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The Ultra-Linear Power AmplifierAn adventure between triode and pentode

Rudolf Moers

1 IntroductionIn 95, David Hafler and Herbert Keroes introduced a pentode power amplifier, in which a tap of theprimary transformer winding was connected to the screen grid of the power pentode [2]. They calledthis the Ultra-Linear power amplifier. This power amplifier shows the advantages of a triode, lowanode AC internal resistance and low distortion, as well as the advantages of a pentode, large deliv-ered anode AC power and good efficiency. The narrative given by David Hafler and Herbert Keroesis good and substantiated in practice; this is very important.What I personally missed in their narration is a theoretical explanation of the operation of the ultra-linear circuit. I have several electronics books including the well known seven parts of the electrontube book range, written by scientists of the Philips Gloeilampenfabrieken Company at Eindhovenin the Netherlands. I also have all the electronics books of the company school written byA.J. Sietsma. In none of these books did I find a theoretical explanation of the operation of the ultra-linear circuit. I do not suggest that such an explanation does not exist; I just have not been able tofind it. Therefore I went on an adventure between triode and pentode myself. In this adventure, the-ory will be checked against practice.

posted with permission from Linear Audio www.linearaudio.net

Figure 1. Homework exercise from the great book from 1959 by A.J. Sietsma [3].

When doing research for my book [], I was pleasantly surprised to find the homework exercise of fig-ure 1. Unfortunately, it is in Dutch but you should be able to understand the circuit.

Philips never published information concerning ultra-linear power gain because they never pro-duced such an amplifier. I contacted Sietsma about the why and how of this homework exercise, buthe is too old to be able to answer. His son told me that his father used to make up all homework ex-ercises himself. He probably wanted to check the knowledge of his students concerning “screen gridnegative feedback” which is the technical name for the marketing name Ultra-Linear.It was this homework exercise which motivated me to do a close investigation of the ultra-linear poweramplifier. Thanks to Sietsma I developed my own network analysis of the circuit, which he probablyalso did, although it was never published. Using my own network analysis method I solved this exer-cise in 2006, and achieved the same results as Sietsma. During the European Triode Festival (ETF) 200,I presented a paper on this subject and for an extended narration I recommend reference [].

2 An adventure between triode and pentodeYou seldom encounter a single ended ultra-linear power amplifier. In principle, it is very well possi-ble to construct one, but I do not know whether these power amplifiers perform satisfactorily. How-ever, the single ended ultra-linear power amplifier is very suitable to explain the Ultra-Linear concept.We will see later that a separate explanation of the push pull ultra-linear power amplifier in classesA, B and AB with their calculations of powers and efficiencies is not required. This seems too good tobe true, but I will show it to be so. In figure 2we have the single ended topology with anode AC ex-ternal resistance ra. The related anode characteristics Ia = f (Vak) with the Vg1,k-curve which lies halfwayinside the control grid base are also given (see sidebar for explanation of terms and symbols). This isthe most favorable working point because we are then in the middle of the upper and lower bendsof the anode static/dynamic transconductance Ia = f (Vg1,k). We must avoid these bends because of thedistortions they cause. The triode connection gives Vg2,k = Vak ≠ constant and the pentode connec-tion gives Vg2,k = Vb = constant. The reason that both anode characteristics are not linear is also visi-ble with the related Child-Langmuir equations above in the anode characteristics of figure 2.With the triode connection, we see a faint concave curvature. With the pentode connection, we seea steep convex curvature and after the knee it changes into an almost horizontal flat line. Anticipat-ing what will come later, an x-coordinate is shown along the primary winding of the output trans-former. The transformer terminal connected to Vb is the point where x = 0. Because Vb is a short circuitfor AC currents, we can say that x = 0 = grounded. The terminal of the transformer connected to theanode is where x = . Scale x is divided linearly along the primary transformer winding.

What would we do, if we would want a linear anode characteristic in the form Ia = kultralinear∙Vak ?If the triode and pentode anode characteristics are concave and convex respectively, we can thenimagine that between concave and convex there is a linear compromise. Screen grid g2 connected tothe anode makes the anode characteristic concave and connected to Vb makes the anode charac-teristic convex.

2

Rudolf Moers


Thus, it is obvious that the connection of screen grid g2 to the primary transformer winding, some-where in between the anode and Vb, will give a more linear anode characteristic and that is shownin figure 3.

The impedance between the screen grid primary transformer tap x and Vb is called x∙ra and the im-pedance between this tap and the anode is called (−x)∙ra. Because Vb is a short circuit for AC currents,we can say that screen grid cathode AC voltage vg2,k is a tap of anode cathode AC voltage vak. Thescreen grid cathode DC voltage Vg2,k still applies to the screen grid, but from here on, screen grid cath-ode AC voltage vg2,k is superimposed. (Vg2,k + vg2,k) changes dynamically and because of this, the at-tractive force on the electrons in the electron cloud around the cathode changes dynamically. Thescreen grid behaves slightly adversely as does the anode with triodes, but with a less attractive forcethan in a real triodes.You can also see this in the pentode equation: see reference []

The Ultra-Linear Power Amplifier


b

2.akg1k

VI = ka + Da.V

3 3

V.a

D+

Vg2k

HALF

Vg1k

CONTROL GRID BASE

g1kIa

k

x=0

x=1

ra LRo

C

g1

g3

g2

aI I

g1R

V

Ivi

g1kV

k

g2

g1

v

kIIk

v

g1

g2

k

PENTODE AS TRIODE PENTODE AS PENTODE

Vg1k

iv I

V

Rg1

II a

g2

g3

g1

C

o RLar

x=1

x=0

k

akV

aI

Vak

V

HALF

g2kV

CONTROL GRID BASE

IS CONSTANT

a kI = pentode. V

g1k g2+D .V

g2k ak. 2

triode

b

IS NOT

a a

CONSTANT

0 0

Figure 2. Pentode as triode and pentode as pentode in a power amplifier.

Because µ is large for pentodes, the factor vak/µ can be neglected. In addition, as long as the screengrid is decoupled by a Cg2 or by an external voltage source Vg2,k, then vg2,k = 0 and due to this factor,vg2,k/µg2,g1 = 0. However, vg2,k ≠ 0 and µg2,g1 is not large thus factor vg2,k/µg2,g1 can no longer be neglectedand gives a significant contribution to anode AC current ia. Output signals vak and vg2,k are oppositein phase to the input signal vg1,k = vi and counteract anode AC current ia. This is a classic case of volt-age negative feedback. Figure also shows the linear anode characteristic Ia = f (Vak) and again withthe Vg1,k-curve which lies halfway inside the control grid base. Once again, this is the most favorableworking point because here we are in between the upper and lower bends of the anode static/dy-namic transconductance Ia = f (Vg1,k). Thus, the constant kultralinear is a real constant, and independentof Vg2,k and Vak. When we neglect the primary transformer copper resistance (Rp = 0), we can sayVb = Vak = Vg2,k. We will see later that vg2,k is almost equal to x∙vak. This equation seems obvious, but

is not fully correct, although in practice it can be ap-plied without large errors. I will come back to this issuelater.The next question is, at which screen grid tap or forwhich value of x do we get a linear anode characteris-tic? Figure 4 shows the answer: for x = 0..

Rudolf Moers


.

.

r

Ia

Vak

akI = ka

g1k

Ik

v

g1

g2

k

Vg1k

iv I

V

Rg1

II a

g2

g3

g1

C

o RL

k

V

HALF

g2kV

b

IS NOT

a

CONSTANT

GRID BASE

CONTROL

V.

rx

x=1

x=0

a

a

PENTODE AS ULTRA-LINEAR

1-x

ultra-linear

0

Figure 3. Pentode as ultra-linear power amplifier.

akVaI

GRID BASE

Ia

Vg1k

FOR ALL THESE CURVES

HALF CONTROL

1.00.7

0.4

0.2

0.0

VALUES OF X

f( )

Vak

=

0

Figure 4. Dynamic ultra-linear anodecharacteristic Ia = f (Vak) with x as parameter.

The value x = 0.4 is an “average opinion” of the manufacturers of output transformers and electrontubes. Some of them use x=0.33 as an“average opinion”. Actually, x is different for each type of elec-tron tube, sometimes on each specimen of one type. So what is the ideal value of tap x for a certainapplication? You must be pragmatic in this situation, because what if the ideal value would bex = 0.8? Should we then get a specific output transformer for this value? Or can we make do withan output transformer with several taps to choose x = 0.0, x = 0.5 or x = 0.0? All these taps do notcontribute to the transformer bandwidth and other quality aspects. Maybe you should just choosex = 0. and accept that you don’t have an ideal linearity for each pentode specimen.In section 5 of this article we will do a nice practical determination of x for a specific pentode speci-men.

3 Power and efficiencyFigure shows that we have a pentode behaving as a pentode for x = 0.0 and a pentode behavingas a triode for x = .0.This corresponds with the x-values shown in figures 2 and . Additionally, all Vg1,k-curves lie halfwayinside the control grid base. How would it look for other Vg1,k-curves? That can be seen in figure 5.With a reasonable triode, see figure 5.a, curve Vg1,k = 0 goes through the origin of the anode charac-teristic. With a reasonable pentode, see figure 5.c, curve Vg1,k = 0 lies almost at the top of the anodecharacteristic. Purely hypothetical, imagine the screen grid tap is adjustable with a slider on the pri-mary winding of a variable output transformer. When the slider moves from x = 0 to x = , the anodecharacteristic goes from pentode to triode, see figures 5.c and 5.a respectively. When the slider movesback to x = 0., you can see the situation of figure 5.b. Here, the Vg1,k-curve which lies halfway insidethe control grid base, goes through the origin of the anode characteristic and curve Vg1,k = 0 lies wellabove the origin. Even with an ideal triode, curve Vg1,k = 0 never lies above the origin. This gives greatexpectation and promise when we apply full-power drive to control grid g.Driving the control grid beyond Vg1,k = 0 is not desirable due to control grid current which must beavoided. We have the lowest drive level with vap (anode peak AC voltage) with the triode, because weare limited by curve Vg1,k = 0. We have the highest drive level with vap with the pentode, despite thelimit of the knee which lies not far from the Ia-axis. With ultra-linear, the drive level with vap is signifi-cantly more than with the triode and is just slightly less with the pentode. The limit for ultra-linear iscaused by the constriction of the Vg1,k-curves.

In the ideal case of ultra-linear mode, the Vg1,k-curves between 0 and halfway in the control grid basewill end at the Ia-axis, and the Vg1,k-curves between halfway in the control grid base and the com-plete control grid base will end on the Vak-axis. Furthermore, curve Vg1,k = ½∙Vg1,k0 will go straightthrough the origin of the anode characteristic. However, ideal pentodes do not exist; but we can re-cognize the following relationship: vap,triode << vap,ultra-linear< vap,pentode

5



Figure 6 from [6] shows the practical anode characteristics Ia = f (Vak) of a KT88 pentode in triode,ultra-linear with x = 0. (0 % tap) and pentode mode. The lower right in figure 6 shows how themanufacturer specifies the ultra-linear anode characteristics Ia = f (Vak) in practice. In this case, theVg1,k-curves lie between 0 V and −60 V. With some interpolation, the center curve Vg1,k = −0 V goesrather nicely through the origin. Curve Vg1,k = 0 V starts parallel on the Ia-axis and curves slightly hor-izontal at the top of the anode characteristic. Curve Vg1,k = −60 V lies almost flat against the Vak-axis.The constrictions of all Vg1,k-curves to the origin are not shown correctly. This part of the anode char-acteristic is probably different for each specimen, and moreover we must avoid drive levels in thatvap range. Let us make a comparison between the distances of the curves Vg1,k = 0 and the Ia-axis fortriode, ultra-linear and pentode mode (table 1):Note: The vertical position of the Vg1,k-curves in Ia = f(Vak) depend on the magnitude of Vg2,k. For ultra-lin-ear and for pentode this is similar.

6

Rudolf Moers


g1k

12

V.g1k0V =

g1kV =0

g1kV = V

g1k0

akVvapvap

W

V

g1k0g1k0V .V

21

g1k

aI

0

W

V = g1k0.V

21

g1k

g1k0VV =

g1k

V =0g1k

g1k12

V.Vg1k0 g1k0

apvapvVak

g1k

g1k

12

V.g1k0

W

g1k0

apv

aTRIODE

cPENTODE

ULTRA-LINEAR

vapakV

I

g1k0V .V

21

W

Vg1k

V =

g1kV =0 V = V

g1k0

0

a

0

bW

Ia

V

W

Figure 5. Comparison of the dynamic transconductance and dynamic anode characteristics for triode, ultra-linearand pentode mode.



Triode Vg2,k=Vak

; Ia =100mA Vg1,k = 0 to Ia -axis: 75V

Ultra-Linear Vg2,k =276 V; Ia =100mA Vg1,k = 0 to Ia -axis: 30V

Pentode Vg2,k =300 V; Ia =100mA Vg1,k = 0 to Ia -axis: 20V

TTable 1. Voltage distance between Vg1,k = 0 and the Ia-axis.

Figure 6. KT88 Beam Power Tetrode in triode, ultra-linear (x = 0.4 = 40%) and pentode mode.

Figure 7 shows the theoretical ideal versions of the practical figures 5 and 6. Anode AC peak voltagevap and anode AC peak current iap, which determine the delivered anode power, are smaller in triodemode than in ultra-linear mode. However, in pentode mode, anode AC peak voltage vap and anodeAC peak current iap are equal to those in ultra-linear mode. This means that the delivered anode powerin ultra-linear mode is equal to the delivered anode power pentode mode. This is very desirable. Fur-thermore, we can see that the Vg1,k-curves in ultra-linear mode have the same linearity as the Vg1,k-curvesin triode mode. This too is very desirable.

Figures .b and .c show two “fictive rotation points”:When we rotate all the Vg1,k-curves of figure .b clockwise 50 we get figure .c.When we rotate all the Vg1,k-curves of figure .c counterclockwise 50 we get figure .b.

Once again, anode AC peak voltage vap and anode AC peak current iap are the same in ultra-linearmode and in pentode mode. Both modes have the same delivered anode power.This means that we do not need to derive separate equations for ultra-linear mode; we can just takethe results from the pentode case. This is applicable for single ended or push pull in classes A, B andAB, but only in theory, of course. How should we handle this in practice? We can not use the situa-tion of figure , but we can use the situation of figure 6.Earlier we saw that: vap,triode<< vap,ultra-linear < vap,pentode

In reality, the mentioned “constriction” in ultra-linear mode is larger than the “knee area” of the pen-tode mode. We must not use these areas, to avoid non-linear distortions. Thus, if you want to calcu-late the delivered anode power in ultra-linear mode, first calculate the delivered anode power inpentode mode and decrease it by a certain factor. But how much should it be decreased?

It seems to me that an estimate of between 20 % and 0 % should be subtracted from the deliveredanode power in pentode mode. Now where does your author get this insight?In reference [], some design examples are shown with the following results for output power:Two EL with VDV600PP transformer: ptriode = W, pultra-linear = W and ppentode = 0 WFour EL with VDV00PP transformer: ptriode = 0 W, pultra-linear = 0 W and ppentode = 80 WThus, the estimate of between 20 % and 0 % decrease seems reasonable. In addition, the deliveredpower in ultra-linear mode is quite sufficient for listening to in your living room. It is obvious thatthe efficiency of ultra-linear mode lies between the efficiencies of triode and pentode mode. In thepractical section of this article we will see that the power behavior and the efficiency of ultra-lin-ear mode come closer to pentode mode than to triode mode.

8

Rudolf Moers


9



ap

iap

i

Vb

vap apv

vapapv

bV

S

W

W

g1kpv

Vg1k 1

2V.V

g1k0 g1k0

vg1kp

g1kpv

Vg1k 1

2V.V

g1k0 g1k0

vg1kp

W

W

00

00

aaI I

aaI I

g1kV =0

2

3

4

4V = g1k0.V

1

g1k

g1kV.g1k0V = 4

4V = g1k0.V

g1k

g1kV.g1k0V = 4

Vak

Vak

V =0g1k 2

3

4

4 g1k0.V

1

g1k

g1kV.g1k0V = 4

4V = g1k0.V

g1k

g1kV.g1k0V = 4

4V = g1k0.V

g1k

g1kV.g1k0V = 4

4V = g1k0.V

g1k

g1k

1V.g1k0V =

g1kV =0

apv

IIa

ap

i

g1kpv

g1k0g1k0V .V

21g1k

TRIODE

b

c

ULTRA

a

LINEAR

PENTODE

V

vg1kp

dS

W

VakVb

vap

4

4

3

2

V =

a

0 0

W

POINT

ROTATION

POINT

ROTATION

S

S

iap

iap

iap

Figure 7. Comparison of the dynamic transconductance and the dynamic anode characteristics for an idealtriode, an ideal ultra-linear configuration and an ideal pentode.

4 Network analysisConsider again the ultra-linear circuit of figure . My goal is to show you anode AC gain

, circuit AC gain and circuit output AC resistance rout = ƒ(x) as function

of the screen grid tap position x on the primary transformer winding.Before we apply a network analysis for the ultra-linear power amplifier, a review of the pentode char-acteristics and pentode quantities is necessary. Especially so because current manufacturers of pen-todes deliver poor and inconsistent datasheets. One quantity has several names worldwide:conductance, transconductance, mutual conductance, slope, steilheid (Dutch) and steilheit (Ger-man) with symbol g, gm and S. Another one is anode AC internal resistance which can be called ri orplate resistance rp or Rp or anode resistance ra. It’s important to have these definitions clear to un-derstand the following narrative. I have listed the various expressions and symbols I use in this arti-cle in the sidebar.

Figures 8 and 9 show how the various pentode quantities can be determined from the pentodecharacteristics. There’s noting new here; you can find the same information in many vintage elec-tronics books.

0

Rudolf Moers


n

g1k

Ia

akV

akV

aI

aa

0

=200V

=200VV

V

i

-4-6

V (V)

-2 50 100 150 200 250 300

V (V)

1

2

3

4

5

6

7I (mA)a

g1k

I =f(V )akg1k

EF86

=1,0Wa,maxP

a:150V-300V

b:100V

c: 20V

Vakg2k

a

b

c

S=V

Ia

V

V=

Vak

r =

Vak aI

-6.0V

-5.5V

-5.0V

-4.5V

-4.0V

-3.5V

-3.0V

V =-2.5Vg1k

g2k

I =f(V )

Vg1k

ak

g1k

g1k

Figure 8. Determination of the anode quantities.

Figure 10 shows anode current Ia and screen grid current Ig2 in one characteristic. We see that the cut-off points of both transconductance curves are positioned equally on the Vg1,k-axis at a certain Vg2,k.So both control grid bases are equal: ∆Vg1,k for S = ∆Vg1,k for S2

This gives and the relationship between anode current and screen grid current

is:

We have already seen pentode equation:

But now we can see a second one:

You can now see the beginning of this section as an introduction for the next part of the narrationand to recognize equations and symbols. From now on, in the rest of this section much will “fall fromthe sky”and normally I do not like that, but I do not want to bore you with equation derivation. In ref-erence [] all following mathematics are derived in small and easy steps. A piece of cake really, butnow I will show you only the direction of the network analyses.



g2I

V

g1kV

V

V

I

V

=200VVg2k

0-4-6

V (V)

-2 50 100 150 200 250 300

V (V)g1k ak

V =300V

2S =

i2

I =f(V )g1kg2 I =f(V )akg2

EF86ak

2

1

Vg2k

a: 200V

b: 180V

c: 160V

d: 140V

e: 120V

f: 100V

g: 80V

h: 60V

g1k

b: -4.0V

c: -4.5V

d: -5.0V

e: -5.5V

f: -6.0V

a: -3.5V

a

b

c

d

f

egh

fe

dc

ba

g2

Vg1k

g1k

V

g2k

g1k

r =

g2kV

g2I (mA)

Ig2

g2k

g g2 1

=

Figure 9. Determination of the screen grid quantities.

and"

With help of both pentode equations and some mathematical tricks it is possible to obtain acurrent source equivalent circuit and a voltage source equivalent circuit for the pentode.When we apply these equivalent circuits with an output transformer with screen grid tap, we thenobtain the current source equivalent circuit and a voltage source equivalent circuit for the pentode asultra-linear power amplifier.These equivalent circuits have as original the circuit of figure , and are shown in figure 11.

We neglect the copper resistances of the transformer windings. Furthermore, we consider that trans-former efficiency ηtransformer = 00%. Kirchhoff’s first law is still ik = ia + ig2 for AC and load resistor RL ispurely resistive. Using some mesh-network rules we can derive the important equation:

Important note: total AC current itotal is not the same as cathode AC current ik!

Anode AC current ia and a fraction x of the of screen grid AC current ig2 deliver the primary power toanode AC external resistance ra. This is really an algebraic approach. The approach from figure isas follows:ia and ig2 together are active in the primary part x∙ra and ia alone is active in primary part ( – x)∙ra.What we do algebraically is to define a total AC current itotal which flows through the total anode ACexternal resistance ra and which does not ‘see’ the tap to the screen grid.

2

Rudolf Moers


V = 250Vak

g2k

g2k

for

I

a,yI

g2,yI

I

V (V)g1k

I =f(V )g1kg2

g2

aI =f(V )g1k

EF86

6

5

4

3

2

1

0-1-2-3-4-5-6

CONTROL GRID BASE Y

CONTROL GRID BASE X

I (mA)a

I (mA)

Ig2,x

Ig2,y

Ia,y

Ia,x

V = 160V

g2,x akV = 250V

V = 100V

a,xfor

Figure 10. Anode DCcurrent and screen grid DCcurrent in a single steepnessgraph.

Anode AC current ia and screen grid AC current ig2 , which, in reality, see partially different AC resist-ances, are replaced by itotal = (ia + x∙ig2) which flows through one AC resistance. However, ra withoutscreen grid tap and itotal are both fictional. Admittedly, our imagination is put to the test.In section 8, I will show you that these assertions are actually allowed.

Further it would be nice if but in that case the current through xra must be the same as

the current through (-x)ra. Unfortunately that is not the situation, but in practice x = 0. andig2 ≈ 0.2×ia.

Thus becomes

Thus, statement is allowed.

Now we have all mathematical tools to derive anode AC gain , circuit AC gain



.pn

k

g g.

g1kv +

v +g1k.

s

LRov

oi

spn

x

x.

.

ar

.

1-x.

1-x

ra

n

g2

a

i

i

I

v vak

g2k

g2

i2rr

i

g1

g1kiv =v

PENTODE

ir

akv v

2 1g g

g2k.

.2

g2kv

k

n

a

p

r

1-x

.

a

b

1-x

.

ra

x

x

np

io

vo RL

I

i

i

a

g2

k

g2k

vS

S g1kv +

g1kv + ak

vvri2

ri

v =vi g1k

PENTODE

CURRENT SOURCE EQUIVALENT NETWORK

g1

ri2

a

g2

a

n and n are

s

number of windings

vak

2 1g g

g2kv

ak

2 1

k

np

.

VOLTAGE SOURCE EQUIVALENT NETWORK

Figure 11. Current source equivalent circuit (a) and voltage source equivalent circuit (b) of the ultra-linear poweramplifier.

g

.

,

and circuit output AC resistance rout = ƒ(x).

In 959, Sietsma probably achieved the same results as I did in 2006. Unfortunately, he did not pub-lish it, and I had to derive it independently; just a matter of brave calculations.In section 6 I will prove the following equations:

Anode AC gain:

Circuit AC gain:

Circuit AC output resistance:

The quantities shown in these equations have already been explained and are constant at a certainworking point. The only variable quantity is screen grid primary transformer tap x. When you applyx = 0 and x = in these equations, you get the anode AC gain, circuit AC gain and circuit AC outputresistance for pentode and triode respectively. Again, in reference [] these are derived in small andvery easy steps.

5 Practical determination of the screen grid tapIt would be nice if figure could be made visible on an oscilloscope screen. During the European Tri-ode Festival 200, Yves Monmagnon demonstrated his Tube Curve Tracer. Later I saw some results ofthis equipment on the internet, see reference [], but at that time I was not aware of the ETF event.Many years before, while attending secondary technical school, I learned how to display transistorcharacteristics on an oscilloscope screen, but making voltage sources for control grid, screen gridand anode which can increase from 0 V to an adjustable maximum voltage of more than |00| Vseems to me not easy. Before I had seen photos of Yves’s presentation in 200, I had already devel-oped another method, see figure 12.

Supply voltage Vb is a short circuit for AC current, and the amplitudes of anode cathode AC voltageVak and screen grid cathode AC voltage Vg2,k start from point Vak = Vb on the Vak-axis of figure 2.On curve xTR = .00 for the triode, Vg2,k = Vak is always valid. To get Vak = 5 V in point TR at an anodeDC current of Ia = mA, we must get Vg2,k = 5. By coincidence that is also Vak.

On curve xPE = 0.00 for the pentode, Vg2,k = Vb = 00V is always valid. To get Vak = 5 V in point PE atan anode DC current of Ia = 2 mA, we must get Vg2,k = 00 V. By coincidence that is also Vb.The curves Vg1,k = ½ control grid base for the triode and the pentode cross at working point W

Rudolf Moers


at Iaw = 80 mA and Vakw = 00 V. We can now draw a straight line, ultra-linear, between working point Wand the origin. We call this line xUL.From point xUL at Vak = 5 V, we can read Ia = mA. Now we must offer a certain voltage of Vg2,k toget Ia = mA at Vak = 5 V. In this case Vg2,k = 269 V.

The characteristics for triode and pentode of figure 2 are measured with the test circuit of figure 13.

5



0

g2k

WHEN V =175Vak

akWHEN V =175V

g2k

2

1g1k0

.

GRID BASECONTROL

HALF

V = Vg1kFOR ALL CURVES

100 150 200 250 300 350 400

V

ap=v

b

ak

V (V)ak

LINEAR

ULTRA

TRIODE

x =1.00TR

x =0.25UL

PE

V =300V

b

a

W

bV =V =300V ADJUSTED

TR

TO OBTAIN I =72mA

PENTODEPE

I (mA)a

20

60

80

g2kV

V

g2kp

ak

v

vap

x= =

V =V -175=125V

akI =f(V )a

g2k

TO OBTAIN I =14mAa

0

40

100

50

UL

g2k

TO OBTAIN I =47mAa

WHEN V =175Vak

x =0.00

V =V =175V ADJUSTEDak

V =269V ADJUSTED

Figure 12. Explanation of the method to determine the screen grid tap x.

V

mA

Ig3

f

a

uA

fk

g1

g2mA

I

g2

g1

Vg1k Vg2k ak

INDIRECTLY HEATED PENTODE

TEST CIRCUIT FOR

Figure 13. Test circuit for research into the static pentode characteristic.

We can now determine screen grid primary transformer taps xTR, xUL and xPE.

At point PE: vg2.kp = ∆Vg2,k = Vb – 00 V = 0 Vvap = ∆Vak = Vb – 5 V = 25 V

At point UL: vg2.kp = ∆Vg2,k = Vb – 269 V = Vvap = ∆Vak = Vb – 5 V = 25 V

At point TR: vg2.kp = ∆Vg2,k = Vb – 5 V = 25 Vvap = ∆Vak = Vb – 5 V = 25 V

If the explanation of this method is not 00 % clear, it will be soon because we now apply this methodin a practical case. Figure 14 shows the anode characteristics for five different values of screen gridprimary transformer tap x of specimen KT88 no..

Line 1 is measured in advancewith the pentode in triode mode: x = .00.

Line 2 is drawn afterwards “freehand”, but we do not know yet that the corresponding x = 0.2.

Line 3 is drawn afterwardswith a straight ruler, but we do not know yet that the correspondingx = 0.25.Line 4 is drawn afterwards “freehand”, but we do not know yet that the corresponding x = 0..

Line 5 is measured in advancewith the pentode in pentode mode: x = 0.00.

From all lines we can read Ia for each Vak. We must now search for the necessary value of Vg2,k at each pointon these lines. Therefore, we need the test circuit of figure 13 which I have used to measure the lines 1 and5. At a certain anode DC current Ia and at an adjusted anode cathode DC voltage Vak, the value of screengrid cathode DC voltage Vg2,k which I have measured, must be subtracted from Vb = 300 V.Also Vak must be subtracted from Vb = 300 V. This gives you ∆Vg2,k and ∆Vak respectively.

6

Rudolf Moers


ill be soon because we now apply this method in a p

The next five tables show the method of figures 2 and explained in practice and deliver the ev-idence that for all measured values (the dots on the lines), the screen grid primary transformer tap xis the same for the corresponding line. We also measure the screen grid DC current Ig2 for later use.



LINEAR

ULTRA

:

:

:

:

LINE 5

LINELINELINELINE

g2kV

(V)

g2kV

(V)

g2kV

(V)

g2kV

(V)(V)

V

300

300

300

300

300

300

300

300

300

300

300

300

300

275

250

225

200

175

150

125

75

100

50

25

a ak

g1kFOR ALL CURVES: V =-26V

25

50

100

75

125

150

175

200

225

250

275

300

181

208

223

225

230

235

242

254

267

276

289

300

206

237

251

254

259

263

269

275

281

288

294

300

236

264

274

278

282

284

287

289

292

294

296

300

akV

(V)

g2k

LINE

1 5432

KT88-no.1

LINE 1

LINE 2

LINE 3

LINE 4

LINE 2

LINE 3

LINE 4

LINE 5

LINE 1: X = 1.00

X = 0.42

X = 0.25

X = 0.13

X = 0.00

TRIODE

ULTRA

LINEAR PENTODE

TRIODE

PENTODE

40035030025020015010050V (V)ak

00

20

40

60

80

aI (mA)

100

120

140

160

180

200I =f(V )

W

Figure 14. Anode characteristic of KT88 no.1 for different values of screen grid primary transformer tap x. Thecorresponding values of Vg2,k at each measured point is shown in the table.

8

Rudolf Moers


Vak (V) adjusted

Ia (mA) read on Ia-axis

Ig2 (mA) measured

Vg2,k (V) adjusted to

read Ia

!Vak (V)

[300V – Vak]

!Vg2,k (V)

[300V – Vg2,k]

0 0 0 unknown 300 unknown unknown25 2 0,9 181 275 119 0,4350 5 5,5 208 250 92 0,3775 9 8,9 223 225 77 0,34100 12 7,6 225 200 75 0,38125 17 5,9 230 175 70 0,40150 22 4,2 235 150 65 0,43175 28 3,6 242 125 58 0,46200 36 4 254 100 46 0,46225 46 4,7 267 75 33 0,44250 55 5,3 276 50 24 0,48275 66 6,2 289 25 11 0,44300 78 7 300 0 0 unknown

Table 3. Measured values of line 2, fig 14. The average value of all screen grid primary transformer taps xaverage = 0.42.

Vak (V) adjusted


Ig2 (mA) measured


read Ia

!Vak (V)

[300V – Vak]

!Vg2,k (V)

[300V – Vg2,k]

0 0 0 0 300 300 125 0 0 25 275 275 150 0 0 50 250 250 175 0 0 75 225 225 1100 0 0 100 200 200 1125 0 0 125 175 175 1150 0 0 150 150 150 1175 2,6 0,1 175 125 125 1200 8,5 0,7 200 100 100 1225 19,2 1,6 225 75 75 1250 35,6 2,9 250 50 50 1275 55 4,6 275 25 25 1300 79 7 300 0 0 unknown325 110 9,2 325350 140 12,1 350375 170 16,5 375400 200 21 400

Table 2. Measured values for line 1, fig 14. The adjustment of Vg2,k happens automatically of course, because the screen grid is connected to the anode. The screen grid primary transformer tap x = 1.00 but that will surprise nobody, so this is the pentode in triode mode.

Not further than point W

9



0 0 0 unknown 300 unknown unknown25 6,5 3,8 206 275 94 0,3450 13 12,5 237 250 63 0,2575 19,5 16 251 225 49 0,22100 26 13 254 200 46 0,23125 32,5 10,4 259 175 41 0,23150 39 8 263 150 37 0,25175 45,5 7 269 125 31 0,25200 52 6,5 275 100 25 0,25225 58,5 6,5 281 75 19 0,25250 65 6,5 288 50 12 0,24275 71,5 6,5 294 25 6 0,24300 78 7,1 300 0 0 unknown

Table 4. Measured values of line 3, fig 14. The average value of all screen grid primary transformer taps xaverage = 0.25. For this specimen KT88 no.1 we have pure ultra-linear at x = 0.25.

Vak (V) adjusted


Ig2 (mA) measured


read Ia

!Vak (V)

[300V – Vak]

!Vg2,k (V)

[300V – Vg2,k]

0 0 0 unknown 300 unknown unknown25 15 9,5 236 275 64 0,2350 26 19,7 264 250 36 0,1475 34 20,6 274 225 26 0,12100 41 17,7 278 200 22 0,11125 49 14,2 282 175 18 0,10150 55 11,2 284 150 16 0,11175 60 9,4 287 125 13 0,10200 64 8,1 289 100 11 0,11225 68 7,6 292 75 8 0,11250 71 7,1 294 50 6 0,12275 74 7 296 25 4 0,16300 78 7 300 0 0 unknown

Table 5. Measured values of line 4, fig 14. The average value of all screen grid primary transformer taps xaverage = 0.13.

!Vg2,k (V)

[300V – Vg2,k]

!Vak (V)

[300V – Vak]


read Ia

Ig2 (mA) measured

Ia (mA) read

on Ia-axis

Vak (V) adjusted

With this method you can determine screen grid primary transformer tap x for each specimen pen-tode and from each curvature in Ia = f (Vak). In practice, we are only interested in the ultra-linear ap-plication.Lines 2 and in fig , drawn“freehand”, are just an illustration to show how the value of x can lie be-tween triode and ultra-linear and between ultra-linear and pentode.

I have also recorded screen grid DC current Ig2 during this measurement because it is interesting tosee the influence of screen grid primary transformer tap x on Ig2, see figure 15 for the results.Line 1 shows triode behavior. Screen grid DC current Ig2 increases the same as anode DC current Ia.Less steeply of course, because screen grid static transconductance S2 is smaller than anode statictransconductance S.

Line 5 shows pentode behavior. Because Ik = Ia + Ig2 ≈ constant, the curvature of screen grid DCcurrent Ig2 is mirrored with respect to anode DC current Ia. The strange “step” of specimen KT88-no.in the area where 25 V < Vak < 50 V, which is typical for Beam Power Tetrodes, can be found in bothcurrents mentioned. We already know the curvature of Ig2, see figure 9.

Lines 2, 3 and 4 are very different. We first see“fast”triode behavior at low values of Vak because nowthe positive screen grid is seen as the“anode”by the electrons of the electron cloud around the cath-ode. Hence, Ig2 is increasing. Thereafter pentode behavior is more dominant. The result is a maximumvalue of Ig2 at approximately Vak = 5 V.

20

Rudolf Moers


0 1 54 300 300 0 025 60 30 300 275 0 050 60 30 300 250 0 075 61 28 300 225 0 0100 63 22 300 200 0 0125 65 19 300 175 0 0150 68 14 300 150 0 0175 70 12 300 125 0 0200 72 9,5 300 100 0 0225 74 8,5 300 75 0 0250 75 7,8 300 50 0 0275 76 7,2 300 25 0 0300 77 7 300 0 0 unknown325 78 6,5 300350 79 6,3 300375 80 6 300400 80 6 300

Not further than point W

Table 6. Measured values of line 5, fig 14. The adjustment of Vg2,k happens automatically of course, because the screen grid is connected to Vb. The screen grid primary transformer tap x = 0.00 but that will surprise nobody; this is pentode mode.

Vak (V)adjusted

Ia (mA) read

on Ia-axis

Ig2 (mA) measured

Vg2,k (V) adjusted

to read Ia

!Vak (V)

[300V – Vak]

!Vg2,k (V)

[300V – Vg2,k]

6 Practical anode AC gain and circuit AC output resistance as function of the screen grid tapIn the network analysis of section , we have seen the influence of the screen grid primary trans-former tap x on the anode AC gain, circuit AC gain and the circuit AC output resistance: Aa = f (x),A = f (x), and rout = f (x). Now it is time to find out what happens in a real circuit. Figure 16 shows thetest circuit. What immediately is apparent is the output transformer with the 0 taps. Once, before Ihad ever heard about the ultra-linear power amplifier, I did an investigation about the maximum de-livered anode power of a 00B triode versus the normalized anode AC external resistance ra/ri. Whenyou know that for a 00B in normal operation ri = 00 Ω, then it does not seems strange that thetaps of the primary transformer winding (ra) of figure 6 are a multiples of 00 Ω. Although thatanode power investigation was quite interesting, it is beyond the scope of this article. See chapter of reference [] for that investigation.For those of you who want to do the same experiments I did, you can order this test output trans-former from the Dutch transformer manufacturer AE-europe. The type number is 28 and its max-imum DC current is 200 mA. Do not expect enough bandwidth and other audio qualities, but it isuseful for power investigations at medium audio frequencies.I again used pentode specimen KT88-no. at the following working point: Vak,w = 00 V, Ia,w = 80 mA,Vg1,kw = − 26 V, Vg2,kw ≈ 00 V and Ig2,w ≈ 8 mA

2



LINE 5

LINE 4

LINE 3

LINE 2

LINE 5

LINE 4

LINE 3

LINE 2

LINE 1

LINEAR

ULTRA

:

:

:

:

: X = 1.00

X = 0.42

X = 0.25

X = 0.13

X = 0.00

TRIODE

PENTODE

40035030025020015010050V (V)ak

0

g1k

g2

FOR ALL CURVES:

akI =f(V )

V =-26V

KT88-no.1

LINE 1

LINE 2

LINE 3

LINE 4

LINE 5

0

10

20

30

40

50

I (mA)g2

W

60

LINE 1

Figure 15. Characteristic of Ig2 = f (Vak) for different values of screen grid tap x.

Note that if working point W changes slightly with other values of screen grid primary transformertap x, we must change Vg1,kw slightly to achieve the nominal setting. There is a voltage drop across theprimary transformer winding of (Ia + Ig2) • (1 - x)• Rp which depends on the screen grid primary trans-former tap x. It varies and is approximately 0 V. At each value of x, the working point is adjusted asnecessary.Looking at the test circuit of figure 6 we would expect the following values of x at each tap:

We define and measurements will determine whether x = xmeasured.

How linearly are the taps divided over the primary transformer winding? What is the influence of Ig2

and ig2 on the function of the tap? What is the influence of screen grid AC internal resistance ri2 on x?We must realize that this test transformer is not designed and produced for ultra-linear applications,but it is available so let us try. Hence the introduction of quantity xmeasured :vg2,k = x∙vak vg2,k = xmeasured ∙vak

We start with anode AC gain Aa = f (xmeasured).

22

Rudolf Moers


DC

AC

DC

30W

LR

g

3

2

f

g

1

1400

700

2100

2800

3500

4200

4900

5600

6300

7000

5

10

30W

Vb

200mA

OR

AC

KT88

no.1

DC DC

DC

AC

ACvi

ffV

g

100V 100k

220k

2k2

6,3V

f

Vg1Vg1k

A

K

LR

Figure 16. Test circuit to determine the dependence of the anode AC gain and the circuit AC output resistance on thescreen grid tap x.

; ; ; ; . . . .

You will observe that the output voltages and powers are rather low. Please do not judge that tooharshly. In the other applications with KT88 pentodes, the supply voltage can be 00 V instead of00 V. Realize that the delivered output power is proportional with (Vb2/ra).OK, here we go: anode AC external resistance ra = 000 Ω. Fraction Ri = Vak/Iaw = 00 V/80 mA = 50 Ω.That give us the fraction ra/Ri = 000/50 = .8 and reference [] shows that this value is very un-favorable to achieve large output power. But I promise you; all will eventually be well concerning theoutput power; please be patient.

We also need equation and for x we substitute in xmeasured.

We can get the following quantities from the datasheets of the KT88:S = .5 mA/V and ri = 2 kΩ and µg2,g1 = 8. Unfortunately, S2 is not given, but that is (not) to be ex-pected from the current manufacturers of electron tubes. In the previous measurements, we haveseen that at Vak = 00 V, Ia ≈ 0∙Ig2. So I make the assumption that S = 0∙S2 and that gives us S2 = .5 mA/V.We now have all the necessary quantities to substitute in the equation together with xmeasured.We start with vg1,k = .2 VRMS = 5.25 Vp, to avoid vap clipping at x = xmeasured = 0.0.

Output power will be very poor, but as promised will be well in theend.

The results of the measurements and calculations are shown in table 7 and as expected, x ≠ xmeasured,because the taps are not perfectly linearly divided over the primary transformer winding. We will seelater that with an actual toroidal-core transformer, x = xmeasured.

Figure 17 shows plots of the table results of the ninth and tenth column as a function of the fifthcolumn, or in other words the functions Aa,measured = f (xmeasured) and Aa,calculated = f (xmeasured) respectively.The agreement between theory and practice is good. Only at low values of xmeasured there are somedifferences.

2



p

and

x vg1,k

(VRMS)

vg2,k

(VRMS)

vak

(VRMS)

pa

(W) vRL

(VRMS)

pRL

(W) |Aa

|

with

formula

0.0 3.72 0.0 158.0 0.00 3.60 4.01 3.20 42.4 50.6

0.1 3.72 19.2 60.8 0.32 0.53 1.51 0.45 16.3 16.8

0.2 3.72 21.3 47.7 0.45 0.33 1.22 0.29 12.8 13.3

0.3 3.72 22.3 40.7 0.55 0.24 1.01 0.20 10.9 11.3

0.4 3.72 23.2 36.1 0.64 0.19 0.92 0.16 9.7 10.1

0.5 3.72 23.6 33.4 0.71 0.16 0.83 0.14 9.0 9.3

0.6 3.72 23.9 30.9 0.77 0.14 0.78 0.12 8.3 8.7

0.7 3.72 23.2 28.9 0.84 0.12 0.73 0.11 7.8 8.1

0.8 3.72 24.2 27.3 0.89 0.11 0.69 0.10 7.3 7.7

0.9 3.72 24.6 26.1 0.94 0.10 0.65 0.09 7.0 7.3

1.0 3.72 25.0 25.0 1.00 0.09 0.62 0.08 6.6 7.0

Table 7. The results of measurements and calculations based on figure 16.

ak

kg

measuredv

vx

,2=

kg

ak

av

vA

,1

=

This test transformer has no taps at0.00 < x < 0.0 and 0.00 < xmeasured <0.2. In the other ranges we seethat the decrease in |Aa| almost per-fectly tracks the increase in x andxmeasured. The larger x and xmeasured, thegreater the screen grid negativefeedback and the decrease in |Aa|.A low anode gain delivers low val-ues of vak and vRL and thus, a low pa

and pRL, see columns 6 and 8 oftable . However, no one can stopus to leave the value vg1,k = .2 V asit is for each value of x. The largerthe value of x the more we move to-ward triode and the less the upperbend in transconductance charac-teristic Ia = f (Vg1,k). Hence, the con-

trol grid base increases and can be used with a larger value of vg1,k.

Figure18 shows pa = f (xmeasured) for vg1,k = .2 V, the second column of table , and shows pa = f (xmeasured)with adjusted vg1,k which is as large as possible without causing non-linear distortion visible on theoscilloscope. The anode power then lies between 2.5 W and 5.5 W and that will provide reasonablesound levels. More power can be obtained by increasing Vakw = Vb and Iaw, but I will not do that here.Of course, we must choose fraction ra/Ri optimally, see reference []. As promised, those power num-bers will all turn out to be fine.The dashed lines in fig show the gain for xmeasured =0.25 and that is the ultra-linearmode for this specimen KT88-no.. See also line of figure and the seventh column oftable .

2

Rudolf Moers


v

0

=f(x )measured

KT88-no.1

rms

Aa

60

50

40

30

20

a

10

00.2 0.4

A

0.6 0.8 1.0

INTO FORMULA

MEASURED AND CALCULATED

akWITH

v =3.72V =constantg1k

g1k

v

CALCULATED WITH x

xmeasured

measured

U

Figure 17. pa = f (xmeasured) for a constantvg1,k , calculated and measured.

0 0.2 0.4 0.6 0.8 1.0xmeasured

measured=f(x )

KT88-no.1

a(W)

0.0

1,0

2.0

3.0

4.0

5.0

6.0

6.5

rmsg1kv =3.72V =constant

without distortion

as large as possibleg1k

v

a

Figure 18. pa = f (xmeasured) for aconstant vg1,k and for an adjusted

vg1,k.

We now continue with the circuit AC output resistance as a function of the actual screen grid pri-mary transformer tap x, or rout = f (xmeasured).

In theory, we can apply Thevenin’s but in practice this is dangerous.

Shorting iRL is permissible for a short time, but VRL,open is dangerous. When a secondary load on the out-put transformer is removed suddenly, an inductive high voltage may appear which can destroy thepower tube. (This is the reason you should never disconnect the loudspeakers from the outputs ofyour electron tube amplifier when it is not switched off). We will determine rout according to figure19.

The voltage source is the secondary side of the output transformer and we want to know the valueof rout. Use a wire-wound adjustable resistor of 0Ω/0W as the load resistor RL and set the slider atmid-position; now RL = 5 Ω.

From figure 9 we can derive :

We now use the following equations:

By adjusting the slider slightly clockwise or counterclockwise, we can create ∆vo and ∆io and apply thisfor each value of x and xmeasured. At larger values of x and xmeasured, when the gain is low and thus the val-ues of vo and io are also low, we can increase vi = vg1,k to achieve larger values of vo and io.If vo ≈ 5 V then io ≈ A because RL = 5 Ω. These values are very easily measured with a voltmeter anda current probe. For each value of x and xmeasured we can make a table for vo1, vo2, io1, io2 and rout.

25



oo

ii

o

V (V)

vv

o,open

LR

10

30W

v

oirout

vo,open

o1

o2o

i (A)

0 o1 o2

v

o

v = f(i )

Figure 19. Voltage source model to determine circuit AC output resistance rout.

We also need equation and substitute xaverage for x.

The values of S, S2, µ and µg2,g1 have already been determined. The square of the transformer wind-ing ratio is of course (ns/np)2. When you look at the design impedances of the test transformer you getthe square of the winding ratio as 5Ω/000Ω = /00. To get the actual values, it is better to look atthe measured values of vRL at the primary side and vak at the secondary side, in table . When you cal-culate this fraction for each x and xmeasured you get vRL/vak = 0.025 so the square of the winding ratio is(vRL/vak)2 = /600. All the ‘ingredients’ of this equation are now known and we will apply this eleven

times as we step x from 0.0 to.0 in 0. increments. We willput all results of rout-calculated

and rout-measured in the sametable as the measured valuesand then draw the graphs asshown in figure 20.

The difference between rout-cal-

culated and rout-measured for eachxmeasured is approximately 0.5Ω, which is caused by the pri-mary and secondary copperresistances of the test trans-former and the wire/contactresistances of the test circuit.In the ultra-linear mode, forxmeasured = 0.25, we find an out-put impedance of rout-calculated

= . Ω (dashed lines). Know-ing the importance of rout onthe damping factor, audio-philes can be expected tohear the difference in soundcharacter due to the differ-ences in rout caused by differ-ent xmeasured values.

At last, we can conclude thatthe network analysis of sec-tion 4 matches reality!

26

Rudolf Moers


0 0.2 0.4 0.6 0.8 1.0xmeasured

measured=f(x )

KT88-no.1

MEASUREDrout

CALCULATEDoutr

0.75

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

outr

rout

Figure 20. rout = f (xmeasured), calculated and measured.

7 Practical comparison of a triode, ultra-linear and pentode power amplifierIn this section we will compare the output power and efficiency, the frequency behavior and thenon-linear distortion of an existing electron tube amplifier which we can make to work as a triode,ultra-linear or pentode amplifier by changing some jumpers. The schematic, from reference [], isshown in figure 21.

2



I=60mA

i

i

1W

150E

1W

150E

g3

g2

1g

100k

100k

100k

10

TURN

LOG

1000V

100nF

16V

1000uF

1k2

K

A

g1

ECC82

0,5x

0,5x

ECC82

10TURN

1g

A

K

100nF

1000V

1000V

100nF

10uF

100V

-29V

-29V

100V

10uF

UL

UL

TR

g

K

3 2

A

g

LR

10

TURN

1

PE

PE

TR

50V

EL34

220uF

385V

100k

10k

100k

A

K

100k

22k

100k

33k

47k

gJUMPERS

JUMPERS

EL34

5E

2k7

2k7

1W

18k

1W

1W

1W

1W

1k

a1

VDV6040PP

i

g2,1

a2

g2,2i

ag1k

HEATER

SUPPLY

IS

NOT

SHOWN

SUPPLYCIRCUITS

OF

ADJUSTMENT:

V=-29V

I=60mA

AND

Vg1

VbARENOTSHOWN

a2=60mA

I

a1

Vb

380V

Vg1

Figure 21. Circuit of one monoblock of my first amplifier, thedesign is from reference [4].

First I will start with the comparison of output power and efficiency.For each mentioned configuration the working point is set to Iaw = 60 mA at vg1,kp = 0 V.In reference [] W is promised for the triode, W for ultra-linear and 0 W for pentode. Tests afterconstruction showed some distortion at those levels so I decreased these powers to 2 W for triode,2 W for ultra-linear and 25 W for pentode. With these values there were no non-linear distortions vis-ible on the oscilloscope screen and these powers are very large for use in a living room. Despite the“easy EL” and the “standard circuit”, the sound quality is fantastic.Figure 22 shows output power and efficiency as function of the control grid cathode AC peak volt-age vg1,kp for the mono block of figure 2. The vertical axes show, on a common scale:Input power - Pin

Anode dissipation - Pa

Delivered anode power - pa

Anode efficiency - ηanode

The reason that Pin increases slowly is because Ia increases from 60 mA to 2 mA, to 80 mA and to86 mA in the configurations triode, ultra-linear and pentode respectively. The working point movesfrom class A to class AB. The differences in output power between the triode and ultra-linear modesare relatively large. The differences in output power between the ultra-linear and pentode configu-rations are very small, as I have noted before.

Furthermore, you can see the differences in control grid base for the triode, ultra-linear and pentodeconfigurations. The value of maximum vg1,kp to obtain maximum delivered anode power pa is differ-ent. In order to be able to use the same preamp again in all cases, I used a “select-jumper” in serieswith the slider of the volume potentiometer. With three different values of resistors in series with theslider I could select three different input voltage levels.

Next, I continue with the comparison of the frequency behavior.Figures 23 through25 show the amplitude-frequency characteristic and the phase-frequency char-acteristic for triode, ultra-linear and pentode configuration respectively. During the measurements,the input of the amplifier was terminated by a resistor of 600 Ω and the input signal offered was5 mVRMS = 0 dB, thus mW input power.The AC output voltage was measured across the load resistor of 5 Ω and thus, the output power canbe calculated by the equations shown below. The powers which are then obtained are less than thepowers of figure 22 because the input signal is now limited to 5 mVRMS = 0 dB, mW input power.When you increase the input level to .6 VRMS, the power levels of figure 22 can be reached easily.When we want these maximum power levels at 0 dB at the input, the voltage gain of the preampli-fier and the phase shifter must be increased.

28

Rudolf Moers


29



1

a

anode

aP

in

P

P

0v (V)

2824201684 12

0v (V)

2824201684 12

60

a

aP

inP

anode

(W)(W)

(W)(%)

60

40

a

aP

inP

anode

(W)(W)

(W)(%)

P

Pa

a

a

(%) (W)

(W)

20

40

60

(W)

124 8 16 20 24 28(V)

anode

Pin

Pa

a

v

in

anode

0

c

0

b

00

class Aclass AB

a

class Aclass AB

class A

anode

a

class AB

2xEL34 TRIODE

2xEL34 ULTRALINEAR

2xEL34 PENTODE Pin

20

40

20

g kp1

g kp1

g kp

Figure 22. The output power, dissipation and the efficiency of the mono block of figure 22. Top to bottom: triode,ultra-linear and pentode mode.

Power gain :

Voltage gain:

Comparison of figures 2 through 25 shows that the crossover points at the lower end of the audiospectrum are almost the same for triode, ultra-linear and pentode mode. At the upper end of theaudio spectrum, the crossover points are significantly different. The bandwidth increases from tri-ode, via ultra-linear to pentode. We could believe that the larger Ca,g1 and the Miller-effect would havea large negative effect for triodes, but triodes have a low-value anode AC internal resistance ri. Pen-todes have a very low Ca,g1, but their anode AC internal resistances ri are very high. The balance withthe quantities Ca,g1 plus Miller-effect versus ri tips towards triodes. Regarding the ultra-linear config-uration, the bandwidth lies between those of triodes and pentodes. Furthermore, expect no slopesof 6 dB/octave or 20 dB/decade because this complete amplifier circuit with its several stages is a“patchwork” of separate amplitude-frequency characteristics and phase-frequency characteristics.

0

Rudolf Moers


dB

5

frequency (Hz)

43210

110 10 10 10

o

o

101010

50

45

40

35

30

25

20

15

0

101

102 3 4

frequency (Hz)

+100

+150

+50

o

0

o

-50

-100

o

-150

o

5

dB

v

A

A

p

TRIODE

5

10

o

TRIODE

A =f(frequency)p

A =f(frequency)v

=f(frequency)

Figure 23. Measured frequency response of the mono block of figure 21 in triode configuration.

We see that in figures 2 through 25 the power bandwidth is slightly smaller than the voltage band-width; this can be understood from the following calculations:



A =f(frequency)p

A =f(frequency)v

1 2 3 4 5

dB

o

o

50

45

40

35

30

25

20

15

10

0

+100

+150

+50

o

0

o

-50

-100

o

-150

o

dB

v

A

A

p

10101010 10

frequency (Hz)

5

frequency (Hz)

43210

110 10 10 10

5

o

ULTRALINEAR

=f(frequency)

ULTRALINEAR

Figure 24. Measured frequency response of the amplifier of figure 21 in ultra-linear configuration.

; g

The power gain factor is:

The voltage gain factor is:

Imagine 10 VRMS is measured across load resistance RL of the pentode amplifier, see figure 25.

Ap = 43 dB

Av = 22 dB

The difference between Ap and Av is 2 dB and you can see that in figure 25. The slopes are differentbecause log14.1 of Ap is not equal to log12.9 of Av.

Lastly, I will compare non-linear distortions, see figure 26.• If we accept just visible distortions on the oscilloscope, we can take the maximum power shown

as delivered by the anode, pa, multiplied by the transformer efficiency of about 9 %.

Configuration TRIODE:• The triode amplifier generates mainly even harmonics (2nd) and that meets theory.• A push pull power amplifier should eliminate the even harmonics, but not in the actual case of this

amplifier. This is because although the anode DC currents are equal, the power tubes (and theirparameters) are not identical.

• The figures for the distortion are not so bad, but opinions about this differ.• This triode amplifier sounds very good, even at full-power drive. Of course, this is my personal

opinion.

2

Rudolf Moers


p

v

1 2 3 4 5

dB

o

o

o

50

45

40

35

30

25

20

15

10

0

5

+100

+150

+50

o

0

o

-50

-100

o

-150

o

dB

v

A

A

p

10101010 10

frequency (Hz)

5

frequency (Hz)

43210

110 10 10 10

PENTODE

A =f(frequency)

A =f(frequency)

PENTODE

=f(frequency)

Figure 25. Measured frequency response of the amplifier of figure 21 in pentode configuration.

Configuration ULTRA-LINEAR:• The ultra-linear amplifier has almost the same figures for distortion as the triode configuration. This

is with a delivered anode power of 5 W, double the power of the triode configuration. Personally,I find this a very good result, but your opinion is possibly different.



ddd

d

d

35302520

L

150 5 10

(W)pR

353020

L

150 5 10

(W)pR

d

d (%)

6.0

4.0

2.0

0.0

d (%)

6.0

4.0

2.0

0.0

0.0

2.0

6.0a

d (%)

b

c

Rp (W)

1050 15

L

20 25 30 35

ddd

d

2xEL34 PENTODE

d

d

4d

d

d

total

3

452

total

235

total2

354

25

2xEL34 ULTRALINEAR

2xEL34 TRIODE

4.0

Figure 26. The harmonic distortions d2, d3, d4, d5 and dtotal (= THD) as function of output power pRL of the circuit offigure 21 in the configurations triode, ultra-linear and pentode.

• The maximum power is almost the same as that of the pentode configuration, but with half thedistortion figures of the pentode configuration.

• Up to 0 W delivered anode power, this configuration leans slightly toward the triode configura-tion due to the even harmonics (2nd). Above this 0 W, the configuration leans more to the pen-tode configuration with its strongly increasing rd and 5th harmonics. Due to this, dtotal increasesstrongly

• 20 W anode power gives a lot of sound volume and with % distortion this is quite good.• This ultra-linear amplifier sounds very good, also even at full-power drive. Of course, this is again,

my personal opinion.

Configuration PENTODE:• The pentode amplifier is known for its odd harmonics (rd) and these are not (partially) cancelled

by the push-pull configuration. The 2nd harmonic is half that of the ultra-linear configuration andis cancelled better by the push pull configuration. This is a pentode property. It seems that thepentode characteristics of these specimens of the EL tube are more equal than those of the tri-ode characteristics of these same specimens.

• The pentode has too much distortion at maximum delivered anode power, but 25 W withdtotal = 2 % is not bad.

• My listening opinion says that at full-power drive this pentode amplifier does not sound verygood, but at 25 W output power, your author cannot hear any disturbances.

8 Contribution of the anode AC current and screen grid AC current to ultra-linear power

In the network analyses of section we have seen equation:

As explained previously, itotal is a fictive AC current flowing through the anode AC external resistancera without screen grid primary transformer tap x. It delivers the same power as the real existing anodeAC current ia and the real existing screen grid AC current ig2 in their relationship . They de-liver power to anode AC external resistance ra with a screen grid primary transformer tap x.We will now study these real existing anode AC current ia and the real existing screen grid AC currentig2 in their relationship . Therefore, we use the test amplifier of the previous section (fig 2)where we select the ultra-linear mode. We use two current probes to achieve an oscilloscope picturefor the currents. The results are shown in figure 27.

When you connect these current probes to both a DC and an AC voltmeter, you then can measurethe currents Ia1 , Ia2, Ig2,1, Ig2,2, ia1, ia2, ig2,1 and ig2,2 respectively. These currents are also mentioned in theschematic of figure 2. We will do the calculations with the AC currents. For the VDV600PP outputtransformer, raa = 6000 Ω and x = 0.0. Table 8 shows x = xmeasured. In contrast to the test transformer,this one has a real screen grid primary transformer tap.

Rudolf Moers


.

The measured values are also shown in figure 2 where vak = 9.6 V and vg2,k = 8.0 V:• ia1 = ia2 = ia = 59 mARMS

• Ia1 = Ia2 = Ia = 80 mADC

• ig2,1 = ig2,2 = ig2 = mARMS

• Ig2,1 = Ig2,2 = Ig2 = 5 mADC

If we substitute these measured values of ia and ig2 in the equation for itotal we get the measured fic-tive AC current:

We can also read anode power pa for full-power drive ultra-linear from figure 22: pa = 25W

For each power pentode this is:AlsoSubstitute all:

5



itotal = 64.6 mARMS

pa-EL34 = 12.5Wand ra = #·raa = # 6000' = 3000'

itotal = 64.5 mARMS

DC-VOLTMETER

AC-VOLTMETER

dcII

i rmsi= =

== CURRENT PROBE ON

CURRENT PROBE ONa1 a2= =

=

I

iI

+

+=g2,1+

=23Wkpg a RL1SITUATION:

a1CHANNEL A:

CHANNEL B:

+

g2,1I i

I

g2,2 g2,2

CHANNEL A: 50mA/DIV

CHANNEL B: 25mA/DIV

TIME BASE:

TRIGGER :

v =24V

ia1 a2 a2i

=25W

=

= ia2 59mArmsa1i

I I 80mAdc

CURRENT PROBE ONAC-VOLTMETER

DC-VOLTMETER

g2,1

g2,1

g2,2

g2,2

14mA

15mA

0A-A

0A-B

0,2ms/DIV

CHANNEL A

CURRENT PROBE ON

U

Figure 27. Anode currents and screen grid currents for the ultra-linear power amplifier

vak (VRMS) vg2,k (VRMS)

given x of power transformer VDV6040PP

31,1 12,5 0,402 0,4100,0 40,1 0,401 0,4193,6 78,0 0,403 0,4

Table 8. Actual anode- and screen grid voltages and xmeasured for nominal x=0.4

Calculated differently

Substitute

Apply equation

Substitute

I’m sure you will allow me to neglect the difference of 0. mARMS.The effect of this fictive itotal is an anode power of 2.5 W for one power pentode.The effect of (ia,measured + 0.4 x 1g2, measured) is also an anode power of 2.5 W for one power pentode.

Thus, a piece of network analysis has been proven: quod érat demonstrándum

References[] Fundamental Amplifier Techniques with Electron Tubes; st edition 200; Rudolf Moers;

Published by Elektor International Media BV; ISBN 98-0-90505-9-[2] An Ultra-Linear Amplifier; David Hafler and Herbert I. Keroes; article in Audio Engineering; No-

vember 95[] Radio Technique part 1; 2nd edition 959; A.J. Sietsma; Published by H. Stam, Haarlem[] Modern High-End Valve Amplifiers based on toroidal output transformers; st edition;

Menno van der Veen; Published by Elektor International Media BV; ISBN 0-90505-6-[5] Lehrbuch der Elektronenröhren und ihrer technischen anwendungen; 8th edition 928;

Dr. H. Barkhausen; Published by S. Hirzel Verlag Leipzig[6] www.svetlana-tubes.com[] www.triodefestival.net ETF200 Tube Curves Tracer

6

Rudolf Moers


:

:

:

itotal = 64.5 mARMS

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