Analog Dithering Techniques for Wireless Transmitters

154 Pages·2012·4.71 MB·English

by  Foad Arfaei Malekzadeh

Analog Circuits and Signal Processing
Series Editors
Mohammed Ismail
Mohamad Sawan
For furthervolumes:
http://www.springer.com/series/7381
Foad Arfaei Malekzadeh
Reza Mahmoudi Arthur H. M. van Roermund
•
Analog Dithering
Techniques for Wireless
Transmitters
123
FoadArfaei Malekzadeh Arthur H.M.van Roermund
Universityof Waterloo Technische Universiteit Eindhoven
1001-545BelmontAve Postbus 513
Kitchener 5600MBEindhoven
ONN2M5G7 Netherlands
Canada
Reza Mahmoudi
Technische Universiteit Eindhoven
Postbus 513
5600MBEindhoven
Netherlands
ISBN 978-1-4614-4216-5 ISBN 978-1-4614-4217-2 (eBook)
DOI 10.1007/978-1-4614-4217-2
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2012939482
(cid:2)SpringerScience+BusinessMediaNewYork2013
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Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Dithering Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Problem Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Book Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Dithering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Dithering Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Equivalent Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 High and Low Frequency Dithering. . . . . . . . . . . . . . . . . . . . . 13
2.4 Rotating Vector Representation. . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Fourier Series Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.1 High Frequency Dithering . . . . . . . . . . . . . . . . . . . . . . 16
2.5.2 Low Frequency Dithering . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Statistical Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6.1 Equivalent Nonlinearity for High
Frequency Dithering . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6.2 Equivalent Nonlinearity for Low Frequency Dithering. . . 22
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Describing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 Sinusoidal DF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Single Sinusoidal DF. . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.2 Two Sinusoidal Input DF. . . . . . . . . . . . . . . . . . . . . . . 30
3.1.3 Multiple Sinusoidal Input DF. . . . . . . . . . . . . . . . . . . . 32
3.1.4 Frequency Translated DF. . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Random Input Describing Function . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 Real Gaussian Input DF. . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 Complex Gaussian DF. . . . . . . . . . . . . . . . . . . . . . . . . 34
v
vi Contents
3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Architectures and Topologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1 Architecture Level Considerations. . . . . . . . . . . . . . . . . . . . . . 38
4.1.1 Open-Loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.2 Closed-Loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.3 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.4 Common Mode Dither. . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.5 Possible Dithering Locations . . . . . . . . . . . . . . . . . . . . 40
4.1.6 Slope Gain Considerations. . . . . . . . . . . . . . . . . . . . . . 41
4.2 Circuit Topologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.1 Voltage Mode and Current Mode Class-D . . . . . . . . . . . 42
4.2.2 Design Aspects of Voltage Mode Class-D . . . . . . . . . . . 43
4.2.3 Design Aspects of the Current Mode Class-D. . . . . . . . . 50
4.3 Dithering Limitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 Linearity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1 Existing Methods and Shortcomings . . . . . . . . . . . . . . . . . . . . 58
5.2 Signal Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.1 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.2 Multisine Representation of Signals . . . . . . . . . . . . . . . 59
5.2.3 DFT Method to Extract Multisine. . . . . . . . . . . . . . . . . 61
5.2.4 Statistical Synbook Methods. . . . . . . . . . . . . . . . . . . . . 62
5.3 Proposed Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4 Correlated Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.4.1 Open Loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.4.2 Closed Loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.5 Nonlinear Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.5.1 Open Loop Real Gaussian . . . . . . . . . . . . . . . . . . . . . . 67
5.5.2 Open Loop Complex Gaussian. . . . . . . . . . . . . . . . . . . 69
5.5.3 Closed Loop Distortion . . . . . . . . . . . . . . . . . . . . . . . . 71
5.5.4 Nonlinear Metrics Calculation . . . . . . . . . . . . . . . . . . . 72
5.6 Memory Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.6.1 Volterra Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.6.2 Wiener-Hammerstein Models. . . . . . . . . . . . . . . . . . . . 74
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6 Spurious Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.1 Existing Analysis Methods and Problems. . . . . . . . . . . . . . . . . 80
6.2 Proposed Optimization Approach . . . . . . . . . . . . . . . . . . . . . . 82
Contents vii
6.3 Optimization Technique for Multi-Sine . . . . . . . . . . . . . . . . . . 83
6.3.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3.2 Common Mode Dithering Topology . . . . . . . . . . . . . . . 85
6.3.3 Harmonic Multi-Tone Dither Effects. . . . . . . . . . . . . . . 86
6.4 Case Studies and Validations . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.5 Applications in Linearity-Efficiency Trade-Off. . . . . . . . . . . . . 87
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7 High Frequency Dithering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.1 Open Loop VMCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.1.1 Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.1.2 Measurement and Validation . . . . . . . . . . . . . . . . . . . . 93
7.2 Self-Oscillating Class-D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.2.1 Topology Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.2.2 Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.2.3 Measurement and Validation . . . . . . . . . . . . . . . . . . . . 103
7.2.4 Generic Design Procedure . . . . . . . . . . . . . . . . . . . . . . 105
7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8 Low Frequency Dithering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.1 Open Loop VMCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.1.1 Fine Tuning of the Dithering Frequency . . . . . . . . . . . . 109
8.1.2 Measurement and Validation . . . . . . . . . . . . . . . . . . . . 110
8.2 Open Loop CMCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.2.1 Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.2.2 Fine Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.2.3 Measurement and Verification . . . . . . . . . . . . . . . . . . . 116
8.3 Generic Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9 Novel Interpretations of Dithering . . . . . . . . . . . . . . . . . . . . . . . . 121
9.1 Dynamic Load Modulation and Dithering. . . . . . . . . . . . . . . . . 121
9.2 Area Modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.3 RF-ADC with Dithering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.4 Mixer as Dithering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.4.1 Driving State Equations. . . . . . . . . . . . . . . . . . . . . . . . 129
9.4.2 Taking Averages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
9.4.3 Solution of the Differential Equations . . . . . . . . . . . . . . 131
9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
viii Contents
Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Chapter 1
Introduction
Poweramplifiers are the mostpowerhungry and perhapsthe most expensive part
of the wireless transmitters in the RF chain. The key differentiators among dif-
ferentPAsarecost,yield,weight,efficiency,easeofdesign,reliability,ruggedness
and high temperature operation. Generally, the most important of these require-
ments are linearity and efficiency. Modern communication systems employ high
crest factor signals as a result of the urgent need of higher bandwidth efficiency.
Achieving mandatory linearity constraints along with competitive efficiency
requirements becomes more difficult with increased signal crest factor [1–3].
In the field of PA design, for linear and efficient operation, two distinct trends
exist, which are either using an inherently linear PA (with poor efficiency) with
supply or load modulation techniques (e.g. envelope tracking) to enhance their
efficiency,whileretainingthelinearity(withpre-distortionorCartesianfeedback),
or using inherently nonlinear (but power efficient) PAs and try to linearize them.
A sub-class of the efficient power amplifiers is known as the class of switched
mode PAs (SMPA). These PAs have different classes of operation, while all of
them have one thing in common: they move fast between the saturation and
off-stateofthedevices,whichmakeseitherthevoltageorthecurrentofthedevice
terminalsoftheseamplifiersnegligible,hencedecreasingthepowerloss,andthus
increasing the efficiency. Among them, operation classes D, E, F, F-1 etc. can be
named. Another similarity among them is that they all suffer from very poor
linearity, i.e. because they switch between cut-off and saturation levels, they
cannotreflecttherealenvelopevariationsoftheinputsignalontheoutputsignal,
which is usually switching between two constant levels. There are a couple of
techniques, for linearization of SMPAs; among them are EER and out-phasing.
F.ArfaeiMalekzadehetal.,AnalogDitheringTechniquesforWirelessTransmitters, 1
AnalogCircuitsandSignalProcessing,DOI:10.1007/978-1-4614-4217-2_1,
(cid:2)SpringerScience+BusinessMediaNewYork2013
2 1 Introduction
1.1 Motivation
In order to obtain the required linearity-efficiency compromise with switched
modepoweramplifiers,varioustechniquesarebeingemployedincurrentwireless
systems.Amongthemarepolarmodulation[4,5]andout-phasingtechniques[6].
Thesehavebeendiscussedindetail.Theyusetherealenvelopesignaltomodulate
aswitched-modeamplifieroutput,orconvertthemodulatedsignaltoasummation
of two constant-envelope signals to be processed by switched mode PAs. The
majordrawbackofallthosetechniquesisthecomplicatedsignalprocessingthatis
needed for wave shaping and the poor efficiency of the tracking amplifier, which
affects the overall linearization efficiency.
Besidesthesetechniques,therearealsotime-domainencodingtechniques,like
sigma-delta modulators (SDM) or pulse-width modulators (PWM). They show
good linearity-efficiency performance. In those techniques, the amplitude and
phase information of a digitally modulated message signal is encoded in limited
number of quantized levels of an output pulse train (e.g. zero and one for binary
encoding) and their zero crossings. This makes it possible to use an efficient
switched mode power amplifier like class D. The major drawback is a relatively
high clocking (or sampling) frequency, which in turn will degrade the power
efficiency due to more reactive power loss.
There is also a class of signal processing techniques which use an external
signal to change the linearity behavior of hard nonlinearities, pruned as dithering
techniques.Thegenericnameof‘dithering’isusedforthisphenomenon,whichis
explained in the following section.
1.2 Dithering Concept
The term ‘dither’ was published in books on analog computation and hydraulic
controlledgunsshortlyafterthewar[7,8].In[9],itisstatedthatoneoftheearliest
applications of dither came in World War II. Airplane bombers used mechanical
computers to perform navigation and bomb trajectory calculations. These
mechanical computers performed more accurately when flying on board the air-
craft, and less well on ground. Engineers realized that the vibration from the
aircraft reduced the error from sticky moving parts. Instead of moving in short
steps, they moved more continuously. Small vibrating motors were built into the
mechanical computers, and their vibration was called dither from the Middle
English verb ‘‘didderen’’ meaning ‘‘to tremble’’ [9]. Dither successfully makes a
digitization system a little more analog in the good sense of the word.
The concept of dithering to reduce quantization patterns was first applied by
Lawrence G. Roberts in his 1961 MIT master’s book [10] though he did not use
the term dither. By 1964 dither was being used in the modern sense, described in
[11].
1.2 DitheringConcept 3
Fig.1.1 a The problem of dithering, as the dither signal dðtÞ; combined with a generic input
signal rgðtÞ is applied to an single input single output transfer characteristic y¼fNLðxÞ. b The
equivalent problem formulation, and c The relationship between the smoothed equivalent
functionandoriginalfunction
The concept of dithering as a linearization technique is exploited in many
applications. As an example, dithering has applications for linearization and for
quantization noise reduction. Many analog-to-digital converter applications
requirelowdistortionforaverywidedynamicrangeofsignals.Unfortunately,the
distortion caused by digitizing an analog signal increases as the signal amplitude
decreases,andisespeciallyseverewhenthesignalamplitudeisofthesameorder
asthequantizingstep.Indigitalaudioapplications,forexample,low-levelsignals
occur often, sometimes alone and sometimes in the presence of larger signals.
If these low-level signals are severely distorted by the quantization process, the
usefulnessofthesystemisgreatlydiminished.Itis,infact,possibletoreducethe
distortion,andalsotoimprovetheresolutionbelowoneLSB(leastsignificantbit),
by adding noise (or dither) to the signal of interest. For ideal converters, the
optimum dither is white noise at a voltage level of about 1/3 LSB rms.
The addition of dither effectively smoothes the ADC transfer function, which
normallyhasastaircase-likeappearance,butitcomeswithaslightreductionofthe
signal-to-noise ratio [11, 12].
1.3 Problem Statement
The topic of the current book lies in the realm of linearized SMPA design.
Assuming that we have a static nonlinear input output transfer function, the
problem is illustrated in Fig. 1.1. We have a signal that is called r ðtÞ which is a
g
band-limited(eitheralowpassorband-passsignal),andwehaveastaticnonlinear
input–output characteristic y¼f ðxÞ; which is a single input single output
NL
mappingfunctiontodescribethenonlinearblock.Theblockresemblesmanytypes
ofcommon switched mode poweramplifiers inwhich the switching device in the