The Ultra Linear
Power Amplifier
An adventure between triode and pentode
by Rudolf Moers
1
Who am I
Born in 1955 in Veldhoven and now living in Eindhoven in the Netherlands.
Education:
Primary Technical School
Secondary Technical School
High
Technical School
Summary of work experience:
 electrical engineering
 electronics
 electronics
 Analog video modification (RGB-keying)
Analog audio circuits with semi-conductors
Philips Optical Disk Mastering  Compact Disk mastering electronics
Compact Disk signal processing electronics
And a lot more
Philips Medical Systems
 Diaphragm control of Röntgen camera
Philips Electron Optics
 Vacuum pump control for electron microscope
Secondary Technical School  Teacher electronics, theory and practice
ASML
 Architecture of electronic hardware
Infrastructure of cabling and racks with
electronic boards and supplies.
Halin
Hobby :
electron tube amplifiers and radio’s
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Contents of this presentation
1.
Introduction and history
2. Comparison of the static characteristic for Triode, Ultra Linear and
Pentode
3.
Comparison of the powers for Triode, Ultra Linear and Pentode
4.
Network analyses of the Ultra Linear Power Amplifier
a. Repetition of the pentode characteristics
b. Repetition of the pentode quantities
c. Current source and Voltage Source equivalent circuits of the
Pentode
d. Current source and Voltage Source equivalent circuits applied
Ultra Linear
5.
Determination of the screen grid tap
3
Contents of this presentation
6. Test equipment
7. Practical evidence 1 of the network analyses of the Ultra Linear
Amplifier
8. Comparison of practical powers and efficiency of an amplifier in
Triode mode, in Ultra Linear mode and in Pentode mode
9. Practical evidence 2 of the network analyses of the Ultra Linear
Amplifier
10. Comparison practical frequency behavior of an amplifier in Triode
mode, in Ultra Linear mode and in Pentode mode
11. Comparison practical non-linear distortion of an amplifier in Triode
mode, in Ultra Linear mode and in Pentode mode
12. Bibliography
4
1. Introduction and history
David Hafler & Herbert Keroes (not the inventors) published
their Ultra Linear story in 1951.
Publishing in 1959 of the Dutch book “Radio Technique part 1”
written by A. J. Sietsma of the Philips company.
The Philips company has never published an Ultra Linear story, but A. J. Sietsma
made a homework exercise about screen grid negative feedback for students.
Rudolf Moers solved this homework exercise about negative feedback in 2006
with his own formulae which gave the same results as A. J. Sietsma.
5
6
Screen grid tap of the
primary transformer
winding : x
x
vg 2, k
vak
x
vg 2, k
vak
vg 2,k  x  vak
0.0 ≤ x ≤ 1.0
x = 0 : pentode
0 < x < 1 : ultra-linear
x = 1 : triode
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2. Comparison of the static characteristic for Triode, Ultra Linear
and Pentode
Same load lines
with different
scales for Vak
triode
Constriction 40V
Constriction 100V
pentode
Constriction 50V
Ultra-linear
8
3. Comparison of the powers for Triode, Ultra Linear
and Pentode in theory.
Vap,triode
Vap,triode
Iap,triode
Iap,triode
<< Vap,ultralinear
<< Vap,pentode
<< Iap,ultralinear
<< Iap,pentode
Va,pentode = Va,ultralinear
Ia,pentode = Ia,ultralinear
By this:
Pap,triode << Pap,ultralinear
Pap,triode << Pap,pentode
Pa,pentode = Pa,ultralinear
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Comparison of the powers for Triode, Ultra Linear
and Pentode in practice.
In Menno’s first book some design examples are shown which use with jumpers to configure
the circuit into triode, ultra-linear and pentode.
Power results:
2x EL34 with transformer VDV6040PP:
4x EL34 with transformer VDV3070PP:
ptriode = 13W, pultralinear = 33W and ppentode = 40W
ptriode = 30W, pultralinear = 70W and ppentode = 80W
ptriode = 13 W  20 W  pultralinear = 33 W versus pultralinear = 33 W  7 W  ppentode = 40 W
ptriode = 30 W  40 W  pultralinear = 70 W versus pultralinear = 70 W 10 W  ppentode = 80 W
Reason
:
vap,triode << vap,ultralinear < vap,pentode
The constriction of the vg1,k -curves in the anode characteristic Ia = f (Vak)
near the Ia –axis is slightly more with ultra linear than with a pentode.
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4. Network analyses of the Ultra Linear Amplifier
4.a. Repetition of the pentode characteristics
Anode current
11
Screen grid current
12
13
4.b. Repetition of the pentode quantities
Anode steepness is also called mutual conductance gm.
Definition of anode steepness
:
For small signals
:
Definition of screen grid steepness :
For small signals
:
S
S
I a
with constant Vak and Vg2,k
Vg1,k
ia
v g1,k
S2 
S2 
I g 2
Vg1,k
ig 2
with constant Vak and Vg2,k
with constant Vak and Vg2,k
with constant Vak and Vg2,k
v g1,k
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Definition of anode
amplification factor :
Vak

V g1,k
For small signals

:
Definition of screen grid
amplification factor :
v ak
v g1,k
 g 2, g1 
For small signals
:  g 2, g1 
Anode
:
penetration factor
Screen grid penetration factor
V g 2 , k
V g1,k
v g 2,k
v g1,k
Da = µ-1 = 1/µ
with constant Ia and Vg2,k
with constant Ia and Vg2,k
with constant Ig2 and Vak
with constant Ig2 and Vak
(Anode
Durchgriff )
: Dg 2   g12, g1  1/  g 2, g1 (Screen grid Durchgriff)
15
Definition of anode
AC internal resistance
: ri 
Vak
I a
with constant Vg1,k and Vg2,k
For small signals
: ri 
vak
ia
with constant Vg1,k and Vg2,k
Definition of screen grid
Vg 2,k
AC internal resistance : ri 2 
I g 2
For small signals
: ri 2 
v g 2, k
ig 2
with constant Vg1,k and Vak
with constant Vg1,k and Vak
16
Barkhausen’s anode
formula :
  S  ri
Barkhausen’s screen grid formula :  g 2, g1  S 2  ri 2
µpentode
as triode
≈ µg2,g1
At the anode:
Anode AC internal resistance:
ri
(or plate resistance)
Anode AC external resistance:
ra
(external load at the anode)
Screen grid tap of the primary transformer winding : x
17
S
I a
Vg1,k
μ
ΔVak
ΔVg1, k
Vg1,k
I a
Vak
I a
Vg1,k
Vak
Anode current
r i
ΔVak
ΔI a
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S2 
I g 2
Vg1,k
ri2 
ΔV g2,k
ΔI g2
Vg 2,k
Vg 2,k
I g 2
Vg1,k
Screen grid current
Vg1,k
μ g2,g1 
ΔVg2,k
ΔVg1,k
19
S
S2 
I a
Vg1,k
I g 2
Vg1,k
∆Vg1,k
Vg1,k
for S
= ∆Vg1,k
for S2
I a I g 2


S
S2
I g2 
S2
 Ia
S
ig 2 
S2
 ia
S
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4.c. Current and Voltage Source equivalent circuits for the Pentode
For triodes:
According to the definitions, AC voltage vg1,k causes anode current :
According to the definitions, AC voltage vak causes anode current :
Superposititon of ia1 and ia2 gives
The triode equation
cc
: ia  S  v g1,k
ia1 = S·vg1,k
ia2 = vak / ri
vak
apply Barkhausen’s

ri
  S  ri
v 

: ia  S   v g1,k  ak 
 

For pentodes:
Factor
v ak

contributes to the anode current slightly because µ is large
see anode steepness characteristic Ia = f (Vg1,k).
Factor
v g 2, k
 g 2, g1
contributes significantly to the anode current because µg2,g1
is small, see screen grid steepness characteristic Ig2 = f (Vg1,k).
The pentode equation

v g 2,k

 g 2, g1
: ia  S   v g1,k 

v ak 
 
21
The pentode equation
:

v g 2,k
v ak 

ia  S  v g1,k 



 
g 2, g1

Equal control grid base for anode current and screen grid current :
Apply this in the pentode equation :
ig 2

v g 2, k
v 
i g 2  S 2   v g1,k 
 ak 

 g 2, g1  

S2
  ia
S
After some mathematical magic tricks we get the current source and voltage source models.
Anode
current source
:

v g 2,k  v ak


ia  S  v g1,k 

 g 2, g1  ri

vak  v g 2,k

 
 S 2   v g1,k 
  ri 2

Screen grid current source
:
ig 2
Anode
:

v g 2, k 

  v ak
ia  ri    v g1,k 



g
2
,
g
1


:
v 

i g 2  ri 2   g 2, g1   v g1,k  ak   v g 2,k
 

voltage source
Screen grid voltage source
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23
4.d. Current source and Voltage Source equivalent circuits
applied to Ultra Linear
x
vg 2, k
vak
x
vg 2, k
vak
vg 2,k  x  vak
0.0 ≤ x ≤ 1.0
TARGET:
A = vo /vi = f (x) and rout = f (x)
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25
Without formulae we see directly :
x of the primary winding  partly contribution to power
ig2 flows through part
ia flows through part (1−x) +x of the primary winding  full
contribution to power
With formulae derivation from the equivalent circuits we achieve :
Anode voltage :
vak  vg 2,k  ia  1  x  ra  ik  x  ra  ia  1  x r a
vg2,k = −(ia + ig2 ) ∙ x ∙ ra and is Kirchhoff’s first law ik = ia + ig2 for AC
Total AC current
:
vak
 ia  x  i g 2   itotal
ra
The total AC current itotal is not the same as cathode AC current ik.
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With the art of magic
formula tricks …….

v g 2,k
v ak 


The pentode equation : ia  S   v g1,k 

 
g 2, g1

vg 2,k  x  vak
vak
 ia  x  i g 2   itotal
ra
ig 2
S2
  ia
S

x  vak vak 
S 

itotal  1  x  2   S   vg1,k 


S 
 g 2, g1  


vak   itotal  ra
.………… we achieve at the anode:
Aa 
v ak

v g1,k
An easy formula derivation in small steps is available.
S  x  S 2   ra
 x
1
1 
   S  x  S 2   ra


 g 2, g1  
27
A
S  x  S 2   ra
Aa 
v ak

v g1,k
vo 
ns
 vak and vi = vg1,k
np
vo
n
 s 
vi
np
 x
1
1 
   S  x  S 2   ra


 g 2, g1  
S  x  S2  ra
 x
1
1 
   S  x  S 2   ra


 g 2, g1  
28
rout 
AC output resistance :
vo ,open
(Thevenin’s theorem)
io , shortcircuit
2
 ns
r

then RL = ∞ with a 
 np

  RL   .


n
When we have io,shortcircuit then RL = 0 with ra   s
 np

  RL  0 .


When we have vo,open
vo ,open

vi
rout 
2
vo ,open
io , shortcircuit
io, shortcircuit 
.………… we achieve at the output:
Again with the art of
magic formula tricks ….
ns
1

np  x
1

 


 g 2, g1  
np 
S 
 1  x  2   S  vi
ns 
S 
rout
n
 s
n
 p
An easy formula derivation in small steps is available.
2

1
 

 S  x  S    x  1 
2


 g 2, g1  
29
Summary
A
rout
vo
n
 s 
vi
np
 ns

n
 p
S  x  S 2   ra
 x
1
1 
   S  x  S 2   ra


 g 2, g1  
2

1
 

 S  x  S    x  1 
2


 g 2, g1  
x is the variable and the other quantities
are almost constant (in theory).
30