Studio Guitar Amp and FX - Ricky-Lee Anderson (UG3 Media Technology Project)

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Studio Guitar Amp and FX – By Ricky-Lee Anderson

BSc (Hons) Sound Engineering and Production

Supervisor: Tom Waterman

May 2012

i

Abstract

Aside from composition skills and playing style, the signature of a recognised guitar player is

their tone. This is formed of amplifying equipment/ effects, in a particular order, driven with a

particular setting which creates a distinct and subjectively pleasing sound.

Tone has become associated with particular artists, eras and styles of playing. And is in-turn

coveted by aspiring and developing artists and producers/engineers within the industry.

This project is an investigation into the stages of guitar amplification and effects pedals that

contribute to guitar tone, and the characteristics thereof, with an objective of proposing a

modular system that enables a user to arrange their own amplification/effect stages and

settings that either emulate or create their desired sound.

ii

Acknowledgements

The author would like to thank Tom Waterman for his guidance as a supervisor/tutor and his

enthusiasm for amplifiers as a guitar player, your subject is taught with excellent context and

has certainly sparked enthusiasm in others.

Further thanks to Tom Evans, Tom Havard and Daisy Pearson for being the coolest and

most supporting housemates since 2010. A large acknowledgement must go to Merlin

Blencowe for the book that guided me through this project, as well as Dave Hunter, Gerald

Weber and RG Keen.

Thank you to Patrick Anderson, Nadia Anderson, Vivian Waters, Sharon Anderson, Tamryn

and Jeandré Henn for help supporting the author as a poverty stricken student.

The most ultimate thanks is awarded to David Gilmour, who's guitar tone and playing was the

first to leave the author slack-jawed, and what has ultimately led to this project.

iii

Contents:

Abstract................................................................................................................................. i

Acknowledgements............................................................................................................... ii

Contents................................................................................................................................ iii

Glossary................................................................................................................................ v

List of diagrams, tables and plates........................................................................................ vi

1.0 Introduction...................................................................................................................... 1

1.1 Guitar Amplifier and Tone History.............................................................................. 1

1.2 Scope......................................................................................................................... 1

1.3 Aims and Objectives.................................................................................................. 2

1.4 Structure of Report..................................................................................................... 2

1.5 Summary.................................................................................................................... 2

2.0 Review of Existing Knowledge......................................................................................... 2

2.1 Literature Review....................................................................................................... 2

2.2 Components Basics................................................................................................... 4

2.2.1 Resistors............................................................................................................ 4

2.2.2 Attenuators with Source and Load..................................................................... 4

2.2.3 Capacitors.......................................................................................................... 5

2.2.4 Impedance and Cables...................................................................................... 6

2.2.5 Filters RC Networks........................................................................................... 6

2.2.6 Tubes................................................................................................................. 7

2.2.7 Transformers..................................................................................................... 8

2.3 Basic Amp Stages...................................................................................................... 9

2.3.1 Input Conditioning.............................................................................................. 9

2.3.2 Preamps Stage.................................................................................................. 11

2.3.3 Tone Stage........................................................................................................ 11

2.3.4 Effects Loop Stage............................................................................................ 12

2.3.5. Phase Inverter Stage........................................................................................ 12

2.3.6 Power Tube Stage............................................................................................. 13

2.4 Biasing Theory........................................................................................................... 15

2.5 Application of Bias..................................................................................................... 16

2.5.1 Designing Simple Triode Stage......................................................................... 16

2.5.2 Choosing a Grid-Leak resistor........................................................................... 16

2.5.3 Transconductance, Amplification Factor and Anode Resistance..................... 16

2.5.4 Mathematical Treatment of Gain Stage............................................................. 17

2.5.5 Cathode Bypass Capacitor................................................................................ 17

2.6 Coupling Networks..................................................................................................... 18

2.7 The Cathode Follower................................................................................................ 19

2.8 The Cascode.............................................................................................................. 20

2.9 The Long Tailed Phase Inverter................................................................................. 21

2.10 The FMV Tone Stack............................................................................................... 22

2.11 Effects Loops........................................................................................................... 23

iv

2.11.1 Active Serial Effects Loop................................................................................ 23

2.11.2 Active Parallel Effect Loop............................................................................... 23

2.12 Guitar Pedals........................................................................................................... 24

2.13 Power Supply System.............................................................................................. 25

3.0 Methodology – Design Process....................................................................................... 26

3.1 Introduction................................................................................................................ 26

3.2 Concept Designs........................................................................................................ 26

3.2.1 Input Conditioning Circuit................................................................................... 26

3.2.2 Distortion Guitar Pedals..................................................................................... 27

3.2.3 Choice of Drivers............................................................................................... 28

3.2.4 Tone Stack Options........................................................................................... 29

3.2.5 Switchable Effects Loop.................................................................................... 30

3.2.6 Phase Inverter/Power Output Circuit................................................................. 30

3.2.7 The Interface...................................................................................................... 31

4.0 Results............................................................................................................................. 31

4.1 Final Design Circuit.................................................................................................... 31

4.2 Discussion.................................................................................................................. 32

5.0 Conclusions..................................................................................................................... 32

6.0 Recommendations........................................................................................................... 33

7.0 References...................................................................................................................... 34

8.0 Bibliography..................................................................................................................... 35

Appendices............................................................................................................................ 36

Appendix A - Resistors 36

Appendix B - Attenuators 37

Appendix C - Capacitors 38

Appendix D - Filters 38

Appendix E - Denominator Reference 39

Appendix F - Tubes 39

Appendix G - Transformers 40

Appendix H - Phase Inverters 41

Appendix I - Biasing Theory 41

Appendix J - Applying Bias 45

Appendix K - Coupling 51

Appendix L - Cathode Follower 55

Appendix M - Cascode 59

Appendix N - Long-Tailed Phase Inverter 62

Appendix O - Feedback Theory 67

Appendix P - Tone Stacks 71

Appendix Q - Distortion Mechanisms 74

Appendix R - Tube Screamer 76

Word Count: 9434

v

Glossary:

AC Alternating Current

DC Direct Current

XL Inductance

XC Capacitance

LF Low Frequency

HF High Frequency

MF Mid Frequency

HPF High-Pass Filter

LPF Low-Pass Filter

BPF Band-Pass Filter

NF Notch Filter

TCR Temperature Coefficient of Resistance

ZIN Input Impedance

ZOUT Output Impedance

RTOT Total Resistance

CTOT Total Capacitance

THD Total Harmonic Distortion

HT High Tension (Voltage)

Gm Transconductance

µ Amplification Factor

Ra Anode Resistor

Rk Cathode Resistor

ra Anode Resistance

rk Cathode Resistance

Cga Capacitance Grid-to-Anode

Cgk Capacitance Grid-to-Cathode

OT Output Transformer

PT Power Transformer

PI Phase Inverter

Vgk Grid-to-Cathode Voltage

ESR Effective Series Resistance

vi

List of diagrams, tables and plates: Fig.1 Voltage Divider & Impedance Circuit Pg.4 Fig.2,3 Current and Voltage against time in a capacitor, and Phase Difference between

voltage and current Pg.5

Fig.4 One Wavelength Pg.6 Fig.5 Cable capacitance and output impedance Pg.6 Fig.6,7 First Order High and Low Pass Filters Pg.7 Fig.8 Triode Tube Pg.7 Fig.9, 10 Transformers Pg.8 Fig.11 Breakdown of the circuit stages of a Fender Deluxe Pg.9 Fig.12 An Equivalent Circuit of a guitar pickup and amplifier Pg.9 Fig.13 Equivalent of a piezo pickup into a load Pg.10 Fig.14, 15 Radial Amp Driver and Jensen Electronics Reamp Box Pg.10 Fig.16 Preamp & tone section Fender Deluxe Pg.11 Fig.17, 18 FMV Tone Stack, James Tone Stack Pg.11 Fig.19, 20 Serial and Parallel Signal flow, Soldano SLO 100 Effects Loop Pg.11 Fig.21 Simple Phase Inverter Pg.12 Fig.22 Fender Super Amp PI Pg.13 Fig.23 Class A Amplification projection Pg.13 Fig.24, 25, 26 Class B, AB, Crossover distortion projection Pg.14 Fig.27 Load Line with voltage input and output swing from a selected bias point C Pg.15 Fig.28, 29, 30 Grid-limiting clipping and cut-off clipping, Maximum level for an ECC83 tube Pg,15 Fig.31 Quiescent current for a given load line/bias Pg.16 Fig.32 Grid Leak Resistor Pg.16 Fig.33 Simple gain stage having max gain at all audible frequencies Pg.17 Fig.34, 35, 36 Roll-off points for variable Ck, Partial Bypass Capacitors, Variable Bypass

Capacitor Pg.17

Fig.37, 38, 39 Coupling Capacitor removing DC, AC&DC Load Lines for the Same Stage, Curves displaying the changes in gain for Ra and Rg

Pg.18

Fig.40, 41 Grid-leak bypass capacitor responses, Anode bypass capacitor responses Pg.19 Fig.42-45 Simple Cathode Follower, Relative Voltage, Operation of a cathode follower,

Voltage Relationships Pg.19

Fig.46, 47 Fixed Bias, Cathode Biasing Pg.20 Fig.48, 49 Simplified Cascode, Lowering screen grid voltages lowers Gm Pg.20 Fig.50, 51 Simple Diagram of Long-Tailed PI, Long Tailed as a PI Pg.21 Fig.52 PI drives into power valves with grid-leak/stopper resistors, so an AC load line

must be drawn Pg.21

Fig.53, 54 Fender tone stack (a) Marshall (b), Frequency Response for an FMV Tone Stack

Pg.22

Fig.55 Defeat/Lift switch/blend circuit and it's frequency response plot Pg.22 Fig.56-58 An active serial effects loop, tone contributing, Active Parallel effects loop,

passive mixing wet/dry, A parallel/series effects loop Pg.23

Fig.59-61 Non-inverting opamp circuit, Inverting Op-amp circuit, Frequency specific gain Pg.24 Fig.62, 63 Two Circuits Showing How Unipolar Power is Obtained from Batteries, Applying

voltage to bias the op-amps, which sets the upper/lower limit of clipping Pg.24

Fig.64-66 Applying voltage to bias the op-amps, which sets the upper/lower limit of clipping, Volume control and ouptput impedance, Two Tone Controls

Pg.25

Fig.67, 68 Pin assignments Radial Workhorse, Workhorse Module Circuit Board Pg.25 Fig.69-71 Lindos interface & ISA828 interface, Lindos and ISA Testing Setup Pg.26 Fig. 72-74 Frequency response curves from HighZ and LowZ settings on ISA828, Input

Conditioning Circuit, Tube Screamer Circuit Pg.27

Fig.75-78 ProCo Rat, Designing Warm Bias Stage, Warm Bias Circuit & Cold Bias Circuit Pg.28 Fig.79-82 Designing Cold Bias stage, Fender/Marshall Switching Tone Stack, Frequency

response Fender option, Frequency Response Marshall Option Pg.29

Fig. 83-88 Series/Parallel Effects Loop Circuit, Series/Parallel Loop Gain Design, Marshall 50W Output, Simple Long Tailed PI, Variable Gain into PI, where previous stage is V1 and first triode of PI is V2

Pg.30

Fig. 89, 90 Proposed idea for front panel of modular amplifier, A rough sketch of card/back pane power/connection ideas

Pg.31

Fig.91 Full schematic, separated into modules by block Pg.31

1

1.0 Introduction

1.1 Guitar Amplifier and Tone History

Amplifiers have evolved plenty over the past 50 years or so, changing their design to suit a changing taste in music and a rapidly growing industry. From the simple Fender “Princeton” and the Mesa Boogie MK1 to Zachary Vex‟s modern Nano Head amplifier that can fit in the palm of your hand.

Players like Chuck Berry and Eddie Cochran from the 1950‟s with “slightly dirty” amplifier sounds have influenced the likes of Jimi Hendrix and Jimmy Page into the 60‟s and 70‟s.

Following the modern era where 7-string guitars and solid-state amplifiers have become popular due to cheaper production costs with „emulations‟ of classic tones....the tube amplifier has become a connoisseur‟s choice to some, and endangered species to others.

There are many musical genres throughout this period that have relied on tube amplifiers as a stable solution to their tonal needs, the tube amplifier is not disappearing – merely evolving to suit the needs of perhaps smaller practice spaces, studio artists and certainly evolving due to the readily available wealth of information online, enabling aspiring designers to become entirely creative with new ideas and even brilliant modifications on existing designs.

The internet has many websites devoted to analysing famous players‟ guitar rigs, which is a complete collection of tools in delivering your sound (Kahn 2011).

[Illustrations opposite (top to bottom): Fender

Princeton, Mesa Boogie Mark1, ZVex Nano Head]

Refs [1, 2, 3]

1.2 Scope

The circuit topologies behind guitar amplifiers and their associated sonic qualities

encompass a large degree of design variation and subjective specification. These are

based on existing amplifiers, pedal, and artists, as well as designing to music-specific

genre.

The scope of this document covers electronic circuit design with basic mathematical

gain/frequency calculations. Innovative power and connectivity solutions must be

2

investigated to make an amplifier/pedal system modular and easy to use, with

consideration for different types of input.

1.3 Aims and Objectives

The aim of this report is to propose a preliminary design for a guitar amplifier with

modular drive, tone and effects pedal options. The design will have a built-in input

conditioning module and power output section, with a suitable system for applying power

to the circuits.

The objectives are:

To briefly discuss the basics of components, networks and supporting calculations

Evaluate existing amplifiers briefly

Analyse input impedance, gain stages, tone stacks, phase inverters, power

outputs, guitar pedals and power supplies

Design a housing system, built in stages and slots for the modules with a

connectivity system

To discuss this design and propose further research

1.4 Structure of Report

The report will assume the reader has basic rudimentary knowledge of electronics, and

will recap this information before highlighting stages of total guitar amplifier schematics

at-a-glance.

Detailed analysis will then be discussed, to form a platform for understanding the design

process, leading into the proposed design and discussion concerning the choices made

in the product. Will then conclude and recommend follow-up projects to further develop

this product.

1.5 Summary

This project is the foundation stage for building guitar amplifiers and understanding how

they influence the sound of a guitar player, or, achieving a desired tone in the studio/live

environment from an amplifier. The project is also intended to be followed-up by primary

research such as experimental builds and testing.

2.0 Review of Existing Knowledge

2.1 Literature Review

Information relating specifically to tube guitar amplifiers often involves acquiring

information from books or journals relating to hi-fi valve amplifiers, such as Morgan

Jones‟ Valve Amplifiers 3rd Edition (Newnes 2003). The information becomes technical

too quickly and assumes a strong knowledge of solid-state electronics and electronics

mathematics with no real emphasis on tone sculpting in the context of instrument

amplification. There is good information concerning build considerations, distortion and

more theory to expand on the research once a foundation of knowledge is created.

3

Oppositely, Scott Kahn‟s book called, Modern Guitar Rigs (Hal Leonard 2011) places

more emphasis on the signal-chain and how it is managed via technology/devices to

influence a guitar player‟s tone and playing. This provides good simple introduction into

thinking about amplifier stages from a player point -of- view...to lead into books such as

Dave Hunter‟s The Guitar Amp Handbook (A Backbeat Book 2005), or, Jack Darr‟s book

with the same title (Howard W. Sams & Co 1971).

The first of these two books provides a small historical enquiry into guitar tube amplifiers

before breaking down simple amplifiers and discussing the components involved, then,

breaking down each amplifier stage into snapshots of existing designs for discussion of

topology in terms of how it sounds (using comparisons to each other).

Whilst Jack Darr‟s book provides good block diagrams, broken-down schematics with

explanations across a range of valve and solid state technology - the specification of this

project is tube-based guitar amplifiers - which is covered more exclusively by Merlin

Blencowe in his book Designing Tube Preamps For Guitar and Bass (Blencowe 2009).

Blencowe assumes basic user knowledge of components from the beginning, going

straight into the fundamentals of gain – biasing triode stages. From here he builds into

coupling stages, cascades, phase inverters and power outputs in variation. The author

does delve into some mathematics, but reinforces it in context of how it affects tone. The

only criticism this book receives is for smaller amounts of detail put into power supply

information – not put into the same degree of context as the other chapters.

All books that have been mentioned are well referenced, linking to journals and projects

which can expand on the referenced information. Online publications such as R.G.

Keen‟s Using the Carbon Comp Resistor For Magic Mojo (Keen 2002) provides useful

information to consider concerning the placement of tone-contributing carbon –composite

resistors in guitar amplifiers – referenced by Hunter.

Blencowe references E. M. Cherry‟s Designing NDFL Amps, which provides a larger

explanation of stabilizing global feedback within amplifiers.

These references are excellent material for developing further knowledge once this

project has concluded.

4

2.2 Components Basics

2.2.1 Resistors

Resistance – the measure of opposition to the flow of current by a piece of electronic

material, dissipates energy in the form of heat. (Ballou 2008)

There are four main equations that derive from Ohms law:

The amount of current through a metal conductor is rationally proportional to the applied

voltage across it. This ratio is defined as the resistance [See Appendix A]:

V = IR

This formula can be rearranged to determine the required variable

P = I2R

P = Power in Watts

I = Current in Amperes

R = Resistance in Ohms

P = V2R

V = Voltage in Volts

Circuit planning – must take into account changes in voltage/current, as resistor values will

remain almost constant, within tolerances of 0.5% to 20% – this is determined by a Voltage

Coefficient. This also varies with temperature, humidity (Temperature Coefficient) and wear –

care must be taken not to exceed the hot-spot temperature of resistors [see Appendix A].

Resistors will contribute their own internal noise to signal due to Johnson noise [see

Appendix A].

Formulas:

Resistors in Series

RTOT = R1 +R2 + R3.....

More than 2 resistors 1

RTOT =

1

R1+

1

R2+

1

R3…

Two resistors in parallel

RTOT = R1 x R2

𝑅1+𝑅2

Several types of resistors are used in circuits, including Carbon-Comp, Carbon-Film, Metal-

Film, Wire wound and Non-Inductive. These are all described in Appendix A, however, the

Carbon-Comp resistor is worth noting for its noise creation effect due to its high Voltage

Coefficient of Resistance – which means the resistance will differ at, e.g. 100v in comparison

to 0v. So if 50vDC was applied with 100v sine wave, it will distort the sine wave, causing

second harmonic distortion „sweetening‟ of tone (Keen 2002).

2.2.2 Attenuators with Source and Load

Attenuation occurs via resistors and voltage dividers such as in Fig.1.

These circuits attenuate to a ratio, and care must be taken to consider the additional effect of the source and load combined with the voltage divider [See Appendix B].

Uses of this circuit include impedance matching, attenuation, gain in feedback loops, biasing.

[Figure 1: Voltage Divider & Impedance Circuit]

Ref [5]

5

Appendix B shows that a potential divider where R1 and R2 are equal values divides a signal in half, using the same formulas we can see that when R2 > R1 the ratio changes, e.g. where R1 = 600Ω and R2 = 6000Ω:

Vd = 1 + (R1/R2) = 1+ (600Ω / 6000Ω) = 1.1

20log(1.5) = -0.83dB

So following the „load ten times source‟ means that the source does not get loaded down, and hence attenuated.

2.2.3 Capacitors

Capacitance – the ability to store charge, attributed to the properties of the two plates, i.e. the potential difference between the two (Gibson 2009) - measured in Farads.

AC Circuits:

- Blocks DC, allowing only AC to pass and inversely blocks AC, allowing only DC to pass

- Discriminates between high and low AC signals – filtering (Capacitive Reactance)

DC Circuits:

- Stores and releases energy, provides an on-demand, single voltage pulse

[Figures 2&3 (left to right): Current and Voltage

against time in a capacitor, and Phase Difference

between voltage and current] Ref [6]

In Fig. 2 we can see that, in a DC circuit, current in a capacitor is maximum when the voltage is minimum. As the capacitor charges the current falls to zero. As a result, the current leads the voltage by 90 degrees (Fig.3), current reaches zero when Vc is at maximum.

Capacitors are influenced by many different factors and as a result add their own tone into circuits, the measure being functionality and taste, see Appendix C for different types and their attributes.

Formulas:

Capacitors in Series

1

CTOT =

1

C1+

1

C2+

1

C3

Capacitors in Parallel

CTOT = C1 + C2 + C3.....

Capacitive Reactance – a capacitors own impedance to AC

XC = 1

2πfc

Where:

F = frequency

C = Capacitance

6

2.2.4 Impedance and Cables

Impedance – resistance against frequency dependant on reactive elements in AC circuits. It can also stem from a combined effect of resistance and capacitive/inductive reactance, denoted as Z, in Ω units.

Single Wires - resistance directly proportional to length

- resistance is inversely proportional to the diameter

- resistance depends on the material

- inductance nearly independent of diameter, proportional to the length

[Figure 4: One

Wavelength]

- One wavelength = λ - Speed of light = 299,792,458m/s - Radio Frequency Wavelengths are electrical signals travelling at the speed

of light - Λ = c/f - Where c = speed of propagation

- and f = frequency

E.g. 1MHz AM Radio wave

λ = 299,792,458/1,000,000

λ = 299,7 meters

A wire can act as an antenna for frequencies four times its length (1/4 wavelength), so wires left too long can introduce noise from RF signals, should not be too much of a problem in guitar amplifiers but is worth noting.

E.g. a 10m cable will act as an antenna for 40m length frequencies

f = c/ λ

f = 299,792,458/40

f = 7.5MHz (approx.)

Studio cables have capacitance of 30pf@ft, or, 100pf@meter.

Formula for capacitance frequency:

fC = 1

2πRC

fC = 1

2π (1 x 10−9)(100 x 10−12) = 1.592Hz

This means the frequencies will roll-off at this frequency – which is very audible. Lowering the value of the output impedance of the 1GigΩ source to 150Ω moves the roll-off to around 1MHz. Output impedance impacts the length of cables that can be used.

[Figure 5: Cable capacitance and output

impedance]

2.2.5 Filters – RC Networks

A filter is largely defined by its pass band; stop band, transition band and centre frequency [see Appendix D for definitions and more], these will determine the output of the circuits from Fig.6&7.

7

[Figure 6: First Order Low Pass Filter] Ref [7]

[Figure 7: First Order High Pass Filter] Ref [7]

The slope is first order, determined by the reactance (XC) of the capacitor, as in Appendix D, this will have inverse effects for LPF versus a HPF, one allowing low frequency to pass by placing reactance (high frequencies) to ground and the other using reactance to block low frequency content and allow high frequency to pass unattenuated. The cut-off frequency for each circuit is determined by:

f = 𝟏

𝟐𝝅𝑹𝑪

The phase will also change by 90 degrees for each „pole‟ or „order‟ of filter [see Appendix D], this will need to be considered when any filters occur in feedback networks (more information on this later).

2.2.6 Tubes

A vacuum tube is used to increase the swing of an input voltage to a larger amount, adding distortion characteristics to change the tone of a signal.

There may also be, depending on the setup of the vacuum tube, a change in phase of the output signal [Appendix F].

There are three main types of vacuum tubes: Triodes, tetrodes and pentodes. Each tube contains a filament, cathode, anode (plate) and a control grid. Additional screen grids, each with their own functions create the difference between the three tubes [see Appendix F].

Uses the heated filament on a separate electrode, which is made more positive. Since the filament is hot and the electrode is cold, current can only flow from filament to the electrode (Barbour 2012).

[Figure 8: Triode Tube] Ref [8]

Vacuum tubes also use transconductance [Appendix F] to translate small voltages into current charge.

Tubes will have their own internal plate resistance and internal capacitance – which coupled with other RC Networks, will produce a tone-shaping effect. This can be put to use in circuit designs, as we will find out.

8

2.2.7 Transformers

[Figure 9: Basic Transformer representation]

The Law of Induction states that a voltage will be induced in a conductor exposed to changing flux, and that induced voltage will be proportional to the rate of the flux change (Whitlock 2008).

Transformers are a pair of electrically insulated windings, magnetically coupled to each other by an iron/ferrous/dust/air core. These are treated to avoid hysteresis – residual magnetic memory keeping the material magnetised (Whitlock 2008).

This increases harmonic distortion for LF signals even at low levels – not desirable for power, but can provide some colour as an output transformer.

Transformers are found in power supply circuits, power outputs and occasionally driving effects loops in guitar amps. They have the advantage of being able to join two circuits in isolation and also change balanced circuits to unbalanced circuits and vice versa.

Their windings ratios can either step-down or step-up voltage, or the same for impedance (reflected by the square of the turn‟s ratio). [See Appendix G for more]

[Figure 10: Audio Line Transformers] Ref [9]

In the output section it‟s job is to convert vacuum tubes high-voltage, low-current output to low-voltage, high-current signal to drive a speaker (Hunter 2005).

The primary coil can be anything from 2kΩ - 10KΩ with a certain wattage potential depending on the type and gain stages used. This is converted to what the speaker sees as 2Ω-16Ω.

The efficiency of the output transformer (OT) , or its lack thereof, plays a large role in the amp‟s overall sound – as it loads the output tubes.

A rule of thumb has been: More iron = more volume and better bass response (Hunter 2005).

Similar principles apply to the power transformer (PT), except it is not handling signal – so size of iron has no immediate relation to frequency response.

Needs to be an accurate, ample supply source to supply the tubes. Ideally over-specified to deal with the current draw and more without over heating (Hunter 2005).

9

2.3 Basic Amp Stages

[Figure 11: Breakdown of the circuit stages of a Fender Deluxe] Ref [10]

Signal in a basic amplifier follows a few basic stages: Input Conditioning, Gain Stages,

Tone Stack, Phase Inverter, Power Output Valves and output transformer (into

speakers, which will not be covered in this project as they are a another project themselves).

Each stage may be repeated and have options built-in to the circuit to provide versatile

control of either the gain or the tone, in some amplifiers different guitar inputs will follow

different routes through the amplifier to provide different tone.

Illustrated in Fig.11 we can see the Fender Deluxe has two gain stages, in between the

different stages are numerous RC networks that serve as passive tone shaping poles, as

well as serving other purposes such as blocking DC, loading down previous stages and

utilizing internal capacitance within the vacuum tubes. To follow is a brief overview of each

stage.

2.3.1 Input Conditioning

Guitars have different styles of pickups, which are, in short, formed of resistance and inductance. Active and passive inductive pickups are common to most electric guitars, whilst piezo pickups can be found on a range of electric, semi-electric and acoustic guitars.

- Each of these pickups must undergo impedance matching from the load the amplifier presents, or face loading down the tone.

[Figure 12: An Equivalent Circuit of a guitar

pickup and amplifier] Ref [11]

10

E.g. in Fig.12 if RS = RL the two resistances would form a potential divider. Following Appendix B this would mean the voltage would be halved.

- power-to-load is at maximum when the resistance is equal

- for maximum voltage-to-load, RL must be much larger than RS [Appendix B, voltage dividers]

(French2009)

The impedance of inductive pickups range roughly 1-12KΩ from single coil to humbuckers, using the rough ratio of source: load = 1:10 [Appendix B], we often find guitar amplifiers using 1MΩ input loads as in Fig.11.

Very high impedance pickups range around 1MΩ+ output impedance (Leon Audio Co. 2012).

So an input impedance of 10MΩ+ is required to prevent these pickups being loaded down into sounding thin and filtered – as piezo pickups have high capacitance – going into a load it resembles a HPF, illustrated in the equivalent circuit in Fig.13.

These buffers can be found in the form of pedals, variable input inside amplifiers and some guitars have active output stages designed to counter this.

[Figure 13: Equivalent of a

piezo pickup into a load]

Vari-Z, or, variable impedance can have a tone shaping effect on the input signal, such as provided in the Focusrite ISA828 audio preamp.

[Figures 14, 15 (left &right): Radial Amp Driver and

Jensen Electronics Reamp Box] Ref [14, 15]

Considering studio-use of guitar amplifiers is “re-amping” a balanced line level signal into an amp.

E.g. send a guitar track from a studio control room into a guitar amplifier (Radial Amp Driver, Fig.14 for recording via microphones.

This changes a balanced signal (XLR socket input) into an unbalanced signal in isolation (transformer), attenuating the signal and setting the impedance to represent a guitar (potentiometers) something more like a guitar. (see Fig.15)

11

2.3.2 Preamplifier Stage

In Fig.16 we can see an input, preamp and tone stack section of the Fender Deluxe from Fig.11.

This amplifier has two switching jack inputs, loaded with a 1MΩ resistor which serves the purpose of loading the source impedance of the guitar, and loads down the input, preventing open-circuit hum when no guitar is connected – switching jack to ground.

Two 68kΩ resistors form a potential divider, also have a tone-shaping function as a LPF paired with the internal capacitance of the 12AY7 triode.

The two triodes are biased with an RC network, which is a frequency-specific bypass network (to be covered in the biasing section).

[Figure 16: Preamp & tone section Fender Deluxe]

Ref [10]

Finally, the preamp stage is separated from the tone stack via a coupling capacitor, which also helps to shape the output tone. This preamp stage is a triode gain stage, these may be situated in many places in the amp as driving stages or recovery stages.

2.3.3 Tone Stage

[Figure 17: FMV Tone Stack]

Ref[16]

Tone shaping occurs around the input stage as we have seen, as well as around cathode/anode bypass, inter-stage coupling with „poles‟, or, RC networks – often stacked on top of each other hence the name Tone Stacks.

Inductive RL circuits are not considered as they are bulky and require large values for LF, which pick up interference and hum.

Tone Stacks normally have low input impedance and high output impedance, which means they need to be driven by a specific type of gain stage, and driven into the correct impedance.

There are a few categories of tone stack, including bass, middle, tilt, Bandmaster, Voigt, James and the popular FMV Tone Stack.

[Fig. 18: James Tone Stack]

Ref[17]

Frequencies are most commonly allocated to three band: Treble – 1KHz and above

Middle – 200Hz to 1KHz, with 600Hz to 800Hz being centre freq.

Bass – 200Hz and below

The position of controls also have common placing:

“One knob “systems – distributes shaping options throughout the amp, this would be seen commonly labelled as „tone‟

Bass Control – placed early as it manages the effects of blocking distortion (to be discussed later)

Treble – placed once all the harmonics have been added to the signal via gain stages, usually at the end

Middle – can be placed anywhere

12

2.3.4 Effects Loops Stage

Effects Loops take different value from where they are placed within the amp schematic, with the placement being relevant to the ideal tone combined with the effects pedals/gear the guitarist will use.

Effects Loops are usually a series or parallel circuit. For series, 100% of the tone goes out of the send and back into the return. Parallel splits the signal two-ways, one leg carrying the pure amp tone, the other going through the effects before summing (actively or passively) back at the return. This is usually controlled by a blend knob, and, because phase shift may occur in the effects leg, a phase control can also be added to correct any issues.

The biggest argument is against serial effects loops as tone generated by the amplifier is

[Figure 19: Serial and Parallel Signal flow] Ref[18]

fed through external circuits, which may be detrimental to the tone.

A simple effects loop is illustrated in Fig.20, which is a passive, un-buffered loop, controlled by the switching input jacks labelled „send‟ and „return‟.

Other effects loops may have a dedicated gain stage driving the signal into the loop and/or a recovery stage to ramp-up the signal lost through the effects chain.

[Figure 20: Soldano SLO 100 effects loop] Ref [19]

A few points need to be considered when planning effects loops into an amplifier (Blencowe 2009):

- Hi-gain amps usually have cleaner output stages, less distorted, good for effects - Low-gain amps usually have dirtier, more distorted output stages, can sound messy with effects - clean sounding amplifiers add less distortion/harmonics to guitar signal, would it need an effects loop?

- The loop needs to be transparent, i.e. not affect the tone of the amplifier - can be designed in to contribute positively to the sound

2.3.5 Phase Inverter Stage

Phase Inverters take one input signal and output this from two paths, each a replica of the input signal phase with one 180 degrees phase flipped, illustrated in Fig.21.

These signals will be sent to their own power output tubes, known as class AB amplification (discussed later).

[Figure 21: Simple Phase Inverter] Ref [21]

13

There are three common types of phase inverter:

- Paraphase [see Appendix H]

- Cathodyne [see Fig.22]

- Long Tail Pair [see Appendix H]

The order listed above also happens to be the dirtiest to the cleanest sounding inverters.

The cathodyne phase inverter (PI) in Fig.22 has a dedicated gain stage driving into it. However due to its higher levels of distortion (lack of large voltage swing) it, along with the paraphrase, are usually unable to drive the output tubes to maximum.

The long tailed pair in Appendix N outputs stronger current to drive into the output tubes, resulting in a more powerful low end and more power tube characteristics.

[Figure 22: Fender Super Amp PI] Ref [20]

2.3.6 Power Tube Stage

Power tubes from each side of the phase inverter amplify signal in a similar manner to most gain stages. There are a few configurations of amplification:

- Push Pull - Single Ended - Parallel Single Ended (fairly rare)

For the purposes of this brief section, the common classes of amplification will be discussed:

In Fig.23, we can see a voltage swing going into Class A amplification, the red spot being the bias point, or where the centre of the output image will be to mirror the input image.

A distinct feature of Class A amplification is that the valve is conducting current at all times – i.e. the „out‟ current never drops to zero at any time (Munro 2007).

[Figure 23: Class A Amplification projection] Ref [24]

14

In Class B amplification, we can see in Fig.24 that the bias point is set to where the valve has almost stopped conducting.

The input signal is a lot larger to drive through the valve hard enough but the output is only one half of the whole waveform.

Class B is used in a push-pull output stage, where each valve will be biased to represent one different half of the input signal each side of the zero-point.

When one valve is on, the other is off; this is more efficient than Class A amplification.

[Figure 24: Class B Amplification projection] Ref [24]

Class AB is somewhere between class A and B, where is up to the setting of the bias point.

A large amount of one peak and a small amount of the other will be the output; again, this class of amplification is used in the push-pull configuration.

Which means one valve will be at maximum power (large peak) while the other is at a lower power (small peak).

Both Class AB and Class B will yield Crossover Distortion:

[Figure 25: Class AB Amplification projection] Ref [24]

- The output of the two PI halves are added together by the OT, and a kink can be seen as in Fig.26. Class AB can suffer from this if the bias is set too low (Munro 2007).

Class A does not suffer from crossover distortion (Munro 2007), but this can trade off more heat generating from the power valve – more harmonic distortion in the signal.

[Figure 26: Crossover distortion projection] Ref [24]

15

2.4 Biasing Theory

[Figure 27: Load Line with voltage input and output

swing from a selected bias point C] Ref [25]

A vacuum tube usually has a static anode characteristics graph [Appendix G] and a transfer characteristics graph [Appendix G] that usually accompanies the packaging.

Using the HT power, anode resistor and Ohms Law we can draw a load line on the first graph which cuts the grid voltage (Vgk) curves, and choose a Vgk curve for biasing. This creates a quiescent voltage and current before the amp processes signal. When a small input signal is processed it causes anode voltage Va to swing.

If the grid goes into grid-limiting (or close towards positive Vgk) or cut-off (maximum quiescent anode voltage), the signal will be warm biased or cold biased, respectively. Each have their own sound characteristics, and this point of clipping either side controls the input sensitivity of the amp. An amp must be centre biased to have more head room and a cleaner sound.

- A 'gain' control can determine how hard the input voltage can swing into clipping.

[Figures 28, 29 (left to right): Grid-limiting clipping and

cut-off clipping] Ref [25]

Fig.28, 29 illustrate these effects on a sine wave.

These effects can be used in different gain stages to create a desired amount of 2nd and 3rd order harmonic distortion blend that will make up an amp's character.

Variable biasing on each stage could be a tool here for even more control of tone.

[Figure 30: Maximum level for an ECC83 tube] Ref [25]

There are limitations on safe biasing to ensure the valve does not degrade or become destroyed.

The maximum continuous power operating for the anode, Pa(MAX) is the curved line.

Maximum voltage the anode can stand at any time Va(0) starts at the black area and is often associated with the power needed to operate the tube - high tension (HT).

The maximum quiescent voltage for the anode is the vertical line Va(max), which is also the cold clipping line.

Appendix I details how to use these graphs more.

16

2.5 Application of Bias

2.5.1 Designing a Simple Triode Gain Stage

The two considerations are the anode resistor (Ra) and the HT.

In Fig.31 we can see 100K has been chosen with an HT of 280V. At a chosen bias point of Vgk = -1.5V:

Ia = ±0.9mA

Va = ±180V

We want the grid to be 1.5V more negative, so given Ia:

1.5V/0.9mA = 1667Ω

(nearest value is 1.5K)

[Figure 31: Quiescent current for given load line/bias] Ref[25]

*The resistors must have sufficient power rating to withstand the power rating they operate at, for example (with quiescent current around 1mA):

P = I

2R

P = (1mA)2 * 100k = 100mW

Could choose the rating at 1/4W, however may choose 1/2W to be on the safe side

2.5.2 Choosing a Grid Leak Resistor

The grid-leak resistor will be a load on the previous stage, so this must be a fairly large value. This is usually around 1MΩ for most stages as well as for loading guitar pickups.

The datasheet provided with the vacuum tube will usually give the maximum allowable value, this value must not be exceeded [see Appendix J for more information].

[Figure 32: Grid-Leak resistor]

2.5.3 Transconductance, Amplification Factor and Anode Resistance

Transconductance, or denoted Gm, is the valve's ability to translate small voltage into current, it is determined by comparing the total change in grid voltage to Ia [see Appendix J]:

Gm = 𝚫𝐈𝐚

𝜟𝑽𝒈𝒌

Amplification Factor (μ) is determined by the small changes in grid voltage (Vgk) causing large changes in anode voltage (Va) [see Appendix J]:

μ = 𝚫𝐕𝐚

𝜟𝑽𝒈𝒌

Anode resistance (ra)is the internal resistance the valve presents to AC, the steeper the grid curves, the lower ra will be. Determined by comparing changes in anode voltage to Ia [see Appendix J]:

ra = 𝚫𝐕𝐚

𝜟𝑰𝒂

17

2.5.4 Mathematical Treatment of Gain Stage

Simply put, the gain is = μ (Blencowe 2009)

Current flows down potential divider Ra||ra and we can only ignore the cathode if it is held constant, however it constantly tries to follow anode (on a much smaller scale).

This pulls down the expected output voltage a bit [see Appendix J].

A = 𝝁𝑹𝒂

𝑹𝒂+𝒓𝒂+𝑹𝒌(𝝁+𝟏)

A cathode bypass capacitor can prevent the voltage swing on the cathode.

2.5.5 Cathode Bypass Capacitor

This bypasses signal to ground dependant on the size of the cathode resistor Rk and the bypass capacitor Ck, Fig.33.

It also helps smooth out changes in signal at the cathode.

Larger - allows more frequencies through to be smoothed

Smaller - only HF

f = 𝟏

𝟐𝝅𝑹𝒌𝑭 ....with F being the chosen roll-off freqency (e.g. 5Hz)

f = 𝟏

𝟐𝝅 𝟏.𝟓𝑲 (𝟓𝑯𝒛)= 21μF (or nearest value 22μF)

This gives all frequencies above this the same gain.

The type of capacitor used here must be chosen with lifespan, distortion and max power rating in mind. Although the cathode does not operate at high levels.

The roll-off point must be considered with reducing LF blocking distortion, [see Appendix J].

[Figure 33: Simple gain

stage having max gain at

all audible frequencies]

Ref[25]

[Figure 34: Roll-off points for variable Ck]

Ref[25]

In Fig.34 we can see different roll-off points for different values of Ck.

However, by placing a resistor or potentiometer (as capacitor Ck keeps DC off this device) in series with Ck. Creating a limited boost, even higher frequencies are not completely shunted to ground by Ck - altering the gain of the circuit [Appendix J].

In circuit B of Fig.35,36 we can see a variable R1 and its variable boost affect on the signal above roll-off point.

So R1: low value = presence/HF boost;

high value = overall boost

[Figure 35: Partial bypass capacitors] Ref [25]

[Figure 36: Variable bypass capacitor, Fig.37] Ref[25]

18

2.6 Coupling Networks

A coupling capacitor is placed between networks with a few purposes:

- removing DC from output signal that superimposes itself on the signal,

Fig.37

- prevents DC from leaking into the next stage

- forms a HPF with Rg

The first stage of coupling should roll off above 50Hz (Blencowe 2009), this reduces mains hum and helps reduce blocking distortion.

The power rating should be able to withstand maximum HT of power transformer.

[Figure 37: Coupling Capacitor

removing DC]

[Figure 38: AC and DC load lines, for the same stage]

Ref[25]

When choosing a grid-leak resistor (Rg)for V2, must keep in mind that it will appear in parallel with Ra for AC signals.

This will mean an AC load line (Fig.38) will need to be created with the bias point located at quiescent current point [Appendix K].

This also proposes a new gain formula that supersedes the previous DC gain:

A = 𝝁(𝑹𝒂||𝑹𝒈)

(𝑹𝒂| 𝑹𝒈 +𝒓𝒂

Also, must not load down the previous stage with size of Rg.

[Figure 39: Curves displaying the changes in gain for Ra

and Rg]

Fig.39 displays the changes in gain that occur for different values of Rg (curves) to anode resistor (Ra) values.

The parallel Ra and Rg also acts as a potential divider, so the gain factor must be considered when limiting signal passed between stages.

Rg could be replaced with a logarithmic potentiometer after the coupling capacitor to regulate gain.

There are a few variations and additional circuits to the coupling capacitor and grid-leak [in Appendix K] that can voice coupling between stages differently. Two examples, Fig.40 & 41, show how LF and

19

[Figure 40: Grid-leak bypass capacitor responses]

Ref[25]

[Figure 41: Anode bypass capacitor responses]

Ref[25]

HF can be attenuated by employing additional bypass capacitors on grid-leak and anode resistors respectively. Care and attention must be paid not to encourage blocking distortion or amplify too much HF content that can lead to amplifier oscillation.

2.7 The Cathode Follower

Output from the cathode side of the valve, the grid swings more positive and the voltage on Rk increases. As opposed to normal anode output, the cathode follower does not invert the phase of the amplified signal.

A = 𝝁+𝑹𝒌

𝒓𝒂+𝑹𝒌(𝝁+𝟏) ...is the gain for cathode follower.

ZIN = Rg

ZOUT = rk||Rk (where rk is resistance of the cathode)

[Figure 42: Simple

Cathode Follower]

[Figure 43: Relative

voltage] Ref[25]

[Figure 44: Operation of a cathode follower]

Ref[25]

[Figure 45: Voltage

relationships Fig.46]

Ref[25]

In Fig.43-45 we can see the valve split up into stages. The total HT is divided up amongst these, as it drops going across the valve. The bias point in Fig.46 is determined by Vga, with line drawn down on the graph, subtracting each Vgk amount from it, forms the curved lines in Fig.44.

The quiescent voltage Vak is read from where it cuts the existing load line, e.g. point Q is bias centre for Vga = 200V.

Note, that if an input voltage of 100Vp-p is input and swings from point P to R, the output will only be ±89V - this means the larger the input the more negative the grid is becoming - a high Gm operation stage. Gain = VOUT/VIN = 89/100 = 0.89

20

[Figure 46: Fixed Bias]

Ref[25]

In Fig.46-47 we can see that the gain is drawn from the cathode and fed back into the grid, at either a fixed (Fig.46) or variable (Fig.47) amount. This is known as Negative Feedback.

In Fig.47 the value of Rg appears larger to AC attached to Rk, this increases the impedance of the circuit and changes the gain, known as bootstrapping.

Fig.46 shows that cathode followers have relatively low ZOUT, which makes them ideal for driving tone stacks or effects loops, which have low ZIN.

(See Appendix L for further depth and variations on existing arrangements.)

[Figure 47: Cathode

Biasing] Ref[25]

2.8 The Cascode

[Figure 48: Simplified

Cascode] Ref[25]

V1 loads into V2's low cathode impedance, V1 acts as a transconductance amplifier (Volts to Amperes).

V2's grid is fixed, common to ground - shields the cathode from voltage swing - no compressed soft edges.

V1= Inverting, V2=Non-inverting -----so overall Cascode is inverting

V1 anode = V2 Cathode and Grid, which is usually around 1/3HT (Blencowe 2009)

Below in Fig.49 shows how lowering the 'screen grid' voltages (voltage at V2 grid) lowers the output current, but widens bandwidth out output swing.

[Figure 49: Lowering screen grid voltages lowers Gm]

Ref[25]

The curves' knee in Fig.49 show the point at which V2 starts conducting.

Due to the nature of the two triodes, the gain, capacitance and ZOUT is more complex than normal. (Appendix M provides formulas for these)

Approximated, ZOUT = Ra

The 'screen' is where biasing takes place, can be fixed by through a potential divider from HT, or, leaked from anode V1 to grid V2.

Adding a capacitor to ground in between the PD, controls the lowest frequency at which voltage is held constant.[see Appendix M]

21

2.9 The Long-Tailed Phase Inverter

[Figure 50: Simple

Diagram of Long-Tailed PI]

Ref[25]

This is the most popular phase inverter used in modern amplifiers (Blencowe 2009), 6 pole circuit (Fig.50) which can be used as a balanced interface.

The Long-Tailed will amplify the difference in voltage between the two inputs (differential amplifier).

Most guitar amps use this as a phase inverter with the second input tied to ground via bypass capacitor - this prevents signal appearing in second grid and unbalancing the output.

The balance of V1&V2 depends on the value of Rk - which should be ideally infinite, but can be rectified by using mismatched anode resistors - balances the gain:

[Figure 51: Long-Tailed as a

phase inverter] Ref [25]

V1 will display output from both its anode (normal inverting gain) and cathode (non-inverting cathode follower) (Assuming Ra1=Ra2=Ra):

Non-Inverting Gain:

A2 = μRa/ (Ra+ra)(2 + Ra +ra

𝑅𝑘(𝜇+1))

Inverting (greater than the non-inverting by):

𝐴1

𝐴2=

Ra + ra

𝑅𝑘(𝜇 + 1)

This is because the cathode of V1 outputs a lower voltage, the same amount will not be passed to V2. The differential gain, assuming A1/A2 balance:

A = 𝛍𝐑𝐚

𝑹𝒂+𝒓𝒂

ZIN = grid-leak resistor

Output Impedance (Balanced Circuit):

ZOUT = Ra||ra

Output Impedance (Unbalanced Circuit):

ZOUT = Ra/2

Because the input signal is split between the anode and the cathode, the input sensitivity is halved.

Because the circuit drives into another gain stage (Power Valves), which have grid-conditioning resistance, the gain will change for AC, so a load line (Fig.52) must be drawn.

Both grids are biased from cathode voltage from the tail, again not exceeding max value given by tube data sheet.

[Figure 52: PI drives into power valves with grid-

leak/stopper resistors, so an AC load line must be

drawn] Ref[25]

V2 has a bypass capacitor, where frequencies down to 'f' will be decoupled to ground [Appendix N]:

Cg2 = 𝟏

𝟐𝝅𝒇𝒁𝒊𝒏

22

2.10 The FMV Tone Stack

There are a few kinds of tone stacks that are used in modern amplifiers such as the Bandmaster (taken from Fender Bandmaster), Voigt (a clean bass amp tone stack), Baxandall and James Tone Stack - the latter used by manufacturers such as Ampeg and Orange (Blencowe 2009).

See Appendix P for more information on these listed tone stacks, for now, the focus will fall onto the most popular tone stack in modern amplifiers (Blencowe 2009), the FMV Tone Stack.

Most commonly used Fender, Marshall and Vox tone stack

are two variations of this stack, in which the "Middle" control is varied

in the Fender stack when all controls are set to minimum the amp is silenced, Fig. 53 (a)

this is not the case with the Marshall Fig.53 (b)

R1 is known as the 'slope resistor' which determines the minimum ZIN

this should be large enough on its own to not load down the previous stage

[Figure 53: Fender tone stack (a) Marshall (b)] Ref

[25]

C3 determines the upper end of the bass control range (with R1 and ZOUT of previous stage)

C2 determines the lower end of the bass control (with R1, P2, P3 and previous ZOUT )

C1 determines the upper end of the control (with P1 and previous stage ZOUT)

adjusting the roll-points of each stage can be done by adjusting values of the capacitors [see Appendix P], or, adjusting the slope resistor - but this impacts on each control

[Figure 54: Frequency response plot for an FMV

tone stack] Ref [25]

FMV stack can be defeated/lifted

allowing the signal to bypass at SW1 (Fig.55) when P3 is at maximum (as resistance is more than R3

otherwise P3 will blend the bypass/Equalized sound

[Figure 55: Defeat/Lift switch/blend circuit and it's frequency response

plot]

23

2.11 Effects Loops

2.11.1 Active Serial Effects Loop

Fig.56 is a serial effects loop enclosed in the same envelope as a dual triode(active), with a gain of ± 50. The triode is an ECC81, which has low ra and high Gm - a strong cathode follower with high gain for the recovery stage.

[Figure 56: An active serial effects loop, tone contributing] Ref[25]

This 1MΩand 22K pot in series preserves the tone of the amplifier by not loading down the previous stage, while the cathode follower attenuates the signal down to instrument level by a factor of 1/50 (inverse of gain recovery, Blencowe 2009).

The design of the circuit, shown by the dashed lines, show the path the signal takes when the effects loop is not engaged - does not affect the tone (in fact, adds more triode harmonic character from recovery tube).

The 100KΩ resistor after the recovery triode simulates the source impedance of a tone stack (Blencowe 2009)

2.11.2 Active Parallel Effects Loop

Parallel loops must be designed to balance wet/dry levels (equal amplitude):

Boost wet before mixing Attenuate dry before mixing

- noisy resistors

Fig.57 shows 1MΩ pot mixing the wet/dry signals.

[Figure 57: Active Parallel effects loop, passive mixing wet/dry] Ref[25]

This is done via two 220KΩ mixing resistors, which prevent each other from shunting to ground if an opposite signal is turned all the way down. If these are made large, the interactions between controls are compromised and has impedance interaction with the next stage.

[Figure 58: A parallel/series effects loop] Ref[25]

Fig.58 illustrates a virtual earth mixer/recovery stage (with a virtual load/grid-leak attached).The 1MΩ pot varies the series resistance of each leg:

Gain = 0.9 to 8 for dry

Gain = 0.9 to 28 for wet

The gain needs to be proportionally higher for the wet signal due to signal loss and

24

attenuation in through effects gear, and also due to the fact that instrument level is smaller.

This circuit is good for mixing between unequal levels, with no significant cross talk (Blencowe 2009).

2.12 Guitar Pedals

Overdriving Transistors:

transistors run at top of operating range

nasty distortion - fuzz

silicon is metallic, germanium sounds a little smoother

[Figure 59: Non-inverting opamp circuit]

Non - Inverting:

gain set with R1||R2

R2 & C1 form LPF

Cannot have gain <1

[Figure 60: Inverting Op-amp circuit]

Inverting:

Gain set with R1&R2 potential divider

To avoid tone loss, input impedance must not be greater than 100KΩ

Therefore R2 = 100KΩ, to have a gain of 10 then R1 = 1MΩ

high value resistor = high noise

[Figure 61: Frequency specific gain]

gain of non-inverting Fig.61 = (10K+1K)/1K = 11

C1 = 𝟏

𝟐𝝅((𝟏𝑲)(𝟒𝟎𝑯𝒛)= 39nF for 40Hz low cut-off

(nearest value = 22nF which makes 72Hz cut-off)

C1 = 𝟏

𝟐𝝅((𝟏𝟎𝑲)(𝟑𝟎𝑲𝑯𝒛)=530pF for 30KHz high cut-off

(nearest value = 470pF which makes 33KHz cut-off)

Power Supply:

Opamp needs bipolar power or to be biased to half-input voltage

a normal battery is unipolar

batteries can be used to create unipolar power

[Figure 62 (left): Two circuits showing how unipolar power is attained from batteries]

[Figure 63 (Right): Applying voltage to bias the op-amps, which sets the upper/lower limit of clipping]

25

[Figure 64: Drive controls for opamp based pedals]

Controls (adjust the amount of distortion):

A - volume is before the opamp, limits the signal into the amp

B - replaces the drive setting resistor of an opamp, alters gain and freq cut-off (HPF)

[Figure 65: Volume control and ouptput

impedance]

affects the signal output of the pedal to an amp or another pedal

the capacitor bocks DC from getting out and off potentiometer

Pot is large for control, and also sets ZOUT

[Figure 66: Two tone controls found in guitar

pedals]

(Fig.66)

A - low pass variable filter

B - LPF = R1 and C1

B - HPF = R2 and C2

B - linear pot R3 controls the blend of two

(Salminen 2000)

2.13 Power Supply Systems

[Figure 67: Pin assignments Radial Workhorse]

Ref [30]

[Figure 68: Workhorse module circuit board] Ref[30]

Unfortunately the project time has come to a close. Briefly, a module card based system like the Radial Workhorse or API Lunchbox would be employed. The circuits would operate on a card (Fig.68), slotting into a port built into the amplifier rack. The voltages and signal are passed via pins (Fig.68), each allocated a different job, much like the Radial Workhorse specifications in Fig.67.

26

3.0 Methodology - Design Process

3.1 Introduction

The modular amplifier's purpose is to provide the user with different ways to voice an amplifier.

Providing a framework with flexible connectivity for input and output with these interchangeable voicing stages for the amplifier demanded a good knowledge of amplifier design, which has now been established.

The next step is selecting a few key qualities of amplifiers and design each stage with buffering to enable them to be shuffled, with variable qualities that allow further tone flexibility within the individual modules.

Like many companies historically, existing designs can provide a good starting point.

3.2 Concept Designs

3.2.1 Input Conditioning Circuit

A Lindos MS10 unit can be utilised to test the ISA828 with constant voltage frequency sweeps – which should be nominally flat.

The signal is sent out through the left mono-out of the MS10 box, into the instrument input jack of the ISA and back out into the right mono-in of the MS10.

An LPT port on the Lindos unit

[Figures 69, 70 (left &right): Lindos interface & ISA828 interface]

Ref[12, 13]

[Figure 71: Lindos and ISA testing

setup]

is connected to the LPT port on a computer to monitor the information, this is illustrated basically in Fig.71.

The levels must be calibrated to be equal levels of signal out from the MS10 unit to signal output of ISA828 (Fig.69).

The instrument-in conections on the ISA828 only allows the use of the High-Z and Low-Z options (Fig.70), this was utilized with the “SweepU” setting the Lin4Win XP controller program, shown in Fig.14.

After Lindos completes the sweeps, it plots frequency response of the signal processed by the ISA828

27

[Figure 72: Frequency response curves from HighZ and LowZ settings on ISA828]

In Fig.72 we can see there are subtle differences between the two input settings, effecting the roll-off. The testing results can also be seen to have other differences in frequency plots, this is due to non-linearity in both the filter poles and transformer circuitry in the ISA828, part of which provides its own individual tone.

The final circuit is shown in Fig.73, which has an added "Reamp" option for studio use.

The selection is controlled by a switch into a solid state buffer which controls the gain by ratio:

VOUT = R2/(R1+R2)

VOUT = 0.09(min) - 1(max)

[Figure 73: Input Conditioning Circuit]

3.2.2 Guitar Distortion Pedals

The operation of the Ibanez Tube Screamer is detailed in Appendix R.

The bypass circuit has been altered to remove the flip-flop circuit and replaced with a simple switch for the front panel.

[Figure 74: Tube Screamer Circuit] Ref [28]

28

The Pro Co Rat is the next pedal.

This pedal uses ground reference clipping, discussed in Appendix Q [Illus.104] and filtered feedback to create tone, as does the Tube Screamer.

[Figure 75: ProCo Rat Circuit] Ref[29]

3.2.3 Choice of Drivers

Both Cold Biasing and Warm Biasing stages will be utilized so both input sensitivity voices are present in the amplifier. Both will operate on an HT = 300V with Ra = 100KΩ.

Warm Bias Module

Load line reads quiescent current/voltage: Ia = 1.4mA and Va = 155V

Biased at -1V (closer to grid limiting when input signal swings)

So for Rk = 1V/1.4mA = 333Ω (330Ω nearest)

Partial bypass gain, 470nF series 4k3Ω pot(with 330Ω seen as series to AC):

FC = 𝟏

𝟐𝝅 𝟒𝟔𝟑𝟎 (𝟒𝟕𝟎𝒏𝑭)= 73.14Hz

low cut-off (Boost all above this)

[Figure 76: Designing Warm Bias stage]

Optional bypass switch for gain control, standard 1MΩ Grid-leak (for Phillips 5751 ECC83)[27], with 22nF coupling cap to enable the module to be attached to any stage. Similarly, another 22nF and 1MΩ are attached to the end to decouple and provide a drain path (decouple and load)to ground should there be nothing attached to the end of the stage.

[Figure 77, 78 (left to right): Warm Bias Circuit and Cold Bias Circuit]

29

Cold Bias Module

Load Line Reads: Ia = 0.5mA and Va = 255V

Biased much closer to cut-off than the warm for harsher effect

Rk = 2.5V/0.5mA = 5KΩ (5K1Ω nearest)

Partial bypass gain, 560nF series 1kΩ pot(with 5k1Ω seen as series to AC):

FC = 𝟏

𝟐𝝅 𝟔𝟏𝟎𝟎 (𝟐𝟕𝟎𝒏𝑭)= 96.63Hz

low cut-off (Boost all above this)

[Figure 79: Designing Cold Bias stage]

With internal plate resistance of Electro Harmonix 12AX7EH[28] of 54K1Ω and Ra, the ZOUT of this stage is ±35.1KΩ. Utilizing anode bypass and HF attenuation resistor, aiming for 3KHz cutoff:

Ca = 𝟏

𝟐𝝅 𝟑𝑲𝑯𝒛 (𝟑𝟓𝑲𝟏Ω) = 1.5nF

The added R1 = 100KΩ pot controls HF attenuation as a shelf, labelled "Presence".

Again, a decouple and load circuit is added to the end of this module and the 12AX7EH data sheet quotes maximum 2.2MΩ grid-leak, a 1MΩ is used. The circuit leading into this was adapted from a gain stage of Mesa Dual Rectifier.

3.2.4 Tone Stack Options

Exploring Weber's A Desktop Reference of Hip Vintage Guitar Amps, many tone stacks from Fender/ Marshall differ by single capacitor values.

A variable tone stack designed by placing a switch for two capacitors, Fig.80.

Fig.81, 82 show frequency responses for both options, Fender showing a scooped MF and Marshall, a larger bass attenuation. The combined value of three pots in parallel with 100KΩ means the ZOUT is similar to a large guitar pickup - no output buffering is necessary.

The input is buffered with a simple cathode follower, adapted from a Marshall 1959 pre-tone stack.

[Figure 80: Fender/Marshall Switching Tone

Stack]

[Figure 81: Frequency response Fender option]

[Figure 82: Frequency Response Marshall option]

30

3.2.5 Switchable Effects Loop

The effects loop ia taken from Blencowe's book [see Fig.60], it is a simple and effective means of implementing a switchable loop, adding a further gain stage:

Ia = 1.2mA; Va = 190V

Centre biased for maximum voltage swing into the phase inverter, also to preserve the tone (disallowing strange effects to clip the gain stage).

[Figure 83: Series/Parallel Effects Loop Circuit]

Rk = 1.5V/1.2mA = 1250Ω (1K5Ω has been chosen)

FC = 𝟏

𝟐𝝅 𝟏𝟐𝟓𝟎 (𝟏𝟎𝟎𝒖𝑭)= 1.27Hz

All frequencies above this will pass, with gain, the stage is controlled by 1MΩ pot preceding the virtual earth recovery stage. Finally a decouple and drain load is added.

[Figure 84: Series/Parallel Loop Gain Design]

3.2.6 Phase Inverter/Power Output

This stage has been kept simple, omitting any global or local feedback.

Unfortunately, a time-limit has been reached for this project, so lesser depth of investigation has been done.

[Figure 85: Marshall 50W Output]

[Figure 86: Simple Long-

Tailed PI]

The gain control appears to be best placed before the PI (Fig.86), perhaps using the ideas displayed in Fig.87 or 88 to drive into the inverter.

A simple power valve output is displayed in Fig.85. Again, little investigation has been done into this so far.

[Figure 87, 88: Variable Gain into PI, where previous

stage is V1 and first triode of PI is V2] Ref [25]

31

3.2.7 The Interface

[Figure 89: Proposed idea for front panel of modular amplifier]

The interface needs to meet the requirements of guitarists who may not have an aptitude for technology.

Fig.89 shows the proposed idea, with simple controls no different to what would appear on an amplifier or effects pedal.

The grilles in the drive and power output stages are for both aesthetic and to vent some heat from the unit.

The back pane Fig.90 is a rough sketch taken from the project logbook, proposing module card system and showing a possible patching 1/4" idea that could be built-in to override the card connections if the user does not wish to move cards around.

[Figure 90: A rough sketch of card/back pane power/connection ideas]

4.0 Results

4.2.1 Full Schematic

[Figure 91: Full schematic, separated into modules by block]

32

4.2.2 Discussion

The first element of designing an amplifier tone is considering what is being plugged in, the

impedance of the input can make a large difference to the first frequency response of the

amp. This can be interpreted into use as well, which is a large part of the reason a 'reamp'

box has been included - as more and more artists are directly connected to recording

studios.

Variable impedance for the input not only gives an amplifier flexibility to host a different range

of guitars and line inputs, but also gives the user an opportunity to adjust this first frequency

response.

The second element that is apparent is the bias settings or the gain stages, whether it be

smashing into power rails on an effects pedal or clipping lightly into cold biased triode. This is

the factor that controls the feel of playing - the input sensitivity. As the guitarist strikes the

strings harder, so the amplifier growls more, or, in extreme tone-freak cases....becomes

more sonically trashy with self-oscillation. This can make the difference between a bland

sounding chord and a harmonically singing, chiming wall of sound.

Interchanging modules is the realm of impedance matching. All the information so far has

stated that the loading down of stages is a detrimental factor, however, given flexible

parameters these issues become quickly subjective to the user. Every generation has a story

of new, strange and exciting artists that have guitar tones that become quickly the must-have

commodity - this generally comes from an artist who is not scared to challenge the status

quo of equipment setup - which is the aim of this project.

The third element of amplifiers that often lacks flexibility, but for the variation of one

capacitor, is the Tone Stack. The proposed design for the switchable Fender/Marshall tone

stack is still very basic, with further consideration, two, three, or even more parallel

capacitors could be added-in, onto a single switch system.

Considering creative use of, again in the studio - equalisation. Tone created from amplifiers,

although advancing fast - does not accurately emulate analogue tone within an analogue

acoustic environment. However, this is not a debate about analogue versus digital.

So retrospectively, having the flexibility to control tone aptly at the source (within the confines

of resistor noise, etc) begins to tackle a number of issues as well as provides a creative tone

outlet.

A smaller system of tone creation is displayed in a guitarists pedal-board, or, rig setup.

Numerous combinations and unorthodox tone shaping is beginning to ask questions of the

traditional guitar amplifier, with manufacturers like Randall responding to this.

The merging of the recording studio with music on an artist level is a another factor to

consider.

5.0 Conclusions

Components play their own individual roles in amplifiers, such as noise contribution,

impedance, reactance

circuits react differently to DC and AC signals

Impedance, RC networks and tone stacks can all be classed as 'poles' or simply put,

tone-shaping networks

triode and power rail biasing influences input sensitivity, i.e. determines the threshold

of clipping

33

a guitar amplifier tone is the sum of good design and it's non-linearity

a modular system requires each stage to be buffered or have correct impedance

matching for possible following, or, preceding stages designed-in

the input &output conditioning stages are the only two stages that should remain fixed

a few key elements of designing a guitar amplifier are impedance, power

requirements, bias theory, transcondutance in triodes, signal phase, class of

amplification and balanced/unbalanced signal.

6.0 Recommendations

Further enquiry needs to be made into aspects of power output, power supply and

interconnectivity of modules (i.e. module cards, EDAC, etc).

Once this has been done, DC coupling, pentodes, parallel triodes and cathodyne phase

inversion need to be explored to complete the basics.

Finally, a recommendation for the future is to build a tube distortion pedal, perhaps with a

basic tone control, i.e. building small stages of the amp for practical use.

34

7.0 References

- Kahn, S, (2011). Modern Guitar Rigs. Hal Leonard Press, pp.01

- Ballou, G, (2008). Handbook for Sound Engineers. Focal Press, pp. 243-262

- Perepelitsa, D, (2006). Johnson Noise and Shot Noise. MIT Dept. Physics, sourced

http://web.mit.edu/8.13/www/JLExperiments/JLExp43.pdf on 18.11.2011

- Gibson, D, (2009). Capacitors. Lecture notes forBSc (Hons) Sound Engineering

- Whitlock, B, (2008) Handbook for Sound Engineers, Chapter 11, Audio Transformer Basics,

Focal Press.

- Leon Audio Company, (2012). Leon Audio Active D.I Box, sourced at

http://www.leonaudio.com.au/active.htm on 20.1.2012

- Blencowe, M, (2009). Designing Tube Preamps for Guitar and Bass, self-published.

- Munro, D, (2007). Amplifier Classes, sourced at

http://www.duncanamps.com/technical/ampclasses.html 15.01.2012

- Weber, G, (1994), A Desktop Referecne of Hip Vintage Guitar Amps, Kendric Books

[1] Image of 1963 Marshall Princeton, sourced http://www.fargenamps.com/vintage-1963-

brownface-fender-princeton-guitar-amp on 22.04.2012

[2] Image of Mesa Boogie Mark1, sourced

http://www.mesaboogie.com/Product_Info/Out_of%20_Production/Mark_I_Reissue/Mark_I_

Closeup/mark_i_closeup.html on 22.04.2012

[3] Image of ZVex Nano Head, sourced http://zvexamps.com/amp_view.html on 22.04.2012

[4] Image of Resistor Colour Code Chart, sourced http://www.williamson-

labs.com/resistors.htm on 22.04.2012

[5] Images of voltage dividers and impedance circuits, Waterman, T, (2010). Passive

Devices, lecture notes for BSc (Hons) Sound Engineering

[6] Images for Current and Voltage against Time and Phase Difference between Voltage and

Current, Gibson, D, (2009). Capacitors. Lecture notes for BSc (Hons) Sound Engineering

[7] Images for First Order LPF and HPF, Gibson, D, (2009), Filter Characteristics, Lecture

notes for BSc (Hons) Sound Engineering

[8] Image of Triode Tube, sourced

http://www.vacuumtubes.net/How_Vacuum_Tubes_Work.htm on 23.04.2012

[9] Image of Audio Line Transformers, sourced http://www.made-in-

china.com/showroom/lotusluo99/product-detailtebxpowEvnTq/China-Line-Matching-Audio-

Transformers-ELM-0250021-.html on 23.04.2012

[10] Image of Fender Deluxe Schematic, Weber, G, (1994), A Desktop Referecne of Hip

Vintage Guitar Amps, Kendric Books, pp.44

[11] Image of Equivalent Circuit of Guitar Pickup and Amplifier, French, R, (2009).

Engineering the Guitar – Theory and Practice, Springer Publishing

[12] Image of Lindos Interface, sourced at

http://www.audistro.ch/store/product_info.php?info=p384_Lindos-MiniSonic-

MS20.html&XTCsid=elbmaeuc2g2n8j8l1t65k8sv87 on 24.04.2012

[13] Image of Focusrite ISA828 interface, sourced at

http://media.soundonsound.com/sos/oct07/images/Focusrite_2_l.jpg on 24.04.2012

[14] Image of Radial Amp Driver, sourced at http://www.radialeng.com/r2011/xamp.php

on24.04.2012

http://web.mit.edu/8.13/www/JLExperiments/JLExp43.pdf

http://www.leonaudio.com.au/active.htm

http://www.duncanamps.com/technical/ampclasses.html

http://www.fargenamps.com/vintage-1963-brownface-fender-princeton-guitar-amp

http://www.fargenamps.com/vintage-1963-brownface-fender-princeton-guitar-amp

http://www.mesaboogie.com/Product_Info/Out_of%20_Production/Mark_I_Reissue/Mark_I_Closeup/mark_i_closeup.html

http://www.mesaboogie.com/Product_Info/Out_of%20_Production/Mark_I_Reissue/Mark_I_Closeup/mark_i_closeup.html

http://zvexamps.com/amp_view.html

http://www.williamson-labs.com/resistors.htm

http://www.williamson-labs.com/resistors.htm

http://www.vacuumtubes.net/How_Vacuum_Tubes_Work.htm

http://www.made-in-china.com/showroom/lotusluo99/product-detailtebxpowEvnTq/China-Line-Matching-Audio-Transformers-ELM-0250021-.html



http://www.audistro.ch/store/product_info.php?info=p384_Lindos-MiniSonic-MS20.html&XTCsid=elbmaeuc2g2n8j8l1t65k8sv87

http://www.audistro.ch/store/product_info.php?info=p384_Lindos-MiniSonic-MS20.html&XTCsid=elbmaeuc2g2n8j8l1t65k8sv87

http://media.soundonsound.com/sos/oct07/images/Focusrite_2_l.jpg

http://www.radialeng.com/r2011/xamp.php

35

[15] Image of Jensen Reamp Schematic, sourced at http://www.jensen-

transformers.com/as/as092.pdf on 24/04/2012

[16] Image of Fender Bassman Schematic, Weber, G, (1994), A Desktop Referecne of Hip

Vintage Guitar Amps, Kendric Books, pp.60

[17] Image of James Tone Stack, sourced at http://www.ampbooks.com/home/amp-

technology/james-tonestack-analysis/ on 24.04.2012

[18] Image of Serial and Parallel Signal Flow, Blencowe, M, (2009). Designing Tube

Preamps for Guitar and Bass, self-published.

[19] Image for Soldano SLO 100 effects loop, sourced at

http://www.prowessamplifiers.com/schematics/post/soldano_slo100.pdf on 24.04.2012

[20] Image of Fender Super Amp PI, Weber, G, (1994), A Desktop Referecne of Hip Vintage

Guitar Amps, Kendric Books, pp.344

[21] Image of Simple Phase Inverter, sourced at http://www.300guitars.com/articles/article-

demystifying-the-phase-inverter/ on 24/04/2012

[22] Image of Classic Paraphase Phase Inverter, sourced at

http://www.dogstar.dantimax.dk/tubestuf/paraph.htm on 24.04.2012

[23] Image of Long Tail Phase Inverter, sourced at

http://www.freewebs.com/valvewizard/acltp.html on 24.04.2012

[24] Images of Class A, B , AB and Crossover Distortion projections, sourced at

http://www.duncanamps.com/technical/ampclasses.html on 15.01.2012

[25] Images for Chapter 2.5, Blencowe, M, (2009). Designing Tube Preamps for Guitar and

Bass, self-published.

[26] Waterman, T, (2011). Distortion Mechanisms. lecture notes for BSc (Hons) Sound

Engineering

[27] Dr.Tube website, Phillips 1970 Dual Triode Datasheet, sourced at,

http://www.drtube.com/datasheets/ecc83-Phillips1970.pdf on 03.05.2012

[27] Dr.Tube website, Electro Harmonix 12AX7EH Dual Triode Datasheet, sourced at,

http://www.drtube.com/datasheets/12AX7EH.pdf on 03.05.2012

[28] Keen, R.G, (1998). The Technology of the Tube Screamer, sourced at

http://www.geofex.com/Article_Folders/TStech/tsxfram.htm on 06.04.2012

[29] DIY Stomp Boxes Website, ProCo Rat Distortion by Keen, R.G, sourced at

http://www.diystompboxes.com/pedals/pcrat.gif on 03.05.2012

[30] Images of Radial Workhorse module card and pin assignments, sourced at

http://www.radialeng.com/r2011/workhorse.php on 03.05.2012

8.0 Bibliography

- Kahn, S, (2011). Modern Guitar Rigs. Hal Leonard Press.

- Ballou, G, (2008). Handbook for Sound Engineers. Focal Press.

- Perepelitsa, D, (2006). Johnson Noise and Shot Noise. MIT Dept. Physics.

- Keen, R.G, (2002). Using the Carbon Comp Resistor for Magic Mojo, sourced at

http://www.geofex.com/article_folders/carbon_comp/carboncomp.htm on 19.11.2012

- Waterman, T, (2010). Passive Devices, lecture notes for BSc (Hons) Sound

Engineering

- Barbour, E (2012). How Vacuum Tubes Work, sourced at

http://www.vacuumtubes.net/How_Vacuum_Tubes_Work.htm on 23.04.2012

http://www.jensen-transformers.com/as/as092.pdf

http://www.jensen-transformers.com/as/as092.pdf

http://www.ampbooks.com/home/amp-technology/james-tonestack-analysis/

http://www.ampbooks.com/home/amp-technology/james-tonestack-analysis/

http://www.prowessamplifiers.com/schematics/post/soldano_slo100.pdf

http://www.300guitars.com/articles/article-demystifying-the-phase-inverter/

http://www.300guitars.com/articles/article-demystifying-the-phase-inverter/

http://www.dogstar.dantimax.dk/tubestuf/paraph.htm

http://www.freewebs.com/valvewizard/acltp.html

http://www.duncanamps.com/technical/ampclasses.html

http://www.geofex.com/article_folders/carbon_comp/carboncomp.htm%20on%2019.11.2012

http://www.vacuumtubes.net/How_Vacuum_Tubes_Work.htm%20on%2023.04.2012

36

- French, R, (2009). Engineering the Guitar – Theory and Practice, Springer Publishing

- Leon Audio Company, (2012). Leon Audio Active D.I Box, sourced at

http://www.leonaudio.com.au/active.htm on 20.1.2012

- Blencowe, M, (2009). Designing Tube Preamps for Guitar and Bass, self-published.

- Salminen, R, (2000). Cook Your Own Distortion, sourced at

http://www.generalguitargadgets.com/richardo/distortion/index.htm on 04.04.2012

- Waterman, T, (2011). Distortion Mechanisms. lecture notes for BSc (Hons) Sound

Engineering

- Keen, R.G, (1998). The Technology of the Tube Screamer, sourced at

http://www.geofex.com/Article_Folders/TStech/tsxfram.htm on 06.04.2012

- Weber, G, (1994), A Desktop Referecne of Hip Vintage Guitar Amps, Kendric Books

Appendices

Appendix A:

Resistors

[Illustration 1: Resistor Colour Code Chart] Ref [4]

Resistance dissipates energy in the form of heat. Conductors have low resistance and low heat.

E.g. 10A current flows through 1Ω resistor = 100W of heat.

P = I2R

P = Power in Watts

I = Current in Amperes

R = Resistance in Ohms

V=IR

V = Voltage in volts

P = V2/R

Changing the voltage while resistance is constant changes power by the square of the voltage.

E.g. 10v to 12v = increase power 44%

P = I2R

Changing current while resistance is constant has the same effect as the voltage.

E.g. 1A to 1.2A = increase power by 44%

Changing the resistance while holding the voltage constant changes power linearly.

E.g. 1KΩ down to 800Ω = 20% increase

500Ω up to 1KΩ = 50% decrease

Changing the resistance while holding the current constant, also linear change.

E.g. 1KΩ to 1.2KΩ = 20% increase

1KΩ to 2KΩ = 100% increase

Voltage Coefficient - Rate of change of resistance due to applied voltage (Ballou 2008).

This is mostly negative, i.e. resistance decreases a voltage increases

Temperature Coefficient - Temperature Coefficient of Resistance (TCR) defined as the change of resistance with temperature.

Hot-Spot Temperature - Max temperature measured of resistor due to internal heat, ambient operating temp and surrounding components (Ballou 2008).

Johnson Noise - Voltage fluctuations due to thermal fluctuations in stationary charge carrier (Perepelitsa 2006). The fluctuations almost act like an oscillator in individual frequency bands:

dP = kTdF

dP = Noise

k = Thermo oscillation

dF = Frequeny Band

http://www.leonaudio.com.au/active.htm

37

Types of Resistors (Ballou 2008):

Carbon-Comp Older and noisier with tolerances not less than ±5%.

“Excess noise, high drift, high pulse power and high variability. They also have a high voltage coefficient of resistance.” (Keen 2002)

Variability heavily influenced by temperature, range from 1Ω to many MEGΩ and rating 0.1-4W. Can handle high surge currents due to loose tolerances.

High in noise, increasing this character with voltage swing, should be placed with discretion.

Carbon-Film Similar to carbon comp but with ceramic cores, slightly tighter tolerances and better temperature coefficients. Still noisy and handle surge currents well.

Metal-Film Quietest and tightest tolerances (1%-5%). Made from nichrome /ceramic/tin oxide/glass/cermet technology. Range 10Ω - 1MΩ and rating 0.125-1W.

Highest temp coefficient, but, drifts out of spec quicker over time.

Wirewound Highest temp coefficient and power handling stability. Resistive wire wound on ceramic core, classed as „air core‟ inductors – some high frequency issues.

Can handle as much as 1500W – known also as instrument-grade products.

Non-Inductive Used for high frequency applications, Ayrton-Perry wiring – two windings connected in parallel in opposite directions.

Appendix B:

Attenuators and Impedance

VIN < VOUT The divider ratio of VIN to VOUT

Va = 1 + (R1/R2)

E.g. Va = 1 + (600Ω / 600Ω) = 2 [NB: This is a ratio, not a voltage]

Take input voltage and divide by the ratio, for example, 1v in:

VOUT = 1v/2 = 0.5v

The loss can be calculated in three ways:

dBLOSS = 20log(Vd) or 20log(VIN/Vd) or 20log(VIN/VOUT)

dBLOSS = -6.02dB

Voltage divider can also be calculated by VOUT = R2/(R1+R2)

[Illustration 2: Voltage Div Ref [5]

[Illustrations (3 left &4 above): Impedance circuits] Ref [5]

The input impedance of the above circuit if:

R1 = R2 = 2500Ω

ZIN = R1 + R2 = 5KΩ

The output impedance is calculated:

ZOUT = (R1* R2)/(R1+R2) = 1K25Ω so.....

*Actual attenuation must be calculated observing the whole circuit!

Equation to Solve Actual Load (Including Source & Load):

ZIN = 5kΩ ZOUT = 1k25Ω

The impedance for input or source going into the circuit should be 500Ω

The impedance for output or load attached to the circuit should be 12k5Ω

dBLOSS = (𝑅2𝑍2)

[ 𝑅2𝑍2 + 𝑍1𝑅2 + 𝑍1𝑍2 + 𝑅1𝑅2 + 𝑅1𝑍2 ]

Therefore, the load should always be at least 10 times greater than the source.

38

Appendix C:

Capacitors

Types of Capacitors:

Mica Capacitors - Metal foil/mica insulation or silver/mica insulation.

Small capacitance, often used in HF circuits.

Ceramic Capacitors - Popular for bypass and coupling because of variety of size, shape and rating. Variety of K-Values/Dielectric Constant.

High K = lower temp stability

Low K = bigger capacitor size and temp stability

Electrolytic Capacitors - Temperature sensitive electrolytic gel - too cold freezes it, too hot dries it out and it can leak + corrode.

Sensitive to surges over rated working voltage, shortens life quickly.

Polarity sensitive: positive leg towards power supply and negative leg towards ground.

Appendix D:

Filters (Ballou 2008)

[Illustration 5: Low Pass Filter and characteristics]

Pass Band – pass through filter with loss < 3dB

Stop Band – pass through filter with loss >3dB

Cutoff Frequency – the point where gain first falls to -3dB moving out of pass band

Bandwidth – difference between upper and lower cut off frequencies either side of the pass band

Transition Band – range of frequencies from cut off frequency to desired attenuation

Centre Frequency – geometric mean of the lowest and highest frequencies of the band

Fm = 𝐹1 X 𝐹2

Where F1 = Cut-off of HPF

And F2 = Cut-off of LPF

[Illustration 6: First Order Low Pass Filter] Ref [7]

[Illustration 8: First Order LPF Response] Ref [7]

[Illustration 10: First Order LPF Phase Response] Ref [7]

[Illustration 7: First Order High Pass Filter] Ref [7]

[Illustration 9: First Order HPF Response] Ref [7]

[Illustration 11: First Order HPF Phase Response] Ref [7]

39

In a LPF (Illus. 8), for frequencies below cut-off, XC is large compared to R, so signal is unattenuated. As signal increases XC decreases and signal is attenuated. The opposite is true for the HPF (Illus. 9) where little or no voltage is developed across the output at LF due to high reactance of XC. As frequency rises reactance is low and voltage is developed across the output (Gibson 2009).

Illustrations 10 and 11 show the phase response to increasing frequency.

Cut-Off Frequency of a filter is determined by formula: f = 𝟏

𝟐𝝅𝑹𝑪

So if R = 150Ω and C = 200µf

f = 𝟏

𝟐𝝅𝑹𝑪=

𝟏

𝟐𝝅 𝟏𝟓𝟎 𝟐𝟎𝟎µ𝒇 = 𝟓.𝟑𝟏𝐇𝐳

Appendix E (Image Ref[5]):

Unit Values

Name Abbreviation Value

Appendix F:

Tubes

Components (Barbour 2012):

Filament - separate coiled element to heat cathode

- coated with electrical insulation so doesn‟t burn-up (aluminium oxide)

- must not directly touch cathode or can put ac into amp output

Cathode - sleeve surrounding filament that emits electrons

- thoriated or oxide coated (different heat peak temps) increases electrons

- must operate inside 20% of rated heat voltage to ensure working longevity

Plate (Anode) - positive element from which the output signal is often taken

- designed to cool itself by radiating heat through glass envelope

Control Grid - plated wire around two metal posts

- has to tolerate a lot of heat, made of tungsten/molybendum/graphite

- placed between plate and cathode, input signal applied

- controls the flow of electrons/current between cathode and anode

Screen Grid - in tetrode (4 element) or pentode (5 element) vacuum tubes

- between control grid and plate

- maintained positive to reduce capacitance between control grid and plate

- accelerates electron flow, increases tube‟s gain

- electrostatic shield, prevents self-oscillation and feedback within tube

Suppressor Grid - between screen grid and plate

- catches stray secondary emission electrons

- generally connected to ground or cathode

Transconductance (Ballou 2008):

- Change in the value of the plate current in µAmperes - Unit for conductance = mho (Siemens)

𝐆𝐦 =𝚫𝐈𝐩

𝜟𝑬𝒈

Ip = Plate Current change

Eg = Applied Voltage change

- E.g. as applied voltage changes from 1v-3v (2v change), so does plate current 1mA-2mA (1mA change).... = 500µmho‟s

- Gain of a circuit is measured by ratio of change in plate voltage to grid voltage

40

- because it is developed across a resistor, the more current varies with a given input signal, the greater the output V = IR

- Gain Vgt = Vg1 * Vg2 * Vg3......(each multiplier is a gain stage)

Polarity (Ballou 2008):

- Polarity between anode plate and control grid changes 180 degrees

- Cathode/control grid are in polarity with each other - Screen grids/plate are 180 degrees out of polarity with cathode/control grid

Internal Capacitance (Ballou 2008):

- Caused by proximity of internal elements between cathode and control grid (Cgk) and control grid and anode plate (Cga)

Plate Resistance (Ballou 2008):

- Internal resistance of the tube - Opposition of passage of electrons from cathode to plate (AC and DC resistance)

Appendix G:

Transformers (Ballou 2008)

The Law of Induction states that a voltage will be induced in a conductor exposed to changing flux, and that induced voltage will be proportional to the rate of the flux change (Whitlock 2008).

A magnetic field is created around any conductor in which current flows, these invisible lines of force are called FLUX, and flow at right angles to the wire

- An instantaneous polarity opposing the original current flow creating a resistance called Inductive Resistance (XL)

- XL = 2πfL

- Where f = frequency and L = inductance (in Henrys)

[Illustration 12: Inductive Coupling]

- Voltage will be induced in any conductor that cuts the flux lines

- Two coils near each other [Illus. 12], and AC current in the primary will induce an AC current in the secondary

- Energy can be transferred from one circuit to another in isolation, without direct connection, i.e. eliminating ground loops, etc

- Consists of many turns called coils, inductance determined by number of turns, physical dimensions of windings and the type of materials used

- Can take full voltage from one or both legs (balanced to unbalanced or vice versa)

Windings/Turns Ratio Coil driven by electrical source called the Primary Winding, the other is called the Secondary Winding

- Same voltage is induced in each winding the ratio is the same as the no. of turns ratio

- Transformers cannot create power, so ideally a 1:1 ratio is the ideal maximum output, unless a resistance load is connected to the secondary V=IR means an increase in power:

E.g. A 20Ω load is connected to a secondary with 1A, making the power (P = I2R) 20W

- This therefore makes the primary 2A, making the input power an equal 20W

- primary 2A with 10v originally applied, R = V/I, makes the primary impedance 5Ω

- impedance of the primary to secondary is 5Ω:20Ω or 1:4

[the SQUARE OF THE TURNS Ratio........TURNS: TURNS2]

- when a transformer converts voltage, it also converts impedance and vice versa

- windings wound in the same direction have the same polarity, inverted windings have inverted polarity (dots indicated which ends have which polarity on schematics)

41

Appendix H:

Phase Inverters

[Illustration 13 and 14: Classic Paraphase Phase Inverter and A Long Tail Phase Inverter] Refs [22, 23]

Appendix I:

Biasing Theory (Blencowe 2009) (Images Ref 25)

In Illus.15 we can see a two input/two output (also called quadripole) terminal triode stage.

An input and an output pole are connected at the cathode, and usually to ground as well – they are common.

Usual Hi-fi amplification is intended to amplify small voltage into large voltage with no distortion or tonal changes. This is not the case for guitar amplifiers, and is deliberately done.

[Illustration 16: Static Anode Characteristics graph of ECC83 triode]

[Illustration 15: Simple common cathode triode gain

stage]

[Illustration 17: Transfer Characteristics of ECC83 triode]

Designing triode stages requires data about the valve; the most useful information is static anode characteristics, seen on graph Illus.16. This shows how a will valve operate in a circuit.

Anode current Ia is on y-axis

- current flowing from anode to cathode

Anode voltage is on x-axis

- voltage dropped across valve between anode and cathode

The curves are the Grid-to-Cathode (Vgk) voltages – or know as grid-curves. All graphs are measured to relative to the cathode at zero volts.

Graph in Illus.17 shows the transfer characteristics (or dynamic characteristics), showing the bias voltage against the anode current for different values of anode voltage.

This conveys the linearity of the valve – the straighter the line the more linear.

A typical triode stage has an anode resistor, Ra, between anode and HT - this forms the load.

For small signal valves, typical Ra = 100kΩ.

The HT is a supply voltage, will depend on the power supply choice. For now, will assume 300Vdc.

Ohms Law shows, if no current flows

42

[Illustration 18: 100kΩ load line on ECC83 anode characteristics with HT 300Vdc. A small

change in Vgk causes change in Ia & Va]

through the valve then there can be no voltage dropped across the resistor (Blencowe 2009).

- the anode must be same potential as HT

This can be therefore marked:

Ia = 0mA; Va = 300V [labelled A, Illus.18]

Conversely if enough current were to flow, we could drop all available voltage across the resistor and none across the valve, Ohm‟s law:

I = V/R = 300V/100K = 3mA

This is the max current that can flow through the valve unless the HT increased or lowered Ra.

This can be marked:

Ia = 3mA; Va = 0V [labelled B, Illus.18]

Ohms Law is a linear equation, so A and B can be linked to form the load line.

Observing Illus.18, we can see a change in Vgk = -2V to Vgk = -1 creates a large changes in Va of around 60V – this is why it is called the control grid.

[Illustration 19: 100kΩ load line showing changes for Va from changes in Vgk centred

on bias point C]

The median point is the middle of a sine wave or voltage swing, this is the starting point on our load line – the median voltage where a Vgk line cuts it [Illus.19 at point C].

So in Illus.19 if we fix Vgk at -1, we are not inputting any signal yet – the valve is in a state of quiescence. At this point:

Ia = 1.4mA; Va = 164V

Inputting a 1Vp-p signal will cause Vgk to swing -0.5V (D) where Va falls to 130V and to the -1.5V(B) line where Va rises to 195V.

So positive input signals produce negative output signals and vice versa – 180 degrees out of phase, called an inverting gain stage.

The 1Vp-p has produced 195-130 = 65Vp-p output. So the gain of the stage is:

A = 𝑽𝒐𝒖𝒕

𝑽𝒊𝒏=

−𝟔𝟓

𝟏= 𝟔𝟓

A (dB) = 20log 𝑽𝒐𝒖𝒕

𝑽𝒊𝒏= 𝟐𝟎 𝐥𝐨𝐠

−𝟔𝟓

𝟏= 𝟑𝟔.𝟑𝐝𝐁

Also note in Illus.19 that Vgk curves get wider apart as Ia increases and closer together as Ia decreases. This means the output gets more squashed on the up-swing, which is a natural compression that generates mainly second order harmonic distortion.

H2% = 𝑪𝑫−𝑪𝑨

𝟐(𝑪𝑫+𝑪𝑨)∗ 𝟏𝟎𝟎 =

𝟑𝟒−𝟑𝟏

𝟐(𝟑𝟒+𝟑𝟏)∗ 𝟏𝟎𝟎 = 𝟐. 𝟑𝟏% 𝟐𝐧𝐝 𝐎𝐫𝐝𝐞𝐫 𝐇𝐚𝐫𝐦𝐨𝐧𝐢𝐜 𝐃𝐢𝐬𝐭𝐨𝐫𝐭𝐢𝐨𝐧

Grid Current Limiting:

Referring to Illus.19, a 3Vp-p is input. The grid can swing down -2.5V to 250V but runs out of grid curves going upwards beyond Vgk = 0V.

This is where grid voltage approaches cathode voltage, resulting in current (and hence voltage) beginning to flow in the opposite direction as electrons are attracted to the grid moving positive.

43

This is known as forward grid current, and causes a

voltage drop across the source resistance, i.e. the ZOUT of the driving circuit so the actual voltage at the grid falls (Blencowe 2009).

As the grid becomes more positive, the impedance of the valve falls from many meg-Ohms to a few kilo-Ohms or less - Grid Current Limiting.

The output signal is squashed or clipped on the negative side.

*It is the grid signal that is clipped, the valve continues to amplify signal appearing here as usual.

(Blencowe 2009)

[Illustration 20: Avg. forward-grid current measured in three valves, HT

= 300V and Ra = 47KΩ]

[Illustration 21: Soft-clipping due to grid current limiting in ECC83]

Ilus.20 shows that forward grid current is not instantaneous and even begins around Vgk = -1V in some tubes.

A point of note is that this will depend on the source resistance - be it a previous triode or guitar ZOUT.

- source resistance low = softer clipping

- source resistance high = voltage drops more suddenly with harder clipping effect.

Illus.21 shows soft-clipping on an ECC83 tube, the

Slightly sharp leading edge indicates onset of grid conduction and the introduction of a few high order harmonics - can be manipulated by adjusting source Z, or, anode voltage (Blencowe 2009).

Cut-Off:

Suppose the bias point is set to Vgk = -2.5V, shown in Illus.22, and a 3Vp-p signal is input.

The anode can swing down to C (165V) but cannot swing above A - which is the HT.

The output signal now clips on the positive side.

[Illustration 23: Clipping produced by cut-off in ECC83] [Illustration 22: Increasing bias votage increases quiescent anode voltage(Va) &

reduces quiescent anode current (Ia), placing valve closer to cut-off]

The input signal makes the grid so negative that electrons are completely repelled by the grid and cannot pass through (Blencowe 2009) - cut off.

In Illus.22 we can see that grid curves become bunched near cut-off, this indicates a compression in the signal peak with added reduction in gain.

The grid does not span the whole of the glass sleeve in a triode, so stray electrons can actually slip through, resulting in cut-off being a little higher than A (Vgk = -4V), this creates a softer, gradual onset of clipping than grid limiting.

Headroom - Threshold of Clipping and Input Sensitivity:

Centre biasing (centre point between cut-off and grid-limiting) is desirable if more headroom is required. This is the cleanest sound, but with little effect to the picking attack of the sound, this measure is called input sensitivity - the voltage required to drive to the point of first clipping (Blencowe 2009).

Increasing the HT increases quiescent Va, moving it right on the graph - more headroom.

The size of the input signal is another consideration for clipping, this can be attenuated before going into the grid - a 'gain' control - to clean/dirty up the sound of a guitar signal.

Clipping Shape:

Asymmetrical Symmetrical

44

- Clipped on one side, or, more on one side than the other

- even order harmonics (2nd)

- harder asymmetrical clipping introduces odd-order harmonics

- Clipped on both sides simultaneously

- mainly odd-order harmonics

- more of a driven tone

[Illustration 24: Symmetrical clipping in ECC83]

Cold Biasing:

- Biased closer to cut-off

- reduces gain of the stage (this can be used)

- resistance to blocking distortion (to follow)

- harder, crunchy more modern hi-gain

Warm Biasing:

- closer to grid-limiting, or, small bias voltage

- makes the valve run physically hot

- warmer sound, blues

- biasing too hot can result in raw/fuzzy sound

Limitations on Bias:

Pa(MAX) = maximum continuous power that can be dissipated by anode.

Exceeded for too long, the anode will glow deep red, referred to as red plating. This will eventually damage or destroy the tube.

This information is published on the data sheets provided with the tube. Alternatively a single figure may be given (e.g. 1W), for which the max allowable current for voltages:

P/V = I

1/500 = 2.0mA

1/400 = 2.5mA

1/300 = 3.3mA

1/200 = 5.0mA

[Illustration 25: Maximum anode dissipation curve & safe operating area]

Above in Illus.25 we can see these points plotted into a curve for max anode dissipation. This can be exceeded only for instants in signal peaks as it is averaged out by dissipation periods.

Va0 = Max voltage the anode can stand at any time.

This must not be reached, and is also usually the point of Max. HT value allowble (Blencowe 2009).

Va(MAX) = Max quiescent anode voltage.

On ECC83 is given as 350V, so bias point must not go to the right of this.

45

Appendix J:

Applying Bias (Blencowe 2009) (Images Ref 25)

- also known as grid bias

- cathode grounded, desired negative voltage applied directly to grid via grid-leak resistor

- should remain fixed and low noise, used more on power valves

- known self/automatic bias

- resistance in series with cathode

- steady anode current flows through valve, voltage develops on the resistance, placing cathode at higher potential than grid

- therefore valve produces its own bias voltage

- self limiting (average current rises, so does bias voltage opposing a rise in anode current – less chance of red plating)

- provides designer control of gain, linearity, ZOUT, freq response.

- also known as contact bias

- develops negative voltage on bridge by using large grid-leak resistor

- during operation electrons strike grid and bleed down grid-leak resistor

- if resistance is large enough the leakage current may be large enough to self-bias (voltage opposing current flow)

- varies from valve-to-valve

- large resistor = more noise & blocking distortion

- voltage wanders with age

- no freq shaping

46

Choosing Cathode Bias Resistor:

A bias of Vgk = -1.5V causes 0.9mA to flow down to the ground [Illus.26] with the grid voltage fixed at zero – which we need to be 1.5V more negative than the cathode.

Choosing the cathode resistor:

R = V/I

R = 1.5V/0.9mA

R = 1667Ω

The closest value resistor is 1.5KΩ.

Drawing a cathode load line to cut the anode load line, start high:

[Illustration 26: Reading Ia value for cathode resistor calculation]

Assume an Ia = 1.5mA flows through the anode, we must work out Vgk point for cathode load line graph (almost superimposed on the same graph).

V = I * R = 1.5mA *1.5KΩ

V = 2.25V

(Point A – Illus.27)

Now need to find the lower point to plot the cathode load line to, assume Ia = 0.5mA :

V = I * R = 0.5mA * 1.5KΩ

V = 0.75V

(Point B – Illus.27)

[Illustration 27: Cathode load line determines actual bias point]

Choosing a Grid-Leak Resistor:

During operation the grid gets hot and will leaks electrons. This can lead to the grid becoming positively charged if all electrons leak off, so a path needs to be made for this lost charge to replenish – between grid and cathode to hold the grid at fixed quiescent voltage.

The grid leak should ideally be large so as to not load down the previous stage like a potential divider.

The maximum value is usually give on the datasheet and is commonly around the 1MΩ - 2MΩ.

With cathode bias the anode current cannot increase dramatically due to its self-regulating nature. This is not the case with fixed bias and the valve may end up if thermal runaway if the max values are not observed.

This maximum value should not be exceeded

[Illustration 28: Grid Leak Resistor]

Power Ratings:

A resistor having insufficient power rating will run hot and drift, eventually failing. Per previous section, quiescent anode current is ±1mA

P = I2R = (1mA)

2 * 100kΩ

P = 100mW

Resistors that have a low wattage rating (1/4W) often have a low voltage rating (250V) before breakdown. An overdriven amp can produce Vp-p = 200V+ signals, so 1/2W is safer.

Cathode resistor has a small voltage across it:

P = (1mA)2 * 1.5KΩ = 1.5mW

[Illustration 28: Power Rating Resistors]

Power will never reach a high value, so 1/4W power rating will be fine.

47

To dissipate 1/4W (0.25W) would require 0.25𝑊 * 1MΩ = 500VRMS

For most, peak signal in a gain stage will be around half of HT, so around 150VRMS for the previous circuit. Lower wattage = less noise.

48

Cathode Bypass Capacitor:

- Bypasses any AC signal on cathode to ground

- DC voltage remains (capacitor will supply any deficit in cathode current)

- this smoothes out any changes in cathode voltage to hold it constant – maintaining maximum gain constant

- no capacitor – slow onset of grid current – smoother creamy sound

- capacitor – removes feedback effect – harder clipping, aggressive sound

[Illustration 29: Gain stage with

max. gain at all audio

frequencies]

The cut-off frequency is where the signal falls to halfway between minimum and maximum (Blencowe 2009), the capacitor value of Illus.29:

F(HALF-BOOST) = 𝟏

𝟐𝝅𝑹𝒌𝑪𝒌

For full bypass of audible frequencies (which is, more gain of audible frequencies), a frequency below audible region should be chosen:

Ck = 𝟏

𝟐𝝅∗𝑹𝒌∗𝑭=

𝟏

𝟐𝝅 𝟏.𝟓𝒌 (𝟓𝑯𝒛) = 21µF

All frequencies being bypassed will have a gain of 58 (per previous calc). This is large value capacitor, electrolytic – limited working life and high Effective Series Resistance (ESR), also, electrolytic capacitors exhibit LF distortion at high AC voltages.

49

Bypassing leaving plenty of LF content leaves too much gain in this area – promotes blocking distortion.

The tone of this stage is determined by the value of cathode capacitor (Ck), see Illus.30.

[Illustration 30: Bass roll off for varied cathode capacitor]

At HF, the 1µF capacitor allows signal to bypass Rk but the 1KΩ series resistor prevents complete bypassing. BUT, Rk is parallel to R1, the effective resistance is therefore 500Ω, therefore the maximum gain of the circuit is:

A = 𝟏𝟎𝟎∗𝟏𝟎𝟎𝑲Ω

𝟏𝟎𝟎𝑲Ω+𝟔𝟐𝑲Ω+(𝟎.𝟓𝑲Ω∗𝟏𝟎𝟏) = 47

To AC, both 1KΩ resistors are in series to the 1µF capacitor, so the cut-off frequency is:

f(HALF-BOOST) = 𝟏

𝟐𝝅 (𝟐𝑲Ω)(𝟏µ𝑭) = 80Hz

In circuit B (above) the potentiometer creates a variable boost circuit:

Low Value Capacitor – HF/Presence boost

High Value – Overall boost (logarithmic pot)

The capacitor also blocks DC – which prevents crackling when pot is turned.

[Illustration 31: Roll-off of variable cathode bypass]

50

[Illustration 32: Loading divider]

Input and Output Impedance:

Preamp mainly concerned with voltage signals, ZIN and ZOUT of stages forms a potential divider. Again a 5-10 ratio should be kept to avoid loading and signal loss, but also can be used to shape the tone of a stage.

The input impedance is Rg (see lllus.33 below).

[Illustration 33: Capacitance between

electrodes lowers input impedance at HF]

[Illustration 34: Thevenin equivalent circuits of

Illus.33 at (A) MF/HF and (B) LF]

Output Impedance:

This will become the source impedance for the next stage.

Ra is parallel to ra and cathode resistors, so:

ZOUT = Ra//ra

(ra calculated earlier to be around 70KΩ)

- Un-bypassed, greatly increases ZOUT - Partially bypassed, high ZOUT at LF, increase bass attenuation

51

Appendix K:

Coupling (Blencowe 2009) (Images Ref 25)

[Illustration 35: The function of a coupling capacitor

removing DC offset]

Fundamentals of AC Coupling:

The output of a guitar pickup is around 30mV – 100mV, and the output of a guitar pedal is 3V-4V. So the objective of the first preamp stage is usually to attain maximum gain.

For example, in Illus.35 the gain of 60 has DC super imposed on it by the normal grid bias voltage in the valve. The coupling capacitor C1 removes this for the next stage.

Also forms a HPF with Rg – tone shaping:

C = 𝟏

𝟐𝝅 𝟏𝟎𝑯𝒛 (𝟏𝑴Ω+𝟒𝟎𝑲Ω) = 15.3nF

52

[Illustration 36: Thevenin Equivalent of Ilus.35]

Where the resistance is equal to Rg + ZOUT of previous stage, using 10Hz as desired roll-off point.

Adjusting the capacitor size can adjust the roll-off frequency to reduce blocking distortion, put less strain on the power supply and the OT/Speaker (if used at the end stage).

Usually the first roll-off stage is well above 50Hz to reduce mains frequency heater hum (Blencowe 2009).

Again, the power rating of the capacitor must match the peak AC power of power transformer, and different types of capacitors have different tone characteristics.

AC Load Line:

Choosing a grid leak for the second gain stage (V1)will form a load on the first (V1), placing it in parallel with V1‟s anode resistor Ra – for AC operation. This is shown in Illus.37:

HT = 260V

Ra = 100KΩ

Rg = 220KΩ

So for DC load (with 100KΩ) the Ia = 260V/100K = 2.6mA

[Illustration 37: Simple Gain stage and equivalent

showing parallel Ra//Rg to AC]

[Illustration 38: DC/AC load lines for Illus.37 where swing is reduced]

For the AC load line Ra//Rg = 69KΩ

- bias point cannot be moved, so this line must intersect it, reading down on graph Va = 150V@

I = V/R = 150V/68K = 2.2mA, plus the quiescent Ia = 1.1mA

AC Load Line Ia = 3.3mA

This line is extended from this point to cut the bias point and extend to Va line.

A few things have happened since converting the DC output to AC:

- The gain has been reduced from 50 to 60 - Output swing is reduced 180Vp-p to 130Vp-p - The input sensitivity increase 3.5Vp-p to 3Vp-p

Illus.38 shows now that there is more Ia than the HT can provide (AC line versus DC line Ia). This is because of the charge the capacitor receives and can supply back into the valve. There is therefore a new gain formula from old DC:

A = µ (𝑹𝒂||𝑹𝒈)

(𝑹𝒂| 𝑹𝒈 + 𝒓𝒂

[Illustration 39: A gain stage heavily loaded by following

Rg causing gain reduction]

This replaces the old gain formula, and must keep in mind impedance matching of stages.

[Illustration 40: Anode resistor to Rg Resistor curves]

53

Blocking Distortion and Grid Stoppers:

Caused by short charging and long discharging of coupling capacitors and possible bypass capacitors – AC voltage created by current going through Rg sets a bias range at V2 (on initial first rise and discharge).

The swing in voltage then changes from initial, e.g. initial charge was 1V from HT and now swings up to 159V then down to -140V.

The first charging sets the bias to clamp while the capacitor charges, and then the swing appears as in Ilus.42 until the capacitor can discharge – appears to cut-off.

[Illustration 41: Current paths in overdrive AC

coupled stage]

[Illustration 42: Output of anode of V2 from Ilus.41, transient causes C1 to charge, blocking the following

signal]

Discharge takes around 10 times longer than charging (Blencowe 2009).

Grid impedance also changes when overdriven, changes the time-constant of C1 allowing it to charge significantly, then V2 stops being overdriven and returns to long discharge state.

This causes a bias shift that moves the point to near cut-off, as shown in Illus.42 almost resembles Class B amplification.

Some Solutions to this are to attenuate long wavelength frequencies (LF) as the longer the wave, the more the distortion artefacts.

A grid-stopper prevents C1 from charging, as well as forming a treble attenuation with V2‟s internal capacitance – tone shaping.

[Illustration 43: Grid stopper R1 must be greater

than 10KΩ]

54

DC Coupling:

Coupling of anodes to the same HT, has some advantages (Blencowe 2009):

- No coupling cap = no blocking distortion - Smooth overdrive even at LF

- No coupling cap = no induced distortion - Reduces resistor noise and phase shift

The disadvantages are (Blencowe 2009):

- Awkward for tone shaping - Max output is limited

- May risk exceeding values allowable for heat-to-cathode-voltage (Vhk(MAX)) - Hard to marry high anode voltage of V1 to grid of following stage without

exceeding voltage ratings or restricting output swing

[Illustration 44: DC Coupling]

55

Appendix L:

Cathode Follower

[Illustration 45: Simple Cathode Follower]

The output is from the cathode of the valve, can act as a good impedance buffer and provides its own unique characteristics. The grid swings more positive and current through the valve increases, also flows in the cathode resistor:

- The voltage on Rk increases - The voltage from this gain stage is in phase

The gain can be said to be 100% negative (cathode current) feedback as all of the output is returned to the input (Blencowe 2009).

A = µ𝑅𝐾

𝑟𝑎+𝑅𝑘 (µ+1) (as there is no anode resistor Ra)

Input Capacitance:

- In a normal gain stage the Miller Effect is Cga * A - Cgk is effectively divided by the action of feedback

Cin = Cga + Cgk (1-A)

Since Cgk(1-A) is extremely small, in the 0.000000.....range, we could approximate Cin = Cga.

In an ECC83 this is around 1.6pF, so there will be a large frequency response.

The ZIN is equal to the grid-leak resistor and can therefore vary depending on the chosen size.

Output Impedance:

- When looking into the cathode, impedances above the cathode appear divided by (µ+1) - When looking into the anode, impedances below the cathode appear multiplied by (µ+1)

rK = 𝑹𝒂+𝒓𝒂

µ+𝟏 .....and if no anode resistor is in place ..... rK = ra/(µ+1)

Rk appears to be in parallel with rK, so

ZOUT = rK||Rk

ZOUT = rk = I/Gm

Transconductance for a Cathode Follower is higher with a lower output impedance. Can source significant current from power supply to dump into the next stage. This allows it to drive heavy and varied loads without insertion loss and is good for driving long cables – possible use in effects loop.

57

[Illustration 46: A common cathode follower in guitar amps]

Cathode Follower in Guitar Amps:

Driving Effects loops as a low ZOUT to drive relatively low ZIN devices such as guitar effects pedals and mixers. They shunt noise from interconnecting cables as they are capacitor coupled and self-biased, and finally, being able to be a built-in stage they do not affect the tone of the amp.

Illus.46 is an example of a Cathode Follower used to drive into a tone stack. It would normally be placed in the same envelope as this, both triodes have 100KΩ resistors at the outputs.

Illus.47 is a cathode follower for a Fender Bassman, this steals current from the previous drive stage, as the grid gets more positive, so current flows down into cathode.

[Illustration 47: Fender Bassman circuit]

58

[Illustration 48: Load lines for gain stage in

Illus.47]

Grid current flowing down into the cathode resistor contributes to the up-going cycle of output signal, and helps the transition into clipping to soften – only the positive cycle is compressed.

Cathode followers are extremely linear in the sense that it amplifies exactly what appears on the grid.

Creates a smooth, rich overdrive.

[Illustration 49: The increase in compression by reducing

the cathode load resistor]

Increasing the grid current too much, however could cause dissipation and melting, as maximum dissipation is ±0.2W (Blencowe 2009).

Per Illus.49&50 we can see lower values of Rk. The graph displays a similar output of Ig for less input voltage (HT) and more smoothing compression.

[Illustration 50: Grid Current in ECC83 cathode follower

with different values Ck and HT]

[Illustration 51: DC coupled cathode follower (A) and

bootstrapping previous stage anode resistor to increase gain (B)]

[Illustration 52: Bootstrapping V1

increases gain]

As previously stated, increasing AC perceived ZIN at cathode follower increases the gain.

Bootstrapping the previous driving anode to the output of cathode follower takes the negative load on the cathode follower and adds onto it:

Rk2 || R1|| (R2+ra)

With Rk1 bypassed by Ck [Illus.51] R1 should be about equal to R2.

Also forms HPF with C1 and R1||(R2+ra).

[Illustration 53: Frequency response of Illus.52 for C1 values]

f = 1

2𝜋𝑅𝐹 where „f‟ is the chosen roll-off

In Illus.53, we can see different roll-off points for different values of C1, also the output swing of V1 is increased by increased load impedance.

This may not increase the output of V2 by much but does add to smooth compressing, more sustain – it is essentially positive feedback.

** Could switch C1/variable for „modern‟ or „vintage‟ setting.

59

Appendix M:

The Cascode (Blencowe 2009) (Images Ref 25)

- Similar to having a screen grid pentode

- V1 into load of V2 [Illus.54] with low cathode impedance of few hundred ohms

- V1 operates as transconductance amplifier (volts to current) with very little gain and Miller Effect reduced. This is suited to HF.

- V2 grid is at fixed voltage, for maximum gain is bypassed with a capacitor

- injecting input at the cathode while the grid is effectively grounded to AC

- known as common grid/grounded grid amplifier

- shields the cathode from voltage swing at anode

- grid does not normally draw grid current so there is no compression or softening

- V1 is inverting and V2 is non-inverting = inverting overall

- seen by the power supply, V1/V2 are in series, to AC they are cascaded

[Illustration 54: Simplified cascade circuit]

[Illustrations 55: Lowering screen grid voltage and effect on Gm]

- the upper triode is biased normally, so the grid must be lower that the cathode

- cathode is at very low voltage, almost equal to grid

- cathode is fed voltage from V1 anode, so further to previous:

V1 anode = V2 Cathode = V2 Grid

- usually around 50-100V or 1/3 HT

- ECC82 is the best performer (Blencowe 2009)

- Illus.55 shows the output of ECC82, readings are from V1 cathode through to V2 anode (across the whole unit)

- if the anode falls below the screen grid there will be no voltage across the upper

[Illustrations 56: Cascode characteristics of common triodes]

triode, as the maximum voltage swing is determined by the HT at Vg2

- in Illus.55,56 the point where we can see the „knee‟ is the point where V2 starts drawing current

- lowering the screen grid voltage squashes the output (lowers the Gm) and curves shift left, increasing maximum output swing voltage

- In the absence of an oscilloscope the output can be plotted by superimposing the readings of each Vgk at reading of Va from the first triode (as it is equal to the grid in the second triode)

- tracing this onto existing static anode characteristics graph of the first triode

- V1 needs to be of high transconductance to input the maximum current into V2

- looking at the abruptness of the curves in Illus.57 we cans see 2 trade-offs:

1) Can enter hard clipping if heavily overdriven, or...

2) have a wide bandwidth of output swing.

- This must be placed according to tone requirements

- somewhere between a true pentode and triode function

[Illustration 57: Deriving cascade characteristics]

61

[Illustration 58: Grid Leak Bias

cascade]

Grid Leak Bias:

During quiescence the grid is zero-biased Signal is applied and the cathode voltage rises Charging current into Cg2 [in Illus.58] via grid-leak Rg2 (small voltage loss through

this) Greater the signal the greater the bias voltage, there will be a compression effect if

the Gm is lowered when driven hard There is a time delay while the bias develops, so transients will not be affected, only

a constant high gain signal The value of Rg2 is not critical, time period produced by Rg2 &Cg2 should be equal

to the lowest frequency to be amplified Cg2 = 1/(f * Rg2)

[Illustration 59: Current boosted

cascade via R1]

Current Boosted Cascodes:

To increase the gain of a cascade, can supply the lower triode with additional current via R1 into cathode of V2 [Illus.59]

Draw a load line for HT = 300/ 47KΩ.

Choose anode voltage of 75V and since we can supply any current, the bias point can be anywhere on dashed line marked A, Illus.60.

The -2V bias chosen, so cathode resistor:

Ia = 3.5mA

R = V/I = 2V/3.5mA

R = 571Ω

[Illustration 60: Supplying the lower triode with more current,

Gm and gain is increased]

Gm = ±2.2mA/V ...and µ = 19 ....so ra = 8.6KΩ

62

Can now select quiescent current for V2 (point of „knee‟ where V2 draws current, i.e. where Vgk 0V cuts load line, dotted line down to point B, Illus.60).

Centre biasing, looks sensibly at Ia = 2mA point B. Selecting resistor R1, we have selected current:

- for the lower triode of 3.5mA - and for the upper triode of Ia = 2mA. - the additional current needed is therefore 3.5-2 = 1.5mA

We chose 75V for V1 anode voltage, the voltage drop across R1 is therefore:

HT – drop = 300 – 75 = 225V

(for V2 feedback resistor) R = V/I = 225/2mA = 112.5KΩ (or nearest value of 120KΩ)

Power dissipation P = I2R = (2mA)

2 * 120KΩ = 480mW

So a 1W rated resistor will be fine.

Appendix N:

Long Tailed Phase Inverter (Blencowe 2009) (Images Ref 25)

[Illustration 61: Simplified Long-Tail Pair

Phase Inverter]

- most popular phase inverter circuit in guitar amps (Blencowe 2009)

- amplifies high-gain input to output on normal HT levels

Is a six pole circuit, seen in Illus.61:

- 2 input

- 2 outut - Shared HT and Rk - Balanced interface

Can have many uses in a circuit, Illus.62, on the premise that each cathode attempts to follow it‟s corresponding grid.

Ideally grid-to-cathode voltage is zero, therefore no voltage to amplify.

The long-tailed pair will only amplify the difference between its two inputs, Illus.62: differential amplifier, V1 also acts as a good cathode follower.

[Illustration 62: Different uses for Long-Tailed PI given by the summing of signal]

63

Overall balance of A1 and A2 depends on value of RK:

If Rk is not infinite balance is improved by high µ valves could use mismatched anode resistors Ra for balance

Input sensitivity:

half the input signal is each on anode and cathode follower of V1 so the input sensitivity is halved normal input of 4Vp-p, long tailed input 8Vp-p – more headroom this still has more input sensitivity than Cathodyne PI

64

- the output swing on the triode is around 2/3 HT = 250V, which is ±170Vp-p

- given Ra = 100KΩ a load line can be drawn of „effective HT‟ 250V

- maximum value of grid-leak for power valves is less than a preamp stage, must also consider the additional grid leak and the load of the next stage in parallel with load of first (for example 220kΩ)

- 100KΩ||220KΩ = 69KΩ

- this determines the AC load line with a smaller output swing of 140Vp-p

[Illustration 63: Partially completed long-

tail PI]

Cold Biasing Warm Biasing

encourages clipping a PI triode but at expense of output swing output valves will be driven less hard tonal balance lost in favour or preamp

distortion

opposite to cold biasing down-going output swing will not be amplified by corresponding power

valve as already in cut-off

66

[Illustration 64, 65 (left to right):

Fender 5F6-A Twin:

- 27V allowed for the tail

- HT 355V with 100KΩ loads

- ECC83

- 470Ω bias (Rb), but since twice the current, a cathode load line of 2*470Ω = 940Ω

- bias point quiescent

Ia = 1.35mA...*2 = 2.7mA

- in tail resistor R = V/I = 27/2.7mA = 10KΩ (small, so imbalance significant)

- Gm at bias point 1.6mA/V, ra = ±62.5KΩ, so gain difference between triodes is:

- i.e. first triode is 16% greater, can be corrected by reducing Ra1 100KΩ/1.16 = 86.2KΩ (nearest value = 82KΩ)

- grid-leak is standard 1MΩ, Cg2 is large 100nF

- negative feedback signal, used four 5881 power valves on output

- resulting in 80W output, biased around -50V

- require 50/ 2 = 35VRMS to drive the signal to full output

Gain to one output of PI = half indicated by AC load line, ±26. For maximum output power the power to PI must be 35/26 = 1.35VRMS.

- this develops down the line 80W into speaker 2Ω (2*4Ω in parallel), voltage is:

- Ratio of input to feedback signal:

- for full power of PI, need 1.35VRMS input, 1.35*0.76 = 1.03V (this is the level of feedback required)

- formed by potential divider of feedback resistor Rf and shunt resistor Rs

voltage at speaker 12.6V required feedback voltage 1.03/12.6 = 0.082 (the gain of the potential divider 𝞫)

- Fender selected a large 5KΩ for Rs

Rf = Rs−Rs∗β

𝛽=

5K−(5K∗0.082)

0.082= 56KΩ

**Feedback resistor depends on power output/speaker tap from which feedback is taken, can just transfer models into each other without altering RF and Rs

67

[Illustration 66: Scope showing 'gain spike' effect of overdriven power

valves]

Gain Spike:

- happens when tail resistance is greater than 100KΩ

- output of the inverting triode is clamped by power valve when it draws current from the inverting anode

held constant the anode is no longer changing and appears 'grounded'

usually half input of PI stage now full goes to non-inverting

- 'spikes' until inverting side recovers

- no too much of a problem in Class AB output

- subdued by a large grid-stopper on power valve, which also helps reduce blocking distortion

Appendix O:

Feedback Theory (Blencowe 2009) (Images Ref 25)

[Illustration 67: Simplified feedback amp]

Open Loop - no physical feedback loop due to internal FB in amp

(Ao)

Closed Loop - physical FB loop controls gain (Ao𝞫)

Closed loop takes open loop and feeds it back via Rf to create a fractional feedback amount 𝞫 to multiply with the original signal:

68

In tube circuits, from anode HT arm:

high value to load valve/preserve Ao blocking cap keeps DC out loop usually minimum Rf is 3 times Ra

*modification of universal feedback equation

Applied in Illus.68 to accommodate the shunting of Rg:

[Illustration 68: Triode with negative feedback]

Closed loop feedback does not affect the tone, just the input signal - increases headroom and also lowers input sensitivity.

Linearity, Noises and Frequency Response:

The output will contain distortion/harmonic distortion:

reduces THD by same amount as the FB factor (17dB last example) reduces frequency distortion by same amount

Internal HPF causes roll-off at 34KHz before feedback begins, fallen by Log-1

(-3/20) = 0.71

Open loop gain 60*0.71 = 42

Frequencies in the feedback loop will be attenuated more than those outside this loop.

This increases the bandwidth of the amplifier.

When the reactance of C1 = Rf, feedback fraction cut-off at frequency (more gain as less passed through FB loop) :

[Illustration 69: Frequency response from circuit in Illus.68 with open/closed-

loop and varied C1]

In Illus.69 we can see the closed loop is flatter to HF, extended by the feeback factor.

Open-loop response decreases due to input capacitances, therefore falls off with a first-order slope.

If the cathode were only partially bypassed, then Ao would be lower at low frequency, this is not recommended due to phase problems - cathodes should be fully bypassed with feedback.

Effect on Input / Output Impedance:

Parallel or Shunt - this is voltage feedback - impedance decreased by the FB factor

Series - this is current feedback - impedance increased by the FB factor

69

Illus.68 circuit was parallel with ra = 65KΩ before feedback. So feedback factor reduces this to:

- need to consider this when choosing a coupling capacitor

Global Negative Feedback - from the secondary of the Output Transformer

impedance of the whole amp is reduced feedback less affected by differing kind of speaker

If the impedance is too low it will load down the previous stage, can be remedied by increasing Rin/Rf (also increases noise). Loops with a high FB factor allow high values of Rin.

Practical Virtual Earth Amplifiers:

This stage has:

almost unity gain (0.97) low output impedance (1.04KΩ) 60/0.97 = 62,or, 32dB reduction in harmonic distortion/noise input sensitivity reduced 60 times

Sometimes called an Anode Follower as has many similar characteristics to a cathode follower.

[Illustration 70: Virtual Earth amp isolation between

channels, and varying gain]

- this stage is difficult to overdrive, therefore it is idea for ramping into a tone stage or effects loop

- Illus.70 is a mixer with variable R inputs, to calculate the gain for one, need to take into account the shunting effect of the others.

- no Rg as grid point is a good virtual Earth due to high Ao

- the two other inputs effectively replace Rg

- input impedance is same for Rin1&Rin2 and lower for Rin3

Effect on Overdrive:

- as mentioned, negative FB loops have lower input sensitivity

- when they do reach the point of overdrive/clipping the feedback loop collapses

70

effectively becoming an open-loop (severe overdrive) negative FB loops have little grey area, either clean or very clipped

- no negative FB has low overdrive at low volume, increasing with gain...this has more user control on input sensitivity, as always...down to choice

[Illustration 71: When FB is applied to same grid as audio

signal, must be between 90-270 degrees out of phase,

180 being ideal]

Stability and Limitations on Feedback:

- gain must be <1 (AB = <1) or infinite gain/oscillation will occur in multiplication

- just below 1amp will oscillate unsustainded at some frequencies

HF = Ringing; LF = Motorboating; VLF = Breathing

- HF ringing can be masked and hard to detect, but can be found in a brittle/peaky/high pitched sound

**Must take into account the phase shift at each pole/network/gain stage when using global negative feedback

±45 degrees for each network, including triodes.

[Illustration 72: Applying FB around three time constants]

Stabilizing Feedback:

- Illus.72, suppose each stage has a gain of 60, ZOUT = 40KΩ and input capacitance 100pF

- wish to apply global FB to input

- mid band gain of the whole amp 60 x 3 = 107dB

- encloses 3 x LPF (ZOUT of each stage||grid-stopper into input capacitance)

- each cut-off of of LPF called a Pole, 45 degree phase shift

[Illustration 73: Idealized frequency response graph assessing FB amp

stability]

- Plotted in Illus.73, starts to roll-off as first order (-6dB per octave) at 8KHz, increases phase shift to 45 degrees

- At 18.3KHz pole 2 increases the roll-off second order (a further -6dB per octave), phase shift increases to 90 degrees

- At 39KHz, increases to third order (another -6dB per octave) and phase shift increases to 135 degrees

- the point at which open-loop gain falls exceeding 6dB per octave marks the feedback stability boundary, Illus.73. The greater the margin the better.

71

**High gain amps are prone to parasitic oscillation and can introduce unwanted feedback, anode bypass capacitors reduce HF gain.

--See Logbook Data Entry on 04.04.2012 for full breakdown of Poles and Zeroes stage design--

Appendix P:

Tone Stacks (Blencowe 2009) Images Ref [25]

The Bandmaster Tone Stack

[Illustration 74: Simple Fender

Bandmaster tone stack]

[Illustration 75: Control layout]

[Illustration 76: Frequency response Bandmaster]

Treble pot stacked on top of bass control

component values yeild less loss driven from a 40KΩ stage such as normal triode

average loss ±10dB, seen in Illus.76

reducing C1 creates a deeper mid scoop but reduces treble control bandwidth

Voigt Tone Stack

[Illustration 77: Voigt tone stack]

[Illustration 78: suggested control layout

Voigt stack]

[Illustration 79: Frequency response of a Voigt tone stack, note

centre freq around 200Hz]

Gain of about -14dB at centre setting

centre frequency around 200Hz

good tone stack for clean bass amps

James Tone Stack

72

[Illustration 80: Frequency response

James stack]

[Illustration 81: Controls]

[Illustration 82: James tone stack]

very similar to Baxandall's circuit (to follow)

-7dB point at centre

bass control doubles as a potential divider - gain loss

used by a range of amp manufacturers such as Ampeg, Dynaco, Magnatone, Orange and Fender 'Blonde' Twin

Passive Baxandall Tone Stack

[Illustration 83: A passive Baxandall tone

circuit]

[Illustration 84: Suggested control setup]

[Illustration 85: Frequency response of Baxandall Tone stack]

R3 usually separates the two circuits, with no R3 present the treble control is rendered useless

flat response in the centre, which shows good isolation between controls, making a good hi-fi tone

Increasing C3 shifts the centre frequency down

a parallel capacitor with C3 would add (series capacitance) to the value and shift centre frequency down - switchable option

FMV Tone Stack

Designing the FMV Tone Stack:

Begin at bottom "middle" control

P3 set to maximum, P2&P1 set to minimum, Illus.87 (a)

at mid frequencies C1 is small enough to be ignored, as in Illus.87 (a)

C2 & C3 appear in parallel, large enough that may assume a short circuit

Illus.87 (b) shows the equivalent circuit to this

supposing previous stage is standard triode ZOUT = 40KΩ, in series with slope resistor R1

ZOUT = (ZOUT + R1) || P3 ...as a potential divider

this determines the degree of attenuation at a flat setting

the greater the attenuation (𝞫), the greater the treble/bass we can 'add back',

For example, chosen -10dB :

[Illustration 86: Controls for FMV]

[Illustration 87: P3 at max, P1&2 at min (a) equivalent

circuit (b)]

73

𝞫 = 10dB/20

= P3

𝑍𝑜𝑢𝑡 +𝑅1+𝑃3 ...but we know 𝞫 = 10

-10/20 = 0.32

Solving for P3 = −β(Zout +R1)

𝛽−1=

−0.32 (40K+100K)

0.32−1= 66KΩ or nearest value 47KΩ

So..... 𝞫 = P3

𝑍𝑜𝑢𝑡 +𝑅1+𝑃3 =

47K

40𝐾+100𝐾+47𝐾= 0.25 ...or -12dB

- with P3 created at maximum value, we can only cut frequency down from -12dB

[Illustration 88: Equivalent circuit with

Mid-min, Bass-max]

choose C3 by assuming 'bass control - maximum', 'middle - minimum'

Equivalent circuit Illus.88

C3 shunts HF to ground and the remaining signal is passed to P2 - which is, the upper end of the bass control

+3dB between mid/bass bands (assuming 200Hz desired):

f = 1

2𝜋𝐹(𝑍𝑜𝑢𝑡 +𝑅1)=

1

2𝜋(200𝐻𝑧 )(40𝐾+100𝐾)= 5nF

nearest value is 4.7nF, which gives +3db frequency 242Hz, and 6.8nF would give +3dB point of 167Hz

it may be easier to adjust the slope resistor

lager value of P2, greater degree of bass-boost, minimum cut is therefore:

𝞫[BASS] = P2+P3

𝑃2+𝑃3+𝑅1+𝑍𝑜𝑢𝑡

C2 determines the lower end of the bass frequency, and is usually set below audibility.

Capacitors C1,2,3 keeps DC off the potentiometers from previous HT (must meet power rating)

with P2 at maximum lowest -3dB freq (with P2 chosen arbitrarily):

f = 1

2𝜋𝐶2 𝑍𝑜𝑢𝑡 +𝑅1+𝑃2+𝑃3 =

1

2𝜋 (10𝑛𝐹 )(40𝐾+100𝐾+470𝐾+47𝐾)= 13Hz

can now choose P1 and C1

P1 must be large enough to make C1 effectively small or MF will be passed via C1 straight to output. If P1 is too large it will create excess resistor noise and C1 will need to be extremely tiny value to avoid stray wiring capacitance

a suggested value is 220KΩ- 470KΩ (Blencowe 2009)

C1 determines the higher end of the control, setting -3dB mid too low will deprive "middle" control of its range (around 2Khz centre):

[Illustration 89: Completed FMV design]

f = 1

2𝜋𝐹 𝑍𝑜𝑢𝑡 +𝑃1 =

1

2𝜋2000 470𝐾+40𝐾 = 156pF

if the previous stage has low output impedance, like a cathode follower, then ZOUT in the above calculations all but drops out

can place a power rated coupling capacitor before the tone stack - eliminates the need for C1-3 to meet HT DC rating, only need to match AC rating

[Illustration 90: Frequency response of FMV stack from Illus.89]

74

HMF - HF are attenuated before reaching the "middle" control

this gives a bass-boost impression

Fender Bassman has a 'deep' switch as in Illus.91

C4=C3

R2 is in parallel to avoid pop/click when switching

[Illustration 91,92: Additional control and circuit frequency resp.]

[Illustration 93: Frequency response for Illus.94(c)]

[Illustration 94: (a) defeat switch, (b) variable lift (c) combination]

Defeat/Lift:

allows the signal to pass without attenuation or equalization

a switch at the bottom of P3 A - a large resistor should be in parallel to reduce clicks and is a grid-leak path to next valve B - a potentiometer placed in stack to progressively bypass/lift, can be blended with equalized C - R2&R3 added, tone stack unchanged in normal mode, has same value as P3 when used as middle control. Switch SW1 allows P3 to elevate the stack when it is adjusted to maximum, C is basically a combination of A&B.

Appendix Q:

Distortion Mechanisms

Harmonic distortion denotes a harmonic relationship to

fundamental and partials.

F0, H2, H3, H4.......

Enharmonic distortion is related to intermodulation

and sum/difference sidebands.

[Illus. 95: Signal hitting the power rails]

Clipping levels set by signals hitting the power rails

in guitar pedals this is ±9V

clipping needs to be controlled so as not to produce so many harmonics - preserve the fundamental (Waterman 2011)

harsh clipping - high order harmonics

smooth clipping has more musicality (Waterman 2011)

[Illus. 96: Power rail in guitar pedals causes earlier clipping]

±15V or 30Vp-p

power rails can 'sag' due to other components

current reducing headroom

reduces on each side, e.g.±1V, so 28Vp-p

14Vpk = 9.899VRMS

20log (9.899/0.775) = 22.1dBu

signals clip around this point

Guitar pedals operate on +9VDC (single rail)

Can also operate on +18V(wall wart)

Requires circuits biased (offset) to half-supply [see previous chapter]

9Vp-p = 4.5Vpk (3.182VRMS)

12dBu of headroom, could be used to drive valves

[Illus. 97: DC Bias offset for clipping in 9VDC pedals]

75

E.g. 90mV signal from guitar is equal to 63.6mVRMS, in a normal pedal of 3.182VRMS

3.182/63.6mV = 50 Amplification factor, or, 33.98dB

As stated earlier, pedals can clip from around 20-40V (Waterman 2011)

[Illus 98: Diode hard clipping] Ref [26]

[Illus. 99: Soft Diode Clipping] Ref [26]

Diode clipping lowers the available headroom by >50 times normal (Waterman 2011).

Non-linear clipping takes place on maximum signal peaks with various knees similar to compression.

[Illus. 100: Symmetrical Clipping] Ref [26]

The more clipped a signal is, the more square a sine wave will appear, the harsh leading edges are similar to the aggressive grid current limiting - odd harmonics

This, being symmetrical on both sides creates an even harder sound.

Asymmetrical clipping can be created from different thresholds of clipping on both sides.

This creates more even order harmonics with some odd harmonics.

[Illus. 101: Asymmetrical Clipping] Ref[26]

[Illus 102: Tube-like clipping] Ref [26]

- Soft symmetrical clipping produces lots of 3rd order harmonics

- Hard symmetrical clipping slews harmonic production up to the 7th order (Waterman 2011), this creates much more extra noise to mask the fundamental

- A nice soft edged compressed sound is similar to the tube sound we have observed in previous chapters

Intermodulation Distortion:

This is the distortion product of two or more waveforms: the sum and difference sidebands

E.g. F1 = 440Hz; F2 = 880Hz

...intermodulates to produce two fundamentals

Sum = 440 + 880 = 1320Hz (Harmonically related to F1)

Diff = 880 - 440 = 440Hz (Fundamental)

** This may sound good for waveforms already relative to each other, but when they are not:

E.g. F1 = 440Hz; F2 = 659.26Hz

Sum = 1099.26Hz (Unrelated to F1)

Diff = 219.26Hz (almost an octave down from F1)

** This is perceived as more harsh distortion sound

[Illus. 103: A signal displaying harmonic distortion elements] Ref [26]

76

Calculating Percent 2nd Harmonic Distortion (per Illus.103):

%Dist(V or SPL) = 100 * 10-dB/20

E.g. 2nd harmonic % = 100*10-50/20

= 0.316%; 3rd harmonic % = 100*10-63/20

= 0.070%

- this is for single harmonic distortion figures

Calculating Total Harmonic Distortion (THD) (per Illus.103):

Total dB = 20log (10dB1/20

+ 10db2/20

+ 10dBN/20

)

[Illus. 104: Ground Reference Clipping] Ref [26]

- harder, harsher more of a 'rock' sound

- one diode for each side of AC signal

- left diode clips positive

- right diode clips the negative

[Illus. 105: V-I curve for silicon diode] Ref [26]

- clamping the opamp output into non-conductive range (forward voltage)

- typical silicon diodes have a forward voltage drop of 0.7V (Fig.79)

- input current causes diode to switch on and create forward voltage drop once Vc reached

i.e. diodes limit the Vc swing

[Illus. 106: Parallel feedback diode clipping] Ref [26]

- clipping is smoother placed in the feedback path (Waterman 2011)

- acts in parallel with the opamp's feedback resistor

- the FB resistor reduces the gain once the signal starts exceeding the diode's threshold

Appendix R:

Pedal Example - Tube Screamer

[Illus. 107: First stage of a Tube Screamer]

type of transistor doesn't change the sound, the gain = 1 (unity)

base of the transistor tied to +4.5V bias through 510KΩ

Actual gain transistor 2SC1815 is 300, multiplied by 10KΩ emitter resistor = 3MΩ

510K||3MΩ means ZIN = ±510K

0.02 cap prevents DC saturating guitar pickups

this stage is always connected to the input

has high enough impedance to avoid loading the guitar pickup

bypass circuit occurs further on

both capacitors under transistor Q1 follow different routes and are small enough not to change the audible signal

77

[Illus. 108: Clipping amp following input buffer]

direct connection to the input buffer except in newer TS10 model, 220Ω resistor Ra separates

gain of the non-inverting amp [1+Zf/Zi]

biased by +4.5V through 10KΩ

Zf = Feedback network impedance to negative pin

Zi = impedance from negative pin to ground

Zi is series capacitor with resistor:

- open circuit at DC

- is frequency selective

- at HF is a short circuit to ground, at LF = impedance

Zf is the parallel clipping diodes, 51pF capacitor and series combination 51kΩ + 500KΩ "Drive" pot:

- diodes 'turn on' voltage is 0.5V to 0.6V

- this is the point where the diode resistance goes from open circuit to low value resistance

- as the diode turns on, the opamp stage gain drops just below 1

- even if "Drive" set to 100, the diodes keep the gain at 1 where input + gain exceeds diode threshold the signal is clipped at forward voltage

Typical guitar voltage signal is around 30mV - 100mV, even this can be amplified to 3V by a pedal alone, this is enough gain to give some distortion.

51pF Capacitor softens the corners of a clipped waveform, this softens the distortion, emulating the onset of grid conduction soft edges we see in triodes. This is more noticeable with the "Drive" up.

The impedance goes down with increasing frequency, more FB equals less gain - softens the edges.

[Illus. 109: Single control Tone stage with volume pot]

1KΩ||0.22μF is LPF of 7230Hz

output of stage is down 20dB (10:1) at 7230Hz

down another 6dB (20:1) at 14KHz

"Tone" is a 20KΩ potentiometer strung from + to - input of second opamp

wiper is tied to 220Ω in series with 0.22μF

active when capacitive impedance is <220Ω (±3.2KHz) in series with 20KΩ attached to wiper end

this varies roll-off 3.2KHz - 36KHz

the more impedance to ground the less roll-off

when + end shunts frequency above 3.2KHz to ground there is less gain

when - end shunts feedback frequency above 3.2KHz to ground there is more gain

Boost/Gain levels off the cut by 220Ω||0.22μF

the opamp is a non-inverting buffer, so there is no net signal loss through the control stage (again gain = 1)

output is through 100KΩ pot, connected to 'hot' lug with the 'cold' lug to ground (Keen 1998)

the signal is taken from the wiper

78

[Illus. 110: Bypass 'flip-flop' circuit]

bypass is done by a JFET 2SK30A (later models use 2SK118)

the source and drain is tied to +4.5V bias through high value resistors

known as N-Channel Devices where "on" looks like 100Ω when voltage between source and gate is zero

"off" looks like a multi-mega ohm resistor and voltage from gate to source is negative (Keen 1998)

the gate of each JFET is tied throught a diode to an electronic sandwich control flip-flop so the gate can be pulled to ground (-4.5V compared to the source)

gate is allowed to float on voltage on the other side of the gate diode, being higher than the 4.5V source

leakage effects let the gate drift up to 4.5V over a few milliseconds - prevents a click when switching on/off

two JFETs connected to out-of-phase outputs made from two NPN transistors

flip-flop set up to change state when "Bypass" switch is pressed

sealed dome momentary switch - computer keyboard technology, available at low cost (Keen 1998)

two out-of-phase outputs (when one high, the other is low) - only one JFET on at a time

one of these JFETs is connected to the input buffer (bypass signal) and the other to previously discussed stages

[Illus. 111: Emitter follower output stage]

emitter follower with a 10KΩ emitter resistor

biased from +4.5V source

emitter follower varies per model

series resistor Rb limits drive to an amp input

in connection to capacitor||shunt resistor

frequency dependant potential divider

this forms the ZOUT, the ZIN of an amp is around 1MΩ, so this follows the 1:10 rule with around 100KΩ output impedance

10KΩ in 808 Model halves the emitter loading of the output buffer and reduces the ZIN of the emitter follower stage

also reduces the negative going output impedance to ±5KΩ - drives the following stage twice as hard

Studio Guitar Amp and FX - Ricky-Lee Anderson (UG3 Media Technology Project)

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