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John
Broskie's Guide to Tube Circuit Analysis & Design

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29 April 2005

April and Eliot
Thomas
Sterns Eliot was right—well, at least when it comes to April and cruelty.
For the first half of the month, I and my family have been ill with the
flu, the mega flu, a flu of solid-state-like cruelty. For the second half
of the month, we have been moving, which was almost as nasty as the flu.

How I envy those who can load their car with all their belongings and
move as easily as Paris Hilton changes boyfriends. After packing and
unloading hundreds of CDs, magazines, electronic parts, tubes, and books,
lots of books, I wish I had been brought up a Buddhist. Well, that's at
least up to and during the move and while unpacking, but once settled, I
cannot imagine not having a good-sized library. Yet, many—maybe most—are
happy to own no more than a few books: a few coffee-table books filled
with glossy pictures, a few self-help titles and cookbooks, a sci-fi novel
that was never finished, the Ann Rice novel that was read twice, well, at
least the good bits were read twice.

Upon entering a nearly book-free house, I feel like the doctor who
performs an autopsy on a body and discovers that it is missing a brain;
and we both ask ourselves the same question: How could anyone live that
way? Yet, I know many intelligent folks that don’t own more than a handful
of books. If you are thinking that web access eliminates the need for
books, this excuse cannot cover that much, as these folks didn't own any
books prior to easy web navigation. In fact, I understand that the
percentage of heavy readers has fallen to an all time low, yet more books
are sold today than ever. How are those two outcomes compatible?

Something like this occurs with audiophiles. Too many times I have seen
$20,000 stereos systems supporting only twenty albums, shoddy albums at
that: mostly test records, a few greatest hits collections, and several of
the audiophile sanctioned group of pop albums played at stereo shows and
audio salon showrooms. On the other hand, I have know committed music
lovers that own thousands of records, tapes, CDs, and have spent no more
than a few hundred dollars on their stereo. One college friend owned over
800 Beethoven record albums, which held at least a dozen different
renditions of Beethoven’s 5th symphony; when he was tested by playing a
small excerpt from one of the recordings, he would always guess the right
conductor. Glenn
Howard owns over a quarter million albums and I have never been able
to stump him on an obscure LP; he just rattles off the list of songs on
albums so rare that I thought that he might not own a copy. Glenn is not
an audiophile. He doesn't worry about his power cords being broken in or
his cartridge not being the current absolute. He just loves music.

Thus, I have come up with Broskie’s Rule: your audio system should
never cost more than your music collection.

Class-AB auto-bias circuits

If the usual DC-servo auto-bias circuit did not work perfectly with a
class-A amplifier, an amplifier operating mode that seems a perfect
candidate for a simple DC servo circuit, what hope do we have for an
auto-bias circuit for class-AB amplifiers? Well, a few techniques have
been tried.

At the complex end, we could build a circuit that only sampled the bias
current when no signal was present or a circuit that ignored error signals
beyond the class-A mode of operation. The first approach would work best
with a small microprocessor-based circuit that would monitor the current
at startup, while the input was shorted to ground, and then would lock the
bias via digital potentiometer until the amplifier was turned off. Of
course, some amplifiers never are turned on and remain on for months and
idle current can drift over a relatively short amount of time. The
alternative technique—throwing away error correction signals that occur
beyond class-A operation—is much simpler to implement, as it only requires
a few extra diodes.

The above circuit appeared in Siliconix’s MOSPOWER Applications
Handbook, 1984, p. 6-106; and originally appeared in a paper in the June
1982 IREE (ICCE). If the circuit does not make any sense to you, you are
not alone. The first time I saw the circuit, I
felt that it was time to tear up my big-brain club card, as I could
not see how this circuit could work. If the top input on the OpAmp is the
inverting input, then the OpAmp amplifies positive-going errors in bias
positively! Watch out; amplifier on fire! If the top input on the OpAmp is
the non-inverting, then the OpAmp applies positive feedback to the
non-inverting input, which must also spell D-A-N-G-E-R. The circuit that
should have appeared is shown below. The transistor at the OpAmp’s output
inverts the OpAmp’s output, making the whole circuit work, as the OpAmp’s
non-inverting input effective becomes the servo’s inverting input.

How does it work altogether? Since class-A operation ends when the
output stage current exceeds twice the idle current, we need a reference
voltage that bisect the clipping voltage produced by the shunting diodes.
Thus, the voltage reference is derived from halving the voltage drop
across the diode at the extreme right. The two 100k resistors define a
50% voltage divider that yields exactly half of the clipping voltage as
the reference voltage. The diode's voltage drop defines the clipping
voltage. Therefore, as long as the amplifier is run in class-A, the
shunting diodes never become forward biased and, thus, never conduct,
effectively falling out of the circuit. Under these conditions, in other
words, under class-A operation, the DC servo strives to maintain an
average idle current equal to the reference voltage divided by resistor
Rs.

When the amplifier is called upon to produce more than a small fraction
of a watt (when it falls out of class-A), the shunting diodes become
forward biased and conduct, clipping the maximum voltage that can be
presented to the OpAmp’s non-inverting input. Since the clipping voltage
is twice the reference voltage, won’t the capacitor at the OpAmp’s
non-inverting input become charged to that value?

No, it cannot; as the input signal presented to it
looks like a square wave with a peak magnitude equal to twice the
reference voltage, as shown below, which averages outs to close to the
voltage reference.

Interestingly enough, this circuit works best when the amplifier is
putting out almost all of its potential power, as at lower signal levels
the square wave looks more like half-wave rectified sine waves, as shown
below.

So, how well does this circuit work? Not that bad, after some tweaking.
The bias voltage does drift during prolonged signal bursts, but with
careful selection of the resistors feeding the shunting diodes, the rate
of drift can be reduced substantially.

Enough already with MOSFETs! What about tubes?

The same circuit can easily be used with triodes, tetrodes, pentodes,
FETs, IGBTs, and transistors—after suitable bias arrangements have been
made, such as a negative bias voltage for the tubes and FETs. The circuit
below works quite well and only uses one OpAmp.

Not perfect, but definitely usable. Below is a SPICE
simulation of the above circuit, with a 6DJ8.

10Vpk, 1kHz tone burst

Not too bad: the bias voltage drifted by only 5.2mV
after the 10Vpk, 1kHz tone burst. A 2Vpk tone burst throws the bias
voltage off by 1.5mV. Of course, the longer the burst, the greater the
bias error.

2Vpk, 1kHz tone burst

2Vpk, 1kHz tone burst

As shown, the circuit can only provide a negative bias voltage down to
the OpAmp's negative rail voltage (well, close to it). Two workarounds
present themselves: add a PNP transistor or add an extra resistor to the
output.

In both cases, an extra negative power supply
will be needed. Note the 2.7-ohm resistor at the cathode and the 300V
plate voltage; these examples are no longer using a 6DJ8.

Morgan Jones' class-AB auto-bias
circuit
Over ten years ago, Morgan Jones created an
extremely clever class-AB auto-bias circuit specifically for tubes that
works on the same principle of clipping the error signal. His circuit uses
an OpAmp to amplify the voltage across a 1-ohm cathode resistor by a
hundredfold. This magnified signal is then clipped at an adjustable level
and fed back into an OpAmp that feeds a grounded-emitter amplifier, which
inverts the voltage. Very slick, however, I wasn't able to get the circuit
to work in SPICE, so I cannot evaluate bias drift under sustained signal
bursts; my guess is that it would perform similarly to the fixed-voltage
auto-bias circuit.

Morgan Jones Auto-Bias Circuit

(By the way, I have been meaning to review Jones' Valve Amplifiers,
3rd Edition, for some time now, but I haven't finished reading it
yet. I will, however, let the 6SN7 out of the box and urge you to buy it,
even if you already own the previous edition. His book makes an excellent
overview of not only tube electronics, but audio electronics in general,
with good, solid information on capacitors, resistors, power supplies, and
plenty more. And I mean plenty more; he covers many small topics that will
inform the most experienced tube fancier. If you like this journal, you
are going to like his book. Buy it.)

I would do his circuit a bit differently, of course, as I even do my
own circuits differently the next time I build them. As shown below, I
would include the PNP grounded-emmiter amplifier in the OpAmp's AC
feedback loop, which would simplify the design slightly and improve
stability.

The future: a non-clipping auto-bias
circuit
We have covered two auto-bias circuits for
class-AB. Both circuits worked by clipping the error signal fed to an
OpAmp. What if we could use all of the error signal? Such a circuit
exists. But it will have to wait until the next blog entry, as once again
I am way over my typing limit.

//JRB

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