The Economic Importance of Power Amplifi ers
Audio power amplifi ers are of considerable economic importance. They are built in their hundreds
of thousands every year, and have a history extending back to the 1920s. It is therefore surprising
there have been so few books dealing in any depth with solid-state power amplifi er design.
The fi rst aim of this text is to fi ll that need, by providing a detailed guide to the many design
decisions that must be taken when a power amplifi er is designed.
The second aim is to disseminate the results of the original work done on amplifi er design in the
last few years. The unexpected result of these investigations was to show that power amplifi ers of
extraordinarily low distortion could be designed as a matter of routine, without any unwelcome
side-effects, so long as a relatively simple design methodology was followed. This methodology
will be explained in detail.
Assumptions
To keep its length reasonable, a book such as this must assume a basic knowledge of audio
electronics. I do not propose to plough through the defi nitions of frequency response, total
harmonic distortion (THD) and signal-to-noise ratio; these can be found anywhere. Commonplace
facts have been ruthlessly omitted where their absence makes room for something new or unusual,
so this is not the place to start learning electronics from scratch. Mathematics has been confi ned
to a few simple equations determining vital parameters such as open-loop gain; anything more
complex is best left to a circuit simulator you trust. Your assumptions, and hence the output, may
be wrong, but at least the calculations in between will be correct . . .
The principles of negative feedback as applied to power amplifi ers are explained in detail, as there
is still widespread confusion as to exactly how it works.
Origins and Aims
The core of this book is based on a series of eight articles originally published in Electronics World
as ‘ Distortion in Power Amplifi ers ’ . This series was primarily concerned with distortion as the
most variable feature of power amplifi er performance. You may have two units placed side by side,one giving 2% THD and the other 0.0005% at full power, and both claiming to provide the ultimate
audio experience. The ratio between the two fi gures is a staggering 4000:1, and this is clearly a
remarkable state of affairs. One might be forgiven for concluding that distortion was not a very
important parameter. What is even more surprising to those who have not followed the evolution
of audio over the last two decades is that the more distortive amplifi er will almost certainly be the
more expensive. I shall deal in detail with the reasons for this astonishing range of variation.
The original series was inspired by the desire to invent a new output stage that would be as linear
as Class-A, without the daunting heat problems. In the course of this work it emerged that output
stage distortion was completely obscured by nonlinearities in the small-signal stages, and it was
clear that these distortions would need to be eliminated before any progress could be made. The
small-signal stages were therefore studied in isolation, using model amplifi ers with low-power
and very linear Class-A output stages, until the various overlapping distortion mechanisms had
been separated out. It has to be said this was not an easy process. In each case there proved to be
a simple, and sometimes well-known, cure and perhaps the most novel part of my approach is that
all these mechanisms are dealt with, rather than one or two, and the fi nal result is an amplifi er with
unusually low distortion, using only modest and safe amounts of global negative feedback.
Much of this book concentrates on the distortion performance of amplifi ers. One reason is that this
varies more than any other parameter – by up to a factor of 1000. Amplifi er distortion was until
recently an enigmatic fi eld – it was clear that there were several overlapping distortion mechanisms
in the typical amplifi er, but it is the work reported here that shows how to disentangle them, so they
may be separately studied and then, with the knowledge thus gained, minimized.
I assume here that distortion is a bad thing, and should be minimized; I make no apology for
putting it as plainly as that. Alternative philosophies hold that as some forms of nonlinearity are
considered harmless or even euphonic, they should be encouraged, or at any rate not positively
discouraged. I state plainly that I have no sympathy with the latter view; to my mind the goal is to
make the audio path as transparent as possible. If some sort of distortion is considered desirable,
then surely the logical way to introduce it is by an outboard processor, working at line level. This
is not only more cost-effective than generating distortion with directly heated triodes, but has the
important attribute that it can be switched off . Those who have brought into being our current
signal-delivery chain, i.e. mixing consoles, multitrack recorders, CDs, etc., have done us proud
in the matter of low distortion, and to willfully throw away this achievement at the very last stage
strikes me as curious at best.
In this book I hope to provide information that is useful to all those interested in power amplifi ers.
Britain has a long tradition of small and very small audio companies, whose technical and
production resources may not differ very greatly from those available to the committed amateur.
I hope this volume will be of service to both.
I have endeavored to address both the quest for technical perfection – which is certainly not over,
as far as I am concerned – and also the commercial necessity of achieving good specifi cations at
minimum cost.The fi eld of audio is full of statements that appear plausible but in fact have never been tested and
often turn out to be quite untrue. For this reason, I have confi ned myself as closely as possible to
facts that I have verifi ed myself. This volume may therefore appear somewhat idiosyncratic in
places. For example, fi eld-effect transistor (FET) output stages receive much less coverage than
bipolar ones because the conclusion appears to be inescapable that FETs are both more expensive
and less linear; I have therefore not pursued the FET route very far. Similarly, most of my
practical design experience has been on amplifi ers of less than 300 W power output, and so heavyduty
designs for large-scale public address (PA) work are also under-represented. I think this is
preferable to setting down untested speculation.
The Study of Amplifi er Design
Although solid-state amplifi ers have been around for some 40 years, it would be a great mistake
to assume that everything possible is known about them. In the course of my investigations, I
discovered several matters which, not appearing in the technical literature, appear to be novel, at
least in their combined application:
● The need to precisely balance the input pair to prevent second-harmonic generation.
● The demonstration of how a beta-enhancement transistor increases the linearity and
reduces the collector impedance of the voltage-amplifi er stage (VAS).
● An explanation of why BJT output stages always distort more into 4 Ω than 8 Ω .
● In a conventional BJT output stage, quiescent current as such is of little importance. What
is crucial is the voltage between the transistor emitters.
● Power FETs, though for many years touted as superior in linearity, are actually far less
linear than bipolar output devices.
● In most amplifi ers, the major source of distortion is not inherent in the amplifying stages,
but results from avoidable problems such as induction of supply-rail currents and poor
power-supply rejection.
● Any number of oscillograms of square waves with ringing have been published that claim
to be the transient response of an amplifi er into a capacitive load. In actual fact this ringing
is due to the output inductor resonating with the load, and tells you precisely nothing about
amplifi er stability.
The above list is by no means complete.
As in any developing fi eld, this book cannot claim to be the last word on the subject; rather it hopes
to be a snapshot of the state of understanding at this time. Similarly, I certainly do not claim that
this book is fully comprehensive; a work that covered every possible aspect of every conceivable
power amplifi er would run to thousands of pages. On many occasions I have found myself about to write: ‘ It would take a whole book to deal properly with. . . . ’ Within a limited compass I have tried
to be innovative as well as comprehensive, but in many cases the best I can do is to give a good
selection of references that will enable the interested to pursue matters further. The appearance of a
reference means that I consider it worth reading, and not that I think it to be correct in every respect.
Sometimes it is said that discrete power amplifi er design is rather unenterprising, given the
enormous outpouring of ingenuity in the design of analog integrated circuits. Advances in op-amp
design would appear to be particularly relevant. I have therefore spent some considerable time
studying this massive body of material and I have had to regretfully conclude that it is actually
a very sparse source of inspiration for new audio power amplifi er techniques; there are several
reasons for this, and it may spare the time of others if I quickly enumerate them here:
● A large part of the existing data refers only to small-signal MOSFETs, such as those
used in (CMOS) op-amps, and is dominated by the ways in which they differ from BJTs,
for example in their low transconductance. CMOS devices can have their characteristics
customized to a certain extent by manipulating the width/length ratio of the channel.
● In general, only the earlier material refers to bipolar junction transistor (BJT) circuitry, and
then it is often mainly concerned with the diffi culties of making complementary circuitry
when the only PNP transistors available are the slow lateral kind with limited beta and poor
frequency response.
● Many of the CMOS op-amps studied are transconductance amplifi ers, i.e. voltage
difference in, current out. Compensation is usually based on putting a specifi ed load
capacitance across the high-impedance output. This does not appear to be a promising
approach to making audio power amplifi ers.
● Much of the op-amp material is concerned with the common-mode performance of the
input stage. This is pretty much irrelevant to power amplifi er design.
● Many circuit techniques rely heavily on the matching of device characteristics possible in
IC fabrication, and there is also an emphasis on minimizing chip area to reduce cost.
● A good many IC techniques are only necessary because it is (or was) diffi cult to make
precise and linear IC resistors. Circuit design is also infl uenced by the need to keep
compensation capacitors as small as possible, as they take up a disproportionately large
amount of chip area for their function.
The material here is aimed at all audio power amplifi ers that are still primarily built from discrete
components, which can include anything from 10 W mid-fi systems to the most rarefi ed reaches of
what is sometimes called the ‘ high end ’ , though the ‘ expensive end ’ might be a more accurate term.
There are of course a large number of IC and hybrid amplifi ers, but since their design details are
fi xed and inaccessible they are not dealt with here. Their use is (or at any rate should be) simply
a matter of following the relevant application note. The quality and reliability of IC power amps
has improved noticeably over the last decade, but low distortion and high power still remain the
province of discrete circuitry, and this situation seems likely to persist for the foreseeable future.
Power amplifi er design has often been treated as something of a black art, with the implication that
the design process is extremely complex and its outcome not very predictable. I hope to show that
this need no longer be the case, and that power amplifi ers are now designable – in other words it is
possible to predict reasonably accurately the practical performance of a purely theoretical design.
I have done a considerable amount of research work on amplifi er design, much of which appears to
have been done for the fi rst time, and it is now possible for me to put forward a design methodology
that allows an amplifi er to be designed for a specifi c negative-feedback factor at a given frequency,
and to a large extent allows the distortion performance to be predicted. I shall show that this
methodology allows amplifi ers of extremely low distortion (sub-0.001% at 1 kHz) to be designed
and built as a matter of routine, using only modest amounts of global negative feedback.
Misinformation in Audio
Few fi elds of technical endeavor are more plagued with errors, misstatements and confusion than
audio. In the last 20 years, the rise of controversial and non-rational audio hypotheses, gathered
under the title Subjectivism has deepened these diffi culties. It is commonplace for hi-fi reviewers
to claim that they have perceived subtle audio differences that cannot be related to electrical
performance measurements. These claims include the alleged production of a ‘ three-dimensional
sound stage and protests that the rhythm of the music has been altered ’ ; these statements are
typically produced in isolation, with no attempt made to correlate them to objective test results.
The latter in particular appears to be a quite impossible claim.
This volume does not address the implementation of subjectivist notions, but confi nes itself to
the measurable, the rational, and the repeatable. This is not as restrictive as it may appear; there
is nothing to prevent you using the methodology presented here to design an amplifi er that is
technically excellent, and then gilding the lily by using whatever brands of expensive resistor
or capacitor are currently fashionable, and doing the internal wiring with cable that costs more
per meter than the rest of the unit put together. Such nods to subjectivist convention are unlikely
to damage the real performance; this is, however, not the case with some of the more damaging
hypotheses, such as the claim that negative feedback is inherently harmful. Reduce the feedback
factor and you will degrade the real-life operation of almost any design.
Such problems arise because audio electronics is a more technically complex subject than it at
fi rst appears. It is easy to cobble together some sort of power amplifi er that works, and this can
give people an altogether exaggerated view of how deeply they understand what they have created.
In contrast, no one is likely to take a ‘ subjective ’ approach to the design of an aeroplane wing or
a rocket engine; the margins for error are rather smaller, and the consequences of malfunction
somewhat more serious.
The subjectivist position is of no help to anyone hoping to design a good power amplifi er.
However, it promises to be with us for some further time yet, and it is appropriate to review it
here and show why it need not be considered at the design stage. The marketing stage is of
course another matter.
Science and Subjectivism
Audio engineering is in a singular position. There can be few branches of engineering science rent
from top to bottom by such a basic division as the subjectivist/rationalist dichotomy. Subjectivism
is still a signifi cant issue in the hi-fi section of the industry, but mercifully has made little headway
in professional audio, where an intimate acquaintance with the original sound, and the need to earn
a living with reliable and affordable equipment, provides an effective barrier against most of the
irrational infl uences. (Note that the opposite of subjectivist is not ‘ objectivist ’ . This term refers to
the followers of the philosophy of Ayn Rand.)
Most fi elds of technology have defi ned and accepted measures of excellence; car makers compete
to improve mph and mpg; computer manufacturers boast of MIPs (millions of instructions per
second) and so on. Improvement in these real quantities is regarded as unequivocally a step
forward. In the fi eld of hi-fi , many people seem to have diffi culty in deciding which direction
forward is.
Working as a professional audio designer, I often encounter opinions which, while an integral part
of the subjectivist offshoot of hi-fi , are treated with ridicule by practitioners of other branches of
electrical engineering. The would-be designer is not likely to be encouraged by being told that
audio is not far removed from witchcraft, and that no one truly knows what they are doing. I have
been told by a subjectivist that the operation of the human ear is so complex that its interaction
with measurable parameters lies forever beyond human comprehension. I hope this is an extreme
position; it was, I may add, proffered as a fl at statement rather than a basis for discussion.
I have studied audio design from the viewpoints of electronic design, psychoacoustics, and my own
humble efforts at musical creativity. I have found complete skepticism towards subjectivism to be
the only tenable position. Nonetheless, if hitherto unsuspected dimensions of audio quality are ever
shown to exist, then I look forward keenly to exploiting them. At this point I should say that no
doubt most of the esoteric opinions are held in complete sincerity.
The Subjectivist Position
A short defi nition of the subjectivist position on power amplifi ers might read as follows:
● Objective measurements of an amplifi er’s performance are unimportant compared with the
subjective impressions received in informal listening tests. Should the two contradict, the
objective results may be dismissed.
● Degradation effects exist in amplifi ers that are unknown to orthodox engineering science,
and are not revealed by the usual objective tests.
● Considerable latitude may be employed in suggesting hypothetical mechanisms of audio
impairment, such as mysterious capacitor shortcomings and subtle cable defects, without
reference to the plausibility of the concept, or the gathering of objective evidence of any
kind.
I hope that this is considered a reasonable statement of the situation; meanwhile the great majority
of the paying public continue to buy conventional hi-fi systems, ignoring the expensive and esoteric
high-end sector where the debate is fi ercest.
It may appear unlikely that a sizeable part of an industry could have set off in a direction that is
quite counter to the facts; it could be objected that such a loss of direction in a scientifi c subject
would be unprecedented. This is not so.
Parallel events that suggest themselves include the destruction of the study of genetics under
Lysenko in the USSR [1] . Another possibility is the study of parapsychology, now in deep trouble
because after some 100 years of investigation it has not uncovered the ghost (sorry) of a repeatable
phenomenon[2] . This sounds all too familiar. It could be argued that parapsychology is a poor
analogy because most people would accept that there was nothing there to study in the fi rst place,
whereas nobody would assert that objective measurements and subjective sound quality have no
correlation at all; one need only pick up the telephone to remind oneself what a 4 kHz bandwidth
and 10% or so THD sounds like.
The most startling parallel I have found in the history of science is the almost forgotten affair of
Blondlot and the N-rays [3] . In 1903, Rene Blondlot, a respected French physicist, claimed to have
discovered a new form of radiation he called ‘ N-rays ’ . (This was shortly after the discovery of
X-rays by Roentgen, so rays were in the air, as it were.) This invisible radiation was apparently
mysteriously refracted by aluminum prisms; but the crucial factor was that its presence could only
be shown by subjective assessment of the brightness of an electric arc allegedly affected by N-rays.
No objective measurement appeared to be possible. To Blondlot, and at least 14 of his professional
colleagues, the subtle changes in brightness were real, and the French Academy published more
than 100 papers on the subject.
Unfortunately N-rays were completely imaginary, a product of the ‘ experimenter-expectancy ’
effect. This was demonstrated by American scientist Robert Wood, who quietly pocketed the
aluminum prism during a demonstration, without affecting Bondlot’s recital of the results. After
this the N-ray industry collapsed very quickly, and while it was a major embarrassment at the time,
it is now almost forgotten.
The conclusion is inescapable that it is quite possible for large numbers of sincere people to
deceive themselves when dealing with subjective assessments of phenomena.
A Short History of Subjectivism
The early history of sound reproduction is notable for the number of times that observers reported
that an acoustic gramophone gave results indistinguishable from reality. The mere existence of such
statements throws light on how powerfully mindset affects subjective impressions. Interest in sound
reproduction intensifi ed in the postwar period, and technical standards such as DIN 45 – 500 were
set, though they were soon criticized as too permissive. By the late 1960s it was widely accepted
that the requirements for hi-fi would be satisfi ed by ‘ THD less than 0.1%, with no signifi cant
crossover distortion, frequency response 20 Hz– 20 kHz and as little noise as possible, please The early 1970s saw this expanded to include slew rates and properly behaved overload protection,
but the approach was always scientifi c and it was normal to read amplifi er reviews in which
measurements were dissected but no mention made of listening tests.
Following the growth of subjectivism through the pages of one of the leading subjectivist magazines
(Hi-Fi News ), the fi rst intimation of what was to come was the commencement of Paul Messenger’s
column ‘ Subjective Sounds ’ in September 1976, in which he said: ‘ The assessment will be (almost)
purely subjective, which has both strengths and weaknesses, as the inclusion of laboratory data
would involve too much time and space, and although the ear may be the most fallible, it is also
the most sensitive evaluation instrument . ’ This is subjectivism as expedient rather than policy.
Signifi cantly, none of the early installments contained references to amplifi er sound. In March 1977,
an article by Jean Hiraga was published vilifying high levels of negative feedback and praising
the sound of an amplifi er with 2% THD. In the same issue, Paul Messenger stated that a Radford
valve amplifi er sounded better than a transistor one, and by the end of the year the amplifi er-sound
bandwagon was rolling. Hiraga returned in August 1977 with a highly contentious set of claims
about audible speaker cables, and after that no hypothesis was too unlikely to receive attention.
The Limits of Hearing
In evaluating the subjectivist position, it is essential to consider the known abilities of the human
ear. Contrary to the impression given by some commentators, who call constantly for more
psychoacoustical research, a vast amount of hard scientifi c information already exists on this
subject, and some of it may be briefl y summarized thus:
● The smallest step-change in amplitude that can be detected is about 0.3 dB for a pure tone.
In more realistic situations it is 0.5 – 1.0 dB. This is about a 10% change [4] .
● The smallest detectable change in frequency of a tone is about 0.2% in the band 500 Hz –
2 kHz. In percentage terms, this is the parameter for which the ear is most sensitive [5] .
● The least detectable amount of harmonic distortion is not an easy fi gure to determine,
as there is a multitude of variables involved, and in particular the continuously varying
level of program means that the level of THD introduced is also dynamically changing.
With mostly low-order harmonics present the just-detectable amount is about 1%, though
crossover effects can be picked up at 0.3%, and probably lower. There is certainly no
evidence that an amplifi er producing 0.001% THD sounds any cleaner than one producing
0.005%[6] .
It is acknowledged that THD measurements, taken with the usual notch-type analyzer, are of
limited use in predicting the subjective impairment produced by an imperfect audio path. With
music, etc. intermodulation effects are demonstrably more important than harmonics. However,
THD tests have the unique advantage that visual inspection of the distortion residual gives an
experienced observer a great deal of information about the root cause of the nonlinearity. Many other distortion tests exist which, while yielding very little information to the designer, exercise
the whole audio bandwidth at once and correlate well with properly conducted tests for subjective
impairment by distortion. The Belcher intermodulation test (the principle is shown in Figure 1.1 )
deserves more attention than it has received, and may become more popular now that DSP chips
are cheaper.
One of the objections often made to THD tests is that their resolution does not allow verifi cation
that no nonlinearities exist at very low level – a sort of micro-crossover distortion. Hawksford,
for example, has stated ‘ Low-level threshold phenomena . . . set bounds upon the ultimate
transparency of an audio system ’ [7] , and several commentators have stated their belief that some
metallic contacts consist of a net of so-called ‘ micro-diodes ’ . In fact, this kind of mischievous
hypothesis can be disposed of using THD techniques.
I evolved a method of measuring THD down to 0.01% at 200 μ V rms, and applied it to large
electrolytics, connectors of varying provenance, and lengths of copper cable with and without alleged
magic properties. The method required the design of an ultra-low noise (EIN 150 dBu for a 10 Ω source resistance) and very low THD [8] . The measurement method is shown in Figure 1.2 ; using an
attenuator with a very low value of resistance to reduce the incoming signal keeps the Johnson noise
to a minimum. In no case was any unusual distortion detected, and it would be nice to think that this
red herring at least has been laid to rest.
● Interchannel crosstalk can obviously degrade stereo separation, but the effect is not
detectable until it is worse than 20 dB, which would be a very bad amplifi er indeed [9] .
● Phase and group delay have been an area of dispute for a long time. As Stanley Lipshitz
et al. have pointed out, these effects are obviously perceptible if they are gross enough;
if an amplifi er was so heroically misconceived as to produce the top half of the audio
spectrum 3 hours after the bottom, there would be no room for argument. In more practical
terms, concern about phase problems has centered on loudspeakers and their crossovers,
as this would seem to be the only place where a phase shift might exist without an
accompanying frequency-response change to make it obvious. Lipshitz appears to have
demonstrated[10] that a second-order all-pass fi lter (an all-pass fi lter gives a frequencydependent
phase shift without level changes) is audible, whereas BBC fi ndings reported
by Harwood [11] indicate the opposite, and the truth of the matter is still not clear. This
controversy is of limited importance to amplifi er designers, as it would take spectacular
incompetence to produce a circuit that included an accidental all-pass fi lter. Without such,
the phase response of an amplifi er is completely defi ned by its frequency response, and
vice versa; in Control Theory this is Bode’s Second Law [12] , and it should be much more
widely known in the hi-fi world than it is. A properly designed amplifi er has its response
roll-off points not too far outside the audio band, and these will have accompanying phase
shifts; there is no evidence that these are perceptible [8] .
The picture of the ear that emerges from psychoacoustics and related fi elds is not that of a precision
instrument. Its ultimate sensitivity, directional capabilities and dynamic range are far more
impressive than its ability to measure small level changes or detect correlated low-level signals
like distortion harmonics. This is unsurprising; from an evolutionary viewpoint the functions of the
ear are to warn of approaching danger (sensitivity and direction-fi nding being paramount) and for
speech. In speech perception the identifi cation of formants (the bands of harmonics from vocalchord
pulse excitation, selectively emphasized by vocal-tract resonances) and vowel/consonant discriminations are infi nitely more important than any hi-fi parameter. Presumably the whole
existence of music as a source of pleasure is an accidental side-effect of our remarkable powers of
speech perception: how it acts as a direct route to the emotions remains profoundly mysterious.
Articles of Faith: The Tenets of Subjectivism
All of the alleged effects listed below have received considerable affi rmation in the audio press, to
the point where some are treated as facts. The reality is that none of them has in the last 15 years
proved susceptible to objective confi rmation. This sad record is perhaps equalled only by students
of parapsychology. I hope that the brief statements below are considered fair by their proponents. If
not I have no doubt I shall soon hear about it:
● Sine waves are steady-state signals that represent too easy a test for amplifi ers, compared
with the complexities of music.
This is presumably meant to imply that sine waves are in some way particularly easy for an
amplifi er to deal with, the implication being that anyone using a THD analyzer must be hopelessly
naive. Since sines and cosines have an unending series of non-zero differentials, steady hardly
comes into it. I know of no evidence that sine waves of randomly varying amplitude (for example)
would provide a more searching test of amplifi er competence.
I hold this sort of view to be the result of anthropomorphic thinking about amplifi ers, treating them
as though they think about what they amplify. Twenty sine waves of different frequencies may
be conceptually complex to us, and the output of a symphony orchestra even more so, but to an
amplifi er both composite signals resolve to a single instantaneous voltage that must be increased in
amplitude and presented at low impedance. An amplifi er has no perspective on the signal arriving
at its input, but must literally take it as it comes.
● Capacitors affect the signal passing through them in a way invisible to distortion
measurements .
Several writers have praised the technique of subtracting pulse signals passed through two different
sorts of capacitor, claiming that the non-zero residue proves that capacitors can introduce audible
errors. My view is that these tests expose only well-known capacitor shortcomings such as
dielectric absorption and series resistance, plus perhaps the vulnerability of the dielectric fi lm in
electrolytics to reverse-biasing. No one has yet shown how these relate to capacitor audibility in
properly designed equipment.
● Passing an audio signal through cables, printed-circuit board (PCB) tracks or switch
contacts causes a cumulative deterioration. Precious metal contact surfaces alleviate but
do not eliminate the problem. This too is undetectable by tests for nonlinearity .
Concern over cables is widespread, but it can be said with confi dence that there is as yet not a shred
of evidence to support it. Any piece of wire passes a sine wave with unmeasurable distortion, and
so simple notions of inter-crystal rectifi cation or ‘ micro-diodes ’ can be discounted, quite apart from the fact that such behaviour is absolutely ruled out by established materials science. No plausible
means of detecting, let alone measuring, cable degradation has ever been proposed.
The most signifi cant parameter of a loudspeaker cable is probably its lumped inductance. This can
cause minor variations in frequency response at the very top of the audio band, given a demanding
load impedance. These deviations are unlikely to exceed 0.1 dB for reasonable cable constructions
(say, inductance less than 4 μ H). The resistance of a typical cable (say, 0.1 Ω ) causes response
variations across the band, following the speaker impedance curve, but these are usually even
smaller at around 0.05 dB. This is not audible.
Corrosion is often blamed for subtle signal degradation at switch and connector contacts; this is
unlikely. By far the most common form of contact degradation is the formation of an insulating
sulfi de layer on silver contacts, derived from hydrogen sulfi de air pollution. This typically cuts
the signal altogether, except when signal peaks temporarily punch through the sulfi de layer. The
effect is gross and seems inapplicable to theories of subtle degradation. Gold-plating is the only
certain cure. It costs money.
● Cables are directional, and pass audio better in one direction than the other .
Audio signals are AC. Cables cannot be directional any more than 2 2 can equal 5. Anyone
prepared to believe this nonsense will not be capable of designing amplifi ers, so there seems no
point in further comment.
● The sound of valves is inherently superior to that of any kind of semiconductor .
The ‘ valve sound’ is one phenomenon that may have a real existence; it has been known for a long
time that listeners sometimes prefer to have a certain amount of second-harmonic distortion added
in[13] , and most valve amplifi ers provide just that, due to grave diffi culties in providing good linearity
with modest feedback factors. While this may well sound nice, hi-fi is supposedly about accuracy, and
if the sound is to be thus modifi ed it should be controllable from the front panel by a ‘ niceness ’ knob.
The use of valves leads to some intractable problems of linearity, reliability and the need for
intimidatingly expensive (and, once more, nonlinear) iron-cored transformers. The current fashion
is for exposed valves, and it is not at all clear to me that a fragile glass bottle, containing a red-hot
anode with hundreds of volts DC on it, is wholly satisfactory for domestic safety.
A recent development in subjectivism is enthusiasm for single-ended directly heated triodes,
usually in extremely expensive monoblock systems. Such an amplifi er generates large amounts of
second-harmonic distortion, due to the asymmetry of single-ended operation, and requires a very
large output transformer as its primary carries the full DC anode current, and core saturation must
be avoided. Power outputs are inevitably very limited at 10 W or less. In a recent review, the Cary
CAD-300SEI triode amplifi er yielded 3% THD at 9 W, at a cost of £ 3400[14] . And you still need to
buy a pre-amp.
● Negative feedback is inherently a bad thing; the less it is used, the better the amplifi er
sounds, without qualifi cation . Negative feedback is not inherently a bad thing; it is an absolutely indispensable principle of
electronic design, and if used properly has the remarkable ability to make just about every parameter
better. It is usually global feedback that the critic has in mind. Local negative feedback is grudgingly
regarded as acceptable, probably because making a circuit with no feedback of any kind is near
impossible. It is often said that high levels of NFB enforce a low slew rate. This is quite untrue; and
this thorny issue is dealt with in detail in Chapters 4 and 8 . For more on slew rate, see also Ref. [15].
● Tone controls cause an audible deterioration even when set to the fl at position .
This is usually blamed on ‘ phase shift ’ . At the time of writing, tone controls on a pre-amp badly
damage its chances of street (or rather sitting-room) credibility, for no good reason. Tone controls
set to ‘ fl at ’ cannot possibly contribute any extra phase shift and must be inaudible. My view is
that they are absolutely indispensable for correcting room acoustics, loudspeaker shortcomings, or
tonal balance of the source material, and that a lot of people are suffering suboptimal sound as a
result of this fashion. It is now commonplace for audio critics to suggest that frequency-response
inadequacies should be corrected by changing loudspeakers. This is an extraordinarily expensive
way of avoiding tone controls.
● The design of the power supply has subtle effects on the sound, quite apart from ordinary
dangers like ripple injection .
All good amplifi er stages ignore imperfections in their power supplies, op-amps in particular
excelling at power-supply rejection ratio. More nonsense has been written on the subject of subtle
PSU failings than on most audio topics; recommendations of hard-wiring the mains or using
gold-plated 13 A plugs would seem to hold no residual shred of rationality, in view of the usual
processes of rectifi cation and smoothing that the raw AC undergoes. And where do you stop? At
the local substation? Should we gold-plate the pylons?
● Monobloc construction (i.e. two separate power amplifi er boxes) is always audibly
superior, due to the reduction in crosstalk .
There is no need to go to the expense of monobloc power amplifi ers in order to keep crosstalk
under control, even when making it substantially better than the 20 dB that is actually necessary.
The techniques are conventional; the last stereo power amplifi er I designed managed an
easy 90 dB at 10 kHz without anything other than the usual precautions. In this area dedicated
followers of fashion pay dearly for the privilege, as the cost of the mechanical parts will be nearly
doubled.
● Microphony is an important factor in the sound of an amplifi er, so any attempt at vibration
damping is a good idea .
Microphony is essentially something that happens in sensitive valve preamplifi ers. If it happens in
solid-state power amplifi ers the level is so far below the noise it is effectively nonexistent.
Experiments on this sort of thing are rare (if not unheard of) and so I offer the only scrap of
evidence I have. Take a microphone pre-amp operating at a gain of 70 dB, and tap the input capacitors (assumed electrolytic) sharply with a screwdriver; the pre-amp output will be a dull
thump, at low level. The physical impact on the electrolytics (the only components that show this
effect) is hugely greater than that of any acoustic vibration; and I think the effect in power amps, if
any, must be so vanishingly small that it could never be found under the inherent circuit noise.
Let us for a moment assume that some or all of the above hypotheses are true, and explore the
implications. The effects are not detectable by conventional measurement, but are assumed to be
audible. First, it can presumably be taken as axiomatic that for each audible defect some change
occurs in the pattern of pressure fl uctuations reaching the ears, and therefore a corresponding
modifi cation has occurred to the electrical signal passing through the amplifi er. Any other starting
point supposes that there is some other route conveying information apart from the electrical
signals, and we are faced with magic or forces unknown to science. Mercifully no commentator has
(so far) suggested this. Hence there must be defects in the audio signals, but they are not revealed by
the usual test methods. How could this situation exist? There seem to be two possible explanations
for this failure of detection: one is that the standard measurements are relevant but of insuffi cient
resolution, and we should be measuring frequency response, etc., to thousandths of a decibel. There
is no evidence whatsoever that such micro-deviations are audible under any circumstances.
An alternative (and more popular) explanation is that standard sine-wave THD measurements miss
the point by failing to excite subtle distortion mechanisms that are triggered only by music, the
spoken word, or whatever. This assumes that these music-only distortions are also left undisturbed
by multi-tone intermodulation tests, and even the complex pseudorandom signals used in the
Belcher distortion test [16] . The Belcher method effectively tests the audio path at all frequencies at
once, and it is hard to conceive of a real defect that could escape it.
The most positive proof that subjectivism is fallacious is given by subtraction testing. This is the
devastatingly simple technique of subtracting before and after amplifi er signals and demonstrating
that nothing audibly detectable remains.
It transpires that these alleged music-only mechanisms are not even revealed by music, or indeed
anything else, and it appears the subtraction test has fi nally shown as nonexistent these elusive
degradation mechanisms.
The subtraction technique was proposed by Baxandall in 1977 [17] . The principle is shown in
Figure 1.3 ; careful adjustment of the roll-off balance network prevents minor bandwidth variations
from swamping the true distortion residual. In the intervening years the subjectivist camp has made
no effective reply.
A simplifi ed version of the test was introduced by Hafl er [18] . This method is less sensitive, but has the
advantage that there is less electronics in the signal path for anyone to argue about (see Figure 1.4 ).
A prominent subjectivist reviewer, on trying this demonstration, was reduced to claiming that the
passive switchbox used to implement the Hafl er test was causing so much sonic degradation that
all amplifi er performance was swamped [19] . I do not feel that this is a tenable position. So far all
experiments such as these have been ignored or brushed aside by the subjectivist camp; no attempt
has been made to answer the extremely serious objections that this demonstration raises.
The Length of the Audio Chain
An apparently insurmountable objection to the existence of non-measurable amplifi er quirks is
that recorded sound of almost any pedigree has passed through a complex mixing console at least
once; prominent parts like vocals or lead guitar will almost certainly have passed through at least
twice, once for recording and once at mix-down. More signifi cantly, it must have passed through
the potential quality bottleneck of an analog tape machine or more likely the A – D converters
of digital equipment. In its long path from here to ear the audio passes through at least 100
op-amps, dozens of connectors, and several hundred meters of ordinary screened cable. If mystical
degradations can occur, it defi es reason to insist that those introduced by the last 1% of the path are
the critical ones.
The Implications
This confused state of amplifi er criticism has negative consequences. First, if equipment is
reviewed with results that appear arbitrary, and which are in particular incapable of replication
or confi rmation, this can be grossly unfair to manufacturers who lose out in the lottery. Since
subjective assessments cannot be replicated, the commercial success of a given make can depend
entirely on the vagaries of fashion. While this is fi ne in the realm of clothing or soft furnishings, the
hi-fi business is still claiming accuracy of reproduction as its raison d ’ ê tre, and therefore you would
expect the technical element to be dominant.
A second consequence of placing subjectivism above measurements is that it places designers in
a most unenviable position. No degree of ingenuity or attention to technical detail can ensure a
good review, and the pressure to adopt fashionable and expensive expedients (such as linear-crystal
internal wiring) is great, even if the designer is certain that they have no audible effect for good or
evil. Designers are faced with a choice between swallowing the subjectivist credo whole or keeping
very quiet and leaving the talking to the marketing department.
If objective measurements are disregarded, it is inevitable that poor amplifi ers will be produced,
some so bad that their defects are unquestionably audible. In recent reviews [20] it was easy to
fi nd a £ 795 preamplifi er (Counterpoint SA7) that boasted a feeble 12 dB disk overload margin
(another pre-amp costing £ 2040 struggled up to 15 dB – Burmester 838/846) and another costing
£ 1550 that could only manage a 1 kHz distortion performance of 1%, a lack of linearity that would
have caused consternation 10 years ago (Quicksilver). However, by paying £ 5700 one could inch
this down to 0.3% (Audio Research M100-2 monoblocs). This does not of course mean that it is
impossible to buy an ‘ audiophile ’ amplifi er that does measure well; another example would be the
preamplifi er/power amplifi er combination that provides a very respectable disk overload margin
of 31 dB and 1 kHz rated-power distortion below 0.003%, the total cost being £ 725 (Audiolab
8000C/8000P). I believe this to be a representative sample, and we appear to be in the paradoxical
situation that the most expensive equipment provides the worst objective performance. Whatever
the rights and wrongs of subjective assessment, I think that most people would agree that this is a
strange state of affairs. Finally, it is surely a morally ambiguous position to persuade non-technical
people that to get a really good sound they have to buy £ 2000 pre-amps and so on, when both
technical orthodoxy and common sense indicate that this is quite unnecessary.
The Reasons Why
Some tentative conclusions are possible as to why hi-fi engineering has reached the pass that it
has. I believe one basic reason is the diffi culty of defi ning the quality of an audio experience; you
cannot draw a diagram to communicate what something sounded like. In the same way, acoustical
memory is more evanescent than visual memory. It is far easier to visualize what a London bus
looks like than to recall the details of a musical performance. Similarly, it is diffi cult to ‘ look more
closely ’ : turning up the volume is more like turning up the brightness of a TV picture; once an
optimal level is reached, any further increase becomes annoying, then painful.
It has been universally recognized for many years in experimental psychology, particularly in
experiments about perception, that people tend to perceive what they want to perceive. This is
often called the experimenter-expectancy effect; it is more subtle and insidious than it sounds, and
the history of science is littered with the wrecked careers of those who failed to guard against it.
Such self-deception has most often occurred in fi elds like biology, where although the raw data
may be numerical, there is no real mathematical theory to check it against. When the only ‘ results ’
are vague subjective impressions, the danger is clearly much greater, no matter how absolute the
integrity of the experimenter. Thus in psychological work great care is necessary in the use of
impartial observers, double-blind techniques, and rigorous statistical tests for signifi cance. The vast
majority of subjectivist writings wholly ignore these precautions, with predictable results. In a few
cases properly controlled listening tests have been done, and at the time of writing all have resulted
in different amplifi ers sounding indistinguishable. I believe the conclusion is inescapable that
experimenter expectancy has played a dominant role in the growth of subjectivism.
It is notable that in subjectivist audio the ‘ correct ’ answer is always the more expensive or
inconvenient one. Electronics is rarely as simple as that. A major improvement is more likely to be
linked with a new circuit topology or new type of semiconductor, than with mindlessly specifying
more expensive components of the same type; cars do not go faster with platinum pistons.
It might be diffi cult to produce a rigorous statistical analysis, but it is my view that the reported
subjective quality of a piece of equipment correlates far more with the price than with anything else.
There is perhaps here an echo of the Protestant work ethic: you must suffer now to enjoy yourself
later. Another reason for the relatively effortless rise of subjectivism is the me-too effect; many people
are reluctant to admit that they cannot detect acoustic subtleties as nobody wants to be labeled as
insensitive, outmoded, or just plain deaf. It is also virtually impossible to absolutely disprove any
claims, as the claimant can always retreat a fraction and say that there was something special about
the combination of hardware in use during the disputed tests, or complain that the phenomena are too
delicate for brutal logic to be used on them. In any case, most competent engineers with a taste for
rationality probably have better things to do than dispute every controversial report.
Under these conditions, vague claims tend, by a kind of intellectual infl ation, to gradually become
regarded as facts. Manufacturers have some incentive to support the subjectivist camp as they can
claim that only they understand a particular non-measurable effect, but this is no guarantee that the
dice may not fall badly in a subjective review.
The Outlook
It seems unlikely that subjectivism will disappear for a long time, if ever, given the momentum
that it has gained, the entrenched positions that some people have taken up, and the sadly uncritical
way in which people accept an unsupported assertion as the truth simply because it is asserted
with frequency and conviction. In an ideal world every such statement would be greeted by
loud demands for evidence. However, the history of the world sometimes leads one to suppose
pessimistically that people will believe anything. By analogy, one might suppose that subjectivism would persist for the same reason that parapsychology has; there will always be people who will
believe what they want to believe rather than what the hard facts indicate.
More than 10 years have passed since the above material on subjectivism was written, but there
seems to be no reason to change a word of it. Amplifi er reviews continue to make completely
unsupportable assertions, of which the most obtrusive these days is the notion that an amplifi er
can in some way alter the ‘ timing ’ of music. This would be a remarkable feat to accomplish with a
handful of transistors, were it not wholly imaginary.
During my sojourn at TAG-McLaren Audio, we conducted an extensive set of double-blind
listening tests, using a lot of experienced people from various quarters of the hi-fi industry. An
amplifi er loosely based on the Otala four-stage architecture was compared with a Blameless threestage
architecture perpetrated by myself (these terms are fully explained in Chapter 2). The two
amplifi ers could not have been more different – the four-stage had complex lead-lag compensation
and a buffered complementary feedback pair (CFP) output, while my three-stage had conventional
Miller dominant-pole compensation. There were too many other detail differences to list here.
After a rigorous statistical analysis the result – as you may have guessed – was that nobody could
tell the two amplifi ers apart.
Technical Errors
Misinformation also arises in the purely technical domain; I have also found some of the most
enduring and widely held technical beliefs to be unfounded. For example, if you take a Class-B
amplifi er and increase its quiescent current so that it runs in Class-A at low levels, i.e. in Class-AB,
most people will tell you that the distortion will be reduced as you have moved nearer to the full
Class-A condition. This is untrue. A correctly confi gured amplifi er gives more distortion in Class-
AB, not less, because of the abrupt gain changes inherent in switching from A to B every cycle.
Discoveries like this can only be made because it is now straightforward to make testbed amplifi ers
with ultra-low distortion – lower than that which used to be thought possible. The reduction of
distortion to the basic or inherent level that a circuit confi guration is capable of is a fundamental
requirement for serious design work in this fi eld; in Class-B at least this gives a defi ned and
repeatable standard of performance that in later chapters I name a Blameless amplifi er, so called
because it avoids error rather than claiming new virtues.
It has proved possible to take the standard Class-B power amplifi er confi guration, and by minor
modifi cations reduce the distortion to below the noise fl oor at low frequencies. This represents
approximately 0.0005 – 0.0008% THD, depending on the exact design of the circuitry, and the
actual distortion can be shown to be substantially below this if spectrum-analysis techniques are
used to separate the harmonics from the noise.
The Performance Requirements for Amplifi ers
This section is not a recapitulation of international standards, which are intended to provide a
minimum level of quality rather than extend the art. It is rather my own view of what you should be worrying about at the start of the design process, and the fi rst items to consider are the brutally
pragmatic ones related to keeping you in business and out of prison.
Safety
In the drive to produce the fi nest amplifi er ever made, do not forget that the Prime Directive of audio
design is – Thou Shalt Not Kill. Every other consideration comes a poor second, not only for ethical
reasons, but also because one serious lawsuit will close down most audio companies forever.
Reliability
If you are in the business of manufacturing, you had better make sure that your equipment keeps
working, so that you too can keep working. It has to be admitted that power amplifi ers – especially
the more powerful ones – have a reputation for reliability that is poor compared with most
branches of electronics. The ‘ high end’ in particular has gathered to itself a bad reputation for
dependability[21] .
Power Output
In commercial practice, this is decided for you by the marketing department. Even if you can
please yourself, the power output capability needs careful thought as it has a powerful and
nonlinear effect on the cost.
The last statement requires explanation. As the output power increases, a point is reached when
single output devices are incapable of sustaining the thermal dissipation; parallel pairs are
required, and the price jumps up. Similarly, transformer laminations come in standard sizes, so the
transformer size and cost will also increase in discrete steps.
Domestic hi-fi amplifi ers usually range from 20 to 150 W into 8 Ω , though with a scattering of
much higher powers. PA units will range from 50 W, for foldback purposes (i.e. the sound the
musician actually hears, to monitor his/her playing, as opposed to that thrown out forwards by the
main PA stacks, also called stage monitoring) to 1 kW or more. Amplifi ers of extreme high power
are not popular, partly because the economies of scale are small, but mainly because it means
putting all your eggs in one basket, and a failure becomes disastrous. This is accentuated by the
statistically unproven but almost universally held opinion that high-power solid-state amplifi ers are
inherently less reliable than others.
If an amplifi er gives a certain output into 8 Ω , it will not give exactly twice as much into 4 Ω loads;
in fact it will probably be much less than this, due to the increased resistive losses in 4 Ω operation,
and the way that power alters as the square of voltage. Typically, an amplifi er giving 180 W into 8 Ω
might be expected to yield 260 W into 4 Ω and 350 W into 2 Ω , if it can drive so low a load at all.
These fi gures are approximate, depending very much on power supply design.
Nominally 8 Ω loudspeakers are the most common in hi-fi applications. The ‘ nominal ’ title
accommodates the fact that all loudspeakers, especially multi-element types, have marked changes in input impedance with frequency, and are only resistive at a few spot frequencies. Nominal 8 Ω
loudspeakers may be expected to drop to at least 6 Ω in some part of the audio spectrum. To allow
for this, almost all amplifi ers are rated as capable of 4 Ω as well as 8 Ω loads. This takes care of
almost any nominal 8 Ω speaker, but leaves no safety margin for nominal 4 Ω designs, which are
likely to dip to 3 Ω or less. Extending amplifi er capability to deal with lower load impedances
for anything other than very short periods has serious cost implications for the power-supply
transformer and heat-sinking; these already represent the bulk of the cost.
The most important thing to remember in specifying output power is that you have to increase it
by an awful lot to make the amplifi er signifi cantly louder. We do not perceive acoustic power as
such – there is no way we could possibly integrate the energy liberated in a room, and it would be
a singularly useless thing to perceive if we could. It is much nearer the truth to say that we perceive
pressure. It is well known that power in watts must be quadrupled to double sound pressure level
(SPL), but this is not the same as doubling subjective loudness; this is measured in Sones rather
than dB above threshold, and some psychoacousticians have reported that doubling subjective
loudness requires a 10 dB rather than 6 dB rise in SPL, implying that amplifi er power must be
increased tenfold, rather than merely quadrupled [22] . It is at any rate clear that changing from a
25 W to a 30 W amplifi er will not give an audible increase in level.
This does not mean that fractions of a watt are never of interest. They can matter either in pursuit of
maximum effi ciency for its own sake, or because a design is only just capable of meeting its output
specifi cation.
Some hi-fi reviewers set great value on very high peak current capability for short periods. While
it is possible to think up special test waveforms that demand unusually large peak currents, any
evidence that this effect is important in use is so far lacking.
Frequency Response
This can be dealt with crisply; the minimum is 20 Hz – 20 kHz, 0.5 dB, though there should never
be any plus about it when solid-state amplifi ers are concerned. Any hint of a peak before the rolloff
should be looked at with extreme suspicion, as it probably means doubtful HF stability. This is
less true of valve amplifi ers, where the bandwidth limits of the output transformer mean that even
modest NFB factors tend to cause peaking at both high and low ends of the spectrum.
Having dealt with the issue crisply, there is no hope that everyone will agree that this is adequate.
CDs do not have the built-in LF limitations of vinyl and could presumably encode the barometric
pressure in the recording studio if this was felt to be desirable, and so an extension to 0.5 dB
at 5 or 10 Hz is perfectly feasible. However, if infrabass information does exist down at these
frequencies, no domestic loudspeaker will reproduce them.
Noise
There should be as little as possible without compromising other parameters. The noise
performance of a power amplifi er is not an irrelevance [23] , especially in a domestic setting.
Distortion
Once more, a sensible target might be: as little as possible without messing up something else . This
ignores the views of those who feel a power amplifi er is an appropriate device for adding distortion
to a musical performance. Such views are not considered in the body of this book; it is, after all,
not a treatise on fuzz-boxes or other guitar effects.
I hope that the techniques explained in this book have a relevance beyond power amplifi ers.
Applications obviously include discrete op-amp-based preamplifi ers [24] , and extend to any
amplifi er aiming at static or dynamic precision.
My philosophy is the simple one that distortion is bad and high-order distortion is worse. The
fi rst part of this statement is, I suggest, beyond argument, and the second part has a good deal
of evidence to back it. The distortion of the n th harmonic should be weighted by n2 /4 worse,
according to many authorities [25] . This leaves the second harmonic unchanged, but scales up the
third by 9/4, i.e. 2.25 times, the fourth by 16/4, i.e. 4 times, and so on. It is clear that even small
amounts of high-order harmonics could be unpleasant, and this is one reason why even modest
crossover distortion is of such concern.
Digital audio now routinely delivers the signal with less than 0.002% THD, and I can earnestly
vouch for the fact that analog console designers work furiously to keep the distortion in long
complex signal paths down to similar levels. I think it an insult to allow the very last piece of
electronics in the chain to make nonsense of these efforts.
I would like to make it clear that I do not believe that an amplifi er yielding 0.001% THD is going
to sound much better than its fellow giving 0.002%. However, if there is ever a scintilla of doubt
as to what level of distortion is perceptible, then using the techniques I have presented it should be
possible to routinely reduce the THD below the level at which there can be any rational argument.
I am painfully aware that there is a school of thought that regards low THD as inherently immoral,
but this is to confuse electronics with religion. The implication is that very low THD can only be
obtained by huge global NFB factors that require heavy dominant-pole compensation that severely
degrades slew rate; the obvious fl aw in this argument is that once the compensation is applied the
amplifi er no longer has a large global NFB factor, and so its distortion performance presumably
reverts to mediocrity, further burdened with a slew rate of 4 V per fortnight.
To me low distortion has its own aesthetic and philosophical appeal; it is satisfying to know that the
amplifi er you have just designed and built is so linear that there simply is no realistic possibility of it
distorting your favorite material. Most of the linearity-enhancing strategies examined in this book are
of minimal cost (the notable exception being resort to Class-A) compared with the essential heat-sinks,
transformer, etc., and so why not have ultra-low distortion? Why put up with more than you must?
Damping Factor
Audio amplifi ers, with a few very special exceptions [26] , approximate to perfect voltage sources, i.e.
they aspire to a zero output impedance across the audio band. The result is that amplifi er output is unaffected by loading, so that the frequency-variable impedance of loudspeakers does not give an
equally variable frequency response, and there is some control of speaker cone resonances.
While an actual zero impedance is impossible, a very close approximation is possible if large
negative-feedback factors are used. (Actually, a judicious mixture of voltage and current feedback
will make the output impedance zero, or even negative – i.e. increasing the loading makes the
output voltage increase. This is clever, but usually pointless, as will be seen.) Solid-state amplifi ers
are quite happy with lots of feedback, but it is usually impractical in valve designs.
Damping factor (DF) is defi ned as the ratio of the load impedance Rload to the amplifi er output
resistance Rout :
Damping factor load
out
R
R
Equation 1.1
A solid-state amplifi er typically has output resistance of the order of 0.05 Ω , so if it drives an 8 Ω
speaker we get a damping factor of 160 times. This simple defi nition ignores the fact that amplifi er
output impedance usually varies considerably across the audio band, increasing with frequency
as the negative feedback factor falls; this indicates that the output resistance is actually more like
an inductive reactance. The presence of an output inductor to give stability with capacitive loads
further complicates the issue.
Mercifully, damping factor as such has very little effect on loudspeaker performance. A damping
factor of 160 times, as derived above, seems to imply a truly radical effect on cone response – it
implies that resonances and such have been reduced by 160 times as the amplifi er output takes an
iron grip on the cone movement. Nothing could be further from the truth.
The resonance of a loudspeaker unit depends on the total resistance in the circuit. Ignoring the
complexities of crossover circuitry in multi-element speakers, the total series resistance is the sum
of the speaker coil resistance, the speaker cabling and, last of all, the amplifi er output impedance.
The values will be typically 7, 0.5, and 0.05 Ω respectively, so the amplifi er only contributes 0.67%
to the total, and its contribution to speaker dynamics must be negligible.
The highest output impedances are usually found in valve equipment, where global feedback
including the output transformer is low or nonexistent; values around 0.5 Ω are usual. However,
idiosyncratic semiconductor designs sometimes also have high output resistances; see Olsher [27] for
a design with Rout 0.6 Ω , which I feel is far too high.
This view of the matter was practically investigated and fully confi rmed by James Moir as far back
as 1950 [28] , though this has not prevented periodic resurgences of controversy.
The only reason to strive for a high damping factor – which can, after all, do no harm – is the
usual numbers game of impressing potential customers with specifi cation fi gures. It is as certain
as anything can be that the subjective difference between two amplifi ers, one with a DF of 100 and
the other boasting 2000, is undetectable by human perception. Nonetheless, the specifi cations look very different in the brochure, so means of maximizing the DF may be of some interest. This is
examined further in Chapter 8.
Absolute Phase
Concern for absolute phase has for a long time hovered ambiguously between real audio concerns
like noise and distortion, and the subjective realm where solid copper is allegedly audible. Absolute
phase means the preservation of signal phase all the way from microphone to loudspeaker, so that a
drum impact that sends an initial wave of positive pressure towards the live audience is reproduced
as a similar positive pressure wave from the loudspeaker. Since it is known that the neural impulses
from the ear retain the periodicity of the waveform at low frequencies, and distinguish between
compression and rarefaction, there is a prima facie case for the audibility of absolute phase.
It is unclear how this applies to instruments less physical than a kickdrum. For the drum the
situation is simple – you kick it, the diaphragm moves outwards and the start of the transient
must be a wave of compression in the air (followed almost at once by a wave of rarefaction). But
what about an electric guitar? A similar line of reasoning – plucking the string moves it in a given
direction, which gives such and such a signal polarity, which leads to whatever movement of the
cone in the guitar amp speaker cabinet – breaks down at every point in the chain. There is no way
to know how the pickups are wound, and indeed the guitar will almost certainly have a switch for
reversing the phase of one of them. I also suggest that the preservation of absolute phase is not the
prime concern of those who design and build guitar amplifi ers.
The situation is even less clear if more than one instrument is concerned, which is of course almost
all the time. It is very diffi cult to see how two electric guitars played together could have a ‘ correct ’
phase in which to listen to them.
Recent work on the audibility of absolute phase [29,30] shows it is sometimes detectable. A
single tone fl ipped back and forth in phase, providing it has a spiky asymmetrical waveform
and an associated harsh sound, will show a change in perceived timbre and, according to some
experimenters, a perceived change in pitch. A monaural presentation has to be used to yield a
clear effect. A complex sound, however, such as that produced by a musical ensemble, does not in
general show a detectable difference.
Proposed standards for the maintenance of absolute phase have just begun to appear [31] , and the
implication for amplifi er designers is clear; whether absolute phase really matters or not, it is
simple to maintain phase in a power amplifi er and so it should be done (compare a complex mixing
console, where correct phase is absolutely vital, and there are hundreds of inputs and outputs, all
of which must be in phase in every possible confi guration of every control). In fact, it probably
already has been done, even if the designer has not given absolute phase a thought, because almost
all power amplifi ers use series negative feedback, and this is inherently non-inverting. Care is,
however, required if there are stages such as balanced line input amplifi ers before the power
amplifi er itself; if the hot and cold inputs get swapped by mistake then the amplifi er output will be
phase inverted.Amplifi er Formats
When the fi rst edition of this book appeared in 1996, the vast majority of domestic amplifi ers were
two-channel stereo units. Since then there has been a great increase in other formats, particularly
in multichannel units having seven or more channels for audio-visual use, and in single-channel
amplifi ers built into subwoofer loudspeakers.
Multichannel amplifi ers come in two kinds. The most cost-effective way to build a multichannel
amplifi er is to put as many power amplifi er channels as convenient on each PCB, and group
them around a large toroidal transformer that provides a common power supply for all of them.
While this keeps the costs down there are inevitable compromises on interchannel crosstalk and
rejection of the transformer’s stray magnetic fi elds. The other method is to make each channel (or,
in some cases, each pair of channels) into a separate amplifi er module with its own transformer,
power supply, heat-sinks, and separate input and output connections – a sort of multiple-monobloc
format. The modules usually share a microcontroller housekeeping system but nothing else. This
form of construction gives much superior interchannel crosstalk, as the various audio circuits need
have no connection with each other, and much less trouble with transformer hum as the modules
are relatively long and thin so that a row of them can be fi tted into a chassis, and thus the mains
transformer can be put right at one end and the sensitive input circuitry right at the other. Inevitably
this is a more expensive form of construction.
Subwoofer amplifi ers are single channel and of high power. There seems to be a general consensus
that the quality of subwoofer amplifi ers is less critical than that of other amplifi ers, and this
has meant that both Class-G and Class-D designs have found homes in subwoofer enclosures.
Subwoofer amplifi ers differ from others in that they often incorporate their own specialized
fi ltering (typically at 200 Hz) and equalization circuitry.
ไม่มีความคิดเห็น:
แสดงความคิดเห็น