Table Of ContentDIGITALSYNTHESIZERS AND TRANSMITTERS
FORSOFTWARE RADIO
Digital Synthesizers and Transmitters
for Software Radio
by
JOUKOVANKKA
Helsinki University of Technology,
Finland
AC.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-3194-7 (HB) Springer Dordrecht, Berlin, Heidelberg, New York
ISBN-10 1-4020-3195-5 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York
ISBN-13 978-1-4020-3194-6 (HB) Springer Dordrecht, Berlin, Heidelberg, New York
ISBN-13 978-1-4020-3195-3 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York
Published by Springer,
P.O. Box 17, 3300 AADordrecht, The Netherlands.
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© 2005 Springer
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Printed in the Netherlands.
Contents
PREFACE...................................................................................XVII
LIST OF ABBREVIATIONS...................................................XXIII
1. TRANSMITTERS................................................................1
1.1 Direct Conversion Transmitters............................................................1
1.2 Dual-Conversion Transmitter................................................................3
1.3 Transmitters Based on VCO Modulation.............................................3
1.4 Offset-PLL Architecture.........................................................................6
1.5 Envelope Elimination and Restoration (EER)......................................6
1.6 Polar-Loop Transmitter.........................................................................9
1.7 Linear Amplification with Nonlinear Components (LINC)..............10
1.8 Combined Analogue Locked LoopUniversal Modulator (CALLUM)
14
1.9 Linear Amplification Employing Sampling Techniques (LIST).......15
vi Contents
1.10 Transmitters Based on Bandpass Delta Sigma Modulator...........17
REFERENCES.............................................................................19
2. POWER AMPLIFIER LINEARIZATION.....................25
2.1 Feedforward...........................................................................................25
2.2 Cartesian Modulation Feedback..........................................................29
2.3 Predistortion..........................................................................................31
2.3.1 Analog Predistortion..............................................................................33
2.3.2 Mapping Predistortion...........................................................................35
2.3.3 Complex Gain Predistortion..................................................................36
2.3.4 Polar Predistortion.................................................................................38
2.3.5 RF-Predistortion Based on Vector Modulation.....................................39
2.3.6 Data Predistorters..................................................................................41
REFERENCES.............................................................................41
3. DIGITAL COMPENSATION METHODS FOR
ANALOG I/Q MODULATOR ERRORS.......................................49
3.1 Quadrature Modulator ErrorsCompensation...................................52
3.1.1 Symmetric Commmpensation Method........................................................53
3.1.2 Partial Correction of Mixer Nonlinearity in Quadrature Modulators....55
3.1.3 Asymmetric Compensation Method......................................................56
3.1.4 Digital Precompensation Method without Training Signal...................57
REFERENCES.............................................................................58
4. DIRECT DIGITAL SYNTHESIZERS............................61
4.1 Conventional Direct Digital Synthesizer.............................................61
4.2 Pulse Output DDS.................................................................................63
4.3 DDS Architecture for Modulation Capability....................................65
4.4 QAM Modulator....................................................................................65
Contents vii
REFERENCES.............................................................................69
5. RECURSIVE OSCILLATORS.........................................73
5.1 Direct-Form Oscillator.........................................................................73
5.2 Coupled-Form Complex Oscillator.....................................................76
REFERENCES.............................................................................79
6. CORDIC ALGORITHM...................................................81
6.1 Scaling of IIInandQn...............................................................................84
6.2 Quantization Errors in CORDIC Algorithm......................................85
6.2.1 Approximation Error.............................................................................85
6.2.2 Rounding Error of Inverse Tangents.....................................................86
6.2.3 Rounding Error of III andQ ..................................................................87
n n
6.3 Redundant Implementations of CORDIC Rotator............................87
6.4 Hybrid CORDIC...................................................................................88
6.4.1 Mixed-Hybrid CORDIC Algorithm......................................................89
6.4.2 Partitioned-Hybrid CORDIC Algorithm...............................................90
REFERENCES.............................................................................92
7. SOURCES OF NOISE AND SPURS IN DDS.................97
7.1 Phase Truncation Related Spurious Effects........................................97
7.2 Finite Precision of Sine Samples Stored in LUT...............................103
7.3 Distribution of Spurs...........................................................................105
7.4 Phase Noise of DDS Output................................................................108
7.5 Post-Filter Errors................................................................................110
REFERENCES...........................................................................110
viii Contents
8. SPUR REDUCTION TECHNIQUES IN SINE OUTPUT
DIRECT DIGITAL SYNTHESIZER...........................................113
8.1 Nicholas Modified Accumulator........................................................114
8.2 Non-Subtractive Dither.......................................................................116
8.2.1 Non-Subtractive Phase Dither.............................................................116
8.2.2 First-Order Analysis............................................................................117
8.2.3 Non-Subtractive Amplitude Dither.....................................................121
8.3 Subtractive Dither...............................................................................122
8.3.1 High-Pass Filtered Phase Dither..........................................................123
8.3.2 High-Pass Filtered Amplitude Dither..................................................123
8.4 Tunable Error Feedback in DDS.......................................................124
8.4.1 Phase EF..............................................................................................125
8.4.1.1 Phase EF for Cosine DDS........................................................126
8.4.1.2 Phase EF for Quadrature DDS.................................................128
8.4.2 Amplitude EF......................................................................................129
8.4.2.1 Amplitude EF for Cosine DDS................................................131
8.4.2.2 Amplitude EF for Quadrature DDS.........................................132
8.5 Implementations..................................................................................134
8.6 Measurement Results..........................................................................134
8.7 Conclusions..........................................................................................135
REFERENCES...........................................................................135
9. BLOCKS OF DIRECT DIGITAL SYNTHESIZERS..139
9.1 Phase Accumulator.............................................................................139
9.2 Phase to Amplitude Converter...........................................................143
9.2.1 Non-Linear D/A Converter..................................................................145
9.2.2 Exploitation of Sine Function Symmetry............................................145
9.2.3 Compression of Quarter-Wave Sine Function.....................................147
9.2.3.1 Difference Algorithm...............................................................147
9.2.3.2 Splitting into Coarse and Fine LUTs........................................149
9.2.3.3 Angle Decomposition...............................................................150
9.2.3.4 Modified Sunderland Architecture...........................................152
Contents ix
9.2.3.5 Nicholas Architecture...............................................................153
9.2.3.6 Polynomial Approximations....................................................155
9.2.3.6.1 Piecewise Linear Interpolation..........................................156
9.2.3.6.2 High Order Piecewise Interpolation..................................158
9.2.3.6.3 Taylor Series Approximation............................................160
9.2.3.6.4 Chebyshev Approximation...............................................161
9.2.3.6.5 Legendre Approximation..................................................163
9.2.3.7 Using CORDIC Algorithm as a Sine Wave Generator............164
9.2.4 Simulation...........................................................................................167
9.2.5 Summary of Memory Compression and Algorithmic Techniques......167
9.3 Filter.....................................................................................................168
REFERENCES...........................................................................169
10. CURRENT STEERING D/A CONVERTERS..............177
10.1 D/A Converter Specifications.........................................................177
10.2 Static Non-Linearities.....................................................................178
10.2.1 Random Errrrors..................................................................................179
10.2.2 Systematic Errors..............................................................................181
10.2.3 Calibration.........................................................................................183
10.3 Finite Output Impedance...............................................................183
10.4 Other Systematic Errors................................................................185
10.5 Dynamic Errors...............................................................................186
10.5.1 Ideal D/A Converter..........................................................................187
10.5.2 Dynamic Performance Metrics..........................................................188
10.5.3 Dynamic Limitations.........................................................................189
10.6 Inaccurate Timing of Control Signals...........................................191
10.6.1 D/A Converter Finite Slew Rate........................................................193
10.7 Different Current Steering D/A Converters Architectures.........194
10.7.1 Binary Architecture...........................................................................194
10.7.2 Unary Architecture............................................................................195
10.7.3 Segmented Architecture....................................................................196
10.8 Methods for Reduction of Dynamic Errors..................................196
x Contents
10.8.1 Glitches Reduction............................................................................196
10.8.2 Voltage Difference between Control Signals....................................198
10.8.3 Current Switch Sizing........................................................................202
10.8.4 Dummy Switches..............................................................................203
10.8.5 Removing Spurs from Nyquist Band.................................................203
10.8.6 Sample and Hold...............................................................................204
10.9 Timing Errors.................................................................................205
10.9.1 Control Signals Synchronization.......................................................205
10.9.2 Switch Driver Load Matching...........................................................207
10.9.3 Layout................................................................................................209
10.10 Cascode Transistor.........................................................................209
REFERENCES...........................................................................213
11. PULSE SHAPING AND INTERPOLATION FILTERS
219
11.1 Pulse Shaping Filter Design Algorithms.......................................219
11.2 Direct Form Structure of FIR Filter.............................................223
11.3 Transposed Direct Form Structure of FIR Filter........................224
11.4 Hybrid Form...................................................................................225
11.5 Word Length Effects and Scaling..................................................226
11.6 Canonic Signed Digit Format........................................................227
11.7 Carry Save Arithmetic...................................................................228
11.8 Polyphase FIR filters in Sampling Rate Converters....................230
11.9 Half-Band Filters for Interpolation...............................................231
11.10 Cascaded Integrator Comb (CIC) Filter.......................................231
11.11 Pipelining/Interleaving...................................................................234
REFERENCES...........................................................................234
