How to Gain Gain: A Reference Book on Triodes in Audio Pre-Amps

849 Pages·2013·28.24 MB·English

by  Burkhard Vogel (auth.)

Burkhard Vogel
How to Gain Gain
A Reference Book on
Triodes in Audio Pre-Amps
Second Edition
How to Gain Gain
Burkhard Vogel
How to Gain Gain
A Reference Book on Triodes
in Audio Pre-Amps
Second Edition
123
Dipl.-Ing. Burkhard Vogel
Lab 6-11
Stuttgart
Germany
ISBN 978-3-642-33032-2 ISBN 978-3-642-33033-9 (eBook)
DOI 10.1007/978-3-642-33033-9
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012952019
(cid:2)Springer-VerlagBerlinHeidelberg2013
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To my wife Beate1
and all valve enthusiasts
1 Shebecameatriodeenthusiasttoo,afterlisteningtomylatesttriodedrivenphono-amp(The
SoundofSilence,2nd.ed.,Springer,2011),playingFriedemann’s180g‘MemoryLane’(inakustk,
BiberRecords).
Preface Second Edition
After theappearanceofthe second edition of‘‘The SoundofSilence’’(TSOS-2)2
and because of its additional turning to valve electronics, it became clear to me
that an expanded second edition of ‘‘How to Gain Gain’’ should follow as fast as
possible.Atleastitshouldincludeallfindingsonelectronicnoisecalculationsfor
triodes, and additionally, it should allow broad application of the Zwicky mor-
phological box approach with additional gain stage configurations that were not
mentioned in the first edition of this book.
Hence,thecompletereworkingofallchapters,thecorrectionofprintingerrors,
and a broader range of add-ons came into the main focus. The summary of the
news looks as follows:
• Three new Chaps. 1–3 on triode gain stage basics for calculation purposes, the
derivation and explanation of the triode’s generated electronic noise, and the
noise creation of passive components became an essential task.
• Inaddition,eachpresentedgainstagecalculationincludesacompleteelectronic
noise treatment section of that specific gain stage. Based on the many TSOS-2
measurements and calculations, newly developed equivalent circuits for noise
calculations play the major role for the noise calculations. It includes three
different versions of signal-to-noise ratio (SN) calculations too.
• These gain stage calculations are accompanied by extensive calculation work-
sheets based on Mathcad 11.3 With a roughly ±20 % tolerance bandwidth
valvesarenotveryprecisedevices.Therefore,theworksheetsshouldalsoserve
as a kind of simulation tool that allows fast tolerance calculations—as long as
thereisnosoftwaretoolonthemarketthatcoversnoisevoltagecalculationstoo.
All worksheets can be downloaded for free from the Springer website.
• The number of different gain stages and gain stage configurations increased
from 27 to 54.
2 SeeAppendixA.
3 In cases of no access to Mathcad, there is a free download possibility of easy to use
mathematicalsoftwarecalled‘‘SMathStudio’’.
vii
viii PrefaceSecondEdition
• Summary tables in Chap. 34 allow fast comparisons of a variety of calculated
items that are based on equal operating conditions. The variety includes the
various gains of the gain stage, the triode noise voltages, the triode’s 1/f-noise
corner frequency, gain stage SNs, and gain stage worsening factors.
• Nearly, all of the presented gain stages became part of extensive gain, transfer
function, noise voltage, and SN measurements. The SN results of these actions
led to the recommendation tables of Chap. 2.
Iguessthatmostoftheprefacecontentofthefirsteditionisstillworthreading.
Therefore, I have decided to leave it like it is.
Stuttgart, Germany, May 2012
Burkhard Vogel
Preface First Edition
The today’s (2008) audio (or low-frequency) amplifier world is nearly 100%
‘‘contaminated’’bysiliconsolid-statecomponentsthatensureproperamplification
for any signal from any source (CD, DVD, Vinyl, MP3, Radio, TV, etc.) to ones
ears.Abroadrangeofdesignsupportingliterature4andotherinformationsources
and tools like eg. the internet or component producer’s applications help design
engineers world-wide to come up with the right products at the right time on the
right markets - hopefully.
The percentage difference between 100% and nearly 100% is filled with gain
making elements that are far away from silicon: vacuum valves and audio trans-
formers.It’s an interestingfact that stillmany CDand/orDVD producingstudios
work with valve and transformer driven equipment like eg. the compressor types
Teletronik LA-2A or UREI 1176LN or they bring into action valve driven
microphones(eg.NeumannU47orRodeClassicII)andmixersatthefront-endof
the recording chain. Not to forget all the valve powered measurement equipment
(from eg. Brüel & Kjær, Tektronics, etc.) still in use.
Because of their outstanding sound quality (eventually mainly caused by an
evenharmonicsdistortioneffect)mostoftheinvolvedvalvesinpre-ampstagesare
triodesorpentodesconfiguredastriodes.Iwon’tdebatewhethersiliconorvacuum
soundsbetter-thiswouldbepurelysubjective.Buttheworld-widegrowingsales
revenues for vacuum based sound and reproduction equipment is an astonishing
thingformeandgivesasoundrelatedanswerbypurseorcreditcard.Andanother
thing surprises me as well: despite the totally different analogue world there are
enoughyoungengineers(andseniorones—ofcourse)ofourtotallydigitalerathat
are willing to struggle with such an old fashioned technology by creating superb
sounding electronic instruments.
Although it might look as if—but it has nothing to do with Black Art! It’s
simply the transfer of a specific know-how into life by enthusiasts. A know-how
4 Interalia:‘‘ElectronicCircuits’’,U.Tietze,C.Schenk,2ndedition,Springer2008,ISBN978-
3-540-00429-5.
ix
x PrefaceFirstEdition
thatseemstobenolongerpartoftrainingcoursesofuniversitiesandcolleges,that
isthreatenedtogetlostifwedon’tworkhardtostopthisevolutionbybringingout
ready and easy to use modern literature and software tools.
Therefore, the following chapters offer formulae to calculate certain building
blocks of valve amplifiers—but for pre-amp purposes only. In nearly all cases
detailedderivationsarealsogiven.Allwhat’sneededarethedatasheetfiguresof
the triode’s () mutual conductance g , the gain factor l and the internal plate
t m, t
resistance r . To calculate frequency and phase responses of gain stages the dif-
a
ferent data sheet presented input and output capacitances have to be taken into
account as well.
It must be pointed out that all formulae are based on certain assumptions. The
most important one is the one that defines the DC biasing conditions of these
active devices. The conditions were assumed to be those of the A-class operating
point settings: the plate DC current never switches off for positive and negative
parts of the input signal. In other words: the A-class operating point is located in
the(*middleofthe)mostlinearpartoftheV /I versusplatevoltageV diagram
g a a
of the respective valve. This is the only way to guarantee that the triode’s data
sheetfiguresformutualconductanceg ,gainlandinternalplateresistancer can
m a
be taken as so-called constants (always valid: l = g r ) and can be used for our
m a
calculation purposes.
Other biasing classes (B = total plate/cathode current switch-off for negative
signal parts or AB = a tiny quiescent current is allowed toflowthrough plate and
cathodefornegativesignalparts)ortheuseofotheroperatingpointsontheV /I
g a
versusplatevoltageV characteristicplotneedcertainadditionalmeasurementsor
a
graphical approaches to get the right values for the above shown valve constants.
Havinggonethroughtheseprocessesthenewlygeneratedg ,l 5,andr
m.new new a.new
figuresshouldbeusedforfurthercalculationpurposes.Thegivenformulaewon’t
change and will look the same.
Idonotdiveintothevalve’sDCbiasingmechanicsbecausetheycaneasilybe
studiedwiththehelpofabroadrangeofliterature.6Butinthatrangeofbooksand
magazines7 I miss a summary of all the gain producing possibilities of triodes on
one spot. That will be the only matter of the following pages. The respective
formulae were derived from equivalent circuits by application of Ohm’s8 and
Kirchhof’s9 laws. It will be demonstrated in detail in Chapters 4ff. These
approachesleadtocertainampbuildingblocksaroundonevalve.Theformulaefor
5 Incontrasttorespective‘‘ondit(s)’’achangeofthebiaspointalsomeansachangeofl;itis
notaconstantatall.
6 Interalia:‘‘Valveamplifiers’’,MorganJones,Newnes,alleditions.
7 Interalia:‘‘TubeCadJournal’’.
8 a)1X*1A=1Vor-generallyspoken-R*I=V.
9 a) The sum of all currents in a circuit’s node equals zero; b) The sum of all voltages (=
potentialdifferences)inacircuit’sclosedloopequalszero.
PrefaceFirstEdition xi
gain stages that incorporate more than one valve (eg. CCSCF or cascoded gain
stages, etc.) will mostly be derived from these building blocks.
Inaddition,Mathcad10(MCD)worksheetsasapartofeachchapteralloweasy
follow-up and application of the respective formulae for any kind of triode. The
calculationsshowresultswith3digitsafterthedecimalpoint.Theonlyreasonfor
that is to demonstrate—from time to time—(tiny) differences with other calcula-
tionresults.Inreality,evenacalculationresultofonedigitafterthedecimalpoint
wouldn’tpresentthewholetruthbecausethetolerancesofvalvesareamagnitude
awayfromprecision.Butthisfactdidn’t-nordoesn’tittoday—preventengineers
from designing extremely precise working analogue amps and other electronic
valve driven devices. That’s why, on the other hand, the calculation approaches
offered are not far away from reality.
I’msureIonlydidtreatalimitedselectionofpossiblebuildingblocksfortriode
drivenamps.That’swhyallreadersareinvitednottohesitatetosendtotheeditors
their know-how on additional triode amp stage solutions—including the mathe-
matical derivations that are needed to understand how they work (à la the pre-
sented Mathcad worksheets). This book should become the collection of
everything what’s of interest on this specific design field. The next edition will
come out with these additional designs.
To sum-up the aims of this book:
• Building-up a collection of triode amp stage alternatives with satisfactory
mathematical demonstration on how they work via derivations and transfer
functions.
• To make things less complex the transfer functions are derived from rather
simplified equivalent circuits, thus, saving a lot of energy by paying for it with
tiny frequency and phase response errors, especially at the ends of the audio
band.
• It’salwaysbettertocalculatefirst-andspentmoneyforexpensivecomponents
later—instead of playing around with dice-type trial and error.
10 MathcadisaregisteredtrademarkofMathSoftEngineering&EducationInc.,since2006part
ofParametricsTechnologyCorporation(PTC),Ma.,USA.