1. Heinrich Barkhausen Valve Equation
2009
Bonjour Stella
Heinrich Barkhausen
and his
Valve Equation
Jürgen Ewert
Good morning triode lovers from all over the world. First I would like to thank our French group for organnizing the festival at this nice place.

2. Preface I know that ~ we don’t always need to do a lot of calculations
when building Triode Amplifiers, but it may
help you conceptualising a project
For some of you it may be NOS (New Old Stuff)
For some of you it may be interesting
Please let me know if it’s boring
… before you start snoring
Today I will talk about Barkhausen, tube data and curves.
Than I will cover the tube parameters and Barkausen’s Tube Equation.
Later I would like to show how we can apply the tube equation in designing an amplifier.

3. Agenda Heinrich Barkhausen Tube Data & Curves
Tube Parameters
Barkhausen’s Tube Equation
Conceptualising a Small Signal Amplifier
Today I will talk about Barkhausen, tube data and curves.
Than I will cover the tube parameters and Barkausen’s Tube Equation.
Later I would like to show how we can apply the tube equation in designing an amplifier.

4. Heinrich G. Barkhausen Interested in Technology early in his life
Studied at the TU Munich and TU Berlin
1907 Doctorate at the University of Göttingen
1911 Founded “Institut für Schwachstromtechnik”
1923 “Lehrbuch der Elektronenröhren” vol.1
“Textbook of Electron Tubes”
standard textbook
in Germany
b. 1881, Bremen, Germany
Interested in Technology early in his life
Studied at the TU Munich and TU Berlin
1907 Doctorate at the University of Göttingen
1911 Founded “Institut für Schwachstromtechnik”
1923 “Lehrbuch der Elektronenröhren” vol.1
“Textbook of Electron Tubes”
standard textbook
in Germany
later 4 volumes
Heinrich Georg Barkhausen
b. December 2, 1881, Bremen, Germany
d. February 20, 1956, Dresden, Germany

5. Barkhausen’s Book Lehrbuch der Elektronenröhren last edition in 1965
4 volumes
Barkhausens books are not the only ones, but very good books
Im Jahr 1923 erschien der erste Band des Lehrbuchs für Elektronenröhren, welches schon 1924 eine Verbesserung erfuhr folgte der zweite Band über Röhrensender, 1929 der dritte über Röhrenempfänger und schließlich noch ein vierter Band. Dieses Standardwerk war bis zum Ende der Röhrenära sämtlichen Radiokonstrukteuren bekannt, vor allem hierdurch wurde der Name Barkhausen zum Begriff. Es gilt bis heute als das umfassendeste und bedeutendste seiner Art. Barkhausen hat 1955 die 7. Auflage noch selber überarbeitet. Die letzte Ausgabe, bearbeitet von Prof. Dr. Eugen Woschni, ist 1965 erschienen.
vierbändige Monografie Lehrbuch der Elektronenröhren, Elektronenröhren und ihre technischen Anwendungen, Hirzel-Verlag Leipzig
Band 1: Allgemeine Grundlagen
Band 2: Verstärker
Band 3: Rückkopplung
Band 4: Gleichrichter und Empfänger
last edition in 1965

6. Barkhausen at the TU-Dresden
d. 1956, Dresden, Germany
Barkhausen
Dresden, Germany
Barkhausen Bau 1959
Barkhausen recognized the
importance of the Transistor but …

7. Lt. Viktor Ivanovich Belenko
Tubes are still used!
The USSR didn’t make Tubes for Audio!
MIG-25
September 6, 1976
Lt. Viktor Ivanovich Belenko
September 06, 1976 Lt. Viktor Ivanovich Belenko piloted his Mig-25 (USSR Product #84) from
the 513th Fighter Regiment at the Siberian Base of Sakharovka, Soviet Air Defense Command and
defected to the United States. He landing the Mig-25 in Japan
Vacuum tubes are up to 1000 times more able to withstand EMP than solid-state electronics.
Landed in Japan

8. Celebrating the Triode
Tube-Audio
is very popular
300 B
Let’s go back to our triodes

9. About Triodes powering a triode measuring the curves
curves & parameters
Last year’s
WINNER
was
CAROLUS
Like people, tubes are individuals. Some have curves some are more linear than others.
Scientists and engineers found early that all tubes are not equal. saturation current amplification mu, etc
Not all Triodes are equal !

10. Powering a Triode Ia Ua Ug Uk = 0V Three important values Eg Ep Ip
plate voltage
plate current
grid voltage
grid current
Three important values – grid current is not important for small signal behavior of a triode
I’m giving both nomenclatures, the German and English because there are differences in the literature

11. Measuring the Tube Curves
Circuit for measuring the
characteristic curves
of a triode
Transfer Characteristic:
Ua = constant; Ug = var.
Plate Characteristic:
Ug = constant; Ua = var.
We know a better method with Ives curve tracer

12. Yves’s Curve Tracer Did You Bring Your Tubes to get the Real Curves?
Intoduced at the ETF 2007
The Hi-Tech Solution for
measuring the tube-curves
We know a better method with Ives curve tracer
Yves Monmagnon

13. Curves versus Linear A Study revealed: most Men go for curvy girls
~ for Audio signals
we want a linear
characteristic
… men will choose a Rubenesque size 14 over a stick-figure size 8 when it comes to their ideal woman.
individual curves are different

14. The Audio-Flagship ~ 300B
The data sheet of the Western Electric 300B is very detailled. A graet example how a data sheet should be.

15. 300B Plate Characteristic Ia; Ua
NOT LINEAR!
Measuring the tube with either Ua=constant or Ug=constant gives two useful sets of curves.
transfer characteristic and plate characteristic make it easier to calculate the tube parameters for a given working point

16. 300B Transfer Characteristic Ia; Ug
NOT LINEAR!
Measuring the tube with either Ua=constant or Ug=constant gives two useful sets of curves.
transfer characteristic and plate characteristic make it easier to calculate the tube parameters for a given working point

17. 300B Engineering Data … the MAXIMUM RATINGS are very important
we will discuss the tube parameters in the following slides
Start page with NO slide # (covered)

18. 300B Tube Parameters more about 300B parameters later …
Start page with NO slide # (covered)
more about 300B parameters later …

19. 300B Transconductance We will re-visit
Start page with NO slide # (covered)
Higlights of the “White Light” by Dietmar & Jürgen Ewert

20. 300B Plate Resistance We will re-visit
Start page with NO slide # (covered)

21. 300B Amplification Factor
We will re-visit
Start page with NO slide # (covered)

22. The Tube Parameters The Names in English & German
mutual conductance & Steilheit
amplification factor & Durchgriff
plate resistance & Innenwiderstand
measuring the tube parameters
Scientists and engineers found early that all tubes are not equal. saturation current amplification mu, etc

23. Mutual Conductance - Steilheit
or Transconductance gm
Steilheit S 
differential quotient

24. Transconductance - Steilheit
Transfer characteristic Ia/Ug Plate characteristic Ia/Ua
Tangent
Mutual Conductance ~
Steilheit
setting the operating point
differential quotient  very small changes

25. Mutual Conductance - Steilheit
Transfer characteristic Ia/Ug Plate characteristic Ia/Ua
Mutual Conductance ~
Steilheit
Δ IA
setting the operating point
Δ UG
difference quotient  changes in linear range

26. Mutual Conductance - Steilheit
or Transconductance gm
gm = Δ Ip / Δ Eg   | Ep = constant [mMho]
"milli Mho" (mA/V)
… “Ohm” spelled backwards
Steilheit S 
S = Δ IA / Δ UG1  | UA = konstant [mA/V]
Ohm
Mho
Groeg Nomis Mho
Georg Simon Ohm
Mutual Conductance or Transconductance gm
the ratio of variation of plate current
to variation of the control grid voltage
at constant plate voltage
gm  = Δ Ip / Δ Eg   | Ep = constant [mA/V]
[in "milli Mho"] (mA/V) … “Ohm” spelled backwards (Siemens)
Georg Simon Ohm – Groeg Nomis Mho
Steilheit S 
Das Verhältnis von Anodenstromänderung zu
Spannungsänderung am Steuergitter bei konstanter UA
S = Δ IA / Δ UG1  | UA = konstant [mA/V]

27. depends on Grid- and Plate-Voltage
300B Transconductance
depends on Grid- and Plate-Voltage
Start page with NO slide # (covered)
Higlights of the “White Light” by Dietmar & Jürgen Ewert

28. Plate Resistance - Innenwiderstand
Plate Resistance rp
Innenwiderstand Ri
Start page with NO slide # (covered)
differential quotient

29. Plate Resistance - Innenwiderstand
Transfer characteristic Ia/Ug Plate characteristic Ia/Ua
Plate Resistance ~
Innenwiderstand
Tangent
setting the operating point
differential quotient  very small changes

30. Plate Resistance - Innenwiderstand
Transfer characteristic Ia/Ug Plate characteristic Ia/Ua
Plate Resistance ~
Innenwiderstand
setting the operating point
Δ IA
Δ UA
difference quotient  small changes (linear)

31. Plate Resistance - Innenwiderstand
Plate Resistance rp
the dynamic source resistance of the anode
   rp= Δ Ep / Δ Ip   | UG1 =  constant [kΩ]
Innenwiderstand Ri
ist der dynamische Quellwiderstand der Anode
    Ri= Δ UA / Δ IA   | UG1 = konstant [kΩ]
Start page with NO slide # (covered)

32. depends on Grid- and Plate-Voltage
300B Plate Resistance
Start page with NO slide # (covered)
depends on Grid- and Plate-Voltage

33. Amplification Factor - Durchgriff
Amplification Factor µ (mu) = 1/D
(open-loop gain)
Durchgriff D  “inverse amplification factor”
differential quotient

34. Amplification Factor - Durchgriff
Transfer characteristic Ia/Ug Plate characteristic Ia/Ua
Inverse Amplification Factor ~
Durchgriff
No curves with IA=const.
setting the operating point
differential quotient  very small changes

35. Amplification Factor - Durchgriff
Transfer characteristic Ia/Ug Plate characteristic Ia/Ua
Δ UG
Δ UA
setting the operating point
IA=const.
Δ UG
Δ UA
difference quotient  small changes (linear)

36. Amplification Factor - Durchgriff
Amplification Factor µ (mu)
   µ =  Δ Ep / Δ Eg  = 1/D | Ip = constant
('Durchgriff‘ or 'Penetration Factor‘ is uncommon in English literature)
Durchgriff D  “inverse amplification factor”
(Leerlaufverstärkungsfaktor µ)
D = Δ UG1 / Δ UA = 1/µ | IA = konstant [%]
Amplification Factor µ (mu)
reaction of of the anode voltage to changes
of the control grid voltage  (voltage amplification)    µ =  Δ Ep / Δ Eg  = 1/D | Ip = constant
('Durchgriff‘ or 'Penetration Factor‘ is uncommon in English literature)
Durchgriff D  “inverse amplification factor”
Rückwirkung der Anodenspannung durch das Gitter
(Leerlaufverstärkungsfaktor µ)
D = Δ UG1 / Δ UA = 1/µ | IA = konstant [%]

37. 300B Amplification Factor
depends on Grid- and Plate-Voltage
Start page with NO slide # (covered)

38. Tube Parameters & Plate Characteristic
THE TUBE PARAMETER TRIANGLE
Δ UG
Δ UA
Δ UG
µ= 1/D =
Δ IA
Rp = Ri =
Gm = S =
Measuring the tube with either Ua=constant or Ug=constant gives two useful sets of curves.
transfer characteristic and plate characteristic make it easier to calculate the tube parameters for a given working point
Δ IA
Δ UA

39. Measuring the Tube Parameters
Set devised by H.W. Everitt
Old Technology
from 1920
but very smart!
combination of three circuits
New Old Stuff
“The thermionic vacuum tube and its applications”
by Hendrik Johannes Van der Bijl
McGraw-Hill, 1920
FREE!
on Google Books
To measure the tube parameters, we don’t need to measure the curves. A better way is to measure the parameters using a tone signal.
see details about the set at: The thermionic vacuum tube and its applications  by Hendrik Johannes Van der Bijl; page
details about the set at:
“The thermionic vacuum tube and its applications”
by Hendrik Johannes Van der Bijl
McGraw-Hill, 1920
pages
FREE!
on Google Books

40. Measuring the Tube Parameters
Circuit I
r1 = 10 Ω
signal current through
r2 compensates signal
because of 180° phase
Start page with NO slide # (covered)
Amplification Factor µ = r2 / r1
adjust r2 to minimum tone in the receiver

41. µ Circuit I ~ Equivalent µ r2 r1 ~ Ug~ Ua~ Ua~= => Ug~ = Ua~
grid
Ua~=
phase 180°
 I~ = 0
=>
it is possible to obtain the tube parameters with only the plate characteristic available r1 r2
Ug~ =
Ua~
adjust r2 to minimum
tone in the headphone
 I~ = 0
CANCEL

42. Measuring the Tube Parameters
Circuit II
r5 = 10 Ω
r3 = 1000 Ω
Start page with NO slide # (covered)
Plate Resistance rp = 100 R1
r2 is the same value as in circuit I
   adjust R1 to minimum tone in the receiver

43. Measuring the Tube Parameters
Circuit III
R2 = 1000 Ω
r4 = 100 Ω
Start page with NO slide # (covered)
Mutual Conductance  gm =  µ/rp = [r2] x 10000
r2 is the same value as in circuit I & II
  [r2] beeing the reading indicated on the dials

44. French, English & German
The Tube Data Sheet
The Tube Parameters in
French, English & German
Datasheets
facteur de gain
pénétration
Scientists and engineers found early that all tubes are not equal. saturation current amplification mu, etc
amplification factor … Durchgriff

45. Tube Parameters - Röhrenkennwerte
Data Sheet
International
it is possible to obtain the tube parameters with only the plate characteristic available
Amplification Factor µ (mu) is more common
than D in most data sheets

46. Tube Data - Röhrenkennwerte
TELEFUNKEN
Data Sheet
Both,
Durchgriff D
and
Amplification Factor
1/D
are given
in the German
Data Sheet
Only the transfer characteristic was given in ealier data sheet. These are curves with Ua=constant

47. Limits of the Tube Parameters
Keep in mind that …
- it’s assumed that the part of the curve is linear
- the tube parameters are only valid for small signals
- the tube parameters vary at different working points
Questions so far?
Do we need tube Parameters and the Tube Equation?
We can build amps without it!
Start page with NO slide # (covered)

48. Barkhausen’s Valve Equation
Start page with NO slide # (covered)
Barkhausen formulated the basic equation
governing the coefficients of the electron-tube
Higlights of the “White Light” by Dietmar & Jürgen Ewert

49. The Tube Equation - German
Barkhausen formulated:
Δ Ia
Δ Ug
Δ Ua = 1 D Ri S
CANCEL
CANCEL
CANCEL
Start page with NO slide # (covered)
If we know two values we can calculate the third one

50. The Tube Equation - English
The English Version:
µ = gm rp
or:
Δ Ip
Δ Eg
Δ Ep = 1 rp gm
Start page with NO slide # (covered)
If we know two values we can calculate the third one

51. Barkhausen’s Tube Equation
is also called the “inner” tube equation
Transconductance * Inverse Amplification Factor * Plate Resistance = 1
gm · 1/µ · rp = S · D · Ri = 1
Die Barkhausensche Röhrenformel
wird auch als "innere" Röhrengleichung bezeichnet
Steilheit · Durchgriff · Innenwiderstand = 1 
S · D · Ri = 1
Start page with NO slide # (covered)

52. Designing with a Triode
Designing a Triode Amplifier
~ What do we want to know?
we know the amplification that we want
we know the parameters of the tube
we would like to know the component values
Scientists and engineers found early that all tubes are not equal. saturation current amplification mu, etc

53. Triode Amplifier Stage
We have a tube
We know the parameters
We know the gain that we need
We want to know Ra for our gain
Simple Triode Amplifier Circuit

54. Plate characteristic Ia/Ua
Operating Point & Gain
load line
Ug~
Ia~
setting the operating point
Plate characteristic Ia/Ua
The Gain Ua~/ Ug~
Ua~

55. keeping the working point
Plate Resistor & Gain
Ug~
Ia~
setting the operating point
keeping the working point
increase Ra~
Ua~
Gain Ua~/ Ug~

56. keeping the working point increased Gain Ua~/ Ug~
Plate Resistor & Gain
Ug~
Ia~
setting the operating point
keeping the working point
increased Ra~
Ua~
increased Gain Ua~/ Ug~

57. keeping the working point increased Gain Ua~/ Ug~
Plate Resistor & Gain
Ug~
Ia~
setting the operating point
keeping the working point
increased Ra~
Ua~
increased Gain Ua~/ Ug~

58. keeping the working point
Plate Resistor & Gain
Ug~
Ia = const
Ia~ = 0
setting the operating point
keeping the working point
Ra~ = ∞
Ua~ = max.
max. Gain

59. Plate Resistor & Gain µ Plate Resistance Ra Gain Ua~ / Ug~
setting the operating point
Plate Resistance Ra

60. Using the Tube Parameters
Data Sheet
it is possible to obtain the tube parameters with only the plate characteristic available
Tube Parameters for Working Points
recommended in the data sheet

61. Calculating Gain using S (gm)
Equivalent Current Source
Ri~
=>
S Ug~
Ua~
|| Ra~
Ia~
Ra~
it is possible to obtain the tube parameters with only the plate characteristic available
Ua~
Ug~
V = = S
Ra~ Ri
Ri + Ra~ +
Ua~ = S
Ug~
Ra~ Ri

62. Calculating Gain using µ (1/D)
Equivalent Voltage Source
Ra~
Ri~
=>
Ug~
Ua~ ~
; Ra~
Ri~
in series
it is possible to obtain the tube parameters with only the plate characteristic available
Ua~
Ug~
V = = +
Ra~ Ri +
Ua~ =
Ug~
Ra~ Ri
Greater Ra
means greater V!

63. Triode Amplifier Stage
The gain “V “ of
the amplifier is always smaller
than µ!
it is possible to obtain the tube parameters with only the plate characteristic available
Ua~
Ug~
V = + = S
Ra~ Ri

64. Triode Amplifier Stage
When designing an amp you know the gain “V” that you need
and you know the
tube parameters.
You really want
to know Ra !
designing an amp we need to calculate the components around the tube. Here we want to know Ra for the gain that we need with a given tube. It may not work if the tube parameters are not matching e.g. a gain of V=100 =
Ra~ Ri S - V -
Ra~ = Ri V

65. Two Stage Amplifier
it is possible to obtain the tube parameters with only the plate characteristic available

66. Two Stage Amplifier Ua~1 Ug~2 1 2 V = = Ua~2 Ug~1 = Ua~1 = V1 * V2
it is possible to obtain the tube parameters with only the plate characteristic available
Ua~2
Ug~1
V = =
Ua~1
= V1 * V2

67. There is more to an Amplifier
Our Pre-Amplifier …
now we know Ra ~ there is still much more
it is a good start for the amp-concept
planning the signal-levels … use dB 1 2 3 4
Atten.
e.g RIAA
Stage 1
Stage 2
Scientists and engineers found early that all tubes are not equal. saturation current amplification mu, etc
signal
voltage 2 4 3 1

68. of your amplifier are great tools, nothing can replace Experimenting
Why do we have our Lab?
Calculating
and modeling
the behaviour
of your amplifier are great tools,
but
nothing can replace Experimenting
Listening
and Testing!
it is possible to obtain the tube parameters with only the plate characteristic available

69. Discussion Barkhausen, “inner tube equation”
Graphic solution using the tube-curves
Calculating the gain of an amplifier stage
Experimenting, Listening and Testing
Scientists and engineers found early that all tubes are not equal. saturation current amplification mu, etc