Per Asbeck Linearisation of RF Power Amplifiers PhD thesis Nokia Mobile Phones and Department of Information Technology Technical University of Denmark March 2001 Linearisation of RF Power Amplifiers by Per Asbeck This thesis is submitted in partial fulfilment of the requirements for the degree: Doctor of Philosophy (Ph.D.) Ørsted•DTU Technical University of Denmark March 2001 ii Preface In connection with this Ph.D project I wish to thank several people for their help and kindness. Professor Erik Bruun (DTU), Ole Olsen (DTU) and Dan Rebild (Nokia Denmark) for supervis- ing this project. Dan Rebild for starting up this Ph.D. project on behalf of Nokia Denmark A/S and for support- ing me in many different ways throughout the project. Thanks to Ole Olesen for helping me starting and establishing the PhD work and helping me arrange my stay at Stanford University. Thomas Lee for letting me visits his group at SMIRC (Stanford Microwave Integrated Circuits Laboratory) at Stanford University. I have learned a lot though discussion with the people in the group and through participation in many seminars. Thanks to Allan Jørgensen (DTU) for CAD support especially with Cadence problems but also in matters of PC, work stations and networks. His help has been indispensable. Thanks to Nokia Denmark financial support and access to many experienced IC and RF design- ers. Note that when I started this project I was affiliated to Institute of Information Technology that later changed it´s name to Ørsted•DTU, Technical University of Denmark. Thesis written is written in Adobe FrameMaker+SGML 5.5 with 12pt Times New Roman Font. The figures are generated with Visio Technical 5.0+ and Mathcad 2000 Professional. The fig- ures are inserted as objects and windows meta files (WMF) and printed out using Adobe distiller post script driver and Adobe Acrobat 4.0. Many graphs are distinguish though their colour which necessitate a colour printer for the printing. __________________________ Per Asbeck Ørsted•DTU Technical University of Denmark iii PREFACE iv Contents Preface .................................................................................................................................. iii Contents................................................................................................................................. v List of figures ....................................................................................................................... ix Abstract................................................................................................................................ xv Resumé (in danish)............................................................................................................ xvii List of Abbreviations.......................................................................................................... xix List of Notation................................................................................................................... xxi Introduction .......................................................................................................................... 1 1 The transmitter..................................................................................................................... 3 1.1 Transmitter architecture ................................................................................................ 3 1.1.1 Direct conversion ................................................................................................ 3 1.1.2 Super heterodyne transmitter .............................................................................. 5 1.1.3 Offset loop transmitter ........................................................................................ 6 1.2 Representations of RF signals....................................................................................... 7 1.2.1 Band limited RF signal ....................................................................................... 7 1.2.2 Complex envelope representation ...................................................................... 8 1.2.3 Filtering of complex envelope signals ................................................................ 9 1.3 Modulation.................................................................................................................... 9 1.3.1 The modulation process .................................................................................... 11 1.3.2 IQ modulation ................................................................................................... 11 1.3.3 QPSK modulation ............................................................................................. 13 1.3.4 Edge modulation ............................................................................................... 16 1.3.5 Measuring the signal quality ............................................................................. 18 2 Modelling and Characterising Non-Linearities............................................................... 21 2.1 Harmonic distortion .................................................................................................... 21 2.2 Intermodulation........................................................................................................... 23 2.3 Polynomial non-linearities .......................................................................................... 24 2.3.1 Harmonic distortion .......................................................................................... 25 2.3.2 Intermodulation ................................................................................................ 26 2.4 Memory-less bandpass non-linearities........................................................................ 28 2.4.1 Complex envelope bandpass non-linear simulation model .............................. 29 2.4.2 The limiter non-linearity ................................................................................... 30 2.4.3 A non-linearity with hysteresis ......................................................................... 31 3 The Power Amplifier.......................................................................................................... 33 3.1 Classes of operation .................................................................................................... 34 v CONTENTS 3.1.1 Class A .............................................................................................................. 34 3.1.2 Class B .............................................................................................................. 36 3.1.3 Classes described by the conductions angle ..................................................... 37 3.1.4 Class F .............................................................................................................. 42 3.1.5 Class D .............................................................................................................. 42 3.1.6 Class E .............................................................................................................. 43 3.2 Characterisation of the PA .......................................................................................... 43 4 Linearisation Techniques................................................................................................... 45 4.1 The LINC Techniques................................................................................................. 46 4.2 CALLUM.................................................................................................................... 47 4.3 Cartesian Modulation Feedback ................................................................................. 48 4.4 Polar Modulation Feedback Loop............................................................................... 48 4.5 Envelope Feedback ..................................................................................................... 50 4.6 Phase Correcting Feedback......................................................................................... 50 4.7 Feed Forward Linearisation ........................................................................................ 51 4.8 Digital Predistortion.................................................................................................... 51 4.8.1 Mapping Predistortion ...................................................................................... 52 4.8.2 Polar Predistortion ............................................................................................ 53 4.8.3 Complex Gain Predistortion ............................................................................. 53 4.8.4 Polynomial predistortion .................................................................................. 54 4.9 Remarks on PA isolation and sensitivity to external disturbance............................... 54 5 Analysis and design of Linearisation Systems ................................................................. 55 5.1 Amplitude linearity of Cartesian Modulation Feed Back System .............................. 56 5.2 Polar modulation feedback ......................................................................................... 60 5.2.1 Polar linearisation in a digital transmitter. ........................................................ 60 5.2.1.1 Polar loop with an RF-phase shifter..................................................... 61 5.2.1.2 Polar loop linearisation using a VCO..................................................