Headphones
and headphone amplifiers
Ah, headphones: either you
love them or you hate them. I love them. I like not hearing noise from
refrigerators, air conditioners, barking dogs, the subwoofers of rude
neighbors, cars, trucks, and especially loud minibikes and motorcycles.
Moreover, I like hearing normally unfamiliar and uncharted musical
events: the floorboards creaking beneath the 300-pound jazz bass player,
the hall’s reverberation, the guitarist’s fingerprints across the strings,
the vocalist’s gasps for air, the recording engineer’s clumsy edits, the
sheet music’s repeated turnings during every classical performance, George
Harrison’s thick-fingered flubs, the mechanical articulation on a
saxophone, the pianist’s humming—well, strike that last one item—in other
words, the hundred diminutive sonic artifacts harbored by recordings but
seldom heard. Some are annoying, others are embarrassing, others still are
transporting, but all reveal a hidden world unmapped by even the finest
loudspeakers.

What’s wrong with loudspeakers? A loudspeaker’s
crossovers and massive diaphragms smear the sonic minutia, rolling over
the barely audible information, washing away the recording’s sonic
fingerprints, like a blurry photograph that truthfully reveals a dress’s
color, but not its texture. Here is a simple experiment: visit a music
store and listen to the sonic signature of each type of cymbal displayed;
then go home and listen to your loudspeakers. What happened to that
obvious and marked difference in timbre? Now listen to the same recordings
with high-quality headphones. Can you hear more of the distinctions in
size, brand, and composition of cymbals? (Yes, I know that CDs make this
test much harder than LPs or tape did.)

To subtract further, the little that the loudspeaker
can faithfully reproduce pours into a sonic coffin known as your listening
room. Parallel walls, floor, and ceiling reverberate unevenly, stressing
some frequencies, but attenuating others. I imagine that even the air
between a loudspeaker and your ears subtracts from what the ear could hear
directly against the loudspeaker; being no more than a mixture of gasses,
how could we expect it to hold a precise imprint for very long before its
natural sponginess smears the finest details? Here is an additional
experiment: sit in the front row of a concert hall and listen to the
amazing brightness, if not downright harshness of many of the orchestra’s
instruments. Then move to the rear of the hall and sit in an untaken seat
and listen to the soft, murky sound, where many discrete violins meld into
one fat, large violin.

Verily, headphones circumnavigate so many sonic
snares that it is amazing that more are not ardent headphone listeners.

The problem with
headphones
Of course, most headphones sound dreadful,
but then so do most loudspeakers. And of course, many do not enjoy
listening that closely, like those who actually prefer the TV’s small
screen to the grandeur of the movies. If nothing else, TV erases the
wrinkles and thick makeup from faces both aged and worn; for example, Joan
Collins lived on as a sex symbol on TV well into her sixties—I’ll grant
that she was once truly lovely, but the big screen would have not
permitted such a deception for so long. Back on topic, others may claim
that headphones sound unnatural, but I have found that these same critics
often believe that “live” music is what comes out of loudspeakers at
concerts; if that is what is "natural," I’ll gladly take the unnatural.

I know some are thinking: What about electrostatic
loudspeakers? Surely they can match the headphone’s magnifying-glass sharp
detail? And I have to admit that the best electrostatic loudspeakers can
come close to matching the best dynamic headphones, but I hold that they
cannot equal the delicacy of the best electrostatic headphones. So when we
compare apples to apples and oranges to oranges, the same relationships
obtain.

Many shy away from headphones because they miss the
visceral impact that big loudspeakers deliver, the shaking of the floor
and body, which no headphone can reproduce. No debate here. In fact, that
is why I have been using subwoofers with my headphone listening for almost
thirty years. Just limit the subwoofer’s high-frequency bandwidth to 70Hz
to 100Hz and adjust its level to the point where it is only felt, but not
heard with the headphones playing.

Finally, consider this: 99.9% of the headphone
listening you have done in your life has been through solid-state
amplifiers. How many Walkmans have you owned that sported a vacuum-tube
output stage? So, if you dislike headphone listening, are you sure it is
not the miserable little solid-state OpAmps that you actually dislike?

Now, when high-quality headphones meet vacuum tubes,
real magic results. Gone are the obnoxious solid-state artifacts that can
sometimes make dull loudspeakers sound sparkling. Gone are the ridiculous
class-B OpAmps found in most receivers and in all MP3 players. (In an MP3
player, battery life is critical and a class-A output stage would be
lethal to playing time.)

Aikido headphone amplifiers

So is the Aikido amplifier, with its
low distortion, low output impedance, feedback-free design and excellent
PSRR figure, the best choice for driving headphones? No, I don’t think so.
In fact, I would argue against its use as a headphone amplifier, as its
single-ended output stage greatly limits the potential current swings from
the triodes used, and thus a push-pull circuit would
be—regrettably—essential.

But then there are the e-mails from readers who tell
me that they are using an Aikido amplifier as a headphone amplifier and
that they love the sound. Normally, I instinctively discount such
testimony, as just about any circuit or modification can provoke such
enthusiasm. But I am reminded of my once dim view of using the Broskie
cathode follower as a headphone amplifier. One reader
told me that his Sennheiser HD-600s never sounded better than they hooked
up to a 6922-based Broskie cathode follower. I couldn’t see the circuit
being happy driving such a low load impedance, but after modeling it in
SPICE and after being suitably impressed, I tried it myself with the
HD-580s I used at the time. Darned if he wasn't right. Recently, I have
hooked up my HD-650s to a 6SN7-based Aikido amplifier (bypassing my
excellent custom-made Tribute
Audio headphone transformers) and it also sounds great.

Still I worry. Although my wife finds it hard to
believe, of all the audiophiles I know, I listen at the lowest volume
levels. So I fear the that the headphone user who likes to share his music
with those across the street from him will be disappointed by the small
amount of ringing in his ears that an Aikido linestage amplifier can
muster. In other words, I believe that if an Aikido amplifier is going to
drive headphones, it must be designed carefully and robustly
overbuilt.

Getting serious

If only all headphones were high impedance devices, with impedances
closer to 1,000 to 10,000 ohms, rather than 16 to 600 ohms, tubes would
have a much easier load to drive. Unfortunately, portable audio equipment
and low-voltage batteries dictate a low headphone impedance. (If you know
Joe Grado, whom I understand is a marvelous fellow, plead with him to come
out a 2k version of his top-of-the-line headphones, hell, even a 300-ohm
version would be great; I’ll buy one, as will many other tube fans.)
Remember that 16 ohms is only twice the impedance of your loudspeakers, so
can anyone really expect a 6SN7 to drive it without an impedance matching
transformer?

So, our first design objective is to limit expected
load impedance to no less than 300 ohms and to limit our choice of output
tubes to those robust enough to drive 300 ohms effortlessly. In other
words, no 12AU7s or 6SN7s or, even, 6N1Ps need apply. These tubes have
their uses, but none can deliver enough current into a 300-ohm load in a
single ended output stage. (Yes, I know that there is a company that sells
highly respected headphone amplifiers that sport 6SN7s throughout, but I
also know that the output stage is a push-pull one.) Single ended
operation means that the idle current is also the current limit into the
load. On the other hand, a push-pull operation allows peak current to
equal twice the idle current in a class-A amplifier and they sky is the
limit in a class-AB or class-B amplifier.

How much current is needed to drive 300-ohm
headphones? It depends on the headphones. I have played my Sennheiser
headphones at the loudest level I would ever want to withstand; then I
replayed the track into an oscilloscope. The highest peak voltage I ever
saw was about 3 volts, which translates into a peak of 10mA, which in turn
equals 15mW. To buy some extra headroom, let’s double this peak current to
20mA. So, will 20mA always be enough? No, I doubt it, as some 400-ohm
headphones are much less efficient; but at least the sizable Sennheiser
crowd will be satisfied.

Octal Aikido headphone
amplifiers
The best choices for an octal-based Aikido
headphone amplifier are the 6BL7 and the 6BX7. (The 6AS7 or 6080 or 6082
could be used, with a truly low B+ of only 50V, but these tubes are not
nearly as linear and would definitely require a global feedback loop.)
These triodes were designed to be used in vertical-deflection oscillator
and amplifier circuits in televisions. Impressively, they can withstand
high plate voltages and high cathode currents that make lesser tubes
swoon—but at the cost of a 1.5A heater current, the same as an EL34 and
almost three times that of a 6SN7. However, in this application, their
best feature is their ability to conduct 20mA with only 75 volts on their
plates, something a 6SN7 simply cannot do. For example, the 6SN7 can
conduct 20mA, but only with a lot of plate voltage, so much, in fact, that
the plate runs into its dissipation limit. Actually, a 6SN7 could also
conduct 20mA with 75 volts on its plate, but only with a positive grid
voltage. So, there are effectively four operational boundaries: the
0-volts grid line, the plate dissipation curve, the maximum cathode
current limit, and the maximum plate voltage limit (we should add the
bottom of curves because of its gross nonlinearity). Below is the 6SN7’s
curves:

Now, the 6BX7’s curves:

Note how the 6BX7’s 10W plate dissipation limit does
not even intrude into the graph’s confines. At 75V and 20mA, its mu is
9.5, which gives us the ratio of 60.5% of power supply noise to be
injected into the bottom triode’s grid. This ratio can be realized through
a 64.9k resistor standing on top of a 100k resistor, or a 100k resistor
standing on top of a 152k resistor.

Now, what remains is to determine the cathode
resistor values. First of all, we want the lowest output impedance
possible, so we cannot tolerate the added resistance from the cathode
resistor; thus, we forgo using a cathode resistor for the top tube and we
bypass the bottom triode’s cathode resistor.

Well, there it is. The 6SN7/12SN7/12SX7 makes a fine
input tube. Both channels draw a total of 48mA. The (external to the PCB)
417-ohm resistor drops the raw 170V down to a fairly filtered 150V. The
170V power supply is easily built from full-wave-bridge rectifying a
120Vac isolation transformer.

So, how good is this headphone amplifier? I haven’t
actually built it, so I am only guessing here, but I am unhappy about the
added bypass capacitor across the bottom triode’s cathode resistor. One of
the great features of the Aikido topology is that it uses cathode
resistance to its advantage, linearizing the triodes without incurring too
large a penalty in increased output impedance. Besides, always try to
avoid placing an electrolytic capacitor in the cathode circuit, as it can
only harm the signal.

In addition, I worry about the 6BL7 or 6BX7 not being
as linear as the venerated 6SN7, particularly without the top cathode
resistor. So I would first build this circuit with both 180-ohm cathode
resistors in place, unbypassed; if the bass is acceptable, then let it be;
if not, try removing the top cathode resistor and tack solder a bypass
capacitor across the bottom cathode resistor.

iPod trick

If the Aikido headphone amplifier is meant to be used with an MP3 player,
such as the famous Apple iPod, the output volume is set digitally within
the device, so no external volume control is needed. This means that the
Aikido headphone amplifier can include a global feedback loop from output
to input grid, as the Aikido inverts phase. In the schematic below we see
the feedback loop in place. The amplifier’s input impedance is roughly
equal to the 20k feedback resistor at the input. Now 20k sound low for a
tube circuit, but is wildly high for an MP3 player that was designed to
drive a 32-ohm load. In other words, the MP3 player’s internal headphone
amplifier will be so unloaded by 20K, that its output stage might even
remain in class-A operation.

The schematic above shows an iPod-ready Aikido
headphone amplifier that uses a global feedback loop to lower distortion,
noise and output impedance, while keeping the output stage’s cathode
resistors in place, and unbypassed. The 6SL7/12SL7/6SU7 offers much more
gain to power the feedback loop. (Note this circuit will require some PCB
hacking.)

Output coupling
capacitors
A 300-ohm load only requires a 27µF
coupling capacitor to ensure a -3dB frequency of 20Hz. The 47µF coupling
capacitor just extends down to 12Hz. The 0.47µF coupling capacitor
bypasses the large and cheap polypropylene 47µF coupling capacitor (super
high-quality electrolytic capacitors might work, but I doubt it); any
quality capacitor is useful as a bypass, even the same capacitor type and
brand but in the smaller value (less inductance).

Although the Aikido octal PCB will hold some
physically very large capacitors, such capacitors can work their way free
from the board if the amplifier is shaken enough. Thus, I always recommend
using some hot glue or tie strips to hold large capacitors in place. (An
added advantage to holding large capacitors down is that all capacitors
have a microphonic quality, which the glue or strips helps dampen. I
always place a small section of Sorbothane below each coupling capacitor, for this
reason.)

What if you plan on driving both power amplifier and
headphones, but not at once. A rotary switch can be configured to allow
giving the line output only the high-quality 0.47µF coupling capacitor,
but paralleling both coupling capacitors when driving headphones (with a
center position of mute). Below is how to wire such a switch.

Next time

We will cover some 9-pin Aikido headphone amplifiers.

//JRB

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