Norman Koren Audio
page | Home page | Part
1

Feedback
and fidelity  part 2
by Norman Koren

Updated Oct.
9, 2006 (last update December 8, 2003)
.

Negative feedback can be a wonderful thing when done
well,
but it's often done badly. Here's how to use it
properly.

Table

of
contents

Part
1 | Introduction
| Computer
modeling | Models
and measurements | The
trouble with feedback
Instability
| Output
transformers | RF
interference | Part
2 | Clipping
| Harmonic
distortion scam
Better
measurements | Feedback
forever? | Feedback
without fear | Output
connections

In part 1 we
discussed negative feedback concepts and applied them to preamplifiers.

Clipping

When an amplifier is driven to its limits— into saturation— the tops and
bottoms of the output waveforms flatten out. This phenomenon is known as
clipping. Because most music signals contain short-term peaks whose
instantaneous power is much greater than the average, most amplifiers— even
moderately powerful amplifiers— occasionally clip during normal operation. For
this reason, the behavior of an amplifier during clipping has a profound effect
on its sound quality.

The power amplifier of fig. 6 is an excellent platform for studying the
effects of feedback on clipping. It can be built as a modified Dynaco Mark 3, or
from scratch with a 4300 ohm primary impedance output transformer. Due to the
limitations of the evaluation version of PSpice, simplified bias and power
supplies have been shown. I have named this amplifier the "Local Hero" because
of its use of local feedback (and also after one of my favorite movies.). Since
it has outstanding sound quality and makes exemplary use of feedback, we shall
describe its circuit in some detail.

Figure 6. The "Local Hero" amplifier: a modified
Dynaco Mark III.

The Local Hero’s chief feature is the absence of global negative feedback
from the output transformer secondary to the input stage. Instead, balanced
feedback from the output is returned to the cathodes of the driver (TU3, TU4)
and output tubes (TU5, TU6). This eliminates many of the stability problems
associated with a large global loop: The fewer stages in the loop, the easier it
is to control phase shifts at both frequency extremes. The amount of feedback on
the drivers is controlled by voltage dividers (R3F, R3C) and (R4F, R4C). The
resistance ratios may be changed to alter the amount of feedback, but if they
are, the parallel resistance between the driver cathodes (nodes 3C and 4C) and
ground should remain around 3300 ohms. The loop is compensated with capacitors
C3M and C4M, with C34 added to extend the high frequency response. (These
capacitors have the same functions as C3M and C3C in fig. 2.) They do not
transmit RF interference from the output. The effects of RF interference are
further reduced because the signal at the drivers is much greater than at the
input. RLD and R16 are for simulation only-- they aren't physically present. RLD
represents the speaker load. R16 prevents an unconnected node error. Stability
is excellent: Even a 1 microfarad capacitor in shunt with the load results in
little ringing.

The input stage (TU1) uses local current feedback: Gain can be controlled by
adjusting R1B. It is ac-coupled to a split-load phase invertor (TU2), which also
has local current feedback. The split-load phase invertor is an excellent
performer when it doesn’t have to drive output tubes, as it does in the classic
Dynaco circuits. Ac-coupling allows the plate resistors to be chosen for equal
but opposite ac current in TU1 and TU2, so that no net ac current is drawn from
the power supply. This reduces sonic degradation from power supply electrolytic
capacitors, which are notoriously nonlinear. The original Williamson circuit
(the grandfather of the Local Hero) had to be dc-coupled because there were
already too many coupling capacitors in the global feedback loop; another would
have undermined the low frequency stability. Ac-coupling also increases the
phase invertor’s maximum output. A note for experimenters: If you build this
circuit, you may need to make fine adjustments on C3M and C4M, and possibly also
C34, for flat response and good stability.

Note: I haven't actually built the
Local Hero, but I've gotten inquiries. I haven't included the power supply
design. Power supplies for this type of amplifier are pretty standard. The
Hammond 372JX
(300-0-300V, 250 mA) and 373BX (350-0-350V, 175 mA) are good power
transformer choices if you're building Local Hero as monoblocks. The
372JX is more conservative, but the 373BX will should put out about 30%
more power (you'll need 500V power supply capacitors).

If you build it, I recommend
testing it by driving it with a square wave generator, loading it with a
typical loudspeaker load (with cables), and looking at the signal at the
output (and speakers) with an oscilloscope. If there is ringing, increase
the Miller capacitors, C3M and C4M. If the square waves seem excessively
rounded, you may be able to decrease C3M and C4M with no ill effects. The
voltage at test points 5C and 6C should be approximately 0.5 V for 50 mA
bias current (per tube). Remember to be
careful of high voltages when you work inside tube
amplifiers!

A
pleasant surprise! Jorn Loe of Norway built a Local Hero. It took him a
long time (he isn't experienced at building tube amplifiers), but it's
working and sounding fine. You can reach him at n (dot) craft (at) c2i
(dot) net.

A comment from
Jorn, Oct. 8, 2006: I did a small correction in the Local
Hero after oscilloscope measurements showed some oscillation. My layout
made the C3M and C4M paths too long. When I connected C3M and
C4M directly to anodes 3P and 4P the amplifiers went silent. I
talked to other tube builders, and they said that this was a good
change. (Sounds fine to me. —NLK)

The results of driving the amplifier into saturation are shown in figures 7
(without feedback) and 8 (with feedback). Since the gain with an 8 ohm load is
9.46dB lower (a factor of 0.3365) with feedback than without it, the input
signals have been adjusted for the same degree of saturation. The actual amount
of feedback is the difference in gain without the load: 15.4dB. This is a
moderate amount: much more than most single-ended tube amplifiers, slightly less
than classic push-pull tube amplifiers, and much less than mid-fi solid-state
amplifiers.

Fig. 7. Sine wave clipping with no
negative feedback.

When feedback is applied, clipping at the amplifier output ( lower curve,
fig. 8) becomes more severe: its onset becomes more abrupt and the tops and
bottoms of the waveforms become flatter. Since no signal is fed back during
clipping, voltage spikes appear at the grid of the output tubes (upper curve,
fig. 8). The difference between figures 7 and 8 is modest because only 15.4 dB
of feedback has been employed: Had more been applied to emphasize the effects of
clipping, the sound quality would have suffered, and the Local Hero would not
have been such a good example of proper use of feedback. In a mid-fi solid-state
amplifier, with 40 dB or more feedback, the tops and bottoms would have been
cleanly chopped off.

Fig. 8. Sine wave clipping with 15.4 dB
negative feedback.

Hard clipping is the direct cause of the constricted dynamics and much of the
sonic harshness attributed to feedback. The audible degradation can only be
determined by ear: there is no hard and fixed rule, but much can be learned by
correlating SPICE results with careful listening. Sonic degradation is a strong
function of amplifier power and loudspeaker efficiency: the higher the sound
pressure level at the onset of clipping, the less offensive it will be. That,
along with the stability/frequency response issue described above, is the reason
that low powered SE amplifiers have limited tolerance for feedback.

Clipping is rarely a problem in preamplifiers. The figure 2 preamplifier has
enough headroom to drive any commercial power amplifier well beyond saturation—
10 to 30 dB, depending on its sensitivity and input impedance.

Despite its drawbacks in power amplifiers, negative feedback offers one
significant advantage: It reduces the output impedance. High output impedance
can cause irregular frequency response under realistic loudspeaker loads [8] as
well as poor woofer damping, audible as mushy ill-defined bass. The optimum
output impedance and feedback level depends on a number of factors that
ultimately reduce to a tradeoff between mushy bass at one extreme (no feedback)
and harsh clipping at the other (too much feedback). Several aspects of this
tradeoff are discussed in the sidebar.

Despite negative feedback’s disadvantages in single-ended tube power
amplifiers, two local experimenters have chosen to use a small amount of it—
around 3 to 4dB. Without it, the bass was just too sloppy. They did not take
this step lightly: They listened extensively, perhaps obsessively, before adding
feedback, and they wouldn't have done so had they duplicated Martin Colloms’
observation, made on the Cary 805C, that even the smallest amount of feedback
compromises musicality.

I can only speculate on the reasons for this discrepancy. At first I thought
the sound pressure level at the onset of clipping would be slightly higher for
the experimenter’s systems, which use Svetlana SV811-10 output tubes operated in
class A2, driving loudspeakers with 93 and 96dB efficiency in rather small
rooms. But the clipping level of the Cary 805C driving the 93 dB efficient
Wilson WITT should be at least as high. Perhaps the discrepancy can be explained
by differences in the room size and acoustics, amplifier clipping signature, or
loudspeaker damping requirements. But there is another intriguing possibility.

Since I don’t have access to the Cary 805C’s schematic diagram, I can only
speculate that when feedback is switched on, the traditional compensation
technique— a capacitor in shunt with the feedback resistor— may be employed. If
this is so, then all the RF picked up from the speaker cables will be
transmitted back to the input stage, even for the smallest amount of feedback,
but none will be transmitted if there is no feedback. This could well explain
Martin Colloms’ observation.

The great harmonic distortion scam

Any circuit technique that improves an amplifier’s linearity at power
levels below saturation, i.e., reduces total harmonic distortion (THD), will
result in more abrupt, harder clipping. Negative feedback is only one of several
such techniques. The relationship between linearity and clipping can be
examined with the transfer and linearity curves in figures 9 and 10. These
curves are derived from the same PSpice simulations as figures 7 and 8 for
saturated 200Hz sine waves, but instead of using time as the independent
variable (x-axis), they use the input voltage, V(INPUT).

Figure 9. Transfer and linearity curves
for the "Local Hero" amplifier without feedback

Fig. 10. Transfer and linearity curves
with 15.4dB negative feedback.

The transfer curve is simply the output voltage, V(SPKR), as a function of
the input voltage. For small input signals, it rises along a relatively straight
line. As it approaches saturation, it deviates from the straight line to a
greater or lesser degree, depending on how well the circuit is linearized. At
saturation, it flattens out. Since it can be difficult to see the deviation from
the straight line, we introduce the linearity curve.

The linearity curve is the slope, or rate of change, of the transfer curve.
In the language of differential calculus, it is the derivative of the output
voltage with respect to the input, dV(SPKR)/dV(INPUT). For small input signals,
it is a relatively straight horizontal line whose value equals the gain of the
amplifier. As it approaches saturation, it starts to drop. This drop is much
more visible than the corresponding change in the slope of the transfer curve.
At saturation, it drops to zero.

We must now explain the multiple traces in the transfer and linearity curves.
To obtain these curves, we drive the output tubes (via computer simulation, of
course) into hard saturation— hard enough to drive the voltage on the grid of
output tube positive with respect to the cathode for a portion of the cycle.
This causes grid current to be drawn, alternately charging coupling capacitors
C3P and C4P. These capacitors can charge quite rapidly, but their discharge is
governed by the RC time constant that includes the grid resistor: C4P�R6G
or C3P�R5G = 0.05 seconds, corresponding to a -3dB
frequency of 3.2Hz. Since the simulation starts with no signal, and hence no
charge, the charge that accumulates whenever one of the output tube grids
conducts causes the multiple traces.

This is no mere artifact of SPICE simulation: It is a real effect in any
amplifier where the grids of the output tubes are capacitively coupled. In hard
saturation, continuous waveforms behave very differently from a single transient
pulse: They can build enough charge across the coupling capacitors to drive the
output tubes deep into cutoff. This leads to an overload recovery time, governed
by the above-mentioned RC time constant, that can be quite audible. Overload
recovery is eliminated in class A2 or AB2 amplifiers, where the output tube
drivers can source grid current. This can be accomplished either with
transformer-coupling or dc-coupled cathode followers [7], either of which are
costly. An additional advantage of class A2 or AB2 power amplifiers is that they
can put out much more power when the output stage is triode-connected.

Now, back to the transfer and linearity curves. Fourier analysis tells us
that signals on straight line portions of the curves have no appreciable
distortion. Signals on portions of the curves with sharp kinks or abrupt
changes generate lots of high order harmonic distortion. Depending on your
viewpoint, either the kinks or the high-order harmonics are the source of sonic
degradation. Signals on portions of the curves with gradual curvature or gentle
rounding generate mostly low (second and third) order harmonic distortion.

In a circuit with high linearity— the result of large amounts of negative
feedback— the transfer curve is a straight line up to saturation, where is
abruptly levels off. The linearity curve is a horizontal line up to saturation,
where it "hits a brick wall" and abruptly drops to zero. There will be very
little harmonic distortion below saturation, but as soon as the amplifier
saturates, serious high-order harmonic distortion is generated.

Amplifiers are traditionally specified for total harmonic distortion at the
rated power, typically around 1dB below saturation (roughly 90% of saturation
voltage or 80% of saturation power). The difference between the rated power and
the saturation level is the "headroom." An amplifier with relatively soft
clipping, such as the Local Hero without feedback (fig. 9), must start rounding
off the signal at amplitudes well below saturation. At the rated power
therefore, it can have considerable THD, but this distortion is mostly low order
(second and third) harmonics. At power levels above saturation, high order
harmonic distortion components will remain much lower than for a highly linear
amplifier.

The problem of hard clipping is not limited to feedback amplifiers. I once
had an amplifier— obtained in a trade, without careful auditioning— that
featured a circuit called "super-feedforward," intended to eliminate the vices
of feedback. It put out 120 watts per channel at 0.005% THD (one of the lowest
in the 1980 Audio Annual Equipment Directory), had response to 250kHz,
and had sound that can only be described as hateful and irritating, even though
it had no obvious flaws. The only suspicious measurement was the saturated sine
waves: They didn’t just clip; they dipped! I didn’t keep the amplifier long
enough to find out why.

Modest levels of low order harmonic distortion do not seem to harm sound
quality. In SE tube amplifiers, most of which have little or no feedback, the
predominant distortion component is the second harmonic. Push-pull amplifiers
cancel even order harmonic distortion components, resulting in lower THD. The
second harmonic distortion in SE amplifiers may well be responsible for their
alluring sound. It has given rise to the theory that even order harmonic
distortion components are more benign than odd. My own view is that the real
culprit is high order distortion components. Second harmonic distortion may
actually enhance sound quality by adding harmonic content— some call it
"euphonic distortion"— that increases the perception of richness and detail. In
all fairness, I haven’t persuaded my experimenter friends that this is the case.

In the 1950s and early 1960s, high fidelity tube amplifiers had 0.5 to 1.5%
THD at rated power output. In the 1970s, a distortion race took place that
paralleled the automotive horsepower race of the 1950s: If 1% THD was OK, 0.1%
was better, and 0.001% would be really awesome. The more leading zeros, the
merrier. These low THD levels were primarily accomplished by increasing negative
feedback to levels well beyond 40dB. We all know the results: amplifiers that
sounded so bad that— a real silver lining on a dark cloud — they gave birth to
the high-end audio industry we know today.

That brings us to the ultimate audio paradox: In a well-designed high
fidelity power amplifier, the lower the total harmonic distortion at rated
power, the harder the clipping; hence the worse the sound. This runs exactly
counter to the popular belief of the past, a belief still widely held in
segments of the audio industry outside the high-end. Within the high-end
community, the predominant belief has been that THD has little to do with sound
quality, even though most of us have experienced evidence of the inverse
correlation: mid-fi amplifiers with low THD but mediocre sound and old tube
amplifiers much higher THD but wonderful sound.

To minimize the likelihood of misunderstanding— inevitable when the above
statement is quoted out of context— let me emphasize that the power amplifier
must have no serious design flaws (like low-level crossover distortion) and must
be working properly. Extremely high levels of THD, over 5 or 10%, probably
indicate trouble. Low harmonic distortion is still desirable in preamplifiers
and line level amplifiers that have at least 10dB of headroom (a factor of ten
in power) between their rated output and saturation. Low harmonic distortion at
rated output only degrades the sound quality of power amplifiers.

Better measurements

The one conventional measurement that provides some indication of an
amplifier’s saturation behavior— THD+noise as a function of power level— has
several shortcomings. It emphasizes harmonic distortion at levels below
saturation and lacks sufficient detail above saturation to describe actual
clipping. Furthermore, it measures total harmonic distortion; hence it
gives far too much weight to the relatively benign second and third order
distortion components.

The transfer and linearity curves (figures 9 and 10) are more direct
indicators of audio quality and saturation behavior. The transfer curve is easy
to obtain on any oscilloscope with X-Y input capability. The linearity curve is
trickier because it involves differentiating the output voltage with respect to
the input. This requires a digital oscilloscope. A number of issues need to be
resolved before this measurement becomes a standard: How far should the
amplifier be overdriven? What is the ideal waveform for this measurement? We
chose a 200Hz sine wave because, with a 1kHz sine wave, the amplifier’s high
frequency limitations smoothed the curves. Would a 100Hz sine wave or a single
sawtooth pulse have been any better? It would be worthwhile to publish these
curves in equipment reviews, even before a standard is established, to see what
can be learned.

Measurements made inside the circuit, examples of which are found in figures
3-5, have great value for the equipment designer, but little value for the
reviewer because different amplifiers have such different circuit topologies.
There is a real need for measurements that indicate sensitivity to RF
interference. Paul Miller made a good first step by inserting noise-modulated RF
signals into amplifiers and measuring the audible noise spectrum [5], but his
descriptions were incomplete, and I am unaware of any follow-up work.

Feedback forever?

To feedback’s opponents, a well-designed amplifier without feedback is
preferable a similar amplifier with it. Presumably, this also includes
individual devices like tubes or transistors. There is an important, though not
obvious, exception that casts doubt on this view. The triode— the favorite of
audiophiles— has built-in local negative feedback.

In a plate-follower triode gain stage, as the grid voltage (the input signal)
increases, the plate current increases. This causes the plate voltage (the
output signal) to drop. Since the plate current depends on the plate voltage, it
will be lower than it would have been had the plate voltage remained constant.
This, by definition, is degenerative, i.e., negative feedback: It could be
eliminated by making the plate current independent of the plate voltage. This
could be done inside the tube by adding a second grid, connected to a constant
high voltage, between the control grid and plate. To keep the electrons that
bounce off the plate and getting absorbed by the second grid, a third grid,
connected to a low voltage, would have to be added between the second grid and
the plate.

What would such a tube be called? A pentode, of course! With no negative
feedback, its gain and output impedance are much higher and its linearity is
poorer. The sound of the triode is almost universally preferred. Considered in
this light, feedback shouldn’t look so bad. For a tube amplifier to be called
truly feedback-free— in the local as well as the global sense— it would have to
be built entirely of pentodes. Any takers?

Feedback without fear

By incorporating engineering theory into computer simulation, we have been
able learn a great deal— some of it new and unexpected— about the origins of
audio quality. The old theory was fine as far as it went; it just couldn’t
handle the complexity of audio amplifiers, where the devil is truly in the
details.

The use of computer simulation to study subjective sound quality is still in
its infancy. As it progresses, amplifier designs will become simpler, more
elegant, and better sounding. Best of all, amateurs are now in a position to
make real contributions to the art, much as they did in the early days of radio.
Some excellent simulation tools are available for free, including the evaluation
version of PSpice from MicroSim, and Duncan Munro’s excellent web page,
http://duncanamps.simplenet.com/. Relevant articles appear in Glass Audio
and Audio Electronics.

Extensive computer simulation and listening have led me to conclude that
feedback amplifiers can have flawless sound quality, without a trace of
muddiness or grayness, provided that the three dangers of feedback— instability,
RF susceptibility, and sharpened clipping— can be eliminated or minimized. This
can be always be accomplished in well-designed vacuum tube preamplifiers, but
there will always be a tradeoff between clipping and output impedance in power
amplifiers. Because this tradeoff involves many factors— amplifier saturation
level, open loop output impedance, loudspeaker efficiency and damping, etc. —
one solution will never fit all needs. The industry-wide trend towards lower
negative feedback may well continue, but I will hazard the guess that it won’t
go all the way to zero.

Although I cannot prove that feedback has no audible drawbacks— no such proof
is possible when the issue is subjective quality— I can offer the fig. 2
preamplifier line stage as evidence. When implemented with a high quality power
supply, its superb sound should equal anything on the market, with or without
feedback. Details of its construction (as a modified Dynaco PAS) have been
published in Glass Audio [4]. The entire project, which includes a moving
magnet phono stage, can be built for around $300 in parts.

In high fidelity amplifiers, the magic is in the circuit. Premium components
and skilled layout may improve the sound of a good circuit, but they cannot
save a poor one. With the knowledge gained by correlating SPICE simulations
with careful listening, we can confidently apply the right amounts feedback to
the right places— sparingly in power amplifiers, more generously in
preamplifiers— without fear of degrading the sound. Advertising claims of "no
negative feedback" should be treated with the usual skepticism. A well-designed
amplifier can have excellent sound whether or not it has feedback. The ultimate
judge of audio quality is, and always will be, the ear.

Output
connections: impedance and power
tradeoffs

In a power amplifier with pentode output tubes (6L6GC, EL34, 6550,
etc.), output impedance and power depend on the screen grid connection.
The three standard connections are:

Pentode: The screen grids are connected to a constant high
voltage source.

Triode: The screen grids are connected to the plates. Its
performance characteristics are those of a triode; hence it is a triode
in all but name.

Ultra-linear (UL): The screen grids are connected to output
transformer taps intermediate (about 40% of the way) between the center
and plate taps.

The following table compares conventional
expectations with PSpice simulations for the Local Hero amplifier,
changing only the output tube screen grid connections.

TABLE
1. PROPERTIES OF OUTPUT TUBE
CONNECTIONS

Connection
(mode)

PENTODE

UL

TRIODE

Conventional
understanding

Output
power

highest

close to
pentode

1/3
pentode

Output
impedance

highest

1/3
pentode

1/10
pentode

Voltage
gain

highest

intermediate

lowest

PSpice simulation of Local Hero
amplifier

Output power
(Watts RMS)

76

68

33

Feedback
(dB)

20-44

(0.1-10kHz)

15.4

9.5

Output impedance
no NFB

25-370W

11.7W

4.9W

Output impedance
NFB

2.3W

1.9W

1.5W

Power output is measured at clipping for 50mA bias current per tube and
a 480V power supply. Normal rated power output is about 20% lower.

The UL connection is popular in classic designs because it offers a
good tradeoff between output power and impedance. Changing an amplifier
from UL to triode mode is a common modification. Triode mode has lower
output impedance, less sensitivity to loudspeaker loads, and less
feedback (hence softer clipping) if the circuit is unchanged, but also
lower power. If the Local Hero is wired in triode mode, reduce C3M and C4M
to 150pF. A class A2 or AB2 triode output stage [7], which can operate
with grid current, would have much greater output power. It's the best of
both worlds, but it comes at a price: The output stage grid must be driven
by a transformer-coupled gain stage (limited bandwidth and don’t even
think of feedback) or by direct-coupled cathode followers, which greatly
complicates the power supply. This has been accomplished in The
Emperor's New Amplifier.

References

Scott Reynolds, "Vacuum-tube models for PSPICE simulations," Glass Audio,
vol. 5, no. 4, 4/93 p. 17.

W. Marshall Leach, Jr., "SPICE models for vacuum-tube amplifiers," J.
Audio Eng. Soc. Vol 43, No. 3, March 1995, p. 117.

Norman L. Koren, "Improved Vacuum-Tube Models for SPICE Simulations,"
Glass Audio, Vol. 8, No. 5, 1996, p. 18.

Norman L. Koren, "SPICE and the Art of Preamplifier Design," (in two
parts), Glass Audio, Vol. 8, No. 2, p. 1 and No. 4, p. 38, 1997.

Paul Miller, "Resonances and Repercussions," Hi Fi News & Record
Review, June 1989, p. 35.

Paul W. Tuinenga, "SPICE, A Guide to Circuit Simulation & Analysis
using PSpice," Prentice-Hall, 1992 or 1995.

Scott Frankland, "The Magic of Design and Synergy, Part I: The Wavestream
V-8 Triode," Positive Feedback, Vol. 5, No. 5, 1995, p. 23.

John Atkinson, "Real-life measurements," Stereophile, August 1995, p.
168.

About the
author
Norman
Koren, a native of Rochester, NY, received a BA in physics from Brown University
in 1965 and an MA in physics from Wayne State University in 1969. His destiny as
a high-tech nomad has taken him to Boston, Philadelphia, Silicon Valley, San
Diego, and most recently to Colorado, where he worked in research and
development of digital magnetic recording channels through 2001.

E-mail | Norman
Koren Audio page | Part
1.

This page was created
December 8,
2003

Images and text copyright (C) 2000-2012 by Norman
Koren. Norman Koren lives in Boulder, Colorado. Since 2003 most
of his time has been devoted to the development of Imatest. He
has been involved with photography since 1964. Designing vacuum tube audio amplifiers was
his passion between about 1990 to 1998.