Tube Amplifier Circuits (Extract) by Elektor

Tube Ampliﬁer Circuits

From SRPP and Mu-Follower to OTL Designs

Peter Dieleman

Tube Amplifier Circuits

From SRPP and Mu-Follower to OTL Designs

●

Peter Dieleman

● This is an Elektor Publication. Elektor is the media brand of Elektor International Media B.V. PO Box 11, NL-6114-ZG Susteren, The Netherlands Phone: +31 46 4389444

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● Declaration

The author and publisher have made every effort to ensure the accuracy of the information contained in this book. They do not assume, or hereby disclaim, any liability to any party for any loss or damage caused by errors or omissions in this book, whether such errors or omissions result from negligence, accident, or any other cause. The author expresses his sincere gratitude to Arrow Electronics and Trenz Electronic for granting permission to include various tables, figures, and program codes in this book.

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35.4.2

Preface

In 2004 Elektor published my first book: ‘Theorie en Praktijk van Buizenversterkers’.

The book was a success and soon it was translated into French and into German.

‘Théorie & pratique des amplificateurs audio à tubes’ was the French title. The German name was ‘Theorie und Praxis des Röhrenverstärkers’.

I wrote the book because in those days knowledge on tubes was not easily available.

In a German Elektuur book ‘Audio en HiFi-buizen’, the author Rainer zur Linde described an SRPP driver invented by K. Anzai in 1969. I asked myself why such an SRPP would be better than a classic anode resistance amplifier. I started doing calculations on the design. It was wrong. I found out about the most infamous mistake (the cathode elco).

I got interested and later on I learned that the design had three of the errors mentioned in this SRPP book in it.

Although the design was wrong, the idea was inspiring. I did research and one of the designs in my first book had such an SRRP but now without the errors.

In the following years I did more research on SRPPs but also on mu-followers and OTLs.

In 2009 Elektor published my second book on these matters. It was immediately translated into German.

Today Elektor and I still get requests for a reprint. The books are out of stock. Elektor decided no to do another reprint but instead to translate the book into English thus reaching a much larger readers community.

The result is this book. It has been revised a bit. The Dutch version contained a few little errors and my knowledge has grown in the past years.

I consider this version to be much better than the Dutch and the German ones.

It is consequent in style and much more accurate in the details.

I want to thank Jan Didden who inspired Elektor and me to accept the translation and the publishing job. I got in contact with him and he made me publish the article ‘Myths in Tube Circuit Design’ in the audioxpress magazine in May 2023.

I thank Menno van der Veen for his inspiring words and friendship during the past many years.

I thank Elektor’s Patrick Wielders for having transformed the manuscript into a good looking book.

Introduction

Tube amplifiers suffer from distortion. Fortunately, there exist SRPP amplifiers, µ-followers, β-followers etcetera. All these produce a minimal distortion even with output voltages of 50 to 100 Vt.

Often these designs are published with errors in them. It shows to be easy to make a wrong design when we do not have a good understanding of the theory.

In the first section of this book we investigate the origin of the distortion and after that the design of an SRPP and of a µ-follower.

On the internet we can find the most exotic designs. Evaluating them teaches us that these designs often make things worse than they are by nature. In the chapter on wrong SRPPs and µ-followers we sometimes see bizarre but also misplaced designs where a simple, one triode amplifier would perform much better.

There exist push-pull end stages. These are investigated and the similarity with the SRPP are looked at. This is done especially with the theory behind the OTL based on the ‘mother’ of all OTLs, the Philips HF303.

Finally attention is given to the frequency characteristics and technical matters like the supply voltage and the power supply of the filaments

In order to illustrate things there are a few designs that describe the discussed subjects.

This book describes much new theory that has not been published before. Often it is an eye opener as it shows that most things have a beautiful and unexpected simplicity.

Section 1 Prior knowledge

1 Conventions and notations

In scientific publications it is customary that the author call himself ‘the writer’. He also uses the word ‘reader’.

I prefer the more charming ‘I’ and ‘you’ Conveying knowledge is a joint effort.

In this book I will use ‘we have’, ‘we can see’ etcetera.

In this book it is tried to consequently use a number of notations and conventions. These are described below.

Alle DC voltages(tensions), -currents and DC resistances are indicated with italic uppercase letters U, I and R.

Two examples: Uak: the DC voltages between anode and cathode Ra : the anode resistance

In English literature the power supply voltages is often called HT (High Tension) but in this book it is indicated by Ub. This comes from its European origin.

Resistances that are numbered are written as R4 etc.

A resistance is a component in a schematic. A resistor is something you can touch. It may get hot.

The same distinction is made for capacities versus condensers or capacitors

A triode or a pentode again is a component in a schematic. A tube is the glass thing that will break when it falls out of your hands. It gets hot. A tube like an ECC83 or 12AX7 contains two triodes. Compare self-inductions versus the physical coil.

A transformer often is called a trafo.

The value of a resistance is written as 6.8 kΩ. In schematics this often shows up like 6K8. This is an old Dutch Elektor habit.

The maximum value of the power the resistor must be able to withstand is indicated only when this is relevant.

All AC voltages, -currents and -impedances are indicated with a lower case letter.

For AC voltages we use the letter v; not the lower case letter u. The unity of course is volt or V for DC. For AC signals we use ‘volts’.

Except in power supply circuits we never use the effective values like 20 Veff. It makes no sense to give a triode a grid signal of 10 Veff. It is the peak- or top value that counts.

Where needed we use the top values indicate by Vt or Vtt although others may prefer Vp or Vpp. Vp is reserved for a pentode’s Vplate.

In the theory of electrical networks the word excitation is used. It means offering a signal to a circuit.

We will use the more mondain word steering- or driving signal. A car has a steering wheel; a tube has a steering grid, also called control grid.

For AC currents we use the lower case letter i. Here also we use the top values only.

For AC resistances or impedances we use the lower case letter r. In this book there is never a need for complex impedances like �� + ��.

Two AC resistances are of special importance. They are ri and rp. The first one is the AC resistance that we see, looking into a circuit. Usually this means the triode’s internal resistance: �� = ��

With rp the same equation is meant, but then for a pentode. Here the letter p stands for the American word plate; the plate resistance.

In resistances and voltages, the cathode is not written with a ‘c’ but with a ‘k’ like in Uak.

The value of electrolytic capacitors is given in μF. In the text they are called an elco. Both schematic elcos and physical elcos are called elcos. The maximum allowed voltage is only given when relevant.

All other capacities are given in pF or nF.

When we use the word grid we mean a tube’s G1.

The grid DC voltages are always negative relative to the cathode voltages. There exists the term NGV. This means Negative Grid Voltage.

We may have NGV = 4 V or Ugk = -4 V. Please note the minus sign.

In this book we never use positive grid voltages implying a grid current. These positive grid voltages are used in switching electronics and in radar designs.

In fact all the tube’s voltages are relative to the one from the cathode.

The transconductance of a triode or pentode is indicated with a capital letter S.

We use the definition: �� = ��

This is the situation without the presence of an anode resistance. It indicates the behavior of the ‘naked’ triode/pentode.

When discussing the transconductance of a triode/pentode in a circuit we use the lower case letter s, meaning the so called dynamic transconductance

References are like [Dieleman]. They are mentioned in the reference chapter.

Calculating and calculations is about the derivation of equations. I use compute, computing and computations when it’s about getting the numerical values.

2 Prior knowledge

To be able to understand the material in this book, knowledge of tubes and the circuits is necessary.

We could derive all this knowledge here but it can be found in several good books.

As a compromise, some results are presented here, where you find references to [Dieleman].

These books (Dutch, German and French) however are hard to get.

2.1 The 3/2 power law

The relation between the current through a diode and the voltage across it satisfy the so called Child-Langmuir equation.

In fact it is the Child equation which was extended many years later by Irving Langmuir. This Langmuir equation can be found in appendix C.

A is the cathode’s surface and b is the distance between anode and cathode. In (2.1) the letter p stands for the word perveance. This perveance value usually is somewhat larger than 1 having the current I in mA and the voltage U in volts.

So for a current of I = 64 mA we need a tension/voltage of Uak = 16 V.

Figure 2.1 The U-I characteristics of an EZ81 rectifier tube

An EZ81 rectifier (see figure 2.1) ends up almost twice as large and has p ≈ 1.7.

Popular tubes have different perveances. An ECC83 (12AX7) with Uak = 150 V and Ugk = -2 V has a current of Ia = 3 mA, where a 6SN7 in contrast has a current of Ia = 12.5 mA.

We get a high perveance by using a large cathode. Please note that the cathode’s temperature is not in the Child equation (the Child model is somewhat simple).

The perveance however is very dependent on the filament temperature

This is a good reason to never neglect the correct value of this filament voltage.

The tubes characteristics are only valid when using the indicated voltage. In appendix C the perveance is further investigated.

2.2 The characteristics of triodes and of pentodes

Figure 2.2 An ECC82 or 12AU7 It is a German graph; Anodenstrom means anode current

In the above figure 2.2 we see the characteristics of an ECC82. For a number of negative grid voltages the current is shown depending on the anode voltage.

Curve E has Ugk = -16 V, curve F has -20 V. Each curve to the left every time has a 4 volts less Ugk voltage.

The curve through the position A has Ugk = -8 V.

The one in position C has -12 V and the one in position B has -4 V.

The leftmost curve has Ugk = 0 V. It goes through the zero point and it is in fact the characteristic of a diode like te one we saw for the EZ81.

The Child-Langmuir equation for a triode is �� = �� ⋅ (�� + �� ) 3 2 (2.2)

From figure 2.2 we can conclude that with a grid voltage of Ugk = -8 V and an anode voltage of Uak = 175 V, there is a current Ia = 3 mA; the position A.

The bold blue horizontal line through the point A gives us the amplification factor μ.

We select the point (-8; 175) on the 3 mA line

When we now go one curve to the right we find a change of the grid voltage of 4 volts

The corresponding anode voltage is 236 V; the point (-12; 236). Would we go one curve to the left, we would get Uak = 108 V.

So with a constant current of Ia = 3 mA we find a change of 236 – 108 = 128 V.

The ratio of these voltage changes is thus 128 / 8 = 16. By definition this is the μ = 16, where the ECC82’s specs say μ = 17. Those specs do not always hold exactly.

The vertical green bold line through A is about the so called transconductance. When, at 175 V in the point A, we go 2 volts upward the current gets Ia = 6.5 mA; an increase of 3.5 mA. When we go 4 volts downward we find a decrease of 2.5 mA. The total change of Ia is 6 mA.

The grid voltage had a change of 6 volts (4 downward and 2 upward).

Now the fraction of these changes by definition is the transconductance. This is S = 6 / 6 = 1 mA / V. That is not much; most triodes have a larger transconductance.

The tangent in the point A goes horizontally over a distance of 400 – 12 = 273 V. Vertically there is a difference of 17 – 0 = 17 mA.

The internal resistance ri therefore is 273 / 17 = 16.0625 kΩ.

Multiplying the transconductance and this ri gives us 16.06. This must be equal to the value of μ.

This is the famous Barkhausen equation �� = �� ⋅ �� (2.3)

Please be aware that a different quiescent position has different ri and S values.

With small signals we will find the same value for μ. This μ should be a constant; it is about constant. There is a special chapter 3 about this.

Warning:

At point A in figure 2.2 we see a DC grid voltage of Ugk = -8 V. This means that the input signal must have a maximum value of 8 Vt When we exceed this amplitude there will be a so called grid current onset. Where grid current is common in impulse circuits and radar electronics, we never do this in audio amplifiers as it gives an enormous distortion.

In fact there is only grid room for 7.5 Vt This a bit lower value is caused by the existence of the so called electrons space charge. It is approximately 0.5 V in ECC8x tubes For an explanation see appendix C on the extended tube model.

The EF86 is a small signal pentode that is often used in audio pre-amplifiers. The Ug1 = -3 V curve bends downward in the right part of the right graph. The graph’s curve most likely is wrong1.

On the left we see the graphs where the negative grid voltages and the corresponding anode currents are drawn. All of this with a fixed anode voltage of 250 V. You are lucky when this is the anode voltage of your wish. Such a high anode voltage is unusual for an EF86. These left graphs are not used frequently.

1 In the heroic days, when lacking graphic tools and equipment, these graphs were made by gluing small rubber wires onto a piece of white paper. They were then photographed. The -3 V wire probably was glued somewhat wrong. What we have here is a curiosity.

Figure 2.3 The characteristics of the EF86 small signal pentode

For a set of G1 voltages the graphs are drawn in the right part of figure 2.3 From this group of curves we can learn much about the transconductance and the amplification and even about the distortion.

In the right graphs we see the typical shape of pentode curves with the sharp bending at voltages less than 50 V. All graphs are taken using a fixed Ug2 voltage of 140 V.

More to the right we can see that increasing the anode voltages gives almost no extra current.

In other words the pentode has a high rp. A value of 1 to 2 MΩ is easily found. In comparison, the ri of an end triode is 1 kΩ and it is 10 kΩ to 60 kΩ for a small signal triode.

2.3 The tube’s replacement model

Below we see the network substitution schematic of a triode with an anode resistance Ra connected. There is nothing connected to the grid. As known this control grid has an infinite high input resistance.

The anode current has two components. The left one is the contribution of the current source. This contribution is S · vg The second (the right one’s) contribution is of the AC current caused by the changing anode voltage. This contributing current goes through the resistance ri.

Figure 2.4 The triode’s substitution model

The definition of transconductance is �� = ��

The definition of the internal resistance is �� = ��

(2.4)

Multiplying S and ri again gives the classis Barkhausen equation: μ = S · ri. (2.3)

The definition of the amplification factor is �� = ��

2.4 Amplifications and impedances

We start with the elementary schematic below:

Figure 2.5 A non-decoupled resistance amplifier

For this circuit we have an amplification

(2.6)

For short in this book we write û instead of (μ+1). This is just for brevity.

In this equation ra is the switching in parallel of the anode resistance Ra and the load resistance Rload.

Usually the influence of the latter is small as it is a resistance of 1 MΩ (say), where Ra = 100 kΩ.

For an end triode we often have a smaller value like 270 kΩ.

Decoupling the cathode resistance in (2.7) with an elco, rk gets the value 0. So often the amplification reduces to:

�� = �� ⋅ �� + �� or even to �� = �� ⋅ �� + �� (2.8)

Typical values are: ECC81 (12AU7), μ = 60, Ra = 100 kΩ and ri = 15 kΩ.

For the amplification we then find Amp = 52 times. Amp is always less than μ.

2.5 Output impedance

Looking inward from above into the anode we see an output resistance of �� = �� + û ⋅ �� (2.9)

When decoupling the cathode resistance, this reduces to ru = ri, what could be expected looking at the triode’s substitute model.

Figure 2.6 Output resistance seen at the anode.

Looking at figure 2.7 below, we could also look upward into the triode from the cathode.

We then see an AC resistance of �� = �� + �� û (2.10)

Figure 2.7 The output resistance seen from the cathode

The output resistance then is:

�� = �� û = �� + 1 ≈ �� = 1 �� (2.11)

Even for an ECC83 with its small transconductance of 1.2 mA / V, this results in a value less than 1 kΩ which is very small in the world of tubes.

2.6 Operation points of end triodes

A triode in a balanced end stage in class A is said to have an optimal so-called match when ra = 2 * ri and thus in a balanced stage raa = 4 * ri. (2.12) ra and raa here are the transformers primary impedances. The theory can be found in [Dieleman] or in one of the better and complete books.

The theory in the next paragraphs corresponds to a model Please note that this model is not sound. It is useful for making quick estimates. The only correct conclusions can be drawn looking at the graphs/characteristics.

The efficiency in class A is only 25 %. This is the main objection against the usage of triodes in an end stage.

The maximum AC anode voltage is half the one from Uak.

The maximum value of the AC anode current equals the quiescent Ia.

Most designers strive to have a perfect match. It is not so that we always want this.

The efficiency in general is: �� = ½ �� • (1 − 2 ⋅ �� ⋅ �� 2 ) (2.13)

This equation is quite unknown. Pa is the triode’s dissipation.

Equation (2.12) is a special case of (2.13).

So the triode’s efficiency also has a maximum of 50 %, just like the one from a pentode. This is in contrast to what is often published.

We reach this maximum by taking a high value of Uak and a triode with a low ri at the same time.

Switching two triodes in parallel to get half the value of ri does not solve a thing because the value of Pa between the two parentheses also doubles. The product of Pa and ri remains the same.

We really need a triode that has a low ri by design.

�� = 3 �� 4 �� (2.14)

For an EL84 (6BQ5) with Uak = 250 V and μ = 19 this gets vi = 10 Vt.

For an EL34 with Uak = 250 V and μ ≈ 10 we get vi = 19 Vt.

The cathode resistance of an matching triode circuit has a value of: �� = 3⁄�� (2.15)

For an EL84 we then get 270 Ω.

As said, this model is not sound. In reality we often find ra = 3 * ri.

2.7 Efficiency

An end stage absorbs energy from the power supply. Only a small fraction of it is transported to the loudspeakers. The rest is wasted as heat in the tubes

The efficiency much depends on the so called class.

There is class A, B and AB and on the other hand there is the choice between a triode or a pentode.

In [Dieleman] these efficiency percentages are derived completely. In this paragraph the essences are presented.

2.7.1 The pentode in class A

We start with a pentode because that is easiest.

First, we look at the real characteristics of an EL84 pentode. Look at the year in the upper right corner; it may be older than you are .

Please note that the dissipation hyperbolic has the name Wa. In this book the dissipation has the name Wa where the output power to the loudspeakers is called Pa.

With curves like the ones in figure 2.8 the calculation of the efficiency cannot be done. We therefore idealize them getting the model below.

Figure 2.8 The EL84 pentode

INDEX

12SN7 .................................. 218

aluminum oxide ............... 214

amplification 27, 47

open loop .......................... 55

amplification factor ........... 24

Amplimo .............................. 218

balance end stages ......... 175

ballast stabilizer 296

bandwidth ............................. 55

Barium oxide 333

Barkhausen .................... 24, 37

Baxandall ............................ 299

beeldbuis 344

bending ................................. 32

cascode.................................. 95

cathode follower ................ 87

cathode resistance ............ 30

Child 116

Child-Langmuir ................. 327

Langmuir ........................... 21

complex ................................. 19

concertina phase splitter ........................................... 250

constant current source 170

Crowbar ............................... 297 current grid ...................................... 24

Decoupling ........................... 28 dipole 147, 166 dissipation hyperbolic 31, 32 distortion 42, 47 asymmetric ...................... 48 symmetric ........................ 50 distribution noise ............. 228 drain ..................................... 156 ECC84 .................................. 229

............................... 30 EL86 ...................................... 176

344 exit potential...................... 327

............................... 25

negative ............................. 55

factor 55 FET................................. 153, 307

22 Fourier analysis .................. 49

characteristic 187 frequency separation filter ............................................ 181 Futterman ........................... 254 gain ................................. 55, 141 grid .......................................... 19 grid current 328 grid current .......................... 83 GZ34 ..................................... 302 heating ................................. 214

ohmic .......................... 176 hum 163 insolvable ............................ 118 inverse ................................. 317 island effect .................. 37, 134 kathodetemperatuur ....... 329 load line 46, 52 load resistance .................. 176 logarithmic.......................... 318 matched 293 matrix algebra................... 115 Maurice Artzt ..................... 231 microphonic........................ 135 Miller ..................................... 353

Miller capacitance ............ 132

Miller-effect ........................ 224

mismatch ............................ 293

model ................................... 327

noise generator ................ 171 nonlinearities..................... 170

Nyquist ................................ 229

ortho phonic ...................... 299 oscillations.......................... 255

output resistance ............... 29 overdriving ........................... 83 oxide cathode ................... 342

oxidkathode 327

parallel stabilizer ............. 296

perveance ............. 21, 176, 327

phase characteristic ....... 187 pinch ..................................... 292

Pirani 344

power series ................ 50, 345 power-on delay ................ 302 Push-Pull ............................... 75 resistance ............................. 18 RIAA 236 RIAA correction ................ 236 room grid 25, 83

current ............ 343 Schmidt phase splitter ... 257 space charge 25, 327 space charge cloud ......... 328 summator ........................... 189 tangent ............................ 24, 37

153

141 Zener .................................... 171 β 152, 154

Tube Ampliﬁer Circuits

From SRPP and Mu-Follower to OTL Designs

Tube amplifiers su er from distortion. Fortunately, circuits such as the SRPP amplifier, mu-follower, and beta-follower produce minimal distortion even at output voltages of 50 to 100 Vpeak.

These designs are often published with errors. Without a sound understanding of the theory, it is easy to arrive at a flawed design.

In the first section of this book, we investigate the origin of distortion, while in the second we investigate the design of and SRPP and a mu-follower.

On the internet we can find the most exotic designs. Evaluating them teaches us that these designs often make matters worse rather than better. In the chapter on incorrect SRPPs and mu-followers, we sometimes see bizarre and misguided designs where using a simple single-triode amplifier would perform much better.

Push-pull output stages also exist. A great number of them are examined, and their similarity to the SRPP is discussed. This is done especially with the help of the theory behind the OTL based on the ‘mother’ of all OTLs, the Philips HF303.

Finally, attention is given to frequency characteristics and technical matters such as the supply voltage and the filament power supply.

To illustrate these points, there are a few designs covering the subjects discussed.

This book presents much new theory that has not been published before. It is often an eye-opener, showing that many things have a beautiful and unexpected simplicity.

Peter Dieleman studied electrotechnology (‘Electrotechniek’) at Delft University of Technology in the Netherlands. He then earned his living as a television repairman, back when televisions still used tubes. He was a lecturer at the universities of Groningen and Twente in the Netherlands for about 25 years. He has always kept his love for tubes alive. In 2003 Elektor published his first book on the theory and practice of tube amplifiers. In 2009, he finished his second book on tube designs such as SRPPs, mu-followers and OTLs. The first book was translated into German and French; the second into German.

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