Norman Koren Audio
page | Home page | Part
2

Feedback
and fidelity  part 1
by Norman Koren

Updated
August 18, 2001

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

Introduction

I've seen negative feedback attacked, reviled, denounced, and defamed for
so long I can no longer stand idly by. Feedback may be as stylish as a ‘63
Dodge Dart, but it’s a dear friend who’s brought beauty and joy to my life. It
may not be a saint, but we don’t expect Marilyn Monroe to be Mother Theresa, do
we? It’s just misunderstood— often as much by its supporters as by its
detractors. In the ten years I’ve been designing and building amplifiers I’ve
learned how to bring out its best while respecting its limitations. The time has
come to share that knowledge.

In his January 1998 Stereophile article "A Future Without Feedback ,"
Martin Colloms asserts that "measurements do not fully describe sound quality,"
and goes on to suggest that "corrective feedback is fundamentally unmusical." He
poses the question, "has anyone explored the implications of negative feedback
for reproduced sound quality in the absolute sense?" What follows is the results
of such an exploration. We shall describe new measurements that provide improved
insight into the origins of audio quality, and we shall use these measurements
to determine when and where to apply feedback to best advantage. Although we
will use vacuum tube circuits as examples, all observations apply equally well
to solid-state. We shall also revisit traditional measurements. One of them—
harmonic distortion at rated power output— has an unexpected correlation with
sound quality.

Sometimes it seems that so much has been written about feedback’s harmful
effects that it’s easy to forget its benefits. Why do engineers love it?
Improved frequency response, reduced harmonic distortion, better gain control,
increased input impedance (in many circuits), and decreased output impedance
(in circuits with voltage feedback). So why do audiophiles hate it? Harsh,
gritty, grainy, glaring sound. Reason enough.

Now for the BIG question: Are these qualities intrinsic to negative feedback
or do they arise from its improper application? From my experience it’s mostly
the latter. Mostly. There are a few places where feedback runs into
unavoidable problems, and it shouldn’t be a big surprise that one of them is the
single-ended vacuum tube power amplifier. How can we know this? We have an
instrument for looking deep into the heart of amplifiers— an instrument that may
be within your reach this very moment.

Computer modeling

The idea of using the computer— the ultimate digital machine— to design
old-fashioned vacuum tube circuits may seem more than a little incongruous. So
it may be, but in the computer we have powerful tool that wasn’t available in
the glory days of Dynaco, McIntosh, and Marantz; an affordable tool for anyone
interested in high-end audio, and usable by anyone with modest engineering
skill. More precisely, our tool is a computer program called SPICE— acronym for
Simulation Program with Integrated Circuit Emphasis, originally developed at the
University of California Berkeley.

SPICE is widely used in industry to prove integrated circuit designs before
they are cast in silicon, where fixing errors is far more costly than in
concrete. There are several commercial versions of SPICE, all of which start
with the Berkeley algorithms and add user-friendly front-ends and outputs.
Probably the best-known of them is PSpice from Cadence Design Systems (http://www.orcad.com/Product/Analog/analog.asp).
A free evaluation
version that can simulate up to fifty parts is available on CD ROM or can
be downloaded from the web. Fifty parts won’t get you far with semiconductors,
but it’s sufficient for the design of surprisingly sophisticated vacuum tube
circuits. Full versions of PSpice are very expensive. Another excellent program
is Electronics Workbench from Interactive Image Technologies (1-800-263-5552; http://www.interactiv.com/), which comes
in a $299 package (sometimes on sale) that can do some serious simulation. Each
of these programs has its learning curve, and since I’ve taken the trouble to
learn PSpice, I’m stuck with it. I love it.

I’m not the only one who values SPICE. When I escaped from Silicon Valley in
1985, I had a neighbor who was developing a version (HSpice) in his garage.
While I was tinkering with tubes, he was quietly taking over the market for
large-scale integrated circuit simulation. In August 1997 I read that he had
sold his company— Meta Software— for one hundred and sixty million dollars.
(That was before the dot com boom, when hardware still got some respect.) Can
there be a lesson here? I suppose we tube lovers must be content to receive our
reward in heavenly sound. None of us will become another Bill Gates. Besides,
the only reproduced sound he ever hears is digital.

Many readers may wonder how well digital simulation can unlock the secrets of
analog electronics. In my experience it can do so astonishingly well. I never
cease to be amazed by how closely measurements match SPICE simulations.

Models and measurements

No matter how strongly you believe that measurements don’t or can’t
correlate with sound quality, you must agree that electrical signals inside
circuits obey the laws of physics. If a computer program has accurate enough
device models, it will simulate the signals with precision. If you examine the
details of those signals with enough care, you may begin to find patterns that
shed light on sound quality.

What is wrong with conventional measurements? Two things. The first is that
most of them are made in frequency domain. The real world happens in time
domain. Frequency domain measurements are derived from a mathematical construct
called the Fourier transform, which is defined for linear systems. When a system
becomes seriously nonlinear— as an amplifier does when it saturates— frequency
domain measurements their meaning. Time domain measurements, such as pictures of
clipped sine waves, are needed to tell the real story. The one time domain
measurement frequently seen in equipment reviews is the 10kHz square wave. This
measurement is usually made with a small signal— far from saturation— and
provides the same information as the frequency response curve. SPICE produces
output in both time and frequency domain.

The second problem is that conventional measurements are taken only at an
amplifier’s external connections: A signal is fed into the input terminals and
measured at the output terminals. What happens inside the circuit can make the
difference between sonic mediocrity and distinction. With SPICE, you can probe
deep inside of circuits. I’ve made measurements that would be difficult,
expensive, and time-consuming with hardware instruments; measurements rarely if
ever seen in equipment reviews; measurements that correlate much more closely
with sound quality than such old standbys as harmonic distortion and frequency
response. We’ve known for a long time they didn’t hold the secrets.

A program’s performance is only as good as its models— sets of equations that
simulate device behavior— and SPICE does not have built-in models for vacuum
tubes. External models must be added. For many years tubes were modeled by the
Langmuir-Childs law [1,2], which represents a tube as a voltage-controlled
current source whose current is proportional to the three-halves power of the
voltage on the controlling elements. This model approximates tube performance
fairly well in the middle of the operating range, but fails miserably near
cutoff, a region particularly critical to the performance of class AB push-pull
amplifiers. It works well for calculating frequency response but not for
distortion.

A new set of models, accurate enough to match experimental tube behavior in
all critical regions, has recently been published [3] and applied to the design
of a modified Dynaco PAS preamplifier [4] with stunning sonic results. We shall
use the old and new PAS line amplifiers (figures 1 and 2) as examples of
problems and solutions related to feedback.

To you non-technical readers, I offer an apology. Feedback cannot be
discussed intelligently without getting somewhat technical. I shall try to keep
this exposition as readable as possible— There will be no heavy formulas, and
you may safely skip over circuit descriptions and references to resistors and
capacitors.

Before we proceed, a few definitions are needed: There are two types of
negative feedback, or degenerative feedback as it is sometimes called: local and
global. Local feedback is connected within or around a single gain stage; global
feedback is connected around several gain stages, usually from the amplifier’s
output to its input. Local feedback is generally regarded as benign, and with
this view I concur. The amount of feedback, expressed in decibels (dB), is the
ratio of the gains without and with feedback (the open and closed-loop gains):
6dB is a factor of 2 in voltage (4 in power); 20dB is a factor of 10 in voltage
(100 in power), etc.

The trouble with feedback

Despite its advantages, negative feedback can degrade amplifier sound
quality in three ways: First, it can lead to instabilities that appear as
response peaks or even oscillations at an amplifier’s frequency extremes.
Second, it can increase susceptibility to RF interference. Third, it makes
clipping more abrupt: This rarely affects preamplifiers, which have plenty of
headroom, but it is always a concern in power amplifiers. With proper design,
the first two problems can be eliminated and the third can be controlled. We
shall examine each of them closely with the help of SPICE.

Instability

Negative feedback operates by subtracting a portion of an amplifier’s
output signal from its input. This is quite straightforward for the middle
frequencies where an amplifier’s open-loop gain is relatively flat. Bode’s
theorem tells us that there is very little phase shift in this region. But
things can get ugly at the frequency extremes. Every RC (resistor-capacitor)
network that contributes to an amplifier’s rolloff adds up to 6dB per octave to
the rolloff and up to 90 degrees to the phase shift. Not all of these RC
networks are obvious in the schematic: Many involve stray capacitances within
the tubes. If the total phase shift exceeds 180 degrees at any frequency where
the loop gain (A/G-1, where A is the open-loop gain and
G is the closed-loop gain) is greater than one, the amplifier will
oscillate [5]. If it merely approaches 180 degrees, a peak will appear in the
frequency response curve that corresponds to ringing in the time-domain. This
will definitely degrade sound quality.

To make matters worse, capacitance in shunt with the load increases the phase
shift. Interconnect cables have around 20pF per foot, and electrostatic
loudspeakers are nothing more than big honking capacitors-- as large as 2
microfarads-- that know how to move. So load capacitance is always
present. An amplifier that performs nicely with a purely resistive load (widely
used in equipment reviews) may misbehave in the real world. Amplifiers have a
property called phase margin— the difference between the maximum phase
shift and 180 degrees— that indicates how well they can tolerate capacitive
loads. A qualitative estimate of phase margin may be obtained by measuring the
response with capacitance in shunt with the load. This is particularly easy with
SPICE.

To keep phase shift under control, a single RC network must dominate the
rolloff. For global feedback loops, this usually involves adding a capacitor to
the circuit. This is accomplished in the original PAS line amplifier (fig. 1)
with 33pF capacitor CLFB connected in parallel with feedback resistor RLFB, and
in the new design (fig. 2), with 7pF capacitor C3M in the input circuit.
Although these capacitors reduce the high frequency cutoff (-3dB point), it is
still around 100kHz in both circuits— well beyond the limits of human hearing.
Most well-designed preamplifiers achieve good frequency response and stability
at the same time— but this is not always the case for power amplifiers with
output transformers.

Figure 1. The original PAS line
amplifier.

The line amplifier of fig. 2 differs in just one respect
from the previously published version [4]: the addition of 150 ohm resistor ROUT
in series with the output. I had always objected to such a resistor because it
increases the output impedance, worsening the high frequency rolloff in the
presence of shunt capacitance from cables. But with negative feedback, phase
shift due to shunt capacitance boosts the high frequency response up to
the resonant peak, just over 100kHz. In extreme cases, this can even result in
oscillation. Increasing the compensation capacitor fixes this problem at the
expense of high frequency rolloff for short cables with low capacitance. ROUT
solves the problem by isolating the amplifier from the load capacitance. If the
correct value is chosen (easily done by trial-and-error with SPICE), the high
frequency loss due to the increased output impedance will balance the boost due
to feedback, making the response below the resonant peak nearly independent of
the load capacitance— even for cables as long as 100 meters. This neat little
trick cannot be accomplished without negative feedback.

Figure 2. The modified PAS line
amplifier.

If we observe the response of the original PAS line amplifier (fig. 3;
simulated with Evaluation PSpice 6.3, which tolerates more components than the
newer evaluation versions), we find that the output signal is fairly flat to
below 1Hz, but the signal at the plate of the first gain stage plate (node 3P)
has a huge resonant peak at 0.4Hz— 35dB above the mid-frequency level. This peak
is present because there is no feedback at dc: It is blocked from reaching the
output terminal by coupling capacitor C4P.

Fig. 3. Original PAS line amplifier frequency
response (first plate 3P and output LINE_OUT).

Now you might ask what effect a resonant peak far below the limits of human
hearing and loudspeakers— a peak that doesn’t even appear at the preamplifier
output— can have on sound quality. Quite a lot, it turns out. To begin with, 33
RPM turntables rotate at a frequency close to 0.4Hz. Signals from mechanical
perturbations at this frequency will be greatly exaggerated inside the
preamplifier. Then there is tube-generated 1/f noise, also called flicker
or pink noise— noise whose power spectral density is inversely proportional to
frequency (f). 1/f noise can be very significant at 0.4Hz. These
two noise sources perturb the bias levels of tubes inside the preamplifier.
Since the tubes aren’t perfectly linear, this leads to envelope
modulation— small variations in signal amplitude at the output that muddy
the sound and blur the imaging.

This problem has been solved in the modified PAS line amplifier (fig. 2) with
a dc-coupled negative feedback loop: Cathode resistor R6C of the
cathode-follower also functions as the feedback resistor. It took quite a bit
of trial-and-error with SPICE to get the input tube operating current to the
correct level (0.7mA; much higher than the original). A resonant peak (fig. 4)
is still present in the new circuit, but it is now 3dB below the mid-frequency
signal level— 38dB better than the original. This is a perfect example of how
external measurements can be misleading: The original design has much more
extended low frequency response, but the new design has cleaner bass and better
overall sound.

Fig. 4. Modified PAS line amplifier frequency
response (first plate 3P and output LINE_OUT).

Feedback and output transformers

Reduced to its essentials, an output transformer is a device comprising two
electrical windings— a primary with NP turns and a secondary
with NS turns— coupled by a magnetic core, and used to match
the high impedance of output tubes to relatively low impedance of loudspeakers.
In simulations, transformers are modeled as devices that multiply the signal
voltage by NS/NP, and have a small series
inductance called leakage inductance (LSP), a large shunt
inductance (LP), and a shunt capacitance
(CIP). This terminology is from "Transformers and Tubes in
Power Amplifiers" by Menno Van der Veen, available from Plitron (1-800-754-8766;
http://www.plitron.com)— strongly recommended to anyone who wishes to pursue
this subject further.

Van der Veen defines the quality factor of an output transformer as the ratio
of shunt to leakage inductance, QF =
LP/LSP. QFis roughly
proportional to the ratio of the upper to lower cutoff frequencies. Leakage
inductance LSP arises from imperfect coupling between the
primary and secondary windings, and is a strong function of the type of
transformer. There are three broad categories:

Push-pull EI transformers (named after the shape of the core): used in
most of the classic designs. Typical cutoff frequencies are between 25 and
70kHz. Can be thought of as occupying the middle ground between SE and
toroidal transformers.

Single-ended (SE) transformers: must tolerate the large dc current drawn
by SE triodes operating in class A. They have EI cores with air gaps to keep
them from saturating. The air gap increases leakage inductance
LSP. QF is lower than for the other types.
Cutoff frequencies can dip into the audio range.

Push-pull toroidal (bagel-shaped) transformers: Have the largest
QF: Cutoff frequencies can exceed 200kHz. They are sensitive
to dc-imbalance in push-pull circuits, but techniques are available to
maintain balance.

An output transformer’s high frequency rolloff is
dominated by the LC (inductor-capacitor) network consisting of
LSP and CIP. This type of network has a
second order rolloff— up to 12dB per octave at frequencies above cutoff,
with a phase shift of up to 180 degrees. As a result of this phase shift, even a
few dB of feedback can cause trouble— response peaks or oscillations with
capacitive loads— unless the loop is carefully compensated. The compensation
techniques are the same ones used in the line stages of figures 1 and 2. The
high frequency cutoff of the RC network must be well below that of the
transformer— the higher the feedback, the lower it must be.

For this reason, feedback cannot be used to extend the frequency response of
an amplifier with an output transformer. Sad to say, not all tube amplifiers
apply feedback correctly. Frequency response peaks above 20kHz and ringing in
response to 10kHz square waves have appeared in several Stereophile
equipment reviews, even for some extremely expensive amplifiers. Such
amplifiers can misbehave badly if there is much capacitance in the load.

Feedback is particularly touchy in single-ended circuits because the output
transformer cutoff frequency is so close to the top of the audible range. A
feedback loop must be compensated with extreme care: Too much compensation rolls
off the highs very audibly; too little risks a response peak. Even just the
right balance may have poor phase margin: It might sound wonderful with one
speaker-cable combination but poor with others. This is one of two reasons that
SE amplifiers are poorly suited for feedback. The other— hardened clipping— will
be discussed below.

Radio
Frequency (RF) Interference

Feedback’s least-known side-effect is that it can increase an amplifier’s
susceptibility to RF interference. This is so because the circuit technique
most often employed to stabilize a feedback loop— a capacitor in shunt with the
feedback resistor (CLFB in fig. 1)— allows RF signals picked up by the
output cable to be fed back into the amplifier’s input virtually
without attenuation. Cables are antennas, albeit poor ones, and vary widely
in their sensitivity to RF pickup. Premium interconnect cables should be
exceptionally well shielded to minimize this sensitivity. Speaker cables, which
are usually unshielded, are much better antennas than interconnect cables.

I am convinced that RF interference is a major culprit because every circuit
change I’ve ever made to reduce the RF entering an amplifier has improved the
sound— made it sweeter, smoother, cleaner, and more generally listenable. It is
the apparent cause of the grittiness, graininess, harshness, and listener
fatigue — what Martin Colloms calls "sand in the tweeter" — that can plague
amplifiers with otherwise excellent specifications. The sonic degradation caused
by RF interference is far worse than harmonic distortion.

RF interference comes from a wide variety of sources: radio, TV, digital
cellular phones, microwave ovens, lamp dimmers, flourescent lights, and digital
appliances such as computers and CD players. (It is particularly difficult to
eliminate inside CD players, where it may be as responsible as jitter for
"digititis.") It is virtually omnipresent in urban, suburban, and all but the
most remote rural areas. It varies from time-to-time and place-to-place, and may
be responsible for many of the discrepancies in published amplifier reviews.

The exact mechanism by which RF interference degrades audio quality is not
well-understood. The most likely cause is intermodulation distortion. Paul
Miller [6] described a series of experiments in which he inserted strong RF
signals modulated with random audio noise into several amplifiers and measured
the resulting audio noise spectra (the result of intermodulation). He claimed to
find a strong correlation with the subjective sound quality.

There is a very simple test for determining if an amplifier is overly
sensitive to RF interference: Turn the volume up and listen for a pop when you
turn on a nearby appliance. A well-designed amplifier will remain silent.

The RF problem was solved in the modified PAS line amplifier (fig. 2) by
compensating the feedback loop with an RC network in the input stage— R3GS and
C3M. Due to the Miller effect, the effective capacitance C3M is its
intrinsic capacitance (7pF) multiplied by the gain of tube TU3 after feedback is
applied (not its intrinsic gain). Calculating this gain can be tricky: Global
feedback reduces the gain of the first stage only; all others operate at full
gain. SPICE eliminates the need for tricky calculations. The correct value of
C3M can be quickly determined by trial-and-error. This technique, which we shall
call Miller compensation, has poorer high frequency response than the
traditional technique, but the response can be extended— made as good as the
traditional technique without compromising stability— by adding shunt capacitor
C3C to the input stage cathode circuit. C3C also provides a bit of extra RF
suppression.

The improvement brought about by this technique is illustrated in fig. 5,
which shows the signal on the plate of the first gain stage (node 3P) when input
signal VIN is applied to the line amplifier output terminal, LINE_OUT. In
the critical region above 20kHz, the response of the modified amplifier averages
18dB below that of the original. The actual improvement is even greater because,
with VIN applied to the line amplifier input, the signal at node 3P
(figures 3, 4) is 6dB larger in the modified line amplifier. This is so because
local current feedback decreases the gain of the second stage (TU4), allowing
the first stage to operate at increased gain. The signal-to RF noise ratio of
the modified amplifier is therefore 24dB better than the original— a really
significant improvement.

Fig. 5. RF susceptibility from line amplifier
output (signal amplitude at the
first gain stage plate with an input
signal injected at the preamp output).

The Parts Connection Catalog & Resource Guide (1-800-769-0747; http://www.sonicfrontiers.com/tpc)
contains an excellent collection of schematic diagrams of classic tube
preamplifiers and power amplifiers. Nearly every amplifier with feedback— and
that’s almost all of them— uses the traditional compensation technique with the
capacitor in parallel with the feedback resistor. In all fairness, this
technique is easy to apply and provides good stability with minimum frequency
response loss. The new technique, Miller compensation in the input stage,
requires two capacitors (C3M and C3C in fig. 2) to achieve good frequency
response extension. With the proper component values, difficult to obtain
without SPICE, the new technique has improved stability, i.e., less of a
response peak with capacitance in shunt with the load. Compensating a feedback
loop at the input stage also reduces response peaks at intermediate gain stages
that can occasionally cause such problems as unexpected saturation.

In part
2 we discuss feedback in power amplifiers.

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
2.

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.