A NALOGUE C IRCUITS AND S YSTEMS
Input Stage
Voltage Amplifier Stage
VBE-Multiplier
Output Stage
Vcc+
Input
Output
Vcc+
Feedback Network ( )
Hi-Fi Amplifier
Group 311 - Fall 2013 - Aalborg University
Department of Electronic Systems
Electronic & IT
Department of Electronic Systems
The Faculty of Engineering and Science
Aalborg University
Fredrik Bajers Vej 7
DK-9220 Aalborg Ø, Denmark
Telephone: 9940 8600
Fax: 9940 9840
www.es.aau.dk/
Field of education: Electronic Engineering and IT
Title: Hi-Fi amplifier
Project period: P3, fall 2013
Abstract:
Project group: 311
Participants:
Alexander Ramlov
Bjarke Nørskov Roe-Poulsen
Chris Artur Pedersen
Mathias Rønholt Kielgast
Michael Bo Poulsen
Supervisor: Ole Kiel Jensen
Copies: 7
Pagecount: 78
Appendices: 32
Appendix Type:
Excerpts from standards
Simulation diagrams
Measurement journals
CD
Completed: 18th of December, 2013
This project is concerning the design and construction of a Hi-Fi amplifier, consisting of an
analogue solution based on specifications made
from DIN/IEC standards and some estimations.
The Hi-Fi amplifier is constructed with three
modules, consisting of a volume control that has
the ability to attenuate and amplify the signal, a
tone control circuit to amplify/attenuate both bass
and treble signals and a power amplifier, which
is based on the LIN (three staged) topology with
a differential amplifier, a voltage amplification
stage and an output power stage. The output stage
of the power amplifier is a class AB solution to
compromise between efficiency and the output
signal. The Hi-Fi amplifier is designed to be able
to deliver a minimum of 10 W output power in a
8 Ω load.
The constructed Hi-Fi amplifier meets all
the specifications for the volume control and the
power amplifier, while the bass control circuit
of the tone control deviates slightly from the
requirements. The Hi-Fi amplifier is measured
to deliver at least 10.1 W at a rated input voltage
of 0.5 VRMS with a maximum total harmonic
distortion of 0.162 %.
The contents of this report are freely available, but publication (with reference) is only allowed
with the consent of the authors.
I
Preface
This report is made by the student group 311 at the Department of Electronic Systems at Aalborg University.
The group consists of five third semester students of Electronic Engineering and IT. The report is produced
during the period from the 2nd of September to the 18th of December, 2013. The overall title for the project
period is Analogue Circuits and Systems.
The report begins with a brief introduction, wherein the basic modules of a Hi-Fi amplifier are mentioned,
leading to the problem statement. Hereafter, relevant standards are discussed and specifications are made for the
amplifier, after which the design is made with both theory and simulations. Next, results from measurements
of the circuit are shown in the integration, which leads to a conclusion that describes how the system fulfil
the specifications. Last the error sources and the possible supplements and improvements are described in the
discussion and in the perspective.
The citation in this report is made by use of the American Institute of Physics (AIP) style, with the references
numbered in order of appearance and listed in this order in the bibliography. If the reference is placed before a
full stop, it refers only to that sentence. When placed after a full stop, it refers to the entire paragraph. When
actively referencing in a sentence, the last name of the first author will be used followed by a citation. Figures
and formulas are numbered according to the chapter, in which they are found (i.e. the first figure in chapter
2 is noted as 2.1, the second as 2.2, etc.). All graphs and images are referred to as figures. Figures without
citation are made by the authors. Furthermore, it should be noted that the equations and quantities are written
with respect to the ISO 31 standard.
A CD is attached to the report with the following content: Simulations from LT-Spice, Matlab scripts, and
the PCB design from Altium.
Aalborg University, 18/12-2013
III
Contents
1
2
3
4
5
Introduction
1.1 Hi-Fi Modules . . . . . . . .
1.1.1 Pre-Amplifier . . . .
1.1.2 Signal Modification .
1.1.3 Power Amplifier . .
1.2 Problem Statement . . . . .
Specifications
2.1 Standards . . . . . . . . . .
2.2 Specification Table . . . . .
2.2.1 Output Voltage Loss
2.2.2 Tone Control . . . .
2.3 Acceptance Testing . . . . .
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Design
3.1 Volume Control . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Volume Control Design . . . . . . . . . . . . . . . . . . . .
3.1.2 Test Results . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Tone Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Finding Component Relationships and Values . . . . . . . .
3.2.2 Input Impedance and Output Impedance of the Tone Control
3.2.3 Simulations and Measurement Results . . . . . . . . . . . .
3.3 Power Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Topology and Strategy . . . . . . . . . . . . . . . . . . . .
3.3.2 Output Stage . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Voltage Amplification Stage . . . . . . . . . . . . . . . . .
3.3.4 Supply Voltage . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Input Stage and Feedback . . . . . . . . . . . . . . . . . .
3.3.6 Small Signal Analysis . . . . . . . . . . . . . . . . . . . .
3.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Overload Protection . . . . . . . . . . . . . . . . . . . . .
3.4.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Measurement Results . . . . . . . . . . . . . . . . . . . . .
Integration
4.1 Acceptance Testing Result
4.1.1 Input . . . . . . .
4.1.2 Output . . . . . .
4.1.3 Performance . . .
4.1.4 Tone Control . . .
4.1.5 Volume Control . .
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Discussion
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1
1
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59
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63
V
C ONTENTS
6
Conclusion
67
7
Perspective
69
Bibliography
71
Appendices
i
A Standards
A.1 IEC 61938-3: 1996 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 IEC 581-6: 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3 DIN 45500: 1973 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i
i
i
ii
B Simulation Diagrams
iii
C Measurement Journals
C.1 Volume Control . . . . . . . . . . . .
C.2 Tone Control . . . . . . . . . . . . .
C.3 Power Amplifier . . . . . . . . . . . .
C.4 Acceptance Testing of Hi-Fi Amplifier
VI
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ix
ix
xiv
xx
xxvi
1. Introduction
All recorded music is produced as low-level electrical signals, whether they are produced by a microphone, an
electrical instrument, or by similar ways. These signals have a too low level of power to supply a loudspeaker
and therefore the signal must be amplified; this can be done by a High Fidelity amplifier (Hi-Fi amplifier). The
level of any voltages that are produced before the amplification is called signal level. Before the signal can
be amplified to the actual output to the loudspeaker, the signal level must be amplified to the line level, by a
voltage amplifier. In general, the line level should be the exact same signal as the signal level input in all ways,
except the amplitude, which should be in the magnitude of one to two volts RMS (Root Mean Square). When
the line level is produced, the power amplification is possible. Before the actual power amplification, all the
signal modification that is desired should be made. This customisation can be performed inside the voltage
amplifier or just after. After the wanted customisation, the power amplification of the line level is made, which
produce an output signal, which has been amplified in both voltage and current, so that the output signal is
capable of supplying a loudspeaker. A simple diagram of the levels and modules can be seen in figure 1.1. The
Hi-Fi amplifier is said to be “transparent”, when the output signal only varies from the original input signal
in amplitude; this is of course desired and all changes in the signal beside the user controlled modifications is
called distortion, which for all amplifiers is attempted to be kept at a minimum, often in a compromise with
efficiency. [1]
The basic function of the Hi-Fi amplifier results in a wide use of all components/units, wherein production of
sound by way of electrical signals is apparent. This applies whether it being an audio card of a PC, a television,
all kinds of sound systems, and so on. [1]
1.1
Hi-Fi Modules
A Hi-Fi amplifier may consist of several modules. A general construction could be the one seen below, with
an initial voltage amplifier, followed by a signal modification module, and finally the power amplifier which
produces the output to the loudspeaker.
Sound
Pre-amplifier
Signal level
Signal modification
Line level
Power
Amplifier
Line level
Power level
F IGURE 1.1: Illustration of the basic four modules of a Hi-Fi amplifier.
1.1.1
Pre-Amplifier
The pre-amplifier (preamp) is the voltage amplifier producing the line level and it is only necessary, when the
input comes from low signal sources without built-in preamp.
1.1.2
Signal Modification
The signal modification can consist of several modules, which can be used manually to adjust the output, this
can be to boost or reduce the bass, treble or volume and so on. The signal can also be incorporated in the
preamp. [1]
1
1. I NTRODUCTION
Tone Control
The tone controller is able to adjust the amplification of a chosen range of low frequencies (bass) and a range of
chosen high frequencies (treble) relatively to a reference amplitude of the signal frequencies. There are many
types of tone controllers, either analogue, digital, or a combination of the two. Some are complicated in circuit
structure and have many settings, others are simple and straight forward to use. [2]
An equalizer is a complicated form of tone control, where specific frequency ranges can be changed. It is
often used instead of simple treble/bass adjustment. [2]
Volume Control
Volume control is commonly adjusted by the user to control the level of amplification and thereby the volume of
the sound produced. The control can be analogue, digital, or a combination of the two. Aside from the manual
volume control, an automatic control could be applied. Automatic Gain Control (AGC) has the function of
controlling incoming signals within a dynamic range, to a specific, constant output level by finding an average
of the input signal. There is a lot of different ways and places where AGC can be applied, including the control
of amplification of sound signals. Within a Hi-Fi amplifier, an AGC module can be used to adjust an incoming
signal with high-varying amplitude to a signal with a linear amplitude.
Volume is measured in Decibel (dB), where decibel is one tenth of a Bel. Decibel is a contraction of the
SI-prefix deci and the unit Bel, a unit named after the scientist Alexander Graham Bell. A relation of the sound
is expressed with the following equation for level difference in power:
∆X = 20 · log
P2
[dB]
P1
(1.1)
Where the fraction is the ratio between the two power levels. In this way, the doubling of a sound level
corresponds to ≈ 6 dB. [3]
1.1.3
Power Amplifier
The power amplifier is the last amplifier in the Hi-Fi amplifier system. The term “power amplifier” is used
because the amplifier requires most attention with regards to power efficiency, as the output requires power
enough to produce sound within the loudspeaker. There is a multitude of considerations to take into account
when calculating how much power to use and what type of power amplifier to use. These different types of
amplifiers are divided into a range of classes, each with their strengths and weaknesses. In the following, there
will be a brief summary of the most commonly used classes, their strengths and weaknesses, and examples of
their use. It should be mentioned that all power amplifier designs make use of feedback systems to improve
performance, with regard to distortion, DC-offset, bandwidth, etc.
Commonly Used Classes
The most commonly used classed are:
• Class A
• Class B
• Class AB
• Class G
2
1.1. Hi-Fi Modules
The class G amplifier is an attempt to reduce the amount of power dissipation in the class AB amplifier by using
several power sources. In this section, only class A, B and AB will be discussed though there are other power
amplifier classes which are worth mentioning briefly, such as class C and D. The class C amplifier is usually
only used in radio frequency circuits, where the distortion issues can be dealt with, and the class D amplifier
involves a great deal of practical problems (such as the implementation of large inductors to deal with high
frequency signals). [4]
Class A
The output stage of a class A amplifier is biased with a current greater than the amplitude of the current
of the input signal. This means that there is always a current flow through the output transistor(s) and that the
transistor(s) will conduct during the entire period of the input signal [5]. In other words, the sound output suffers
very from distortion, as the amplification is linear [6]. However, the class A amplifier has poor efficiency, the
maximum efficiency of this class with ideal components is 25 % [5]. A higher efficiency can be achieved by
using inductive coupling, though the inductors needed will be large and thereby costly. The reason why the
efficiency is so poor, is because the output transistor(s) always has current flowing through it. This means that
even when there is no signal through the output transistor(s), it will never turn “off”, meaning it will always
consume the same amount of power, independent of the output.
Beside the economic and environmental issues of the power consumption, the wasted power forms a problem
in the shape of heat. Class A amplifiers usually require some sort of heat sink [6], but despite this problem, the
class A amplifier design is much simpler than other classes (such as class AB).
Vcc+
vo
I
Vcc
C
vS
VS
G vs
iC
vo
t
vs
iL
Rload
t
Vcc-
F IGURE 1.2: Diagram of class A power amplifier, with an incoming signal with DC-voltage VS and an ACsignal with amplitude vS . The AC-signal is amplified with a gain, G, resulting in an output vo with amplitude
G · vS . The diagram to the right illustrates the waveform of a full signal output with an ideal transistor.
The circuit illustrated in figure 1.2 is a simple, biased BJT amplifier circuit. The transistor conducts for the
entire length of the input signal and thus the output signal is (as illustrated on the right of the diagram) clear.
Summary of the class A amplifier:
+ The output signal is linear, thereby no significant distortion in the output signal.
+ The design is simple compared to other classes.
- The maximum efficiency is ideally 25 %.
- Heat issues.
3
1. I NTRODUCTION
Because of its traits, the class A power amplifier is most commonly used by audio enthusiasts or musicians
wanting the best output sound. Though its poor efficiency it does not often make up for its clear sound, so in
most applications it is not chosen over other classes of power amplifiers.
Class B
The class B amplifier makes use of two transistors in the output stage (one npn- and one pnp-transistor). One
transistor conducts during the positive period of the signal and one transistor conducts during the negative
period of the signal [5, 6]. The class B output stage is not supplied with a constant bias like the class A output
stage, instead, the transistors are only activated when the voltage reaches higher than the base-emitter voltage
(and only one transistor can be turned on at any time). Silicon based transistors have a base-emitter voltage of
about 0.7 V [5], so when there are signals below 0.7 V the transistors do not conduct, resulting in much greater
efficiency than the class A design. Furthermore, there are no bias current in the class B power amplifier, which
results in a higher efficiency.
Vcc+
vo
vS
C
vs
G vs
vo
t
t
Dead band
iL
Rload
Vcc-
F IGURE 1.3: Diagram of class B power amplifier, with an incoming AC-signal with amplitude vS . The
amplifier consist of an NPN and a PNP BJT, each amplifying half of the signal, resulting in a dead band as
seen on the output, due to the base-emitter saturation voltage.
The maximum efficiency is 78.5 %, which is much better compared to the efficiency of a class A amplifier
(ideally 25 %). The problem of the class B amplifier is, however, that the constant switching between transistors
causes the output signal to be distorted to a high degree. This is due to the problem of cross-over distortion,
which is illustrated in the output signal on figure 1.3 and in figure 1.4. This problem occurs because both
transistors cannot be turned on at the same time, so a small gap occurs, when the signal changes polarity and
the transistors switch on and off, due to the base-emitter saturation voltage. The effects of this are most notable
when the amplitude of the input signal is small, as the base-emitter saturation voltage then will be large in
comparison. [5]
4
1.1. Hi-Fi Modules
Input and output of a class B amplifier
2
1.5
Amplitude / V
1
0.5
0
−0.5
−1
−1.5
−2
0
0.5
1
Time / ms
1.5
2
F IGURE 1.4: Illustration of the input voltage (red) versus the output voltage (blue) for a class B power
amplifier. It is seen how base-emitter saturation voltage results in cross-over distortion, where the smallest
voltages are lost in the output signal.
Summary of the class B amplifier:
+ Efficient, ideally up to 78.5 %
- Cross-over distortion
- Difficult to design
The class B amplifier design is commonly used in portable radios or other battery-driven devices, where quality
is not as important as longevity. Due to the distorted output signal, it is rarely used amongst musicians or audio
technicians.
Class AB
The most commonly used amplifier design is the class AB design. It is a compromise between efficiency and
sound quality. It works much like the class B design, but instead of the two transistors in the output stage
switching on and off at each half of the input signal, they now conduct for a little bit over the half, resulting in
the elimination of the cross-over distortion. This is possible, because the transistors, like in the class A design,
receive a bias current, albeit a small bias current compared to the bias current in the class A design.
Class AB amplifier output wave
1
Load
Upper transistor
Lower transistor
0.8
0.6
Current / I
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.1
0.2
0.3
0.4
0.5
Time / s
0.6
0.7
0.8
0.9
1
F IGURE 1.5: The input and output of a class AB push-pull amplifier, where load (blue) is the output signal,
the upper transistor (green) and the lower transistor (red). Notice that the cross-over distortion from the class
B amplifier (see figure 1.4) has been eliminated because the transistors conduct through the length of the dead
band (though the signal still can suffer from some degree of distortion).
5
1. I NTRODUCTION
Summary of the class AB amplifier:
+ More efficient than the class A design
+ Less distorted output than the class B design
- Not as efficient as the class B design
- The output signal is not as clear as with the class A design
- Complicated design
The class AB amplifier design is mostly used, as it is a good compromise between efficiency and sound quality.
It is used in almost any loudspeaker system where a power amplifier is necessary.
Efficiency of Classes A, B, and AB
As has been mentioned, the three classes have their own strengths and weaknesses. Class A has low distortion,
but its low efficiency makes it unsuitable in applications with a power above 1 W [7]. Class B has a good
efficiency, but has problems with distortion. Class AB can be almost as efficient as a class B amplifier, with a
lower distortion level. A comparison of the efficiency of the three classes is seen in figure 1.6.
Efficiency of Class A,B and AB power amplifiers
80
Class AB
Class B
Class A
70
Maximum efficiency 78.5 %
Efficiency / %
60
50
40
Maximum efficiency 76 %
30
Maximum efficiency 25 %
20
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Peak output voltage / V
0.7
0.8
0.9
1
F IGURE 1.6: Plot of the theoretical efficiency of the three amplifier classes: A, B, and AB. It is seen, how their
efficiency increases with the output voltage, and how the AB amplifier theoretically can perform compared to
the B amplifier.
The class G amplifier is, as mentioned earlier, a class AB amplifier with more than one supply voltage. This
makes the amplifier more efficient when the output is low, which is often the case in everyday use, making this
a substantial improvement.
1.2
Problem Statement
With the wide range of options available for the use of a Hi-Fi amplifier it has been decided to narrow the scope
of the project according to the resources, time and learning goals for the semester. This has led to cover the
following amplifier modules within the project:
6
1.2. Problem Statement
• AB Class Power Amplifier
And the following signal modification modules.
• Tone Control
• Volume Control
Notice that the pre-amplifier is left out, which means that the project delimits from low voltage input sources,
such as electrical instruments, analogue record-playing units and microphones. This leaves line level voltage
digital audio-playing units as possible input sources for the Hi-Fi amplifier, such as MP3 players, computer
audio outputs, and audio outputs from mobile phones. Furthermore, it has been determined from the learning
goals of the semester, that multichannel inputs and outputs are not necessary to demonstrate the purpose of the
Hi-Fi amplifier.
The problem statement is defined:
“How does one build a single channel input and output Hi-Fi amplifier with the user control modules consisting
of a tone and volume control, and the power amplifier module consisting of a class AB, and which specifications
should it meet?”
7
2. Specifications
As described in the problem statement, it is desired to design and build a class AB Hi-Fi power amplifier with
user controls, to adjust the speaker volume and a function to amplify/attenuate a frequency range nearly without
affecting the other frequencies at the same time. A simple block-design for this can be seen below.
User control
Sound
Volume
Control
Tone
Control
Power
Amplifier
F IGURE 2.1: The delimited Hi-Fi amplifier with the relevant modules
In order to determine a specific design, which can be tested, a specification for the product is made from
relevant standards.
2.1
Standards
A table with the relevant standards are listed in table 2.1. Those standards are used in order to set up a
specification for a Hi-Fi amplifier with tone and volume control. A description of the relevant details in the
standards are located in appendix A.1.
The three selected standards are from IEC (International Electrotechnical Commission) and DIN (Deutsches
Institut für Normung) and are all available in the Aalborg University Library. Newer versions of the standards
may be found at the representative organisations websites, but these were deemed sufficient.
Standards
Description
IEC 61938-3: 1996 [8]
Audio, video, and audiovisual systems - Interconnections and matching values Preferred matching values of analogue signals.
IEC 581-6: 1979 [9]
Amplifiers.
DIN 45500: 1973 [10]
Hi-Fi audio equipment and systems - Minimum performance requirements.
TABLE 2.1: Used standards with titles and descriptions.
9
2. S PECIFICATIONS
2.2
Specification Table
A specification table is set up by use of selected relevant standards, which the Hi-Fi amplifier should meet in
order to fulfil the problem statement. The specification table will later be used to determine the design of the
Hi-Fi amplifier.
Specification no.
Description
Min
Rated
Max
Requirements
Input
Source impedance a
Input impedance a
EMF a
Overload source EMF a
1.
2.
3.
4.
2.2 kΩ
22 kΩ
0.2 V
2.8 V
0.5 V
Output
5.
6.
7.
Source impedance
Load impedance
Output power b
0.8 Ω
8Ω
10 W
Performance
8.
Gain deviation in effective
frequency range b
Effective frequency range
THD c
9.
±1.5 dB
Relative to 1 kHz
0.7 %
20 Hz to 20 kHz
±13 dB
±13 dB
20 Hz to 112 Hz
8.9 kHz to 20 kHz
±3 dB
500 Hz to 2 kHz
20 Hz to 20 kHz
Tone control
10.
11.
12.
Bass amplification
Treble amplification
Gain deviation in nonequalized frequencies
±10 dB
±10 dB
Attenuation
−46 dB
Volume control
13.
Relative to 1 kHz
a Values
from the IEC 61938 standard
from the IEC 581-6 standard
c Values from the DIN 45500 standard
b Values
TABLE 2.2: Specification table with all the selected requirements for the Hi-Fi amplifier.
2.2.1
Output Voltage Loss
The attenuation factor, α, is the ratio between the load impedance, Zload , and the output source impedance,
Zsource . This factor can be used to define the ratio between the load voltage VL and the source voltage VS , which
is the voltage loss ρ.
α=
Zload
Zsource
⇒
ρ=
VL
=
VS
Zload
Zsource
Zload
Zsource
Zsource + Zsource
=
α
α +1
(2.1)
According to the IEC 61938 standard, the attenuation factor should be greater than or equal to ten. To achieve
this with a load impedance of 8 Ω, the output source impedance must be less than or equal to 0.8 Ω:
α=
10
8Ω
= 10
0.8 Ω
(2.2)
2.2. Specification Table
So the chosen source must meet this requirement. From this, the maximum voltage loss can be found:
ρ=
2.2.2
VL
10
=
≈ 0.91
VS
10 + 1
(2.3)
Tone Control
As an estimation, the tone control has been set to minimum ±10 dB in both bass and treble. This is for the ideal
tone control and without compensating for the deviation in practice; based on this, the tone control has been set
to maximum ±13 dB in both bass and treble to make op for the cut-off frequency. In that way the tone control
will amplify/attenuate with between ±10 dB to ±13 dB in both low and high frequencies. To make a smooth
transition from the frequencies which are amplified/attenuated and those that are not, a first order filter will be
adequate.
Sound
Frequency Range
Infrasonic
0 Hz to 20 Hz
Low frequency sounds (Bass)
20 Hz to 200 Hz
Mid range frequency sounds
200 Hz to 2 kHz
High frequency sounds (Treble)
2 kHz to 20 kHz
≥20 kHz
Ultrasound
TABLE 2.3: Frequency range classification of sound waves. [11]
From table 2.3, it is seen that the frequency range of interest in relation to bass is 20 Hz to 200 Hz, and
for treble 2 kHz to 20 kHz. It is decided that the frequencies between 500 Hz and 2000 Hz should not be
amplified/attenuated, and the frequencies amplified/attenuated with ±10 dB to ±13 dB is limited to be 20 Hz to
111.93 Hz and for the high frequencies 8933.67 Hz to 20 kHz, due to following calculations:
νgiven · 10decade = νnew
500 Hz · 10−0.65 = 111.93 Hz
0.65
2000 Hz · 10
(2.4)
= 8933.67 Hz
Where νgiven is the given frequency and νnew is the frequency 0.65 decade away from the given.
With a first order filter, the filter will amplify/attenuate with ±20 dB per decade. In this case the
13
amplification/attenuation is ±13 dB which is adequate to 20
decade or 0.65 decade. The characteristic in relation
to amplification/attenuation, with the chosen values is seen on figure 2.2.
Amplification /dB
-20
13
10
c
/de
dB
3
0
3
Frequency /Hz
111.93
500
2000
8933.67
-10
-13
F IGURE 2.2: Tone control characteristics
11
2. S PECIFICATIONS
From this figure the tone control frequency response is defined.
2.3
Acceptance Testing
The test conditions for the specifications, will be explained in this section. During the tests, the system will
often be specified to be in rated conditions. Rated condition for this system is as follows:
• The source EMF is set to 0.5 V.
• The input signal is set to a frequency of 1 kHz.
• The volume control output is set to the voltage chosen to be line level in relation to 10 W output at the
power amplifier.
• The tone control is set to neutral position (0 dB amplification/attenuation).
Source Impedance
Because the Hi-Fi system will be operating with several different input sources, the input source impedance will
deviate. It is required that the rated source impedance is 2.2 kΩ (see table 2.2). When the system is specified
to be in rated condition, the rated source impedance is set to 2.2 kΩ.
Input Impedance
The input impedance is measured with an audio analyser card, which produces a frequency sweep from 20 Hz
to 20 kHz. The measured real impedance value should not fall below 22 kΩ in order to prevent an early signal
loss.
Output Impedance
The output source impedance is measured with an audio analyser card, which produces a frequency sweep from
20 Hz to 20 kHz. The measured real impedance value should not be measured above 0.8 Ω in order to prevent
a late signal loss.
Output Power
The characteristics for distortion-limited output power can be written as:
Pout =
2
Vout
Zload
(2.5)
Where Vout is the distortion limited output voltage, Zload is the rated load impedance, and Pout is the distortion
limited output power.
When measuring the output power, the first step is to bring the amplifier to rated conditions with the
appropriate load impedance and a suitable harmonic distortion measuring device connected to an output
terminal. If necessary, the source EMF is readjusted so that the maximum total harmonic distortion is produced.
The distortion limited output voltage Vout can now be measured, where after the distortion limited output power,
Pout , can be calculated with equation (2.5). In rated conditions this value should be ≥10 W.
12
2.3. Acceptance Testing
Deviation in Effective Frequency Range
In sub-clause 14.11.2 of standard IEC 60268-3 it is described, how to measure the deviation in effective
frequency range (in this case the frequency range 20 Hz to 20 kHz). The deviation describes the deviation
in decibel of the output voltage (the voltage output equalling a frequency in the range 20 Hz to 20 kHz) in
proportion to a reference output voltage at 1 kHz, Vref . To calculate the deviation, the following equation is
used:
∆V = 20 · log
Vout
[dB]
Vref
(2.6)
The deviation must not surpass the deviation of ±1.5 dB. The first thing to do is to measure the Vout and
the source EMF at the frequency of 1 kHz. Secondly, Vout values in the frequency range 20 Hz to 20 kHz is
measured. To do this, the source EMF gain must be hold at the same gain level, as for the measurement of
the reference output voltage. Also a sweep of audio frequencies 20 Hz to 20 kHz, are send into the circuit by
the source EMF. The Vout values yields all the values equalling every single frequency in the sweep of audio
frequencies. Thirdly, the deviation values in decibel is calculated, by use of equation (2.6). These deviation
values are represented as a function of the frequencies in the range 20 Hz to 20 kHz.
Total Harmonic Distortion
When measuring total harmonic distortion (THD) at effective frequency range 20 Hz to 20 kHz, the first
step is to bring the system to rated conditions, whereupon the reference output voltage, Vout , is measured.
Subsequently, the system is subjected to a sweep of frequencies ranging from 20 Hz to 20 kHz. The THD is
calculated with the use of the following equation:
0
V
T HDtot = out · 100 %
Vout
(2.7)
0
Where Vout is the measured output voltage and T HDtot is the total harmonic distortion. During the length of
the sweep, the THD must not exceed 0.7 %.
Tone Control
The tone control is measured separately for bass and treble control. Firstly, the treble is measured at maximum
amplification. From this setting, the amplification must not exceed 13 dB or drop below 10 dB at frequencies
between 8.9 kHz to 20 kHz. The gain in the non-equalized frequencies at 500 Hz to 2000 Hz must not exceed
3 dB.
The same measurements are done for full attenuation. From this setting, the attenuation must not drop below
−10 dB or exceed −13 dB at frequencies between 8.9 kHz to 20 kHz. The gain in the non-equalized frequencies
at 500 Hz to 2000 Hz must not drop below −3 dB.
The bass control are measured at maximum amplification. From this setting, the amplification must not
exceed 13 dB or drop below 10 dB at frequencies between 20 Hz to 112 kHz. The gain in the non-equalized
frequencies at 500 Hz to 2000 Hz must not exceed 3 dB.
The same measurements are done for full attenuation. From this setting, the attenuation must not drop below
−10 dB or exceed −13 dB at frequencies between 20 Hz to 112 Hz. The gain in the non-equalized frequencies
at 500 Hz to 2000 Hz must not drop below −3 dB.
13
2. S PECIFICATIONS
Amplification /dB
-20
13
10
c
de
/
dB
3
0
3
Frequency /Hz
111.93
500
2000
8933.67
-10
-13
F IGURE 2.3: Tone control characteristics
Volume Control
The volume control is set to its rated condition. From this setting, the volume control must be able to attenuate
the output to 46 dB at every frequency from 20 Hz to 20 kHz.
14
3. Design
Within the introduction and specification chapters it has been determined, which issues that lies with the
problem statement (section 1.2) and which standards should be met in order to solve the problem statement
with the use of the specifications (section 2.2). With this information it is possible to implement a design.
In this following chapter the process of designing the modules for the Hi-Fi amplifier will take place. Each
section includes circuits which meet the specifications and interface requirements for each module. A figure
with the interfaces included can be seen below.
Gtone
THDvol
Gvol
Volume control
Vline
EMF
Vline
8.9 k
500 2k
+14 dB
- 32 dB
Power
Amplifier
Pout
f /Hz
Zload
-13 dB
Zvol, out
Ztone, in
Ztone, out
Zamp, in
Zamp, out
Design values
Specifcation values
Zsignal = 2.2 k
Zvol, in
22 k
Zamp, out 0.8
Zload
=8
THDamp
13 dB
112
Zvol, in
Gamp
Tone control
Av /dB
Zsignal
THDtone
EMF = 0.2 V to 2.8 V
Pout 10 W
Zvol, out
Ztone, in
Ztone, out
Zamp, in
10
1k
10
1k
Vline = 1 V
Gvol ± 0.5 dB
Gamp ± 0.5 dB
Gtone ± 0.5 dB
THDvol
THDtone
THDamp
0.1 %
0.1 %
0.5 %
F IGURE 3.1: The Hi-Fi amplifier divided into the chosen modules with both design and interface values
illustrated.
The specification values seen on figure 3.1 are from the specifications table, while the design values are
chosen in order to ease the design process of the individual modules. The input impedances have been
determined to be much greater than output impedances in order to prevent a voltage dividing of the line level
voltage, Vline . The line level has been set to 1 V in order to appoint a relation between the line level and output
power of 10 W. Furthermore, this value will be of use to produce a simple design for the volume control
module.
The maximum gain deviation in the effective frequency range is set to ±1.5 dB throughout the Hi-Fi
amplifier. In order to make sure that this specification is met the value ±1.5 dB is distributed between the
blocks. Each block must meet a maximum value of ±0.5 dB. The design parameters of the blocks are Gvol for
volume control, Gtone for tone control and Gamp for the power amplifier.
The total harmonic distortion values for the Hi-Fi amplifier are distributed between the blocks. The volume
control THD, THDvol , and tone control THD, THDtone , are chosen to 0.1 % each, while the value for the
amplifier, THDamp , is 0.5 %. These values are chosen based on the expected ratio of THD by the blocks.
15
3. D ESIGN
3.1
Volume Control
The volume control module is the first module within the Hi-Fi amplifier, and its function is to attenuate/amplify
a given signal in order to control the output audio level at the speaker(s). The specifications for the volume
control are listed in the following table.
Description
Source
Minimum value
Input impedance
Section 2.2.
22
Output impedance
Figure 3.1.
Gain range
Figure 3.1.
Gain deviation
Figure 3.1.
Input voltage
Section 2.2.
Output voltage
Figure 3.1.
THD
Figure 3.1.
Rated value
Maximum value
Unit
kΩ
≤ -32
0.2
10
Ω
≥ 14
dB
±0.5
dB
2.8
VRMS
1
VRMS
0.1
%
TABLE 3.1: Specifications for the volume control.
A voltage attenuation can be obtained with a voltage divider, while the amplification can be done with an
operational amplifier (op-amp). This has lead to the design of the circuit seen on figure 3.2.
3.1.1
Volume Control Design
ZG
2200 Vcc+
VG
V+
Op-Amp
Rpot
Vout
Vcc-
R2
R1
F IGURE 3.2: Design of volume control with the use of an OPAMP and a voltage divider.
Input Impedance for the Volume Control
As the volume control is the first module within the Hi-Fi amplifier, the input impedance Zin , has to be 2.2 kΩ
to prevent loss of signal and therefore the Rpot is chosen to be 100 kΩ. The input impedance, for the volume
control circuit can be found with a parallel connection of Rpot and the op-amp input impedance, ZinA . However,
generally ZinA Rpot , so that:
Zin = Rpot ||ZinA ≈ Rpot ≈ 100 kΩ
(3.1)
It should be noted that ZinA is complex, where as Rpot is real. However, it is the modulus of the input impedance
that is of interest. The input capacitance of the op-amp, which defines the imaginary part, is low, so that it
barely affects the modulus, which therefore is approximated to be the real part in this circuit. In the case of
Rpot → 0, the input impedance will continue to be Rpot due to the rest of the circuit being grounded.
16
3.1. Volume Control
Voltage Control
In order to control the output voltage to be the chosen line level, the minimum input voltage of 0.2 V is used,
denoted as V+ . This is obtained with a voltage divider of the generator impedance ZG and the input impedance,
which has been defined to Rpot .
V+ =
Rpot
·VG
Rpot + RG
(3.2)
Where VG is the signal voltage. With this, any value of the signal generator can be reduced to 0.2 V.
Now when any value of the signal can be attenuated to 0.2 V, the desired amplification to reach the desired
line level can be found with a simple transfer function for the volume control circuit.
A=
Vout
R2
' 1+
= 5.5
V+
R1
(3.3)
The amplification value is set to 5.5 instead of 5 in order to regulate for any voltage loss in the voltage divider.
This way the specified value of 1 V output voltage is ensured. The corresponding value of amplification in dB
can be found as:
20 · log10 (5.5) ≈ 15 dB
(3.4)
From this, the size of R2 and R1 can be chosen and calculated. A value for R1 is chosen to 1 kΩ, so that R2 can
be calculated. This is done with the following equation:
R2 = (A − 1) · R1 = (5.5 − 1) · 1 kΩ = 4.5 kΩ
(3.5)
Op-Amp Values
Apart from the component values found in the volume control circuit, there is yet the op-amp and its relevant
values to determine. The values deemed relevant to meet the specifications is the op-amp input impedance,
ZinA , output impedance, ZoutA , slew rate, SR, and the small-signal differential voltage amplification, Ao . The
selected op-amp is the TLE 2071, due to its high slew rate and small-signal differential voltage amplification
throughout the effective frequency range. The values can be seen in table 3.2 and in the data sheet for the TLE
2071 [12].
Parameter
Minimum value
Typical value
Maximum value
Unit
ZinA
1012
Ω
ZoutA
80
Ω
35
V
µs
SR
23
Ao
50 @ 20 Hz
110 @ 20 kHz
dB
TABLE 3.2: Shows the relevant values for the TLE 2071, from the data sheet [12].
Output Impedance for the Volume Control
The output impedance, Zout , which should be ≤ 10 Ω is obtained with a feedback consisting of β , Ao , and ZoutA .
Zout =
ZoutA
1 + β · Ao
(3.6)
Where the value β is defined by the non-inverting resistors R1 and R2 .
β=
R1
2
=
R1 + R2 11
(3.7)
17
3. D ESIGN
It should be noted that output impedance of the op-amp is complex and the small-signal differential voltage
amplification, Ao , is calculated at the lowest specified effective frequency range value (20 Hz) and the highest
(20 kHz). The small-signal differential voltage amplification is read off table 3.2. Both the maximum and the
minimum value of the small-signal differential voltage amplification is found with equation (3.8).
110
Ao = 10 20 = 316230 ∠ − 15◦
Ao = 10
50
20
= 316.23 ∠ − 90◦
@ 20 Hz
(3.8)
@ 20 kHz
Equation (3.6) is used with the two different Ao values to obtain the highest and the lowest possible output
impedance for the volume control circuit.
|Zout | = 1.39 · 10−3 Ω
|Zout | = 1.37 Ω
@ 20 Hz
(3.9)
@ 20 kHz
Beside the specifications there is another relevant factor to consider when working with an op-amp: The
slew rate is defined as a multiplication of the angular frequency, ω, and the peak amplitude of the voltage V .
Slew rate defines how fast the op-amp can change the output voltage in time. The slew rate required for the
volume control circuit can be calculated with the following equation:
√
SR = ω ·V = 2 · π · (20 · 103 Hz) · ( 2 · 1 V) = 0.178 V/µs
(3.10)
V
In the data sheet for the TLE 2071 the slew rate is defined to have a minimal value of 23 µs
which is much more
than required [12].
It has been determined that simulations for the volume control circuit is out of relevance, due to the
simplicity of the circuit behaviour.
3.1.2
Test Results
Within this subsection the measured data for the volume control is listed. From table 3.3, the data required to
determine, whether the volume control meets the specifications or not is listed. The test procedure and all the
test results can be found in appendix C.1.
Description
Minimum value
Input impedance
Gain deviation
THD
Measured Value
Unit
60
kΩ
10
0.18
Ω
≥ 14
-78 to 14
dB
±0.5
±0.036
dB
0.1
0.008
%
22
Output impedance
Gain range
Maximum value
≤ -32
TABLE 3.3: Measured data for for the volume control.
From this, it is concluded that the volume control meets the interface specifications seen in figure 3.1.
3.2
Tone Control
To design the tone control one can look at existing circuits, that have the ability to attenuate/amplify low and
high frequencies, and weigh up the pros and cons. The specifications for the tone control is listed in the
following table.
18
3.2. Tone Control
Description
Source
Minimum value
Input impedance
Figure 3.1.
1
Output impedance
Figure 3.1.
Gain range for bass
(20 Hz to 112 Hz)
Section 2.2.
Gain range for treble
(8.9 kHz to 20 kHz)
Section 2.2.
Gain deviation in
nonequalized frequencies
(500 Hz to 2 kHz)
THD
Maximum value
Unit
kΩ
10
Ω
±10
±13
dB
±10
±13
dB
Section 2.2.
±3
dB
Figure 3.1.
0.1
%
TABLE 3.4: Specifications for the tone control.
Baxandall Tone Control
In the control of high and low frequency sound waves, the Baxandall tone control circuit is of significance. The
Baxandall tone control circuit has the ability of attenuation or amplification by adjusting two potentiometers,
as these two potentiometers adjust a low pass and a high pass filter, respectively. When the Baxandall tone
control is passive, it will attenuate all frequencies, while the active Baxandall amplifies specified frequencies.
An amplifier is therefore necessary. [13]
C3
R2
RP
R3
Bass
Increase
Decrease
Vcc+
Vin
Vout
Increase
Decrease
Vcc-
Treble
C1
R1
C2
F IGURE 3.3: Diagram of an active Baxandall tone control circuit with an operational amplifier. The figure is
made with inspiration from Carter [13].
Alternative Tone Control Circuit
Instead of an active Baxandall circuit, where the treble and bass controls make use of one single operational
amplifier, the two controls can be separated with an amplifier each. While it may be attractive to keep the
amount of used components down, this alternative circuit is a more simple solution.
19
3. D ESIGN
Z1
Vin
R1
Z2
C1
C2
RP
R2
Z2
Z1
Vout
Vin
R3 Increase Decrease R4
R1
RP
Increase
C1
R2
Decrease
C2
Vcc-
VccVout
Vcc+
Vcc+
(a) Treble control
(b) Bass control
F IGURE 3.4: Diagrams of the alternative tone control circuits where treble and bass are separated in contrast
to the unified Baxandall circuit.
It is clear that these circuits are easier to grasp, when component value calculations must be made.
3.2.1
Finding Component Relationships and Values
The alternative to the Baxandall circuit is preferred because of its simplicity, and therefore these circuits are
used to produce the design for the tone control.
Treble Control
In the alternative treble circuit, seen in figure 3.4(a), the relationship between the input voltage, Vin , and the
output voltage, Vout , is given as:
Vout = −
Z2
Vin
Z1
(3.11)
Where Z2 are the total impedance of RP2 , C2 , R2 and R4 , as seen on 3.4(a), and Z1 is the total impedance of
RP1 , C1 , R1 and R3 , respectively. The parts of the potentiometers is defined as:
RP
RP1
RP2
F IGURE 3.5: Illustration of the denotation of the potentiometer.
By use of this, the transfer function can be expressed:
HT ( jω) =
Z2
Vout
=−
Vin
Z1
(3.12)
As can be seen from the circuit diagram, the two impedances can be written as:
Z1 = R1 +
1
+ RP1
jωC1
Z2 = RP2 +
20
1
+ R2
jωC2
k R3 =
k R4 =
1
jωC1 + RP1 )R3
1
R1 + jωC
+ RP1 + R3
1
1
(RP2 + jωC
+ R2 )R4
2
1
RP2 + jωC2 + R2 + R4
(R1 +
(3.13)
3.2. Tone Control
With the impedances expressed in equations (3.13), the transfer function can be rewritten:
1
(RP2 + jωC
+R2 )R4
2
HT ( jω) = −
1
RP2 + jωC
+R2 +R4
2
1
(R1 + jωC
+RP1 )R3
1
R4 (R2 + RP2 +
=−
R3 (R1 + RP1 +
1
+RP1 +R3
R1 + jωC
1
1
jωC2 )(R1 + R3 + RP1 + jωC1 )
1
1
jωC1 )(R2 + R4 + RP2 + jωC2 )
(3.14)
1
From this it can be seen that for the frequency independent amplification to be unity (0 dB), the ratio between
R4 and R3 must also be unity, so that R3 = R4 = Rb . Now, the limit of this transfer function for jω → 0 is unity,
as wanted for a treble control. The transfer function can now be simplified to:
HT ( jω) = −
(R2 + RP2 +
(R1 + RP1 +
1
1
jωC2 )(R1 + Rb + RP1 + jωC1 )
1
1
jωC1 )(R2 + Rb + RP2 + jωC2 )
(3.15)
The frequency dependent amplification is meant to be unity, when the potentiometer is set at a value that cause
RP1 to be equal to RP2 . This means that C1 = C2 = C and R1 = R2 = Ra ; thereby the transfer function can be
further simplified to:
HT ( jω) = −
(Ra + RP2 +
(Ra + RP1 +
1
1
jωC )(Ra + Rb + RP1 + jωC )
1
1
jωC )(Ra + Rb + RP2 + jωC )
(3.16)
From the transfer function, the zeros and poles can be seen:
1
(Ra + Rb + RP1 )C
1
P1 = −
(Ra + Rb + RP2 )C
1
(Ra + RP2 )C
1
P2 = −
(Ra + RP1 )C
N1 = −
N2 = −
(3.17)
In the alternative treble circuit seen on figure 3.4(a), the two Rb resistors are not necessary for the circuit to
work in theory. In practice, however, the circuit will not work without these resistors, because the capacitors
make a DC decoupling between the input and the op-amp, which need an input current to work. To make sure
the resistor Rb does not interfere with the filter, it is chosen to be much bigger than Ra (Rb Ra ). This means
that the pole and zero N1 and P1 are almost equal (N1 ≈ P1 ), and thereby will not have any influence on the
amplification or attenuation. The figure 3.6 illustrates that the pole and zero of significance are N2 and P2 .
Amplification /dB
P2
13
10
3
0
N2
0
P1 N1
2000
8933 Frequencies /Hz
F IGURE 3.6: Illustration of the position of poles and zeros with full amplification.
21
3. D ESIGN
With focus on amplification, the potentiometer is placed at full amplification, so that RP1 is zero at the pole
P2 and RP2 is the full value of RP at the pole N2 . For full amplification N2 must be placed at −2π · 2000 Hz and
P2 at −2π · 8933 Hz. This gives the following relationships:
−2 · π · 2000 Hz = −
1
(Ra + RP )C
− 2 · π · 8933 Hz = −
1
Ra ·C
(3.18)
Which can be rewritten as:
Ra + RP =
1
2 · π · 2000 Hz ·C
Ra =
1
2 · π · 8933 Hz ·C
(3.19)
To find a relationship between the resistor value Rb and one of the other components Ra , RP or C, the transfer
function for jω → ∞ is used:
lim HT ( jω) = −
jω→∞
(Ra + RP2 )(Ra + Rb + RP1 )
(Ra + RP1 )(Ra + Rb + RP2 )
(3.20)
For full amplification (4.4668 or 13 dB), RP2 is the value of RP and RP1 = 0. The transfer function can be
simplified to equation 3.21:
A( jω) = |HT ( jω)| =
(Ra + RP )(Ra + Rb )
= 4.4668
(Ra )(Ra + Rb + RP )
(3.21)
By replacing Ra and RP with their relationship to C from equation (3.19), the transfer function gives a
relationship between C and Rb :
A( jω) = |HT ( jω)| =
1
1
( C·2π·2000
Hz )( 2π·8933 Hz·C + Rb )
1
1
( 2π·8933
Hz·C )( C·2π·2000 Hz + Rb )
= 4.4668
⇒ Rb =
0.9195 Hz−1
C
(3.22)
Component Values for Treble
With the found component relationships, the component values for treble can be calculated. In the treble control,
the capacitor value has great influence on the amplification and attenuation. Therefore the other components
RP , Rb and Ra are calculated through the relationship to the capacitor value. The capacitor value C is chosen to
be 15 nF, because its an available component. As seen in table 3.5, the component values, which are calculated
on the basis of C, is shown along with the nearest available values. Notice that the calculated value of Rb differ
highly from the available chosen value, but this is nearly without influence. The value of potentiometers are
not to be trusted because of a big value tolerance. Therefore the table also shows a measured value for the
potentiometer.
Values calculated on the basis of C
Nearest available value
C
15 nF
15 nF
Rp
4.118 kΩ
4.7 kΩ
Ra
1.188 kΩ
1.21 kΩ
Rb
59.847 MΩ
10 MΩ
TABLE 3.5
22
Measured value
4.36 kΩ
3.2. Tone Control
Bass Control
The basic relationship (eq. (3.11)) between Vout and Vin , which is valid for the inverting amplifier in the treble
control, is valid for the bass control circuit as well. Therefore the transfer function can be written similarly:
HB ( jω) =
Vout
Z2
=−
Vin
Z1
(3.23)
Now the impedances must be given by (seen from fig. 3.4(b)):
Z1 = RP1 k
1
iωC1
Z2 = RP2 k
1
iωC2
+ R1 =
+ R2 =
1
RP1 iωC
1
1
RP1 + iωC
1
1
RP2 iωC
2
1
RP2 + iωC
2
+ R1
(3.24)
+ R2
These expressions are inserted in the transfer function:
1
jωC2
1
RP2 + jωC
2
1
RP1 jωC
1
1
RP1 + jωC
1
RP2
HB ( jω) = −
+ R2
=−
+ R1
(1 + jωC1 RP1 )(RP2 + R2 + jωR2C2 RP2 )
(1 + jωC2 RP2 )(RP1 + R1 + jωR1C1 RP1 )
(3.25)
When jω → 0, then the system amplification should be 13 dB when the potentiometer is at the maximum value,
as this is the amplification wanted for the lowest frequencies in the effective frequency range. It is assumed that
the frequencies at 20 Hz behave approximately as for signals with ω → 0. The limit of the transfer function for
jω → 0 is:
lim A( jω) = lim HB ( jω) =
jω→0
jω→0
R2 + RP2
R1 + RP1
(3.26)
From this it can be seen, that R1 = R2 , or else the amplification will differ from zero when RP1 = RP2 . The
value of 13 dB amplification corresponds to a ratio of ≈ 4.47 between output and input, therefore:
A( jω) = |HT ( jω)| =
R + RP
= 4.47 ⇔ Rp = 3.47R
R
(3.27)
Where R = R1 = R2 .
From the transfer function expressed in equation (3.25) the poles and zeroes can be seen:
1
C1 RP1
1
P1 = −
C2 RP2
N1 = −
RP2 + R
RC2 RP2
RP1 + R
P2 = −
RC1 RP1
N2 = −
(3.28)
At full amplification, N1 and P2 are equal and zero, which means that they have no influence on the
amplification. The zero and pole of significance for full amplification are therefore P1 and N2 , where N2 gives
the highest value (highest frequency). The second zero, N2 , must therefore be placed at f = 500 Hz:
3.47R + R
RP2 + R
= 2π · 500 Hz ⇔
= 2π · 500 Hz
RC · RP
RC · 3.47R
⇒ R = 0.000 41 C−1
(3.29)
Where C is the capacitance of both C1 and C2 , as these should be equal, so that the amplification is unity for
RP1 = RP2 .
The figure 3.7 illustrates that the pole and zero of significance are P1 and N2 for full amplification.
23
3. D ESIGN
Amplification /dB
13
10
3
0
P2
N2
112
0
500
Frequencies /Hz
F IGURE 3.7: Illustration of the position of poles and zeros with full amplification.
Component Values for Bass
With the found component relationships, the component values for bass can be calculated. In the bass control,
the potentiometer value has great influence on the amplification and attenuation, because of a low quantity of
available component values. The other components R and C are therefore calculated through the relationship
to the potentiometer value. The potentiometer value Rp is chosen to be 4.7 kΩ, as it is an available component.
Table 3.6 shows the component values which are calculated based on Rp along with their nearest available
values. The value of potentiometers has large value tolerances, therefore the table also shows a measured value
for the potentiometer.
Values calculated on the basis of C
Nearest available value
C
302.702 nF
330 nF
Rp
4.7 kΩ
4.7 kΩ
R
1.354 k Ω
1.33 k Ω
Measured value
4.36 kΩ
TABLE 3.6
Op-Amp Values
The op-amp which is chosen for the tone control circuit is a TLE 2072, which is similar to the TLE 2071.
However, the TLE 2072 has two built in TLE 2071 op-amps. The relevant values are the as in the volume
control design. These can be seen in table 3.2 and in the data sheet for the TLE 2072 [12].
24
3.2. Tone Control
3.2.2
Input Impedance and Output Impedance of the Tone Control
Treble Control
The input impedance for the treble circuit Z1 can be found with equation (3.13). However, the lowest impedance
possible required to be ≥ 1 kΩ, Zin is equal to Z1 with the potentiometer RP1 → 0, because any higher value
increases Zin . Furthermore ω is set to the highest possible frequency, which is 2π · 20 kHz.
|Zin | =
Ra +
1
jωC1
k Rb = 1.321 kΩ
(3.30)
The output impedance is calculated similar to the volume control output impedance:
|Zout | =
ZoutA
1 + β · Ao
(3.31)
The highest allowed output impedance is Zout ≤ 10 Ω can be found when Ao is at the lowest value of
amplification as seen in equation (3.27). The lowest value of the amplification Ao = 316 is found at the highest
frequency 20 kHz, in equation (3.8).
|Zout | = 1.116 Ω
(3.32)
Bass Control
The input impedance for the bass module can be found with equation (3.24). In order to make sure that this
impedance never falls below 1 kΩ, RP1 is decreased to its minimal value RP1 → 0, which short-circuits the
capacitor. This leaves the R1 as the input impedance:
Zin = R1 = 1.33 kΩ
(3.33)
Calculations for the output impedance in bass control is not of relevance as Ao will only increase when going
down in frequencies. The impedance value for bass will therefore always be below the impedance value for
treble, which can be seen in equation (3.32).
3.2.3
Simulations and Measurement Results
With the calculated values from section 3.2.1, the tone control circuit can be simulated with LT-Spice. The
purpose with the simulations is to give an idea about what happens with the amplification or attenuation, when
the potentiometer is being adjusted to different values. Notice that phase shifting through the circuit is not of
relevance because the sound signal is the same before and after the circuit, only shifted, which a listener will
not notice. It could be of interest to show if there are any differences in a simulated and calculated plot of the
amplification dependent on frequencies. Yet the calculations and simulations of the amplification dependent on
frequencies for both bass and treble are exactly the same. Based on that, only the calculations are shown. The
calculations are made with the previously deduced equations in MatLab. Furthermore the measured data for
the tone control in relation to the simulations is plotted for both bass and treble.
Treble Control
In figure 3.8, the amplification and attenuation with the treble control can be seen. Between the limits with full
attenuation and full amplification, the treble control deviates in amplitude as expected. According to the figure
below it fulfils the specifications given in section 2.2.
25
3. D ESIGN
Measurement and calculation of the treble control frequency respons
15
Calculated max attenuation
Calculated RP1=3kΩ and RP2=1.36kΩ
Calculated R =2.18kΩ and R =2.18kΩ
P1
10
P2
Calculated R =1.36kΩ and R =3kΩ
P1
5
Amplification / dB
P2
Calculated max amplification
Measured max attenuation
Measured RP1=3kΩ and RP2=1.36kΩ
Measured RP1=2.18kΩ and RP2=2.18kΩ
Measured RP1=1.36kΩ and RP2=3kΩ
0
Measured max amplification
−5
−10
−15
20
100
1000
Frequency / Hz
10000
F IGURE 3.8: The frequency response of the amplification on a logarithmic scale with a calculated and a
measured data set, where the amplitude varies in the higher frequencies. The value of the amplitude varies
from ±3 dB to ±12.5 dB in the frequencies from 2 kHz to 20 kHz at the maximum values in both the measured
and the calculated data sets.
Bass Control
At figure 3.9, the amplification and attenuation of the bass control can be seen. Between the limits with
full attenuation and full amplification, the bass control deviates in amplitude in a way which is not expected.
According to the figure below it seems to deviate from the specifications given in section 2.2. Notice that, when
RP1 = 1.36 kΩ and RP2 = 3 kΩ, the amplification induces a attenuation at the frequencies 300 Hz to 3000 Hz.
The same is valid for the attenuation (induce an amplification), when RP2 = 1.36 kΩ and RP1 = 3 kΩ. The
reason for this behaviour is that the pole and zero that has no influence during full amplification or attenuation
as described in section 3.2.1.
Measurement and calculation of the bass control frequency respons
15
Calculated max attenuation
Calculated RP1=3kΩ and RP2=1.36kΩ
Calculated RP1=2.18kΩ and RP2=2.18kΩ
10
Calculated RP1=1.36kΩ and RP2=3kΩ
Calculated max amplification
Measured max attenuation
Measured RP1=3kΩ and RP2=1.36kΩ
Amplification / dB
5
Measured RP1=2.18kΩ and RP2=2.18kΩ
Measured RP1=1.36kΩ and RP2=3kΩ
0
Measured max amplification
−5
−10
−15
20
100
1.000
Frequency / Hz
10.000
F IGURE 3.9: The frequency response of the amplification on a logarithmic scale with a calculated and a
measured data set, where the amplitude varies in the lower frequencies. The value of the amplitude in the
measured varies from below ±12.5 dB to ±3 dB in the frequencies from 20 Hz to 500 Hz at the maximum
values in the measured data, which can be found in appendix C.2.
26
3.3. Power Amplifier
Compared to the Specifications
From table 3.7 it is determined whether the tone control meets the specifications or not. The test procedure and
all the test results can be found in appendix C.2.
Description
Minimum value
Input impedance
Maximum value
Measured Value
Unit
> 1000
kΩ
10
2.8
Ω
1
Output impedance
Gain range for bass
(20Hz to 112Hz)
±10
±13
±9.5 to ±12.5
dB
Gain range for treble
(8.9kHz to 20kHz)
±10
±13
±10.7 to ±12.5
dB
Gain deviation in
nonequalized frequencies
for bass
(500 Hz to 2 kHz)
±3
+2.6 and -2.2
dB
Gain deviation in
nonequalized frequencies
for treble
(500 Hz to 2 kHz)
±3
±3
dB
THD
0.1
0.275
%
TABLE 3.7: Measured data for for the tone control.
It is concluded that the tone control meets the interface specifications seen in figure 3.1, but not all of the
specifications in section 2.2.
3.3
Power Amplifier
In order to reach a high output power level and a relatively clean output signal, a compromise between efficiency
and signal distortion is necessary. As explained in section 1.1.3, class A amplifiers deliver an output with
very little distortion, but is very energy inefficient. A class B amplifier is much more efficient, but its output
signal suffers greatly from output distortion. The class AB amplifier is the scope of this report, and it a good
compromise between the A and B class amplifiers. By assembling a class B push-pull amplifier and then
attempting to cancel the cross-over distortion with a small quiescent bias, a class AB amplifier with good
efficiency and clean output signal should be achievable. The specifications for the power amplifier are listed in
the following table 3.8 (from table 2.2 and figure 3.1):
Description
Source
Minimum value
Maximum value
Unit
0.8
Ω
Output source impedance
Section 2.2
Input impedance
Figure 3.1.
1
kΩ
Output power
Section 2.2
10
W
Gain deviation
Figure 3.1.
±0.5
dB
THD
Figure 3.1.
0.5
%
TABLE 3.8: Specifications for the power amplifier module.
27
3. D ESIGN
The line level at which the output power should reach the minimum 10 W is 1 VRMS set by the volume
control, as chosen previously in this chapter.
3.3.1
Topology and Strategy
One of the most commonly used amplifier architectures (and the one which will be used for this design) is the
LIN three stage amplifier architecture [7]. An illustration of the architecture can be seen in figure 3.10.
Signal
Input Stage
Voltage
Amplification
Stage
Unity
Gain
Stage
Output
Feedback
F IGURE 3.10: Basic illustration of the three stage amplifier topology with feedback.
The input stage typically consists of a differential amplifier, which will serve to ease the implementation of
feedback and reduce DC-offset. The voltage amplification stage (VAS) will have to ensure the necessary output
voltage level, as the output stage is a unity voltage gain stage. As the output stage will amplify current and not
voltage, the VAS is usually required to have high voltage gain. The output stage has a high input impedance and
a low output impedance, which allows the power amplifier to work with low impedance loads such as speakers.
The design begins at the output stage of the power amplifier, where requirements for the transistors will
be determined with regards to large signals. From these large signal values, the circuit will be dimensioned
and fitting transistors for the output stage will be chosen and thermal relations are taken into account. Once
the transistors have been chosen, the bias can be designed. Subsequently, the VAS will be designed to deliver
the necessary signal to allow the output stage to reach the requirement of minimum 10 W through the speaker.
Subsequently, the differential input stage along with the feedback system is designed to make sure the output
distortion is reduced, so that the output signal meets the performance requirements. Following this, small signal
analysis is used to determine gain as well as input and output impedances. The stability of the system will then
be examined and overload protection is implemented. Finally, the calculated and simulated values will be
compared to measurements.
Input Stage
Voltage Amplifier Stage
Output Stage
+Vcc
QD1
QNPN1
QD2
QNPN2
QVAS
Input
QD3
QD4
Output
QPNP2
ID
RB2
RB1
QPNP1
IBIAS
-Vcc
Feedback Network ( )
F IGURE 3.11: Diagram of simplified power amplifier with a differential amplifier in the input stage, voltage
amplifier stage (VAS) and a simple biased B class output stage, along with a feedback β system.
28
3.3. Power Amplifier
3.3.2
Output Stage
The basic output stage of the class AB power amplifier can be seen on figure 3.11.
The calculations in the following equations are done without taking cross-over distortion into account,
approximating the signal output to be a sine wave. Furthermore, the relations and equations used are for class
B output stages, as for large signals the class AB efficiency is very similar to a class B, as the bias will have low
influence on the efficiency. Given that the load is set to 8 Ω and that the minimum power dissipated through the
load is 10 W, the minimum voltage required through the load resistance can be calculated as follows [5]:
PL =
Vbo2
2 · RL
(3.34)
Where PL is the power dissipated in the load resistance, Vbo is the peak output voltage and RL is the load
resistance. Inserting the known values:
Vbomin =
p
√
2 · PL · RL = 2 · 10 W · 8 Ω = 12.649 V ≈ 12.65 V
(3.35)
Where Vbomin is the minimum peak voltage necessary to generate 10 W across the load resistance. To be certain,
an extra 0.5 V is added to the peak voltage to make sure that any small deviation in low voltages, will not cause
the power dissipated in the load resistance to go below 10 W. This means that the peak voltage and output
power has changed for further calculations:
Vbomin ≡ 0.5 V + 12.65 V = 13.15 V
PL =
(13.15 V)2
= 10.806 W ≈ 11 W
2·8Ω
(3.36)
The minimum current through the load resistance can be calculated by the following formula [5]:
13.15 V
Vbo
Ibomin = min =
= 1.644 A ≈ 1.65 A
RL
8Ω
(3.37)
Where Ibomin is the minimum peak current required through the load resistance to generate the necessary power.
To determine the supply voltage, a series of considerations are to be made. These considerations are
dependent on choices of components and design and will therefore be discussed later (section 3.3.4); until
then a supply voltage of 18.5 V is deemed adequate.
To make sure the chosen transistors can withstand the power, it will be necessary to calculate the highest
possible power dissipated in them, so worst case scenario calculations are made.
The power of the power supply is [5]:
Pcc =
2
π
·
Vbo
2 13.15 V
·Vcc = ·
· 18.5 V = 19.3592 W ≈ 19.4 W
RL
π
8Ω
(3.38)
The average power dissipated in the output stage, PD , is then [5]:
PD = Pcc − PL
(3.39)
Where PL is the power dissipated in the load. Substitution of equations (3.38) and (3.34) into equation (3.39)
yields:
PD =
2 Vbo
Vb 2
·
·Vcc − o
π RL
2 · RL
(3.40)
29
3. D ESIGN
Differentiating this expression with regards to Vbo , and equating to zero yields the value of Vbo , for which the
output voltage creating the worst-case average power dissipation in the output stage will be [5]:
∂ PD
∂
=
∂ Vbo
∂ Vbo
Vb 2
2 Vbo
·Vcc − o
·
π RL
2 · RL
!
=0
⇒
2
Vbo = ·Vcc
π
(3.41)
This expression is then substituted into equation (3.40) which yields the following:
( π2 ·Vcc )2
2 ·V 2
2 π2 ·Vcc
·Vcc −
= 2 cc
PD,max = ·
π
RL
2 · RL
π · RL
(3.42)
This means that the worst-case average power dissipation in the output transistors is:
PDmax =
2 · (18.5 V)2
= 8.669 W ≈ 8.7 W
π2 · 8 Ω
(3.43)
In the simple AB power amplifier output stage (fig. 3.11), this power will be evenly divided between the two
transistors due to symmetry.
With such relatively high currents and power dissipation in the output stage, it will be necessary to chose
capable transistors and design short-circuit protection. Some transistors which are capable of such currents
and powers are known as power transistors; they can withstand high degrees of power dissipation, though they
usually suffer from low current gain values, which will result in high base currents, as will be obvious from
following relation [5]:
IB =
IC
β
(3.44)
Where IB is the base current and IC is the collector current. If β is small (say β < 100), the bias current could
reach values well above 100 mA, which is not preferable, as it will result in gain difficulties, bias difficulties
and even thermal difficulties in the design of components prior to the power transistors.
Transistor Coupling
As illustrated earlier in figure 3.11, the output stage of the amplifier consists of a complimentary npn- and pnptransistor. However, it is possible to reduce the amount of base current necessary by using a composition of a
driver transistor and a power transistor; such a coupling could be the Darlington transistor [5]. The coupling is
illustrated in figure 3.12.
30
3.3. Power Amplifier
Vcc+
QNPN1
QNPN2
RL
8
QPNP2
QPNP1
VccF IGURE 3.12: Two complimentary npn- and pnp-darlington pairs in an amplifier output stage.
In this coupling, a power transistor along with a so-called driver transistor is used. In figure 3.12 the driver
transistors are Q3 and Q4 whilst the power transistors are Q1 and Q2. Using a driver and a power transistor
in this way will greatly enhance the current gain, because (as mentioned in the previous subsection 3.3.2) the
current gain value of a power transistor is usually low, but with the Darlington coupling the combined current
gain is:
βTotal ' βDriver · βPower
(3.45)
However, a drawback is that the base-emitter voltage increases:
VBE = VBE1 +VBE2
(3.46)
This means that the bias voltage will have to be increased.
Another way to couple the transistors in the compound configuration is shown in figure 3.13. This coupling
is most commonly used in IC design [5], though it is not limited to IC designs. This design can also be used
in discrete design and will save the use of one pnp-transistor compared to the Darlington, and thereby one
base-emitter voltage drop. However, for the design developed in this report, the Darlington is used, due to
availability of available Darlington IC components.
31
3. D ESIGN
Vcc+
QNPN1
QNPN2
QPNP1
RL
8
QPNP2
VccF IGURE 3.13: An alternative coupling method to the Darlington called compound configuration.
To summarise, the requirements for the transistors in the push-pull output stage are the capability to deliver
peak output current of 1.65 A and peak output voltage of 13.15 V, while withstanding a total power dissipation
of approximately 8.7 W. To meet these requirements, an npn Darlington transistor, with a complementary pnp
Darlington transistor, is chosen, namely the MJ11016 (npn) and MJ11015 (pnp). These consists of a driver and
a power transistor in one IC-component in a SMD-case. From the data sheet [14] for these components, some
extreme worst case specifications are found, which will be used in the design of the output stage:
• VBE,sat ≈ 2 V (base-emitter saturation voltage).
• VCE,sat ≈ 1.2 V (collector-emitter saturation voltage).
• βDC = hFE ≈ 5 k (DC current gain).
The saturation values are estimations of the worst case from plots of the typical values, and taken at the critical
points. The current gain differs for MJ11016 and MJ11015 by about 500, though the value of 5000 is chosen
because it is the worst case and thus would be the most relevant to take into account. For these components,
the small signal current gain will begin to decrease at about 30 kHz, which is more than sufficient to meet the
specifications for the effective frequency range (no. 8 in table 2.2). From this, it is seen that biased base current
A
C
= 1.65
should be IB = βIDC
5000 ≈ 0.33 mA. Which is quite high, though achievable.
Bias design
There are several ways to deliver a quiescent bias to a transistor. A common and effective bias design in power
amplifier designs is the VBE -multiplier [5], which is seen below in figure 3.14.
32
3.3. Power Amplifier
IBIAS
NPN Darlington
+
VBB
Signal Input
RVBE1
QVBE
VBE
+
RVBE2
PNP Darlington
F IGURE 3.14: Diagram of the VBE -multiplier.
This bias design makes use of a constant current source (IBias ), a resistor (RVBE1 ) connected between
collector and base of QVBE and a resistor (RVBE2 ) connected between base and emitter. If the base current
is neglected, the current through RVBE1 and RVBE2 can be approximated to:
IR =
VBE
RVBE2
(3.47)
Where IR is the current through both RVBE1 and RVBE2 . By use of the same approximation, the voltage across
RVBE1 and RVBE2 (VBB , illustrated of figure 3.14) is:
VBB = IR · (RVBE1 + RVBE2 )
Substituting equation (3.47) into equation (3.48), following relationship is obtained:
VBE
RVBE1 RVBE2
RVBE1
VBB =
· (RVBE1 + RVBE2 ) = VBE ·
+
= VBE ·
+1
RVBE2
RVBE2 RVBE2
RVBE2
(3.48)
(3.49)
It becomes clear
that this design amplifies the base-emitter voltage, VBE (justifying the name of the design),
by a factor of RRVBE1
+ 1 and by adjusting the ratio between the resistances, it is possible to obtain a suitable
VBE2
value of VBB to accommodate the base-emitter voltage drops in the output stage.
The Darlington components require a base-emitter voltage of 2 · 2 V = 4 V to activate; this is the voltage
the VBE -multiplier should deliver, however, it is deemed necessary to make sure that the VBE -multiplier can
deliver slightly more than this voltage, as the later issue of stabilising the system might require the insertion
of additional components. Therefore, the voltage, which the VBE -multiplier should deliver, is chosen to be
adjustable. The resistance R2 is chosen to be 1 kΩ and the resistor RVBE1 is chosen to be a potentiometer. By
using equation (3.49) and expecting a VBE saturation voltage of approximately 0.7 V the relationship between
the sizes of RVBE1 and RVBE2 can be calculated:
RVBE1
RVBE1
4V
VBB = 4 V = 0.7 V
+1 ⇔
=
− 1 = 4.71
(3.50)
1 kΩ
1 kΩ
0.7 V
The value of RVBE1 should then be at least RVBE1 · 4.71 = 4.71 kΩ, though to enable adjustments the
potentiometer chosen should be slightly larger than this value. The VBE -multiplier should now be easily
adjustable during construction of the circuit and thus a final value can be concluded once the circuit has been
constructed and determined to be functional.
The constant current source can be made in the shape of a current mirror. Especially, the Wilson current
mirror [15], which can be seen in 3.15(b), because it has a reduced current ratio dependence on the current
33
3. D ESIGN
gain of the transistors compared to the basic current mirror seen in figure 3.15(a). Furthermore, the Wilson
mirror is less thermally unstable, as most of the power will be dissipated in the third transistor (Qw3 ), which is
preferable, because both Qw1 and Qw2 must conduct the same current. This demands that the two transistors
must therefore be matched, which is a requirement for both types of mirrors. The Wilson current mirror is also
favourable in the way that the output impedance is much larger than for the basic mirror and the output current
is less dependent on the resistance that is connected to the output. [5]
Vcc
Iref
Vcc
Out
Iref
Rref
Out
Rw
Qw3
Qcm1
Qcm2
Qw1
(a) Basic current mirror.
Qw2
(b) The Wilson current mirror.
F IGURE 3.15
In the Wilson mirror, a current, IRw , will pass through Rw :
IRw =
Vcc −VBE1 −VBE3
Rw
(3.51)
Where IRw is the current through Rw , VBE1 is the shared base-emitter voltage drop of Qw1 and Qw2 and VBE3 is
the base-emitter voltage drop of Qw3 . Assuming that Qw1 and Qw2 conduct the same current, the relationship
between the input current and output current is[5]:
IOut
1
'
IRw
1 + β22
(3.52)
Where IOut is the resulting current drawn from “Out” in figure 3.15(b) and β is the DC current gain of
the matched transistors. For transistors with a high value of current gain, this ratio is approximately unity,
which means that IRw1 ' IOut . The Wilson mirror will draw an extra voltage drop from the extra transistor in
comparison with the basic current mirror, but this does not outweigh the advantages which the design brings.
To prevent thermal runaway further in the Wilson mirror, emitter resistances can be added. This will,
however, also cause a voltage drop of VRe , resulting in a reduced mirrored current, so that equation (3.51)
must be revised. Making the approximation that the current through the emitter resistance and the reference
resistance, I = IRw = IRwe , then the voltage drop across the current mirror distributed as follows:
Vcc = VBE1 +VBE3 + I(Rw + Rwe )
(3.53)
Which results in an expression for the output current as IOut ' I:
IOut '
34
Vcc −VBE1 −VBE3
Rw + Rwe
(3.54)
3.3. Power Amplifier
To ensure that enough current always can be drawn from the Darlington stage, while still maintaining a constant
voltage across the VBE -multiplier, following component values are chosen: Rwe1 = Rwe2 = 200 Ω and Rw = 3 kΩ.
This results in following output current, expecting a base-emitter voltage drop of approximately 0.7 V in the
transistors:
IOut '
18.5 V − 2 · 0.7 V
≈ 5.3 mA
3 kΩ + 200 Ω
(3.55)
These values are chosen, as the current should be much greater than the current, which must be drawn from
the pnp Darlington transistor, so that the DC values for the VBE -multiplier will not change. Also, this current is
drawn through the VAS, which means that it should be large enough to allow proper amplification in the VAS
stage.
Implementing the Wilson mirror into the VBE -multiplier yields the circuit illustrated in figure 3.16.
VAS
NPN Darlington
RP
RVBE2
1k
QVBE
VBE
+
PNP Darlington
Rw
3k
Qw3
Qw1
Qw2
Rwe2
200
Rwe1
200
Vcc-
F IGURE 3.16: The VBE -multiplier with a Wilson mirror as current source.
The Wilson-mirror along with the VBE -multiplier ensures a bias current and a constant voltage so that the
output stage may function as a class AB push-pull configuration. This will serve to reduce cross-over distortion
significantly, although the bias current and constant voltage will result in a loss in efficiency.
Thermal Examination
The efficiency of the transistors used in the Darlington coupling is not ideal, resulting in power dissipated in
them. When the transistors are heated, the base-emitter saturation is decreased, making thermal runaway a
possibility. For that reason it is necessary to make precautions for this phenomenon.
To prevent thermal runaway, two approaches are used: Attaching and dimensioning a heat sink to the
transistors and implementing emitter resistors that are placed in extension of the power transistors. First of
all, the output stage must be examined which leads to the dimension of the heat sink. In the next section, the Re
is examined.
35
3. D ESIGN
From equation (3.43) it is seen that maximum power dissipated in the transistors PDmax , is approximately
8.7 W in both Darlingtons.
If the provided power, PQ , to the power transistors is larger than PDmax , it will induce thermal runaway.
Therefore the provided power must be lower or equal to PDmax (PQ ≤ PDmax ).
A way to express the power PDmax thermally is by following equation [5]:
ΘJA =
◦C
TJmax − TA 200C ◦ − 35C ◦
=
= 37.932
8.7W
PDmax
W
( 2 )
(3.56)
Where ΘJA is the total thermal resistance from the circuit in the transistor to the ambient air. TJmax is the
maximum temperature, the transistor can handle, which is given from the data sheet [14]. TA is the surrounding
temperature(worst case). The components of ΘJA are ΘJC , ΘCS and ΘSA , where ΘJC is the thermal resistance
from the inner circuit to the case, the value ΘCS is the thermal resistance of the isolation between the case and
the heat sink, and the value ΘSA is the thermal resistance from the heat sink to the ambient air. The value ΘJC is
◦
given from the data sheet [14] and is 0.875 WC . The value ΘCS is given from [16], where the chosen isolation is
◦
sil pads and thermal paste with a thermal resistance of 1 WC . The value ΘSA is the only one that is unknown and
also the one of interest because it is required to dimension the heat sink. From equation (3.57), the maximum
value for ΘSA is therefore found:
ΘJA = ΘJC + ΘCS + ΘSA ⇔ ΘSA = ΘJA − ΘJC − ΘCS = 37, 932
◦C
W
−1
◦C
W
− 0.875
◦
◦C
W
= 36.057
◦C
W
(3.57)
◦
C
C
Since there are two transistors, the maximum value for ΘSA must be 36.1
2 W ≈ 18 W . This means that the
◦C
heat sink must have a thermal resistance value below 18 W to make sure that PQ is below PDmax .
It is decided, that the heat sink should not be heated further than a temperature of 65 °C more than the
surrounding environment. From equation (3.58) a new value for ΘSA is calculated, which the heat sink thermal
resistance value must be below.
ΘSA =
◦C
65°
=
7.472
8.7
W
2 W
(3.58)
◦
The chosen heat sink is of the type SK 402, which jas a maximum thermal resistance value of 3.4 WC at the
length of 25 mm [17]. This means that the heat sink SK 402 easily fulfil the given requirements.
Emitter Resistance
In order to keep the circuit thermally stable, a maximum value for the emitter resistor is calculated for each of
the two Darlington couples following equation[16]:
Re ≥ 4
mV
VT
·Vcc · θJA −
°C
IC
(3.59)
Where IC is the maximum the current defined as:
IC ≤
VT
26 mV
= mV
= 18.526 mA
−KVCC ΘJA 4 ◦C · 18.5 V · 18.965 ◦C
W
(3.60)
Where ΘJA is half of the value found in equation (3.56), as the power is shared between the two Darlingtons.
Thereby the emitter resistance is found:
Re ≥ 4
mV
°C
26 mV
· 18.5 V · 18.965
−
≈ 0Ω
°C
W 18.526 mA
(3.61)
The very low value of the resistor is due to the size of the heat sink used. However, a emitter resistance of 1 Ω
is used.
36
3.3. Power Amplifier
3.3.3
Voltage Amplification Stage
The VAS should distort the signal as little as possible whilst still amplifying the voltage to ensure the wanted
output voltage, as the output stage will have unity voltage gain. It is therefore favourable to include as few
components as possible in the amplifier configuration. A simple pnp-transistor amplifier can be used (fig.
3.17).
Vcc
Input Stage
Unity Gain Stage
F IGURE 3.17: A simple pnp-transistor used as an amplifier.
When the input stage has been developed, the VAS will be further analysed, when the stability of the system
is examined.
3.3.4
Supply Voltage
Previously, the power supply was chosen as 18.5 V. Figure 3.18 illustrates the distribution of the supply voltage
at maximum output.
MJ11016
Vcc+
VAS
2V
+
1
RP
BC547B 1
+
1k
3k
BC547B
1.8 V
+
Output: 13.15 V
+
1.8 V
-
2V
+
0.3V
MJ11015
-
+
0.7V BCM847BV
+
1.06V
200
200
-
Vcc-
F IGURE 3.18: The distribution of the supply voltage through the output stage.
The transistors which are used in the Wilson current mirror are the matched transistors (Matched SMD
NPN-Pair) BCM847BV [18] and the NPN transistor BC547B [19]. The closely matched transistors are used to
make sure that the difference between β in the two transistors is as small as possible. A BC547B is also used in
the VBE -multiplier. The minimum voltage required to ensure a power of 11 W is 13.15 V as shown in equation
37
3. D ESIGN
(3.36). The voltage drop across the two Darlingtons are ±2 V for the NPN and PNP pairs respectively, though
these are compensated for by the VBE -multiplier. The emitter resistances in the Wilson-mirror cause a voltage
drop of 1.06 V and the emitter resistances between the NPN Darlington and the PNP Darlington cause voltage
drops of 1.8 V. The voltage across the Wilson current mirror is then 1.06 V + 0.7 V + 0.3 V = 2.06 V and the
voltage drop across the Darlington pair stage per half-cycle is 13.15 V + 1.8 V + 2 V = 16.95 V. Comparing the
voltage drops and the supply voltage chosen:
Vcc − (VDarlington +VWilson ) = 18.5 V − (16.95 V + 2.06 V) = 0.49 V
(3.62)
Which means that the supply voltage is sufficient for the system to operate properly.
3.3.5
Input Stage and Feedback
As described earlier, the input stage consists of a differential amplifier, which amplifies the input signal
compared to the feedback signal. The differential amplifier is required to operate as a small signal amplifier,
which means that the signal to be amplified (the difference between the two input signals) is limited to a low
voltage (≤ VT ), so that the amplifier operates in the linear region, illustrated at figure 3.19. [5]
Normalised collector current
iC
I
}
Linear Region
1
0.8
0.6
0.4
0.2
0
-4
-2
0
2
Normalised differential input
vd
V
4
T
F IGURE 3.19: The transfer characteristic of the differential amplifier with normalised axes. [5]
The two input signals will in this case be the signal from the previous block (the tone control) and the
feedback signal from the unity gain stage, denoted as Input (Vin ) and Feedback (Vβ ) in figure 3.20.
38
3.3. Power Amplifier
Vcc+
Vcc+
QD1
QD2
Output
QD3
Input
QD4
Feedback
Rref
10 k
Qcm1
Qcm2
Rcme1
Rcme2
5k
5k
Vcc-
Vcc-
F IGURE 3.20: A differential amplifier with active load.
At the bottom of the circuit, transistors Qcm1 and Qcm2 along with resistances Rref , Rcme1 and Rcme2 compose
the constant current source in the shape of a basic current mirror. The Wilson mirror is not used, as the thermal
stability of this current mirror will not be an issue, nor any other of the benefits of the Wilson mirror, so
instead the transistor is omitted. At the top of the circuit, transistors QD1 and QD2 form another current mirror,
which are used as an active load. For the input stage, the Matched SMD NPN-Pair BCM847BV [18] is used
in the differential amplifier, with the BC547B [19] transistors in the current mirror and the pnp BC557B [20]
transistors in the active load.
The current mirror driving the differential amplifier is designed, so that the following current will be drawn:
IOut ' IRef =
Vcc −VBE 18.5 V − 0.7 V
=
≈ 1.18 mA
Rref + Re
10 kΩ + 5 kΩ
(3.63)
This approximation is more rough than for for the Wilson mirror in the output stage, as the output current is
more dependant on the DC gain value of the transistors in this basic current mirror. Furthermore, the transistors
used is not matched, but it is deemed adequate nevertheless.
The entire power amplifier must for 1 VRMS input, at the least, deliver an output peak voltage of 13.15 V,
so the feedback network is required to adjust the signal to a suitable level, making the difference between the
input voltage and the feedback voltage ≤ VT .
The amplifier can be depicted using a simple signal model with one module amplifier module with a
feedback network, this model is depicted as seen in the following illustration, figure 3.21.
xi
+
vd
A
xo
- xf
F IGURE 3.21: Simple amplifier system with feedback network (β ).
39
3. D ESIGN
In this system, the output signal, xo , will be characterised as:
xo = Avd = A f xi
(3.64)
Where A f is the amplification of the amplifier system (wherein the feedback system is taken into account):
Af =
A
xo
=
xi
1+βA
(3.65)
If the amplifier gain is large, this expression can be simplified:
Af =
A
1
'
1+βA β
(3.66)
From this expression, the feedback network can be designed; for xi = 1 VRMS =
xo ≥ 13.15 V, so:
13.15 V
Af ≥ √
≈ 9.3
2V
⇒
β.
1
≈ 0.1
9.3
√
2 V, it is specified that
(3.67)
Using a voltage divider, such a feedback can be obtained.
Differential
Amplifier
8.4 k
1 k
Output
Feedback
100 F
F IGURE 3.22: The feedback circuit.
The capacitor seen in figure 3.22 is placed in the feedback network, so that all the DC-offset is accounted
for in the differential amplifier, by only grounding the AC-signal in the voltage divider of the feedback system.
The chosen components give rise to the following voltage division:
1 kΩ
1
=
1 kΩ + 8.4 kΩ 9.4
(3.68)
Thereby the feedback network meets the requirement found in equation (3.67).
3.3.6
Small Signal Analysis
The small signal analysis is carried out at middle frequencies where capacitors are considered AC short circuits.
The purpose of the small signal analysis is to make sure that the open loop gain (β · A) is much greater than one
in order to stabilise the system. It is also necessary to determine the input and output impedances throughout
the system.
Small Signal Analysis: Output
The gain is approximately equal to one in the output stage, however, it is also of interest to find the input and
output impedance of this part of the system. A circuit of the output stage is shown in figure 3.23.
40
3.3. Power Amplifier
MJ11016
Vcc+
VAS
1
REN
BC547B 1
REP
RP
Rw
ß
RL
RVBE2
1k
3k
Out
MJ11015
BC547B
Qw3
Qw1
200
Qw2
BCM847BV
Rwe1
200
Rwe2
Vcc-
F IGURE 3.23: The output stage.
In the case of small signals, only one of the Darlington pairs conduct during each half-cycle. This means
that to determine the output impedance, it will only be necessary to look at one of the Darlington pairs. Figure
3.24 shows the small signal equivalent circuit of the npn Darlington transistor.
NPN Darlington
IB1
roVAS
Vcc+
r1
ß1.IB1
ß2.IB2
r2
Out
F IGURE 3.24: Small signal equivalent of the NPN Darlington transistor
Notice that the emitter resistances REN and REN and the feedback have been neglected for the moment. Their
influence will be examined later, for now, a voltage is applied at the output. To find the output impedance, it
will be necessary to find the output current. The output voltage must be:
Vo = −VBE1 −VBE2 +VroVAS
(3.69)
Which also can be written as:
Vo = −IB1 · rπ1 − IB1 · (1 + β1 ) · rπ2 − IB1 · roVAS
(3.70)
Where β1 is the current gain of the driver transistor. The current can be expressed as follows:
Io = −(1 + β2 ) · IB2 = −(1 + β2 ) · (1 + β1 ) · IB1
Where β2 is the current gain of the power transistor. An expression for
(3.71)
Vo
Io
can then be made:
Vo −IB2 · rπ1 − IB1 · roVAS − IB1 · (1 + β1 ) · rπ2
rπ2
rπ1 + roVAS
=
=
+
Io
−(1 + β2 ) · (1 + β1 ) · IB1
(1 + β2 ) (1 + β2 ) · (1 + β1 )
(3.72)
41
3. D ESIGN
Assuming that β1 1 and β2 1 equation (3.72) can be rewritten:
Vo
rπ2
rπ1 + roVAS
rπ2 rπ1 + roVAS
=
+
'
+
Io
(1 + β2 ) (1 + β2 ) · (1 + β1 )
β2
β2 · β1
Where rπ =
β
gm
⇒
rπ
β
=
1
gm ,
(3.73)
which means the expression further can be rewritten:
Vo rπ2 rπ1 + roVAS
1
rπ1
roVAS
1
1
roVAS
'
+
'
+
+
'
+
+
Io
β2
β2 · β1
gm2 β1 · β2 β1 · β2 gm2 gm1 · β2 β1 · β2
It is seen that
1
gm2
roVAS
β1 ·β2
and
1
gm1 ·β2
roVAS
β1 ·β2 ,
(3.74)
which means that equation (3.74) can be expressed as:
Vo
roVAS
roVAS
'
'
Io
β1 · β2 βDarlington
(3.75)
However, so far, the emitter resistances and the feedback have been neglected. Including them into the
calculations leads to the following expression:
Zo '
roVAS
βDarlington
+ REN
2
(3.76)
1+β ·A
And because REN = 1 Ω, equation (3.76) becomes:
Zo '
roVAS
βDarlington
+ 12 Ω
(3.77)
1+β ·A
Where β · A is the open loop amplification and not the current gain of the Darlington transistor.
Small Signal Analysis: VAS
A small signal equivalent of the VAS is shown in figure 3.25.
VAS
B
Power Amp
C
gm .V
r
ro
ZinOS
E
F IGURE 3.25: The small signal equivalent of the VAS circuit.
The gain of the VAS is equal to gm · ro ||ZinOS , where ZinOS is the input impedance of the power amplifier.
Small Signal Analysis: Diff. Amp.
In the differential amplifier circuit illustrated in figure 3.26, Vin is the 1 VRMS input and Vβ is the feedback input.
The transistors chosen for this operation are the matched transistors (Matched SMD NPN-Pair) BCM847BV
[18] and (Matched SMD PNP-Pair) BCM857BV [21].
42
3.3. Power Amplifier
Vcc+
BCM857BV
QD1
QD2
VAS
BCM847BV
Vin
QD4
QD3
Vß
10 k
8.4 k
BC547B
13.15 V
1 k
BC547B
100 F
5 k
5 k
VccF IGURE 3.26: The differential amplifier.
To determine the small signal gain of the differential amplifier it is necessary to look at an equivalent small
signal diagram. The circuit seen in figure 3.27 is the equivalent small signal circuit for the differential amplifier
(the constant current source is not included in the analysis). First step is to find the general transconductance
(Gm = Vioin ). The single-ended output is grounded and a differential input signal of Vin is applied to the inputs.
Assuming that QD1 , QD2 , QD3 , and QD4 are matched in pnp and npn transistor pairs respectively, virtual
(symmetry) ground occurs between the two emitters of QD3 and QD4 .
ro1
r1
gm1.VB
re2||ro2
Out
Vin/2
B3
ro3
gm3.Vin/2
ro4
gm4.Vin/2
r3
B4
Vin/2
r4
F IGURE 3.27: The small signal equivalent.
The circuit can be further reduced as illustrated in figure 3.28.
43
3. D ESIGN
ro1
re2
gm1.VB
Out
Vin/2
B3
ro3
gm4.Vin/2
gm3.Vin/2
rπ3
B4
Vin/2
rπ4
F IGURE 3.28: The reduced small signal equivalent.
Notice that re2 consists of re2 ||ro2 ||ro4 ||rπ1 , though as re2 is significantly smaller than the other resistances,
it will dominate and thus the resistance can be approximated to re2 . The voltage VB is the base voltage of QD1
shared with QD2 , resulting in that VB1 = VB2 = VB , which is why it is simply denoted as VB . It can be calculated
as follows: [5]
Vin
(3.78)
Vb = −gm4 · re2 ·
2
The collector current of QD1 can then be calculated:
Vin
Ic1 = gm1 ·VB = −gm1 · gm4 · re2 ·
(3.79)
2
Then, the output current can be found as:
Vin
iout = gm3 ·
− gm4 ·VB
(3.80)
2
Inserting equation (3.79) into equation (3.80) yields:
Vin
Vin
iout = gm3 ·
+ gm1 · gm4 · re2 ·
(3.81)
2
2
V−0.7 V
The current source in figure 3.26 draws a current of Iref ≈ 18.5
10 kΩ+5 kΩ = 1.18 mA and, assuming the transistors
are matched, the current will divide evenly through
QD3 and QD4 , meaning that every transistor is biased with
approximately the same current. This means
because gm =
Ire f
2
VT
that gm1 = gm3 = gm4 = gm =
1.18 mA
2
26 mV
=
0.023 S which is the general transconductance of the differential amplifier.
Now, to determine the output resistance of the differential amplifier, the two inputs are grounded and a signal
is sent into the output as illustrated in figure 3.29.
re2
ro1
QD1
Out
Node X
i
ix
Vx
QD3
ro3
ro4
QD4
F IGURE 3.29: Circuit for determining the output impedance.
44
3.3. Power Amplifier
The resistor re2 is actually re2 ||ro2 , however, as re2 is very small, it dominates and thus the resistance is
approximately equal to re2 . The output impedance Ro3 of transistor QD4 can be calculated by the following
equation [5]:
Ro3 = ro3 + (Re ||rπ3 ) + (gm · ro3 ) · (Re ||rπ3 )
(3.82)
The total emitter resistance, Re , is approximately equal to re3 and since the output resistance usually is very
high, gm · ro3 should be very high as well, which means that the first occurrence of Re ||rπ3 can be neglected.
Equation (3.82) then becomes:
Ro3 ' ro3 + (gm · ro3 ) · (re3 ||rπ3 )
(3.83)
The value of re3 ||rπ3 is approximated to re3 because, as stated before, re3 is much smaller than rπ3 , so the is
simplified:
Ro3 ' ro3 · (1 + gm · re3 )
(3.84)
1
Also, because re3 ' gm
equation (3.84) can be further simplified:
gm
Ro3 ' ro3 · 1 +
= 2ro3
gm
(3.85)
The current ix can now be found via a node equation at node X:
Vx
Vx
+
ix =
ro3 ro1
From which the output impedance can be determined as follows:
Vx
Vx
1
1
ix
1
= Vx ⇒
⇒ Ro =
ix = Vx ·
+
⇒ 1
= 1
= ro3 ||ro1
1
1
ro3 ro1
ix
ix
ro3 + ro1
ro3 + ro1
Thus, the differential gain Ad = VVino can be determined. Recall that Gm =
equation for the differential gain can be written as follows:
Io · Ro
Vo
=
= gm · Ro = gm · ro3 ||ro1
Ad =
Vin
Vin
Which is the gain of the differential input stage.
io
Vin .
(3.86)
(3.87)
Seeing that Io · Ro = Vo , the
(3.88)
The input impedance of the differential stage can be determined by looking at the circuit in figure 3.28. The
input impedance is 2 · rπ , however, taking the feedback into account the expression becomes:
Zin = 2 · rπ · (1 + β · A)
(3.89)
Where β · A is the open loop gain.
Small Signal Analysis: Summary
The voltage gain of the power amplifier is illustrated in figure 3.30.
ro3||ro1
Vin
Zin
+
Ad
-
Vout
+
VAS
-
ZinOS
Vß
F IGURE 3.30: Illustration of the voltage gain between the different stages.
45
3. D ESIGN
Notably, the gain of the output stage has been omitted, because the voltage gain is unity and thus is irrelevant
to the total voltage gain of the power amplifier. The gain in the differential stage is, as derived earlier, equal to
Ad = gmd · ro3 ||ro1 and the VAS gain is Av = −gmv · ro ||ZinOS . The total gain of the power amplifier is then:
AOS = Ad · Av · 1 = (gmd · ro3 ||ro1 ) · (−gmv · ro ||ZinOS )
(3.90)
Because ro3 k ro1 is relatively large, it can be concluded that the open loop gain of the differential amplifier
will be much greater than one. Likewise with the open loop gain of the VAS, as its collector resistance is quite
sizeable and the impedance it is looking into is, because of the Wilson current mirror, very large.
3.4
Stability
The power amplifier so far is illustrated in figure 3.31.
Input Stage
Voltage Amplifier Stage
VBE-Multiplier
Output Stage
Vcc+
BCM857BV
RP
BC547B
BC557B
1
1 k
Input
MJ11016
Output
BCM847BV
3 k
10 k
BC547B
BC547B
8.4 k
BC547B
1
1 k
MJ11015
BCM857BV
100 F
5 k
5 k
200 200 VccFeedback Network ( )
F IGURE 3.31: The power amplifier so far.
To determine whether the system is stable or not, it is brought into open loop mode (see appendix B.1 for
the LTSpice simulation diagram). The input is grounded and there is no AC feedback. A negative input signal
is then applied to the feedback system so that the open loop gain is positive (purely done to make it easier to
graphically determine whether the system is stable or not). The phase shift at 0 dB should not exceed ±180°,
else the system will be unstable. Ideally, it should not exceed ±135°, because issues in the construction of the
actual circuit might shift the value.
46
3.4. Stability
Bode plot
Magnitude in dB
80
DiffAmp
VAS
Output
60
40
20
0
−20
−40
2
10
3
10
4
10
5
10
6
7
10
10
Frequency in Hz
Phase plot
250
Diff. Amp.
VAS
Output
Phase in degrees
200
150
100
50
0
−50
−100
−150
−200
2
10
3
10
4
10
5
10
6
7
10
10
Frequency in Hz
F IGURE 3.32: Simulated Bode plot of the power amplifier as developed until now in open loop mode showing
the open loop gain after each stage thereby showing the total open loop gain.
From the Bode plot (figure 3.32) of the total open loop gain, it can be seen that at 0 dB amplification, the
phase shift is −175°, making the system unstable, as it will oscillate due to the feedback.
Bode plot
Magnitude in dB
80
DiffAmp
VAS
Output
60
40
20
0
−20
−40
2
10
3
10
4
10
5
10
6
7
10
10
Frequency in Hz
Phase plot
250
Diff. Amp.
VAS
Output
Phase in degrees
200
150
100
50
0
−50
−100
−150
−200
2
10
3
10
4
10
5
10
6
10
7
10
Frequency in Hz
F IGURE 3.33: Simulated Bode plot of the power amplifier as developed until now in open loop mode showing
the open loop gain of each stage separately
47
3. D ESIGN
The open loop voltage gain was isolated for each separate module by taking the voltage after the module in
relation to the voltage before the module. From this (figure 3.33) it can be seen that it is the VAS in which the
dominant pole lies, it is this module which will be examined.
To reduce the phase shift, a capacitor is inserted between the base and collector of the VAS transistor. This
reduces bandwidth and extra care is required with regards to slew rate, but it is required to stabilise the system.
To keep the negative influence of the capacitor at a minimum, a small capacitance is aimed for. To be able to
use a smaller capacitor, a resistor is placed in series with the capacitor. The choice of components was made by
use of simulations in LTSpice, and can be seen in figure 3.34.
Vcc+
Differential Stage
QVAS
RVAS
CVAS
220 pF
150
Output Stage
F IGURE 3.34: The VAS with capacitor and resistor implemented.
With this new VAS design, the system is now simulated. The Bode plot of the output of the new design can
be seen in figure 3.35
Bode plot
Magnitude in dB
80
60
40
20
0
−20
−40
2
10
3
10
4
10
5
10
6
10
7
10
Frequency in Hz
Phase plot
250
Phase in degrees
200
150
100
50
0
−50
−100
−150
−200
2
10
3
10
4
10
5
10
6
10
7
10
Frequency in Hz
F IGURE 3.35: Simulated open loop Bode plot of the power amplifier with the new changes implemented in
the VAS.
From the open loop Bode and phase plot of the system with the new VAS implemented, it can be seen that
at 0 dB amplification, the phase shift is −127.5°, which means that the system should be stable. From the plot
it can be seen that the open loop gain, β A, has a maximum value of approximately 80 dB, which is decreased
to 60 dB at 20 kHz.
48
3.4. Stability
As mentioned, this introduced capacitor can result in problems with slew rate. The current through the
dV
capacitor is given as Icap = C , with voltage V̂ = AṼoo sin ωt. Due to the resistor, however, the current through
dt
this series must be calculated using the impedances:
s
V
I=
Z
Z=
V
⇒I= q
R2VAS +
R2VAS +
1
ωC
2
(3.91)
13.15 V
=r
2 = 0.000 364 A ≈ 0.36 mA
2
1
1
2
(150 Ω) + 2π·20 kHz·220 pF
ωC
If this current cannot be drawn from the VAS, there will be slew rate problems. The current must be drawn
from the current sources, of which the one in the input stage is smallest. This current source, however, draws a
current of approximately 1.2 mA (equation (3.63)), so slew rate should not pose any problem.
For further examination, a transient analysis and a Bode plot is made for the closed loop system (see LTSpice
diagram in B.2).
Bode plot
40
Magnitude in dB
30
20
10
0
−10
−20
−30
−40
2
10
3
10
4
10
5
10
6
10
7
10
8
10
Frequency in Hz
Phase plot
250
Phase in degrees
200
150
100
50
0
−50
−100
−150
−200
2
10
3
10
4
10
5
10
6
10
7
10
8
10
Frequency in Hz
F IGURE 3.36: Simulated closed loop Bode plot of the power amplifier with the new changes implemented in
the VAS.
According to the transient analysis (figure 3.37), there is no oscillation nor any other distortion apparent.
Additionally, the peak output value is 13.3 V, which meets the requirements. If the Bode plot is examined
(figure 3.36), it can be seen that the frequency response is very linear in the effective frequency range, though
something strange occurs around 10 MHz. This phenomenon is most likely caused by the internal capacitances
of the transistors and even though the system is designed to operate in the frequency range of 20 Hz to 20 kHz it
would be favourable to make sure the bode plot is more linear. It was found that inserting a capacitor in parallel
with the VBE -multiplier as illustrated in figure 3.38 solves the problem around 10 MHz.
49
3. D ESIGN
Transient Analysis
15
Voltage
10
Voltage
5
0
−5
−10
−15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time in ms
F IGURE 3.37: Simulated transient response at 1 kHz of the power amplifier as designed until now.
RP
BC547B
100 nF
1 k
F IGURE 3.38: VBE -multiplier will a capacitor in parallel to stabilise the system.
The capacitance of the capacitor is chosen to be 100 nF. A bode plot of the improved system is illustrated
in figure 3.39. As the purpose of the VBE -multiplier is to act like an ideal battery while having no influence on
the AC signal, the capacitor helps on the strange behaviour for high frequencies being an AC coupling.
Bode plot
40
Magnitude in dB
30
20
10
0
−10
−20
−30
−40
2
10
3
10
4
5
10
10
6
10
7
10
Frequency in Hz
Phase plot
250
Phase in degrees
200
150
100
50
0
−50
−100
−150
−200
2
10
3
10
4
10
5
10
6
10
7
10
Frequency in Hz
F IGURE 3.39: Simulated closed loop Bode plot of the power amplifier with the new the AC coupling of the
VBE -multiplier.
50
3.4. Stability
Now with the capacitor implemented in the VBE -multiplier, it can be seen that the strange frequency response
for the higher frequencies has disappeared.
3.4.1
Overload Protection
Overload protection avoids damage if the output is short circuited. In figure 3.40, a current limiter is used as
overload protection, using the transistors QOP1 and QOP2 to examine the condition of the output transistors base
current and VBE voltage. When the conditions exceed the permissible current, it draws current from the base of
the two Darlington transistors to reduce the output current. [7]
Vcc+
IBias
QNPN1
D1
ROP1
QOP1
Catching diode
QNPN2
ROP2 ROP5 REN
VBias
Output
ROP3 ROP6 REP
QOP2
D2
ROP4
QPNP2
Catching diode
QPNP1
VAS
VccF IGURE 3.40: Diagram of an example of a simple current limiter. [7]
The diodes D1 and D2 prevents QOP1 and QOP2 from conducting in the wrong half cycle. The catching
diodes are a way to diminish the effect of a “flyback pulse”, where a voltage spike is produced when the load is
suddenly disconnected. [7]
Vcc+
QNPN1
QOP1
ROP1
ROP2
ROP3
QOP2
ROP4
QNPN2
REN
Output
REP
QPNP2
QPNP1
VccF IGURE 3.41: Diagram of a current limiter to the short circuit protection.
51
3. D ESIGN
As seen on figure 3.41 ROP8 and ROP9 from figure 3.40 has been removed because the transistors used is
the Darlington coupling are an IC solution, so the driver emitter cannot be accessed. The diodes D1 and D2
is removed, because of the diodes did not change anything, as the two transistors in the overload protection do
not support current through the emitter.
In the VAS, an emitter resistance of 50 Ω is added to limit the current through the collector. Additionally,
two 1N4148 diodes are added into the circuit between the VCC voltage and the base to limit the base-emitter
voltage to 1.4 V, and thus further limiting the current through the collector.
Overload Protection Calculation
The short circuit is symmetric, so that means that ROP1 = ROP4 , ROP2 = ROP3 and Re = REN = REP . The transistors
chosen are BC547B and BC557B, where the voltage needed is VBE = 0.7 V. The current from the VAS stage is
limited to:
IVAS =
0.7 V
= 14 mA
50 Ω
(3.92)
As the 1.4 V limited by the diodes is split between the base-emitter and the emitter resistance. The current
drawn from the Wilson mirror was found to be 5.3 mA in equation (3.55). The collector current in QOP1 is:
IC = IVAS − Imirror = 14 mA − 5.3 mA ≈ 8.7 mA
(3.93)
Now, the DC current gain for the transistor BC547B can be found, which for IC = 8.7 mA is approximately 240
[19]. The base current of transistor ROP1 is then:
IB =
IC
8.7 mA
=
≈ 36.1 µA
βDC
240
(3.94)
The transistor activates at a base current of 36.1 µA and a VBE voltage of 0.7 V. The emitter resistors are chosen
to be 1 Ω in the thermal examination. The current through the load is to be limited to I = 3 A, for which the
current through the emitter resistor is:
VRe = Re · I = 1 Ω · 3 A = 3 V
(3.95)
To make sure the base of ROP1 has enough current at this point and resistor ROP2 can cause a voltage drop of
0.7 V, the current of IROP1 should be at least ten times the base current, so to be on the safe side a multiplication
of 13 is used:
IROP1 = 13 · IB = 13 · 36.1 µA = 469 µA
(3.96)
Then, ROP1 can be calculated to:
ROP1 =
VRe −VBE
≈ 4.9 kΩ
IROP1
(3.97)
The current over the resistor ROP2 is then calculated:
IROP2 = IROP1 − IB ≈ 433 µA
(3.98)
The resistor ROP2 can be calculated by the following equation, where ROP2 is unknown:
VBE = IROP2 · ROP2
52
⇒
ROP2 =
VBE
≈ 1.6 kΩ
IROP2
(3.99)
3.4. Stability
The calculated components to the overload protection
R1 ≈ 4.9 kΩ
R3 ≈ 1.6 kΩ
R2 ≈ 1.6 kΩ
R4 ≈ 4.9 kΩ
3.4.2
(3.100)
Summary
The system with the implemented overload protection looks as follows from figure 3.42.
Input Stage
Voltage Amplifier Stage
VBE-Multiplier
Output Stage
50 BCM857BV
(Potentiometer)
Vcc+
MJ11016
RP
BC547B
1 k
Input
BCM847BV
10 k
BC547B
150 220 pF
3 k
BC557B
1 k
1.6 k
1
1.6 k
1
Output
4.9 k
BC547B
8.4 k
BC547B
4.9 k
BC547B
BC557B
MJ11016
BCM857BV
100 F
5 k
5 k
200 200 VccFeedback Network ( )
F IGURE 3.42: The power amplifier design so far.
If a (relatively) large DC input signal is sent, it will not pose a problem for the amplifier, but if a loudspeaker
is connected, the diaphragm will be moved to the extreme position, which in the worst case can damage the
loudspeaker without producing any sound. To prevent this, the input is DC decoupled, so that only AC signals
reach the output. A simple high pass filter is used, where a large capacitor is used to ensure that the influence on
the effective frequency range is as low as possible; the chosen value was 47 µF, as this was the largest bipolar
capacitor available.. Additionally, supply decoupling is added to ensure that the supply will act as ideal as
possible. The final design can be seen in figure 3.43.
Input Stage
Voltage Amplifier Stage
VBE-Multiplier
Output Stage
1000 F
100 nF
8.4 k
Input
50 BCM857BV
(Potentiometer)
Vcc+
MJ11016
RP
BC547B
1 k
BCM847BV
47 F
10 k
BC547B
150 220 pF
3 k
BC547B
BC557B
BC547B
8.4 k
1 k
4.9 k
BC547B
BC557B
1.6 k
1
1.6k
1
Output
4.9 k
MJ11016
BCM857BV
100 F
1000 F
100 nF
5 k
5 k
200 200 Vcc+
Feedback Network ( )
F IGURE 3.43: Final power amplifier diagram.
53
3. D ESIGN
The input impedance, output impedance and efficiency are calculated and compared to simulated and
measured values. The gain deviation is not calculated, however, it will be simulated and measured. The THD
will only be measured as simulations and calculations of this are difficult to obtain any precise data from.
Input and Output Impedance
The input impedance, Zin , of the power amplifier can be calculated with a parallel connection between rin and
the input impedance of the differential amplifier. An expression for the input impedance of the differential
amplifier was found with equation (3.89):
Zin = rin k (rπ · 2 · (1 + β · A))
(3.101)
β
Where rin = 8.4 kΩ and rπ is calculated by rπ = gm
. From a simulation of a circuit of figure 3.43, the value of
Ic
0.6 mA
Ic is found to be 0.6 mA. Then, gm = VT = 26 mV = 0.024 S. The current gain, β , is determined by the data
250
sheet for BC547B [19] to be 250. Then, rπ = 0.024
S = 10 416.66 Ω ' 10.41 kΩ. The open loop gain, β · A, is
graphically determined (from a simulation of the open loop gain of the final circuit) to be 34.8 dB at 20 kHz.
Then, Zin can be calculated:
|Zin | = |8.4 kΩ k (10.41 kΩ · 2 · (1 + 34.8 dB))| = 8.34 kΩ
(3.102)
Which meets the requirement of Zin ≥ 1 kΩ. This is then compared with the simulated and the measured input
impedance as shown in figure 3.44. (Spice circuit can be seen in appendix B.3).
Measurement and simulation of the power amplifier Input impedance
8460
|Input impedance| / Ω
8450
8440
8430
Measured
Simulated
8420
8410
8400
8390
20
100
1000
Frequency / Hz
10000
F IGURE 3.44: The simulated and measured input impedances.
The measurements can be seen in figure C.24. The measured input impedance is approximately 8.4 kΩ
at 20 kHz. The calculated value at the same frequency is 8.34 kΩ and the simulated value is approximately
8.38 kΩ at 20 kHz. Simulated, calculated and measured values all fall within the boundary of Zin ≥ 1 kΩ.
The output impedance of the system can be approximated using equation (3.77) as follows:
Zo '
roVAS
βDarlington
+ 12 Ω
1+β ·A
(3.103)
roVAS is calculated by the following formula:
ro =
54
VA
Ic
(3.104)
3.4. Stability
Where VA is the Early voltage and can be determined by the following equation:
VA =
Ic
−VCE
hoe
(3.105)
Where roVAS is the collector impedance of the VAS transistor, βDarlington is the current gain of the Darlington
transistors and β · A is the open loop gain.
The value of βDarlington is 5000 and open loop gain is (as mentioned during the calculation of the input
impedance) equal to 34.8 dB.
Inserting this into equation (3.103) yields the following expression:
Zo '
roVAS
βDarlington
+ 21 Ω
(3.106)
1 + 34.8 dB
VCE and Ic is (from a simulation of the final circuit) equal to approximately 16.33 V and 5.4 mA. From the
data sheet [22] the value of hoe is maximum 60 µS at Ic = 2 mA, though as the Ic of the VAS is 5.4 mA, it would
be safe to say that the value of hoe is at least 60 µS.
Inserting these values into equation (3.105):
VA =
5.4 mA
− 16.33 V = 73.67 V
30 µS
(3.107)
Then, ro can be calculated:
ro =
VA 73.67 V
=
= 13.64 kΩ
Ic
5.4 mA
(3.108)
Inserting these values into equation (3.103):
|Zo | '
+ 12 Ω
= 0.0577 Ω
1 + 34.8 dB
13.64 kΩ
5000
(3.109)
Which is below the requirement of 0.8 Ω (3.8) and thus acceptable.
The simulated and measured output impedances can be seen in figure 3.45 (Spice circuit can be seen in
appendix B.4):
Measurement and simulation of the power amplifier Output impedance
0.7
|Output impedance| / Ω
0.6
0.5
0.4
Measured
Simulated
0.3
0.2
0.1
0
20
100
1000
Frequency / Hz
10000
F IGURE 3.45: Simulated and measured output impedances.
The measurements for the output impedance can be seen in figure C.25. The measured output impedance is
constant at approximately 0.675 Ω, which is quite off from the calculated value of 0.0577 Ω and the simulated
55
3. D ESIGN
value of approximately 0.08 Ω. The measured value is nearly off by a factor of one to ten, though it still meets
the requirement of Zo ≤ 0.8 Ω. The relatively large value of Zo could be explained by the fact that the built
system is far from ideal and that the calculations do not take wire resistances into account. The simulations
most likely use a different value of βDarlington than the calculations as well.
Efficiency
The efficiency of the class AB power amplifier should be between 78.5% and 25% (1.1.3). From equation
(3.38) in subsection 3.3.2 the power of the power supply is 19.4 W. The calculated output power is 11 W which
gives an efficiency of:
η=
PL
11 W
· 100% =
· 100% = 56.70%
Pcc
19.4 W
(3.110)
Figure C.28 shows the measured values. The output power deviates from 11.13 W to 11.25 W which gives an
efficiency of:
η=
11.13 W+11.25 W
2
19.4 W
· 100% = 57.628% ≈ 57.63%
(3.111)
The measured result deviates from the calculated result by 57.6% − 56.7% = 0.9%.
Gain Deviation
The simulated and measured gain deviation is illustrated in figure 3.46 (Spice circuit can be seen in figure B.5):
Measurement and simulation of the power amplifier amplification
23
22.5
Amplification / dB
22
21.5
Measured
Simulated
21
20.5
20
19.5
19
20
100
1000
Frequency / Hz
10000
F IGURE 3.46: Simulated and measured gain during the frequency band 20 Hz to 20 kHz.
The measurements can be seen in figure C.26. The simulated gain at 20 Hz it is 22.43 dB, 1 kHz it is
22.47 dB, and at 20 kHz it is 22.47 dB. The simulated gain deviation is then approximately 0.04 dB. The
measured gain deviation is 0.05 dB, though the maximum gain measured is approximately 19.54 dB at 20 kHz.
Compared to this to the simulated gain at 20 kHz, there is a difference of about 3 dB. The reason why there is
such a difference could well be the fact that the simulations are for the ideal case. There are many deviations
which the simulation cannot compensate for, such as resistor deviations, transistor current gains, transistor
matching and so on. Either way, the gain deviation does not exceed the maximum value of ±0.5 dB, so the
results are acceptable.
56
3.4. Stability
THD
The THD has been measured and can be seen in figure C.27. It varies from 0.002 % to 0.012 % across the
frequency range of 20 Hz to 20 kHz. The maximum THD allowed is 0.5 % and the measured result is within
this boundary.
3.4.3
Measurement Results
Within this section all the measured data for the power amplifier in relation to the interface specifications can be
found. The results can be seen in table 3.9, while the test procedure and all the graphs can be found in appendix
C.3.
Description
Minimum value
Measured Value
Unit
1
8.4
kΩ
Output impedance
0.8
0.675
Ω
Output power
10
11.13
W
±0.5
±0.05
dB
0.1
0.012
%
Input impedance
Gain deviation
THD
Maximum value
TABLE 3.9: Measured data for for the power amplifier.
From this, it is concluded that the power amplifier meets the interface specifications.
57
4. Integration
In the following chapter, the three modules are combined to the Hi-Fi amplifier as seen on figure 4.1 and
measured according to the specifications made in section 2.2. The results of measurements are then compared
to the specifications.
Volume control
Tone control
Power amplifier
Input
Output
F IGURE 4.1: The Hi-Fi amplifier combined with the volume control found in figure 3.2, the tone control
found in the figures 3.4(a) + 3.4(b) and the power amplifier, found in figure 3.43 in the given order.
4.1
Acceptance Testing Result
Specification
Minimum value
Maximum value
Measured Value
Unit
Approved
82
See figure C.36
See figure C.36
kΩ
V
V
Yes
Yes
Yes
0.8
0.6
10.1
Ω
W
Yes
Yes
±1.5
0.7
±0.4
0.16
dB
%
Yes
Yes
±13
±13
±3
±9.5 to ±12.5
±10 to ±12.5
±3
dB
dB
dB
No
Yes
Yes
-79
dB
Yes
Input
Input Impedance
Overload EMF
EMF
22
2.8
0.2
Output
Output Source Impedance
Output Power
10
Performance
Gain Deviation
THD
Tone Control
Bass Control
Treble Control
Gain Deviation in Nonequalized Frequencies
±10
±10
Volume Control
Volume Control Attenuation
-46
TABLE 4.1: Measured data for for the whole Hi-Fi amplifier.
59
4. I NTEGRATION
After setting the requirements for the Hi-Fi amplifier and designing it, there can now be made some
measurement on the final product, which will be described in table 4.1. The measurement results with graphs
and procedures can be found in appendix C.4. All measurements are made at rated conditions, which can be
found in section 2.3, unless described otherwise in the procedures.
4.1.1
Input
Input Impedance
The input impedance for the Hi-Fi amplifier is the input impedance for the first module, which is the volume
control module. The value of this impedance is calculated with equation 3.1 and is ≈ 100 kΩ. The specification
requires a value of ≥ 22 kΩ, and the measured value has a minimal value of 82 kΩ, which meets the standard.
Minimum EMF and Overload EMF
The EMF varies over a high voltage range due to a varying signal source. The Hi-Fi has therefore been set to
be able to deliver a 10 W power output from a signal EMF on 0.2 V to 2.8 V. This signal is controlled by the
volume control to deliver the desired output power, which can be seen on figure C.39.
4.1.2
Output
Output Impedance
The output impedance for the Hi-Fi amplifier is also the output impedance for the last module, which is the
power amplifier module. The value for this impedance is calculated with equation 3.103 found in the power
amplifier design and gives 0.32 Ω. The required specification value for the output impedance is set to ≤ 0.8 Ω
and the measured value is found to 0.6 Ω which meets the specification.
Output Power
The output power for the Hi-Fi amplifier is set to a minimum value of 10 W, whenever the power amplifier input
voltage is ≥ 1 VRMS . This value has been calculated with equation (3.36) and delivers ≈ 11 W. The minimal
measured value however is 10.1 W, which can be seen at figure C.39. The output power meets the requirement
of a value ≥ 10 W.
4.1.3
Performance
Gain Deviation
The gain deviation in the effective frequency range is set to a maximum value of ±1.5 dB with the reference
frequency of 1 kHz. This value has only been simulated for tone control and the power amplifier. However,
all the modules have been designed to have a flat frequency response for rated conditions. The measurement
results shows a deviation of ±0.4 dB, which meets the standard, this can be seen on the graph at figure C.36.
THD
The maximum allowed THD is set to 0.7 %. This value has not been simulated or calculated either. The design
however is made with components to prevent signal clipping and modules to prevent crossover distortion. The
measurement results shows a THD of 0.16 %, which can also be seen on figure C.37. This measurement meets
the specification for THD.
60
4.1. Acceptance Testing Result
4.1.4
Tone Control
The bass control and treble control has been chosen to an amplification/attenuation of ±10 dB to ±13 dB in the
equalized frequencies. Furthermore a requirement for the non-equalized frequencies with a value of ±3 dB has
been made, due to a usual ±3 dB deviation when working with a non ideal filter. The measured graph on figure
3.9 for the frequency response shows an amplification/attenuation which violates the minimal value of ±10 dB
in the bass control and therefore the specifications are not met.
4.1.5
Volume Control
The volume control attenuation is required to be at least −46 dB. This is not calculated, due to the volume
controls ability to ground the signal, which should give the desired value of attenuation. The figure C.7 shows
the attenuation, where the lowest value of attenuation is −79 dB, which meets the specifications.
61
5. Discussion
In the discussion, the uncertainties of measurements, specific for the Hi-Fi amplifier, are being discussed. Those
uncertainties leads to a discussion of possible circuit corrections that can be made to produce a better circuit
and better measurements.
Uncertainty of Measurements Specific for the Hi-Fi Amplifier
Input Impedance
The input impedance shown in the figure C.34 in appendix C.4 is less than the expected (≈ 82.5 kΩ), because
the input impedance for the volume control alone is around 91.4 kΩ as shown on figure C.5 in appendix C.1.
The reason for this is not found. However, it is suspected, that it is due to some parameter in the measurement
tools.
Output Impedance
The spikes in the output impedance shown on the figure C.35 in appendix C.4 for around 50 Hz could be a
consequence of 50 Hz disturbance. The increment of impedance, when going from low to high frequencies, can
be caused by the inner capacitances of the power transistors in the output stage.
Frequency Response
The frequency response for the Hi-Fi amplifier with the input EMF as 0.2 V, 0.5 V, and 2.8 V is shown at figure
C.36 in appendix C.4. The reason for the non-linearity could be that the settings of the tone control is not exact
unity and therefore interfere with the amplification. The power amplifier in figure C.26 in appendix C.3 did
also have a non-linear frequency response which means that it is not only the tone control that induces a nonlinearity but also the inner capacitances of the power amplifier. The reason that the frequency response for rated
conditions is different than those for 0.2 V and 2.8 V, is not found. However, the potentiometer on the volume
control has a very sensitive adjusting handle. A little pull could therefore cause an unwanted adjustment of the
potentiometer value, as the volume control clearly is able to amplify the signal as required, which can be seen
for the input of 0.2 V.
Frequency Dependent THD
This measurement of the Hi-Fi amplifier frequency dependent THD is shown on figure C.37 in appendix C.4.
The peak at 25 Hz THD could be caused by 50 Hz noise, because the THD is calculated from the harmonic
components, for which the 50 Hz is the first harmonic. The sudden fall in THD at ≈ 11 kHz, is caused by
the lack of harmonic components, because the THD measurements only are calculated from the harmonic
components at ≈ 20 Hz to ≈ 50 kHz.
Output Power
The figure C.39 in appendix C.4 shows the Hi-Fi amplifier output power dependent on frequencies for the
following input EMF: 0.2 V, 0.5 V, and 2.8 V. The Hi-Fi amplifier output power behaves like the frequency
response C.36 in appendix C.4, because it is calculated from the same data. The Hi-Fi amplifier output power
63
5. D ISCUSSION
compared to the power amplifier output power C.28 in appendix C.3 is not similar. The reason for this could be
that the tone control and volume control effects the response; possibly, as noted before, this is due to that the
tone control is not set exactly at no amplification.
The THD for the Hi-Fi amplifier shown on figure C.38 in appendix C.4, measured to 0.16 %, is not near
its maximum allowed value (0.7 %), which means that the output power easily could have been adjusted to a
higher level before the THD of the Hi-Fi amplifier reaches the highest allowed value.
Possible Circuit Corrections
Shielding
The THD of the Hi-Fi amplifier is at its maximum at 0.16 % (see figure C.37). Therefore the specification
for THD is approved, but the THD is with little difficulty improved even more and thereby fulfil a more strict
specification. A significant improvement is to cover the circuit with aluminium foil or to enclose the entire
circuit in a metal box which is a shield against noise (especially 50 Hz from the mains) and thereby improve
the EMC (Electromagnetic Compatibility).
The power amplifier is on a wooden board, where the brass nails has the function as junctions for the
components and wires. This circuit structure makes the power amplifier very big and thereby also very receptive
for EMI (Electromagnetic Interference). To prevent the circuit from being receptive of EMI, an option is that
the circuit is being made more compact in form of a functional print, which also is more easy to handle and use.
Durability of the Hi-Fi Amplifier
As mentioned above, the power amplifier is on a wooden board. This construction causes the circuit to be
fragile. The reasons for this are thin wires, small components like SMD that are difficult to handle and easily
break, BNC connectors that easily break under mounting of cables and junctions that easily break. To prevent
this, a good idea is to make the circuit small and compact on a print and encapsulate it, which thereby is
protecting the print paths and components. Also, to make the power amplifier more protected against thermal
runaway, the Darlington components could be thermally coupled to the VBE -multiplier, such that the bias will
decrease, when the output stage is heated.
Component Values
The components available are not the components that are needed, only an approach to the correct values,
which thereby have caused the tone control to work in another way than intended, because the component
relationships are not fulfilled. With more available components, it is possible to meet the specifications for the
bass control. Of that reason it can be fair to implement a extra tolerance in the amplification deviation.
Uncertainty of Potentiometer Values
The potentiometers that are used in the volume and tone control have a large tolerance value and are difficult
to adjust. To prevent that the potentiometer values differ from the values that is wanted after adjusting them, it
can be a good idea to use potentiometers that are easier to adjust precisely. The reason for this is that the tone
control clearly interfere with the Hi-Fi amplifier frequency response and other measurements.
Power Supply
The Hi-Fi amplifier does not have its own power supply. A large external HAMEG 3-channel power supply
is being used. Choosing a more more compact, power supply that matches the Hi-Fi amplifier in power
64
requirements would be preferred. This way, the power supply does not have to be adjusted after every time
of use.
65
6. Conclusion
The project purpose is to make a Hi-Fi amplifier, based on the problem statement:
“How does one build a single channel input and output Hi-Fi amplifier with the user control modules consisting
of a tone and volume control, and the power amplifier module consisting of a class AB, and which specifications
should it meet?”
The specifications made for this product can be found in section 2.2 and are based on the IEC 61938-3, IEC
581-6 and DIN 45500 standards and some estimations on the basis of project related courses.
The volume control is designed to allow the user to control the level of attenuation/amplification of the signal strength in the Hi-Fi amplifier. From the measurement results it is concluded that the volume control meets
all requirements, as it can be seen in table 3.3.
The tone control is designed to enhance or inhibit the bass and treble frequencies between ±10 dB to ±13 dB.
Based on simulations and tests it is concluded that the tone control meets all requirements except gain tolerance
for bass, which should have a minimum value of ±10 dB, but only has a value of ±9.5 dB (see table 3.7).
The power amplifier uses a class AB solution, which is designed from the LIN topology to deliver a high
output power, a low output impedance with feedback and a decent efficiency. Through simulation and testing
of the power amplifier it is concluded that the power amplifier meets the requirements, with a maximum THD
of 0.012 % and a minimum output power of 11.13 W. The results for the power amplifier measurements can be
found in table 3.9.
Finally, from the test of the whole circuit, with the volume control, tone control and the power amplifier connected in series it can be concluded that the system works as desired, with the exception of the bass control.
The output power of the Hi-Fi is measured to 10.1 W and the THD is measured to 0.16 %.
67
7. Perspective
If the Hi-Fi amplifier were to be used or marketed, a proper casing would be needed in order to abide by the
Danish legislation for electronic appliance [23]. Furthermore, a proper user interface and other developments
could be made to the Hi-Fi amplifier.
Most audio signals today are stereo signals. Therefore, it can be of relevance to construct a two (or multi)
channel amplifier, so that the Hi-Fi amplifier can handle stereo signals. In that case, it should be taken into
account that the tone control and volume control must be able to control both the left and right input stereo
signal. Therefore they must be re-designed so that both the left and right audio tracks can be controlled with the
same potentiometer at the volume control, the treble control, and the bass control. Also, when incorporating
stereo, a balance control can be implemented, enabling the user to change the level between the left and right
loudspeaker.
To increase the amount of accepted input sources, a pre-amplifier can be made in order to accept low
signal levels, such as analogue record playing units, microphones, or electronic instruments. Additionally,
the multichannel input availability can be made, so that several sources can be switched between, or even
played from at the same time. Furthermore, a distortion amplifier output can be made to give the opportunity
of using electronic guitars as input sources.
A more advanced tone controller can be developed, such as a equalizer, that can increase/decrease specific
frequency ranges, can be made either analogue or digital. Same goes with the volume control, where a digital
volume control could diminish the problems with the potentiometers, as well as an AGC can be developed to
automatically adjust sound levels to a preferred amplitude.
The efficiency of the Hi-Fi amplifier has not been measured. This can be examined and improved, e.g. by
using smaller thermal emitter resistances in the output stage, as these are larger than required. Also, resistances
throughout the system used to protect against thermal issues can be examined at possibly revised. Additionally,
the output of Hi-Fi amplifier can be further developed to incorporate several supplies, making it a class G
amplifier design, which will increase the efficiency, especially for low output powers.
69
Bibliography
[1]
G. Randy Slone. High-Power Audio Amplification Construction Manual. McGraw-Hill, 1999.
[2]
Learnabout Electronics.
Amplifiers module 4.2, November 2013.
learnabout-electronics.org/Amplifiers/amplifiers42.php.
[3]
NDT Resource Center.
Decibel, November
GeneralResources/decibel/decibel.htm.
[4]
Douglas Self. Audio Power Amplifier Design Handbook. Focal Press, 2009.
[5]
Kenneth C. Smith Adel S. Sedra. Microelectric Circuits. Oxford University Press, sixth edition, 2011.
[6]
Electronics-Tutorials. Amplifier, November 2013. http://www.electronics-tutorials.ws/
amplifier/amp_1.html.
[7]
Douglas Self. Amplifier Design Handbook, 6th Edition. Focal Press, 2013.
[8]
International Electrotechnical Comission. 61938-1, December 1997.
[9]
International Electrotechnical Comission. 581-6, 1979.
2013.
http://www.
http://www.ndt-ed.org/
[10] Deutsches Institut für Normung. 45500, Januar 1973.
[11] Aalborg University Acoustics. Facts about sound, December 2013. http://www.es.aau.dk/
sections/acoustics/press/fakta/fakta-om-lyd/.
[12] Texas Instruments. Op-amp tle 2071, November 2013. http://www.komponenten.es.aau.dk/
fileadmin/komponenten/Data_Sheet/Linear/TLE2071.pdf.
[13] Bruce Carter. An audio circuit collection, part 1, November 2000. From Texas Instruments Incorporated.
[14] ON Semiconductor. High-current complementary silicon transistors mj11015 and mj11016, December 2013. http://www.komponenten.es.aau.dk/fileadmin/komponenten/Data_
Sheet/Transistor/MJ11015.pdf.
[15] G.J Ritchie. Transistor Circuit Techniques. Chapman & Hall, 1993.
[16] Ole K. Jensen & Sofus B. Nielsen Jan H. Mikkelsen.
Slides mm 18, December 2013.
http://sict.moodle.aau.dk/file.php/179/Course_Material_subject_18/
ACD18.slides.pdf.
[17] Fisher Eletronik. Sk 402, December 2013. http://www.fischerelektronik.de/web_
fischer/en_GB/heatsinks/A01/Standard%20extruded%20heatsinks/PR/SK402_
/$productCard/parameters/index.xhtml.
[18] NXP Phillips. Bcm847bv datasheet, December 2013. http://www.nxp.com/documents/data_
sheet/BCM847BV_BS_DS.pdf.
[19] Phillips.
Bc547b datasheet, December 2013.
http://www.komponenten.es.aau.dk/
fileadmin/komponenten/Data_Sheet/Transistor/BC547.pdf.
71
B IBLIOGRAPHY
[20] Phillips.
Bc557b datasheet, December 2013.
http://www.komponenten.es.aau.dk/
fileadmin/komponenten/Data_Sheet/Transistor/BC557.pdf.
[21] NXP Phillips. Bcm857bv datasheet, December 2013. http://www.nxp.com/documents/data_
sheet/BCM857BV_BS_DS.pdf.
[22] General Semiconductor.
Bc556 thru bc559.
http://www.ceia.uns.edu.ar/
integrados/datos/Transistores%20PNP/BC556-BC557-BC558-BC559_General%
20Semiconductor.pdf.
[23] Retsinformation. Begendtgørelse for radioudstyr, teleterminaludstyr og elektriske og elektroniske
apparater og faste anlæg (danish), December 2013. https://www.retsinformation.dk/
Forms/R0710.aspx?id=29302.
[24] Hameg. Triple power supply hm7042-2, December 2013. http://shop.micronplus.ro/pdf/
HM%207042.pdf.
[25] Fluke. Multimeter, December 2013. http://www.testequipmentconnection.com/specs/
FLUKE_37.PDF.
[26] National Instruments. Ni-pci-4461 specification sheet, December 2013. http://www.ni.com/pdf/
products/us/pxi4461.pdf.
72
A. Standards
A.1
IEC 61938-3: 1996
Input
Matching Values
Rated source impedance
2.2 kΩ
≥ 22 kΩ
Input impedance
Rated source EMF
0.5 V
Minimum source EMF for rated output voltage
0.2 V
≥ 2.8 V
Overload source EMF
TABLE A.1: Input interface specifications for audio signals from the IEC 61938-1 standard. [8]
A.2
IEC 581-6: 1979
Requirements
Matching Values
Gain deviation effective frequency range:
1000 Hz
± 1.5 dB
Overload source EMF:
1000 Hz
≥ 2V
Total harmonic distortion for power amplifiers:
At rated output power and ≤ 26 dB
≤ 0.5 %
As long as the the harmonic requirements are met,
the output power is allowed to meet following
requirements compared to rated value:
At 40 Hz - 63 Hz
At 12 500 Hz - 16 000 Hz
≤ 3 dB
≤ 3 dB
≥ 10 W per channel
Rated output power
The amplifier shall be able to deliver the rated output power at rated distortion for at least 10 min with all
channels operating simultaneously at rated output power, and at ambient temperature between 15 ◦ C and
35 ◦ C.
Power amplifier (without volume control):
Wideband signal to-noise ratio
≥ 81 dB
Power amplifier (without volume control):
Weighted signal to-noise ratio
≥ 86 dB
TABLE A.2: Specifications for amplifiers from the IEC 581-6 standard. [9]
i
A. S TANDARDS
A.3
DIN 45500: 1973
Requirements
Matching values
Frequency range (1 kHz as reference)
Harmonic distortion (Pre or Power amplifier)
Valid at the frequency range 40 Hz to 12 500 Hz for output
power 10 W and ≤ 26 dB.
40 Hz to 16 kHz with ±1.5 dB tolerance.
Maximum 0.7 % for 40 Hz to 12 500 Hz
Intermodulation factor (Pre or Power amplifier)
Attenuation factor
Output Power:
Maximum 2 %
Minimum 3 for 40 Hz to 12 500 Hz
Minimum 10 W (Mono)
TABLE A.3: Specification for amplifiers from the DIN 45500. [10]
ii
Q3
BC547B
SINE(0 1.4142 1)
100meg
V2
Vee
R14
.ac dec 300 20 10Meg
Re1
5k
R1
10k
Vcc
Q1
BC547B
Vcc
Q2
BC547B
Re2
5k
Q4
BC547B
Vee
BC557B
Q11
R13
100µF 1k
C1
BC557B
Q10
R12
8.4k
18.5
V3
BC557B
Q9
18.5
V1
Q7
BC547B
Vee
F IGURE B.1: Open loop spice circuit.
R2
200
R6
3k
R5
1
Q8
BC547B
R4
200
Q5
BC547B
Q6
BC547B
R8
1k
R7
2.4k
Vee
iii
Vcc
Vcc
Vee
MJ11015
U1
R11
1
R10
1
U2
MJ11016g
Vcc
Vee
R3
50
100meg
C2
V4
AC 1.414
100meg
L1
R9
8
B. Simulation Diagrams
B. S IMULATION D IAGRAMS
.ac dec 300 10 50Meg
BC557B
Q11
Vcc
Q2
BC547B
BC557B
Q10
R13
R14 220pF
150
Cdom
R3
50
BC557B
Q9
V3
18.5
Vcc
V1
18.5
Q7
BC547B
R6
3k
R2
200
R7
2.4k
R8
1k
R5
1
Q8
BC547B
Q6
BC547B
Q5
BC547B
R4
200
MJ11015
U1
R11
0.25
R10
0.25
U2
MJ11016g
Vcc
Vee
Vcc
Q1
BC547B
C1
100µF 1k
R12
8.4k
Vee
V2
Q4
BC547B
Re2
5k
Vee
SINE(0 1.4142 1K)
AC 1.4142
R1
10k
Re1
5k
Vee
Vcc
Vee
F IGURE B.2: Closed loop spice circuit.
R9
8
iv
Q3
BC547B
Vee
v
Itest
AC 1
47µ
C8
.four 1k V(out)
.ac dec 100 10 1meg
Q3
BC547B
R18
8.4k
Vee
Zout = V(out)/I(Itest)
Re1
5k
R1
10k
BC557B
Q11
Vcc
Q1
BC547B
R13
R12
8.4k
D1
1000µ
100n
C7
C3
220p
150
18.5
100n
C5
C6
1000µ
18.5
V1
BC557B
Q9
R3
50
V2
C2
R14
D
D
Vcc
Q7
BC547B
R2
200
R6
3k
R15
1.6k
4.9k
R17
4.9k
R16
Port8
R4
200
Q5
BC547B
Port10
100n
Port11
C4
Port9
Q8
BC547B
Q6
BC547B
R8
1k
R7
3k
Port11
Out
Port10
F IGURE B.3: Spice circuit for simulation of input impedance.
Re2
5k
C1
BC557B
Q10
100µF 1k
Vcc
Q2
BC547B
Q4
BC547B
Vee
D2
Vee
BC557B
Q13
Vcc
Port8
Port9
R5
1.6k
Vee
BC547B
Q12
Vee
MJ11015
U1
R11
1
R10
1
U2
MJ11016g
Vcc
Vee
Out
R9
8
B. S IMULATION D IAGRAMS
.four 1k V(out)
BC557B
Q11
Q2
BC547B
BC557B
Q10
R13
D2
D1
D
D
R14
150
100n
C7
C3
Vcc
1000µ
C2
220p
R3
50
C6
BC557B
Q13
BC547B
Q12
Port8
Port9
100n
C5
V1
1000µ
18.5
BC557B
Q9
V2
18.5
Vcc
R5
1.6k
R6
3k
R15
1.6k
Q7
BC547B
R16
4.9k
R17
4.9k
Port10
Out
Port8
C4
Port10
100n
Port11
Port9
Q8
BC547B
Port11
R7
2000
R8
1k
Q6
BC547B
Q5
BC547B
R4
200
MJ11015
U1
R11
1
R10
1
U2
MJ11016g
Vcc
Vee
Vcc
Q1
BC547B
C1
R2
200
Vee
Vcc
100µF 1k
R12
8.4k
Vee
C8
R1
10k
Re2
5k
Q4
BC547B
Vee
R18
8.4k
Q3
BC547B
Re1
5k
Vee
F IGURE B.4: Spice circuit for simulation of input impedance.
"Zout = V(Out)"
Out
R9
8
Itest
AC 1
vi
47µ
.ac dec 100 10 30k
Vee
vii
AC 1.4142
V3
47µ
C8
R18
8.4k
Q3
BC547B
.ac dec 100 1 100meg
Vee
Re1
5k
R1
10k
BC557B
Q11
Vcc
Re2
5k
Q4
BC547B
Q2
BC547B
100µF 1k
C1
R13
BC557B
Q10
R12
8.4k
D1
1000µ
100n
C7
C3
220p
150
18.5
1000µ
18.5
100n
C5
C6
VAS
V1
BC557B
Q9
R3
50
V2
C2
R14
D
D
Vcc
Q7
BC547B
R2
200
R6
3k
R15
1.6k
R16
4.9k
R17
4.9k
Port8
R4
200
Q5
BC547B
Port10
100n
Port11
C4
Port9
Q8
BC547B
Q6
BC547B
R8
1k
R7
3000
Port11
Out
Port10
F IGURE B.5: Spice circuit for simulation of input impedance.
Q1
BC547B
Vcc
Diff_Amp_Out
Vee
D2
Vee
BC557B
Q13
Vcc
Port8
Port9
R5
1.6k
Vee
BC547B
Q12
Vee
MJ11015
U1
R11
1
R10
1
U2
MJ11016g
Vcc
Vee
Out
R9
8
C. Measurement Journals
C.1
Volume Control
Within this measurement journal the methods of measurement and all the measured data can be found for the
volume control module (see section 3.1).
Purpose of Measurement
The purpose of the measurement journal is to examine if the produced volume control meet the interface
specifications.
The desired measurements are:
• Input Impedance
• Output Impedance
• Frequency Response
• Total Harmonic Distortion (THD)
The Measured Object
The produced volume control is built with the circuit seen at figure C.1.
Vin
Vcc
Rpot
100 k
V+
TLE 2071
Vout
Vee
R2
4500 R1
1000 F IGURE C.1
Conditions of Measurement
The the conditions for the measurements can be found in section 2.3.
ix
C. M EASUREMENT J OURNALS
Tools of Measurement
Measurement tool
Tool number
Manufacturer / type
Precision
Voltage supply
33907
HAMEG
Found in [24].
Multimeter
33046
FLUKE 37
Found in [25].
N/A
NI-PCI-4461
Found in [26].
PC with Swept Sine
64640
N/A
N/A
BNC and MC cables
N/A
N/A
N/A
Audio analyser
Procedure for Measurements of Input and Output Impedance
NI-4461
Volume control
Ai0
Ao0
Rref
Volin
Volout
Zout
Zin
Ai1
F IGURE C.2: The measurement setup to measure the input impedance for the volume control.
NI-4461
Volume control
Ai0
Ao0
Ai1
Rref
Volout
Volin
Zout
Zin
2.2 kΩ
F IGURE C.3: The measurement setup to measure the output impedance for the volume control.
1. The volume control is connected to the NI-PCI-4461 analyser like seen on figure C.2. The reference
resistor is chosen to 712 Ω in order to meet the measurement specifications for the NI-PCI-4461 analyser
[26].
2. The program Swept Sine FRF VI is used. In “DAQ Configuration”, the AO excitation channel is set to
Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, and the AI response channel is set at Dev1/ai1.
3. In tab “Source Settings”, the amplitude is set to 0.707 V, the start frequency is set to 20 Hz, the stop
frequency is set to 20 kHz, and number of steps is set to 100.
4. The potentiometer, RPot is adjusted to the minimal value and the frequency sweep is commenced, after
which the data is saved.
5. Step 4 is repeated with the potentiometer RPot adjusted to the maximum value of 100 kΩ.
6. The volume control is disconnected and the measurement is done over the reference resistor Rref .
x
C.1. Volume Control
7. The volume control is connected to the NI-PCI-4461 analyser like seen on figure C.3.
8. Steps 4 and 5 are repeated.
9. The volume control is disconnected and the measurement is done over the reference resistor Rref .
10. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
Procedure for Measurements of the Frequency Response of Amplification and THD
NI-4461
Volume control
Ai0
Ao0
2.2 kΩ
Volin
Volout
Ai1
F IGURE C.4: The measurement setup to measure the frequency response for the volume control.
1. The volume control module is connected to the NI-PCI-4461 analyser like seen on figure C.4.
2. The program Swept Sine FRF VI is used. In “DAQ configuration”, the AO excitation channel is set to
Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, the AI response channel is set at Dev1/ai1, and the
sampling frequency is set to 50 000 Hz.
3. In “Source Settings”, the amplitude is set to 0.707 V, the start frequency is set to 20 Hz, the stop frequency
is set to 20 000 Hz, and number of steps at 100.
4. In “Processing Settings” the following parameters are set: Settle time to 25 ms, settle cycles to 5,
integration time to 25 ms, and integration cycles to 5.
5. In “THD settings” the following parameters are set: Maximum harmonic to 5 and THD units to dB (this
will be converted to % with the script attached to the CD).
6. The potentiometer, RPot , is adjusted to the maximum value of 100 kΩ and the frequency sweep is
commenced, after which the data is saved with the save button.
7. Step 4 is repeated with RPot adjusted to the minimal value, and then the sweep commenced again.
Subsequently, sweeps are made where the potentiometer value is increased with one tenth each time.
The potentiometer value is measured with the multimeter to ensure specified values. The frequency
response and THD measurement for the volume control is now complete.
8. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
Measured Data
The measurement results can be seen on the following figures.
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C. M EASUREMENT J OURNALS
Measurement of the volume control input impedance
100k
Input impedance (0 Ω)
Input impedance (91.4 kΩ)
95k
|Input impedance | / Ω
90k
85k
80k
75k
70k
65k
60k
55k
50k
20
100
1000
Frequency / Hz
10000
F IGURE C.5: The input impedance as a function of the frequencies from 20 Hz to 20 kHz. To show if the
value of the potentiometer in the volume control has any influence on the input impedance, two measurements
have been made. One with the potentiometer value of 0 Ω and one with the value of 91.4 kΩ. As seen on the
figure, the potentiometer has nearly no influence. Furthermore, it can be seen, that the input impedance is at
least 60 kΩ or higher for all the frequencies ranging from 20 Hz to 20 kHz.
Measurement of the volume control output impedance
0.55
Output impedance (0 Ω)
Output impedance (91.4 kΩ)
|Output impedance | / Ω
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
20
100
1000
Frequency / Hz
10000
F IGURE C.6: The output impedance as a function of the frequencies from 20 Hz to 20 kHz. To show if the
potentiometer in the volume control has any influence on the output impedance, two measurements have been
made. One with the potentiometer value of 0 Ω and one with the value of 91.4 kΩ. As seen on the figure, the
potentiometer has nearly no influence. Furthermore it can be seen that the output impedance is lower than at
least 0.55 Ω for all the frequencies ranging from 20 Hz to 20 kHz.
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C.1. Volume Control
Measurement of the volume control frequency respons
0.035
Amplification / dB
0.025
0.02
0.015
0.01
0 kΩ
9.14 kΩ
18.28 kΩ
27.42 kΩ
36.56 kΩ
45.7 kΩ
54.84 kΩ
63.98 kΩ
73.12 kΩ
82.26 kΩ
91.4 kΩ
0
−5.5
−20
Amplification / dB
0.03
20
15
9.14 kΩ
18.28 kΩ
27.42 kΩ
36.56 kΩ
45.7 kΩ
54.84 kΩ
63.98 kΩ
73.12 kΩ
82.26 kΩ
91.4 kΩ
0.005
−40
−60
−80
0
−100
−0.005
−0.01
20
100
1000
Frequency / Hz
10000
−120
20
100
1000
Frequency / Hz
10000
F IGURE C.7: The left figure shows the amplitude dependent on the frequencies from 20 Hz to 20 kHz. The
left figure has 11 sampled amplitudes moved to the same amplitude (0 dB @ 1 kHz) where deviation in the
effective frequency range at different amplitudes can be seen. All samples seen on the left figure shows a flat
response. The right figure shows the maximum amplification/attenuation, where the maximum amplification
is ≈ 14 dB and the maximum attenuation varies between −89 dB to −120 dB.
Measurement of volume control THD
900
0,008
0 kΩ (max attenuation)
91.4 kΩ (max amplification)
9.14 kΩ
0,007
800
700
0,006
Distortion / %
Distortion / %
600
0,005
0,004
0,003
500
400
300
0,002
200
0,001
0
20
100
100
1000
Frequency / Hz
10000
0
20
100
1000
Frequency / Hz
10000
F IGURE C.8: The left and the right figure shows the distortion in percent dependent on the frequencies 20 Hz
to 20 kHz. On the left figure, there are two samples, one with the potentiometer value of 91.4 kΩ and one
with 9.14 kΩ. Both of these samples are for all the frequencies between 20 Hz and 20 kHz lower than 0.008 %
distortion. On the right figure there is one sample where the potentiometer value is set at 0 Ω.
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C. M EASUREMENT J OURNALS
C.2
Tone Control
In this measurement journal the methods of measurement, procedure of measurement and all the all the
measurement results for the tone control module can be found.
Purpose of Measurement
The purpose of the measurement journal is to examine if the produced tone control module meets the interface
specifications made in figure 3.1 in chapter 3.
The desired measurements are:
• Input impedance
• Output impedance
• Frequency response
• Total harmonic distortion (THD)
The Measured Object
The produced tone control is built in one as seen at figure C.9.
Vin
Rta
Ct
RtP
Rtb
Rta
Ct
Rb
Cb
Rtb
Rb
RbP
Cb
VCC-
VCCVout
VCC+
Treble control
Bass control
VCC+
F IGURE C.9
Conditions of Measurement
The conditions for the measurements is in accordance with the acceptance testing section (section 2.3).
Tools of Measurement
Measurement tool
Tool number
Manufacturer / type
Precision
Voltage supply
33907
HAMEG
Found in [24].
Multimeter
33046
FLUKE 37
Found in [25].
N/A
NI-PCI-4461
found in [26]
PC with Swept Sine
64640
N/A
N/A
BNC and MC cables
N/A
N/A
N/A
Audio analyser
xiv
C.2. Tone Control
Procedure for Measurements of Input and Output Impedance
NI-4461
Tone control
Ai0
Ao0
Rref
Trebin
Bassout
Zin
Ai1
Zout
F IGURE C.10: The measurement setup to measure the input impedance for the tone control.
NI-4461
Tone control
Ai0
Ao0
Ai1
Rref
Bassout
Trebin
Zout
Zin
F IGURE C.11: The measurement setup to measure the output impedance for the tone control.
1. The tone control is connected to the NI-PCI-4461 analyser like seen on figure C.10. The reference resistor
is chosen to 712 Ω in order to meet the measurement specifications for the NI-PCI-4461 analyser [26].
2. The program Swept Sine FRF VI is used. In “DAQ configuration” the AO excitation channel is set to
Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, and the AI response channel is set at Dev1/ai1.
3. In “Source Settings” the amplitude is set to 1.414 V, the start frequency is adjusted to 20 Hz, the stop
frequency is set to 20 000 Hz, and number of steps at 100.
4. The potentiometer RtP is adjusted to the minimal value and the potentiometer RbP is adjusted to the
maximum value. The sweep is commenced, after which the data is saved.
5. The tone control is disconnected and the measurement is done over the reference resistor Rref . The input
impedance measurement is now complete.
6. The connection is readjusted to the tone control output Trebout like seen on figure C.11 and the frequency
sweep is performed.
7. The tone control is disconnected and the frequency sweep is done once more. The output impedance
measurement is now complete.
8. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
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C. M EASUREMENT J OURNALS
Measurement procedure for frequency response and THD
NI-4461
Tone control
Ai0
Ao0
Trebin
Trebout
Ai1
F IGURE C.12: The measurement setup to measure the frequency response for treble.
NI-4461
Tone control
Ai0
Ao0
Bassin
Bassout
Ai1
F IGURE C.13: The measurement setup to measure the frequency response for bass.
NI-4461
Tone control
Ai0
Ao0
Trebin
Bassout
Ai1
F IGURE C.14: The measurement setup to measure the THD and the frequency response for the tone control.
1. The tone control module is connected to the NI-PCI-4461 analyser like seen on figure C.12.
2. The program Swept Sine FRF VI is used. In “DAQ configuration”, the AO excitation channel is set to
Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, the AI response channel is set at Dev1/ai1, and the
sampling frequency is set to 50 000 Hz.
3. In “Source Settings”, the amplitude is set to 1.414 V, the start frequency is set to 20 Hz, the stop frequency
is set to 20 000 Hz, and number of steps to 100.
4. In “Processing Settings” the following parameters are set: Settle time to 25 ms, settle cycles to 5,
integration time to 25 ms and integration cycles to 5.
5. In “THD settings” the following parameters are set: Maximum harmonic to 5 and THD units to dB (This
is later converted to % with a MatLab script).
6. The treble potentiometer RtP is adjusted to the maximum value and the frequency sweep is commenced,
after which the data is saved.
xvi
C.2. Tone Control
7. Step 6 is repeated with RtP adjusted to the minimal value, half maximum value, 1.36 kΩ, and 3 kΩ. The
potentiometer value is measured with the multimeter to ensure specified values. The frequency response
for treble is now complete.
8. The input and output are reconnected to the tone control like on figure C.13.
9. Steps 6 and 7 are repeated. The frequency response for bass is now complete.
10. The input is reconnected as illustrated on figure C.14.
11. Step 6 is repeated with RtP adjusted to maximum, the half maximum, and the minimum value. The
frequency response and THD measurements for the tone control are now complete.
12. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
Measured data
The measurement results can be seen in the following figures.
Measurement of the tone control input impedance dependent on frequencies
Input impedance in worst case (Treble RP1 = 0 Ω)
|Input impedance| / Ω
5
10
4
10
3
10
20
100
1000
Frequency / Hz
10000
F IGURE C.15: The input impedance in relation to frequencies on a logarithmic scale, where the impedance
drop exponentially as the frequency increases. The end value of the impedance at 20 kHz is above the required
1 kΩ.
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C. M EASUREMENT J OURNALS
Measurement of the tone control output impedance dependent on frequencies
3
Output impedance in worst case (Bass R
p2
= 4.36 kΩ)
|Output impedance| / Ω
2.5
2
1.5
1
0.5
0
20
100
1000
Frequency / Hz
10000
F IGURE C.16: The output impedance in relation to frequencies on a logarithmic scale throughout the entire
frequency range. The value of the impedance varies from 0.1 Ω to 2.8 Ω.
Measurement of the treble control frequency respons
15
Measured max attenuation
Measured RP1=3kΩ and RP2=1.36kΩ
Measured RP1=2.18kΩ and RP2=2.18kΩ
10
Measured RP1=1.36kΩ and RP2=3kΩ
Measured max amplification
Amplification / dB
5
0
−5
−10
−15
20
100
1000
Frequency / Hz
10000
F IGURE C.17: The frequency response of amplitude on a logarithmic scale where the amplitude varies in the
higher frequencies. The value of the amplitude varies from ±3 dB to ±12.5 dB in the frequencies from 2 kHz
to 20 kHz at the maximum values.
xviii
C.2. Tone Control
Measurement of the bass control frequency respons
15
Measured max attenuation
Measured RP1=3kΩ and RP2=1.36kΩ
Measured RP1=2.18kΩ and RP2=2.18kΩ
10
Measured RP1=1.36kΩ and RP2=3kΩ
Measured max amplification
Amplification / dB
5
0
−5
−10
−15
20
100
1000
Frequency / Hz
10000
F IGURE C.18: The frequency response of amplitude on a logarithmic scale. The value of the amplitude varies
from ±12.5 dB to ±3 dB in the frequencies from 20 Hz to 500 Hz at the maximum values. Notice that, when
RP1 = 1.36 kΩ and RP2 = 3 kΩ, the amplification induces a attenuation at the frequencies 300 Hz to 300 Hz.
The same is apparent for the attenuation, when RP2 = 1.36 kΩ and RP1 = 3 kΩ.
Measurement of the tone control THD
0.03
Max amplification
Max attenuation
Neutral position
Distortion / %
0.025
0.02
0.015
0.01
0.005
0
20
100
1000
Frequency / Hz
10000
F IGURE C.19: The figure shows the THD in relation to the frequency at different attenuation/amplification
values in the tone control, where the values are highest in the lowest frequencies The value of THD varies from
almost 0 % to 0.0275 % in total. The neutral position has slightly less distortion in proportion to the maximum
amplification/attenuation. For maximum amplification, there is a sudden fall in THD at the frequency 8 kHz.
The reason for this is probably that the THD is calculated from its harmonic components, but in this case the
measurement goes to 20 kHz which means that some of the harmonic component to 8 kHz is not measured.
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C. M EASUREMENT J OURNALS
C.3
Power Amplifier
This measurement journal contains the methods of measurement, the measurement procedure and all the
measured data for the power amplifier module.
Purpose of Measurement
The purpose of the measurement journal is to examine if the produced power amplifier works as intended with
regard to the interface specifications, which can be found in figure 3.1 and chapter 3.
The desired measurements are:
• Input impedance
• Output impedance
• Frequency response
• Total Harmonic Distortion (THD)
• Output power
The Measured Object
The produced power amplifier is built with the circuit seen at figure C.20.
Input Stage
Voltage Amplifier Stage
VBE-Multiplier
Output Stage
1000 F
100 nF
8.4 k
Input
50 BCM857BV
(Potentiometer)
Vcc+
MJ11016
RP
BC547B
1 k
BCM847BV
47 F
10 k
BC547B
150 220 pF
3 k
BC547B
BC557B
BC547B
8.4 k
1 k
100 nF
5 k
5 k
200 Vcc+
Feedback Network ( )
F IGURE C.20
The Conditions of Measurement
The conditions for the measurements can be found in section 2.3.
xx
1.6 k
1
1.6k
1
4.9 k
MJ11016
BCM857BV
100 F
1000 F
4.9 k
BC547B
BC557B
200 Output
C.3. Power Amplifier
Measurement Tools
Measurement tool
Tool number
Manufacturer / type
Precision
Voltage supply
33892
HAMEG
Found in [24].
Multimeter
33045
FLUKE 37
Found in [25].
N/A
NI-PCI-4461
Found in [26].
PC with Swept Sine
64640
N/A
N/A
BNC and MC cables
N/A
N/A
N/A
Audio analyser
Procedure for Measurement of Input and Output Impedance
NI-4461
Power amplifier
Ai0
Ao0
Rref
Powin
Powout
Zout
Zin
Ai1
Rload
F IGURE C.21: The measurement setup to measure the input impedance for the power amplifier.
NI-4461
Power amplifier
Ai0
Ao0
Rref
Powout
Ai1
Powin
Zout
Zin
F IGURE C.22: The measurement setup to measure the output impedance for the power amplifier.
1. The power amplifier is connected to the NI-PCI-4461 analyser like seen on figure C.21.
2. The program Swept Sine FRF VI is turned on. In “DAQ configuration” the AO excitation channel is set
to Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, the AI response channel is set at Dev1/ai1, and
the sampling frequency is set to 50 000 Hz.
3. In “Source Settings” the amplitude is set to 1.414 V, the start frequency is set to 20 Hz, the stop frequency
is set to 20 000 Hz, and number of steps to 100.
4. The frequency sweep is commenced and the data is saved.
5. The power amplifier is disconnected and the measurement is done over the reference resistor Rref . The
frequency sweep/data save is done once more. The input impedance measurement is now complete.
6. The power amplifier is connected to the NI-PCI-4461 analyser like seen on figure C.22.
7. Step 4 is repeated.
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C. M EASUREMENT J OURNALS
8. The power amplifier is disconnected and the measurement is done over the reference resistor Rref . The
frequency sweep/data save is done once more. The output impedance measurement is now complete.
9. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
Measurement procedure for frequency response and THD in relation to frequency
NI-4461
Power amplifier
Ai0
Ao0
Powin
Ai1
Powout
Rload
F IGURE C.23: The measurement setup to measure the frequency response for the power amplifier.
1. The power amplifier module is connected to the NI-PCI-4461 analyser like seen on figure C.23.
2. The program Swept Sine FRF VI is turned on. In “DAQ configuration” the AO excitation channel is set
to Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, the AI response channel is set at Dev1/ai1, and
the sampling frequency is set to 50 000 Hz.
3. In “Source Settings” the amplitude is set to 1.414 V, the start frequency is set to 20 Hz, the stop frequency
is set to 20 000 Hz, and number of steps to 100.
4. In “Processing Settings” the following parameters are set: settle time to 25 ms, settle cycles to 5,
integration time to 25 ms and integration cycles to 5.
5. In “THD settings” the following parameters are adjusted: Maximum harmonic to 5 and THD units to dB
(This will later be converted to % with a MatLab script).
6. The frequency sweep is commenced and the data is saved.
measurements for the power amplifier is now complete.
The frequency response and THD
7. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
Measured data
The measurement results can be seen on the following figures.
Input impedance
The first measurement for the power amplifier is the input impedance, which is measured with the procedure
found in C.4, step 1 to 5 and 9.
xxii
C.3. Power Amplifier
Measurement of the power amplifier Input impedance
8456
Input impedance for rated conditions
8454
|Input impedance| / Ω
8452
8450
8448
8446
8444
8442
8440
8438
20
100
1000
Frequency / Hz
10000
F IGURE C.24: The figure shows the input impedance which is approximately independent of frequencies
within the effective frequency range. The lowest real value of the impedance is ≈8.4 kΩ at 20 kHz.
Output impedance
The measurement of the output impedance for the power amplifier is measured with the procedure found in
C.4, step 6 to 9.
Measurement of the power amplifier output impedance
0.68
Output impedance for rated conditions
0.675
|Output impedance| / Ω
0.67
0.665
0.66
0.655
0.65
0.645
0.64
0.635
20
100
1000
Frequency / Hz
10000
F IGURE C.25: The figure shows an output impedance dependant on frequencies on a logarithmic scale, where
the impedance only varies approximately 0.3 Ω over the effective frequency range. The highest real value of
the impedance is ≈0.675 Ω.
Frequency response
The measurement of the frequency sweep for the power amplifier is measured with the procedure found in C.4,
step 1 to 7.
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C. M EASUREMENT J OURNALS
Measurement of the power amplifier frequency respons
19.55
Amplification for rated conditions
Amplification / dB
19.54
19.53
19.52
19.51
19.5
19.49
20
100
1000
Frequency / Hz
10000
F IGURE C.26: The figure shows a frequency response with amplitude dependant on frequencies on a
logarithmic scale. The value of the amplitude varies approximately 0.05 dB in the frequencies from 20 Hz
to 20 kHz.
THD
The measurement of frequency dependent THD for the power amplifier is measured with the procedure found
in C.4, step 1 to 7. This measurement is shown on figure C.27.
Measurement of the power amplifier frequency dependent THD
0.014
THD for rated conditions
0.012
THD / %
0.01
0.008
0.006
0.004
0.002
20
100
1000
Frequency / Hz
10000
F IGURE C.27: The figure shows the THD dependant on frequencies where the THD values are highest in the
lower frequencies. The value of THD varies from almost 0.002 % to 0.012 % in total.
Output power
The output power for the power amplifier is plotted with MatLab using equation 2.5 in section 2.3.
xxiv
C.3. Power Amplifier
Measurement of the power amplifier output power
11.28
Output power for rated conditions
11.26
Output power / Watt
11.24
11.22
11.2
11.18
11.16
11.14
11.12
20
100
1000
Frequency / Hz
10000
F IGURE C.28: The figure shows the output power with amplitude dependant on frequencies on a logarithmic
scale. The value of the amplitude varies from 11.13 W to 11.25 W in the frequencies from 20 Hz to 20 kHz.
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C. M EASUREMENT J OURNALS
C.4
Acceptance Testing of Hi-Fi Amplifier
Within this acceptance testing of the Hi-FI amplifier the methods and procedures for each measurement can be
found with the appurtenant measurement results.
Purpose of Measurement
The purpose of the acceptance testing is to examine whether the produced Hi-Fi amplifier works as intended
with regard to the specifications, which can be found in section 2.2.
The desired measurements are the measurable specifications found in sections 2.2, which is the following
five items.
• Input Impedance
• Output Impedance
• Frequency Response
• Total Harmonic Distortion (THD) dependant on frequencies and amplitude.
• Output Power
The Measured Object
The produced Hi-Fi amplifier is constructed with all the modules connected, such that the volume control is
first, the tone control is second and the power amplifier is last like seen at figure C.29.
Volume control
Power amplifier
Tone control
Input
Output
F IGURE C.29: The figure shows the Hi-Fi amplifier, which consists of the volume control, the tone control
and the power amplifier, connected in the mentioned order.
The conditions of measurement
The rated test conditions and the theory for each measurement can be found in section 2.3.
Measurement tools
Measurement tool
Tool number
Manufacturer / type
Precision
Voltage supply
33892
HAMEG
Found in [24].
Multimeter
33045
FLUKE 37
Found in [25].
N/A
NI-PCI-4461
Found in [26].
PC with Swept Sine
64640
N/A
N/A
BNC and MC cables
N/A
N/A
N/A
Audio analyser
xxvi
C.4. Acceptance Testing of Hi-Fi Amplifier
Procedure for measurement of Input and Output Impedance
The following figures and procedure describes how the input and output impedance for the Hi-Fi amplifier is
measured.
NI-4461
Hi-Fi amplifier
Ai0
Ao0
Rref
Input
Output
Zin
Ai1
Zout
Rload
F IGURE C.30: The measurement setup to measure the input impedance for the amplifier circuit.
NI-4461
Hi-Fi amplifier
Ai0
Ao0
Rref
Output
Ai1
Input
Zout
Zin
2.2 kΩ
F IGURE C.31: The measurement setup to measure the output impedance for the amplifier circuit.
1. First the volume control is adjusted to two times amplification, next the tone control is adjusted to unity
amplification in both the bass and treble part.
2. The amplifier circuit is connected to the NI-PCI-4461 analyser like seen on figure C.30.
3. The program Swept Sine FRF VI is turned on. In “DAQ configuration” the AO excitation channel is set
to Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, the AI response channel is set at Dev1/ai1, and
the sampling frequency is set to 50 000 Hz.
4. In “Source Settings” the amplitude is set to 1.414 V, the start frequency is set to 20 Hz, the stop frequency
is set to 20 000 Hz, and number of steps to 100.
5. The frequency sweep is commenced and the data is saved.
6. The amplifier is disconnected and the measurement is done over the reference resistor Rref alone. The
frequency sweep/data save is done once more. The input impedance measurement is now complete.
7. The amplifier circuit is connected to the NI-PCI-4461 analyser like seen on figure C.31.
8. Step 4 is repeated.
9. The amplifier circuit is disconnected and the measurement is done over the reference resistor Rref alone.
The frequency sweep/data save is done once more. The output impedance measurement is now complete.
10. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
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C. M EASUREMENT J OURNALS
Procedure for Measurement of Frequency Response and THD in Relation to Frequency
NI-4461
Hi-Fi amplifier
Ai0
Ao0
2.2 k
Input
Ai1
Output
Rload
F IGURE C.32: The measurement setup to measure the frequency response for the amplifier circuit.
1. First the volume control is adjusted to two times amplification, next the tone control is adjusted to unity
amplification in both the bass and treble part.
2. The amplifier circuit is connected to the NI-PCI-4461 analyser like seen on figure C.32.
3. The program Swept Sine FRF VI is turned on. In “DAQ configuration” the AO excitation channel is set
to Dev1/ao0, the AI stimulus channel is set to Dev1/ai0, the AI response channel is set at Dev1/ai1, and
the sampling frequency is set to 50 000 Hz.
4. In “Source Settings” the amplitude is set to 1.414 V, the start frequency is set to 20 Hz, the stop frequency
is set to 20 000 Hz, and number of steps to 100.
5. In “Source Settings” the amplitude is set to 1.414 V, the start frequency is set to 20 Hz, the stop frequency
is set to 20 000 Hz, and number of steps to 100.
6. In “Processing Settings” the following parameters are set: settle time to 25 ms, settle cycles to 5,
integration time to 25 ms and integration cycles to 5.
7. The frequency sweep is commenced and the data is saved.
8. Readjust the "source settings" amplitude to 0.283 V and the volume control output to 1 V with relation to
this new source amplitude. The frequency sweep and data save is done.
9. Readjust the "source settings" amplitude to 3.959 V and the volume control output to 1 V with relation
to this new source amplitude. The frequency sweep and data save is done. The frequency response and
THD measurements for the amplifier circuit is now complete.
10. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
xxviii
C.4. Acceptance Testing of Hi-Fi Amplifier
Measurement procedure for THD dependants on amplitude
NI-4461
Hi-Fi amplifier
Ai0
Ao0
Input
Output
Ai1
F IGURE C.33: The measurement setup to measure the THD with a single frequency varying amplitude for
the Hi-Fi amplifier.
1. First the volume control is adjusted to two times amplification, next the tone control is adjusted to unity
amplification in both the bass and treble part.
2. The NI-PCI-4461 outputs are readjusted like on figure C.33.
3. The program Swept Amplitude THD VI is turned on. In “DAQ Configuration” the output channel is set
to Dev1/ao0 and the input channel is set to Dev1/ai1.
4. In “Source Settings” the frequency is set to 1000 Hz, the minimum amplitude is set to 0.1414 V and the
maximum amplitude is set to 0.707 V. The number of steps is set to 100.
5. The amplitude sweep is commenced, and the data is saved. The amplitude dependant THD measurement
for the Hi-Fi amplifier is now complete.
6. The measurement results can be plotted in MatLab with the scripts found in the attached CD.
Measured Data
The measurement results can be seen on the following figures.
Input Impedance
The first measurement for the amplifier circuit is the input impedance, which is measured with the procedure
found in C.4, step 1 to 6 and 10.
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C. M EASUREMENT J OURNALS
Measurement of the Hi−Fi amplifier Input impedance
82.65 k
|Input impedance| / Ω
82.6 k
82.55 k
82.5 k
82.45 k
82.4 k
82.35 k
Input impedance for rated conditions
82.3 k
20
100
1000
Frequency / Hz
10000
F IGURE C.34: This figure shows the input impedance for the Hi-Fi amplifier for rated conditions. The lowest
to highest value are ≈ 82.32 kΩ to 82.64 kΩ. The impedance is highest at the low frequencies and lowest at
the highest frequencies, but the deviation from lowest to highest impedance is no more than ≈ 300 Ω to 400 Ω.
Output Impedance
The measurement of the output impedance for the amplifier circuit is measured with the procedure found in
C.4, step 7 to 10.
Measurement of the Hi−Fi amplifier output impedance
0.7
Output impedance for rated conditions
|Output impedance| / Ω
0.6
0.5
0.4
0.3
0.2
0.1
0
20
100
1000
Frequency / Hz
10000
F IGURE C.35: This figure shows the output impedance of the Hi-Fi amplifier at rated conditions. The lowest
to highest value are ≈ 0.07 Ω to 0.55 Ω. Around 50 Hz there is a peak. If the peak are not of importance, the
impedance in general are lowest at the low frequencies and highest at the highest frequencies.
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C.4. Acceptance Testing of Hi-Fi Amplifier
Frequency Response
The measurement of the frequency sweep for the amplifier circuit is measured with the procedure found in C.4,
step 1 to 8.
Measurement of the Hi−Fi amplifier frequency respons
0.15
0.1
Amplification / dB
0.05
0
−0.05
−0.1
Frequency response 0.2 V RMS
Frequency response 0.5 V RMS
Frequency response 2.8 V RMS
−0.15
−0.2
−0.25
20
100
1000
Frequency / Hz
10000
F IGURE C.36: The figure shows the frequency response of the Hi-Fi amplifier for following values: 0.5 V,
0.2 V and 2.8 V. The value of the amplitude varies ≈ 0.38 dB in the frequencies from 20 Hz to 20 kHz. The
frequency response varies throughout the entire frequency range, where the measurement for rated input
(0.5 V) is different that those for 0.2 V and 2.8 V.
THD
The measurement of frequency dependent THD for the amplifier circuit is measured with the procedure found
in section C.4, step 1 to 8.
Measurement of the Hi−Fi amplifier frequency dependent THD
0.16
THD 0.2 V RMS
THD 0.5 V RMS
THD 2.8 V RMS
0.14
0.12
THD / %
0.1
0.08
0.06
0.04
0.02
0
20
100
1000
Frequency / Hz
10000
F IGURE C.37: The figure shows the THD dependant on frequencies for following values: 0.5 V, 0.2 V and
2.8 V. The THD values are highest in the highest frequencies. The value of THD varies from almost 0.005 %
to 0.15 % in total. At 25 Hz there is a peak at all measurements. At ≈ 11 kHz, there is a sudden fall in THD
for all amplitudes.
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The measurement of amplitude dependent THD for the Hi-Fi amplifier is measured with the procedure found
in section C.4, step 1 to 6.
Measurement of the Hi−Fi amplifier amplitude dependent THD
0.036
Amplitude dependent THD for rated conditions
0.034
Distortion / %
0.032
0.03
0.028
0.026
0.024
0.141
0.282
0.423
Source peak amplitude / V
0.564
0.705
F IGURE C.38: The figure shows the Hi-Fi amplifier THD dependant on amplitude for rated conditions @
1 kHz. The value of THD varies from ≈ 0.025 % to 0.0345 % in total, which is a deviation of 0.0095 %.
Because of the low deviation, the response of THD dependent on amplitude is considered flat.
Output Power
The output power for the amplifier circuit is plotted with MatLab using equation 2.5 in section 2.3.
Measurement of the Hi−Fi amplifier output power
11.5
Output power / Watt
0.2 V
0.5 V
2.8 V
11
10.5
10
20
100
1000
Frequency / Hz
10000
F IGURE C.39: The figure shows the Hi-Fi amplifier output power dependant on frequencies for following
values: 0.5 V, 0.2 V and 2.8 V. The value of the amplitude varies from 10.12 W to 11.35 W in the frequencies
from 20 Hz to 20 kHz which is a deviation of 1.23 W.
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