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If an amplifier's passing of a signal is labeled
"function X," then feeding the amplifier inverse
function X (1/X) will equal unity. For example,
if an amplifier adds only gain and no distortion,
then its function is "times 30," let's say. Thus if
given an input signal that is divided by 30, the
inverse of times 30 (1/30), its result is unity. The
inverse RIAA equalization curve that a phono
preamp implements is an example of an inverse
function against the same function equaling a
flat output response. Simple enough, so why the
refusal to apply this principle to audio
amplifiers?
Inverse Complementary
Distortion Cancellation
Adding distortion to eliminate distortion
seems as contradictory as trying to prevent war
by preparing for it. Yet in audio practice,
seeming contradictions abound, feedback
making an amplifier sound less clean, lower
damping factors creating a better bass
reproduction, for example. While these
examples are controversial, adding negative
distortion to distortion to yield no distortion
should not be, yet this technique has few
adherents. In fact, many do not know that this
technique has been suggested. So it was after
reading in
audioXpress's
July issue an article by
Graham Dicker that asked why hasn't the lower
distortion that occurs in amplifiers with an even-
numbered stages and increase with odd-
numbered stages not been noted before, I
decided that the topic of distortion cancellation
by complementary inverse pre-distortion is
worth looking into again. (July--notice how long
it takes me to get around to writing on a topic.)
Half a century ago is the last time this topic
was seriously covered; and the following two
articles are well worth a trip to the library:
"Non-Linearity Distortion,"
Wireless Engineer
,
January 1956, and "Nonlinear Distortion
Reduction by Complementary Distortion,"
IRE
Transactions on Audio
, Sept-Oct 1959. It is
fascinating to read the angry responses to the
last article; but then anger often betrays a lack of
understanding. (Paul Klipsh even got into the
fray and on the wrong side if I remember
correctly.) The argument against lowering
distortion by pre-distorting went along the
following lines: an amplifier that distorts will
only end up distorting the pre-distorted signal,
yielding no advantage, as the result will be a
distorted pre-distortion; or that while it is
possible to cancel 2nd harmonic distortion with
this technique, it not possible to cancel the
higher harmonics. Truly odd arguments; doesn't
a distorted inverse distortion equal no distortion?
And why only the 2nd harmonics?
The answer lies not in the physics behind an
amplifier operation, but rather a psychological
obsession with frequency and sine waves. With
the notable exception of the late Richard Heyser,
few of us working with audio design are
comfortable with anything other than sine
waves. Maybe it is because instantaneous plate
voltages do not seem as important as frequency
response and harmonic distortion. Or maybe the
oscilloscope's inability to display instantaneous
voltages as well it can display sine waves makes
us think exclusively in terms of frequency and
sine waves. Yet at any given moment in time, a
tube's plate voltage can be at only one voltage
potential, just as a loudspeaker's cone can be at
only one absolute fixed position or a resistor can
experience a single absolute current flow at any
given moment. It is only over time that these
discrete plate voltages, cone positions, and
resistor currents all add up to produce the
fundamentals and overtones that we hear.
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If the point of operation is set at -2 volts of
grid bias or at -6 volts, we may never realize that
the triode has a profound break in linearity. In
other words, if we remain within a grid-voltage
window of 0 to -4 volts, the tube's linearity is
impeccable; the same holds true in the window
of -4 to -8 grid volts. But at the -4 volts of grid
bias point of operation, the tube's break in
linearity is easily seen, as the triode offers a
larger gain to positive going input signals than to
negative going signals. In fact, the 2nd harmonic
distortion is readily calculated to be 16.7% from
the following formula:
2nd Distortion =
0.5(Vmax + Vmin) - Vq
Vmax - Vmin
(To some extent, all triodes resemble this
imaginary triode in that their amplification
factors are not constant, decreasing with
increased plate voltage and low plate current.)
Now let's imagine two of these imaginary,
dual-mu triodes used in a line-stage amplifier.
The first triode is used in a standard grounded-
cathode configuration; the second, in a cathode
follower configuration. Both triodes are biased
at the -4 grid voltage point and both see the
same cathode-top voltage and plate current. The
first triode directly cascades into the second
triode. How well will circuit made up of grossly
non-linear triode work?
To get a feel for
instantaneous voltages, take
a thick telephone book and
draw a sine wave on the
open edge. Each page holds
only one small dot of ink in
much the same way that
one slice of time hold only
one plate voltage. (Digital
recordings simply take the
instantaneous voltage value
for any given time-slice and
convert it to binary code.
The next step to understanding how inverse
distortion can lead to less distortion is to
imagine a triode that displays an odd property: it
has two sharply defined amplification factors.
Form 0 to -4 grid volts, the mu is 40, but from -4
grid volts on, the mu is 20. And other than this
break in a consistent mu, this triode is perfectly
linear.
0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
+300vdc
30k
0 Vp 100 200 300 400
300
+150vdc
5965
.5µF
+153vdc
input
300
5965
+2.8vdc
1M
560
30k
1M
Vg
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Constant-Current-Draw-Compound amplifier
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When a cathode follower shares the same
triode and load resistance and plate voltage and
idle current as the grounded-cathode amplifier
that precedes it
, the cathode follower undoes
much of the distortion of the first stage. This
happens because the cathode follower is
retracing the curves that the grounded-cathode
amplifier traced. As the first stage's plate
sluggishly swings positive, its cathode-to-plate
voltage increases and its conduction decreases;
as the cathode follower's cathode swings
positive, its cathode-to-plate voltage
aggressively decreases and its conduction
increases. Inversely, when first stage's plate
aggressively swings negative, the cathode
follower's cathode-to-plate voltage sluggishly
increases and its conduction decreases.
To the degree that a triode is consistently
inconsistent, this circuit will make use of inverse
pre-distortion to yield a lower distortion than
either sub-circuit used independently. If this
technique seems too optimistic, consider what
goes on a multiple stage line amplifier with
feedback; the penultimate gain stage delivers to
the last stage an inverse pre-distorted signal that
undoes the distortion that the last would impose
in the absence of feedback. The feedback
created this inverse pre-distorted signal precisely
for the output device, as it is the output device
that terminates the feedback loop. (It is
interesting to compare a non-feedback amplifier
to one with feedback. In the non-feedback
amplifier, distortion grows larger at each
proceeding stage from the input. In the feedback
amplifier, distortion is largest at the input stage
and grows cleaner with each proceeding stage to
the output.) But feedback is not the only means
to creating an inverse pre-distorting signal.
How do we use this trick to make a power
amplifier? First of all, we must use the same
triode type for both the driver tube and the
output tube. Second, we must use same cathode-
to-plate voltages, load impedances, and idle
currents for both triodes. Third, we must cascade
a grounded-cathode amplifier into a cathode
follower output stage.
+800vdc
+650vdc
3k
+400vdc
5k
100
.5µF
2k
EL34
+37vdc
470k
{
bias V
16
+400vdc
8
4
100
5k
input
1k
EL34
+37vdc
470k
741
CCDC power amplifier
At first glance, it looks like we will have to
lose half of the potential power output in order
to reduce the distortion complementarily, as the
first stage will have to work into the same load
as will the output stage. For example, if the a
single 2A3 output tube sees a load of 2500
ohms, then the 2A3 driver tube will also have to
work into a 2500 ohm load; since both tubes
undergo the same voltage and current swing,
both tubes will deliver the same power into their
loads. But as only one of these loads creates
sound, half of the potential efficiency is lost.
Considering that the average triode based SE
amplifier is only about 20% efficient, we do not
have much efficiency to throw away.
But if we increase the number of output
devices used in parallel, we effectively increase
the efficiency. For example, if we design a
single-ended 300B power amplifier that uses
three 300B output tubes in parallel, then only
one 300B power tube is needed to provide the
complementary inverse pre-distortion. So we
end up throwing away only a quarter of our
potential watts, rather than half. (Of course, the
more output tubes in parallel, the better the
efficiency.)
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+662.5vdc
+800vdc
1720
36.3k
3.75k
+400vdc
.5µF
+300vdc
2k
300B
300B
300B
100k
30k
}
5vdc
Bartolucci 2
+62vdc
{
300
16
+150vdc
+400vdc
8
4
5965
1250
.5µF
1k
+153vdc
300
300B
GND
+2.8vdc
5965
+62vdc
}
5vdc
+52vdc
1M
560
30k
470k
886
247
www.glass-ware.com
In the above schematic, you see an 300B
based cathode follower output stage being
driven by an 300B based grounded-cathode
amplifier, whose plate resistor is three times
greater (3750 ohms) than the reflected
impedance on the output transformer's secondary
(1250 ohms; the 247 ohm biasing resistor's value
will have to be added to the primary impedance,
if this resistor is not bypassed). The key feature
is that the grounded-cathode amplifier stage's
idle current and cathode-to-plate voltage
matches that of each output tube.
The extra power supply voltage comes from a
voltage doubler circuit, as shown below. Lest
those who posses all-knowledge-of-all-that-is-
worth-knowing-about-tube-electronics (a
surprisingly small amount, it turns out, no more
than can fill a few articles from the audiophile
press and the odd rec.tube thread) lose their
composure over the unseemly use of solid-state
diodes, a tube rectifier can be easily used for the
400 vdc power supply voltage and, with some
work, tube rectifiers could be used for the 800
volts power supply as well.
+800vdc
600vac CT
250mA
+400vdc
The 300B-based driver tube must realize a
voltage swing large enough to drive the parallel
cathode followers to full power output. Since the
needed swing is not symmetrical, the potential
swing need not be either. As configured, the
driver stage can potentially swing down more
voltage than up, which is what the output stage
needs to see. This is the result of the triode
requiring more voltage to turn it off than it
requires to increase its conduction.
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So when the driver tube sees an input swing
of +62/-62 volts, its plate will swing -221/+195
volts, which in turn this imbalance will counter
the imbalance that the output tubes will force
onto the its output voltage swing, as it is the
inverse of the output stage's imbalance.
The unfortunate feature of this amplifier is
that because the 300B mu is low, the output
stage never realizes it full potential output, as the
cathode follower output stage's low gain requires
a much greater voltage swing at its grid to bring
out the full output power that the 300B can give.
Thus a better choice for an output tube might be
triode connected 8417 or EL34. In the schematic
below, we see an EL34-based output stage. This
amplifier would provide about 15W of relatively
inexpensive, clean, pure single-ended power.
The power amplifier's input stage also uses
complementary inverse pre-distortion to lower
this stage's contribution to the amplifier's final
distortion figure by not adding excessive
distortion to the mix. Thus the same principle of
inverse-complementary-distortion cancellation
that lowers the output stage's distortion is used
to in the input stage. The same triode, the same
cathode-to-plate voltage, the same load resistor
value--all are used to inverse symmetrically
cancel the distortion from the input stage.
The end result of all these techniques is an
amplifier with a low output impedance and low
distortion and wide bandwidth, an amplifier that
does not use feedback (at least not a global
feedback loop). The cathode follower output
stage deserves some comments. This circuit
employs 100% cathode degeneration of the
output signal to keep the output in inline with its
input. If the cathode fails to move as positive as
the grid moves, then the grid effectively
becomes more positive and the tube's conduction
increases, which will force the cathode to a
greater positive voltage. Conversely, if the
cathode falls less negatively as the grid falls,
then the grid effectively becomes more negative
and the tube's conduction decreases, which
results in the cathode's voltage to collapse. In
other words, the cathode follower output stage
uses all of the output tube's transconductance to
force the output to follow the input signal. This
short, quick feedback mechanism also brings the
output impedance down and extends the
bandwidth. It also serves to lower the
transformer's distortion contribution, as output
transformers distort least with low impedance
input sources. This is an import advantage of
this output stage, as the transformer is not
enclosed in a distortion lowering feedback loop.
+800vdc
+650vdc
35k
2.5k
+400vdc
100
100
100
5k
.5µF
+300vdc
2k
EL34
EL34
EL34
30k
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+37vdc
300
16
+150vdc
+400vdc
100
5965
8
4
.5µF
1k
+153vdc
300
EL34
One Electron UBT-1
GND
+2.8vdc
5965
+37vdc
1M
560
30k
470k
741
85
www.glass-ware.com
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Inne pliki z tego folderu:
Totem-Pole_Output_Stage.pdf
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Accordion_Amplifier.pdf
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CompInvDisAmp.pdf
(376 KB)
Grounded_Cathode_Amplifier.pdf
(227 KB)
ipt.pdf
(193 KB)
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