Srinidhi Embar Ramanujam Intermodulation Distortion Modelling and Measurement Techniques for GaN HEMT Characterization kassel university press This work has been accepted by the faculty of Electrical Engineering and Computer Science of the University of Kassel as a thesis for acquiring the academic degree of Doktor der Ingenieurwissenschaften (Dr.-Ing.). Supervisers: Prof. Dr.-Ing. G. Kompa Prof. Dr.-Ing. A. Bangert Defense day: 09th December 2008 Bibliographic information published by Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.d-nb.de. Zugl.: Kassel, Univ., Diss. 2008 ISBN print: 978-3-89958-654-1 ISBN online: 978-3-89958-655-8 URN: urn:nbn:de:0002-6558 © 2009, kassel university press GmbH, Kassel www.upress.uni-kassel.de Printed by: Unidruckerei, University of Kassel Printed in Germany To my parents and my family for their devotion and prayers Acknowledgements I wish to express my deep gratitude to Prof. Dr.-Ing. G. Kompa who supervised and nurtured me in becoming a researcher. His invaluable support and encouragement gave me confidence in overcoming difficult times. My sincere thanks to Prof. Dr.-Ing. A. Bangert for accepting the task of being my second examiner. Further, I wish to thank Prof. Dr. sc. techn. B. Witzigmann and PD Dr.-Ing. R. Marklein for accepting to be members of the disputation committee. I am thankful to all the members of the department of High Frequency Engineering for their constant support. I wish to express my gratitude to Mrs. H. Nauditt, Dipl.-Ing. J. Weide, Dr. -Ing. A. Z. Markos, Mr. R. Ma, Dipl.-Ing. B. Wittwer, Mr. S. Dahmani, Mr. A. Zamudio, Mr. S. Monsi, and Mr. A. A. Hussein. My sincere thanks to my parents, family members, and friends who are not mentioned by name for their unreserved encouragement and strong support over past several years. This acknowledgement will most certainly be incomplete without thanking the German Research Foundation (DFG) and the European project TARGET (Top Amplifier Research Group in a European Team) for their financial support. Srinidhi Embar Ramanujam Kassel, December 2008 iii Contents 1. Introduction 1 1.1 Research Objectives …………………………………………. 4 2. Nonlinearity and Memory-Effect Characterization 9 2.1 Nonlinear RF Characterization Techniques …………………. 11 2.1.1 Single-Tone Excitation …..…………………………… 11 2.1.2 Two-Tone Excitation ………………………………… 12 2.1.3 Multi-Tone and Spread-Spectra Excitation ……………. 15 2.2 Memory Properties of a Nonlinear System .……………….… 19 2.3 Memory-Effect Manifestation …………………………….… 23 3. Volterra Model of AlGaN/GaN HEMT 28 3.1 Small-Signal Distortion Analysis ……………………….……. 29 3.1.1 Power Series Characterized Memoryless System Analysis 30 3.1.2 Volterra Series Characterized Dynamic System Analysis ... 32 3.1.2.1 Nonlinear Current Method …………………… 33 3.2 Quasi-Linear Small-Signal FET Equivalent Circuit Model …… 40 3.2.1 Taylor Series Coefficient Extraction ..………………… 42 3.2.1.1 Modelling Conductance Nonlinearity .…..….… 42 3.2.1.2 Modelling Capacitance Nonlinearity .………..… 47 3.3 IMD Modelling ……………………………………………… 49 st 3.3.1 1 -order Volterra Kernel ……………………………… 50 nd 3.3.2 2 -order Volterra Kernel ……………………………… 51 rd 3.3.3 3 -order Volterra Kernel .……..………………………. 58 3.3.4 Model Verification ....………………………………… 61 3.4 IMD Vectorial Analysis …..…………………………………. 61 v 3.5 AlGaN/GaN HEMT Linearity Optimisation ………..…………… 63 3.5.1 Gate Field-Plate Based IMD Minimization ………………… 64 3.6 5th-Degree Extension of Volterra Model ………..………………… 66 4. Large-Signal Measurement Technique 71 4.1 Fundamental System Requirements ……………………………… 72 4.1.1 System Description ……….……………………………… 75 4.1.2 System Calibration ………..………………………………. 77 4.2 Termination Properties for IMD Characterization ………...……… 82 4.3 RF Bias Network - Design Guidelines …………...……………….. 85 4.3.1 Characterization Testbench - Baseband and RF Perspective .. 87 4.3.2 Key Design Challenges ….………………..……………… 100 4.4 Broadband Bias Tee Evaluation ………………………………… 111 4.4.1 Memory-Effect Characterization ………..………………… 111 4.4.2 Load-Pull Characterization ………..……………………… 118 4.5 Drain Bias Sensing ……………………………………………… 123 5. IMD Sweet-Spots 130 5.1 Origin …………………………………………………………… 131 5.1.1 Small-Signal IMD Sweet-Spot ………..…………………… 132 5.1.2 Large-Signal IMD Sweet-Spot ..…………………………… 133 5.2 Bias and Load Termination ……………………………………… 138 5.3 Sweet-Spot Reproducibility ……………………………………….. 143 5.3.1 Statistical Process Consistency Evaluation ………………… 143 5.3.2 Experimental Characterization of Large-Signal IMD Sweet-Spots ………………………………………………. 145 5.3.2.1 Two-Tone Stimuli ………………………………… 145 5.3.2.2 Multi-Carrier W-CDMA Stimuli …………..……… 148 vi 6. Conclusion and Future Work 154 Appendices 162 A. FET Based IMD3 Phasors …..……………………………… 162 B. Measurement Accuracy Enhancement Criteria ..……………… 170 C. Pitfalls in Characterizing Device Inherent IMD Behaviour …… 172 D. Correlation Between IMR and ACPR Characteristics ………… 176 References 181 Publications of the Author 191 vii List of Abbreviations 3GPP third generation partnership project ACPR adjacent channel power ratio ADC analog-to-digital converter AM-AM input amplitude modulation to output amplitude modulation conversion AM-PM input amplitude modulation to output phase modulation conversion ANN artificial neural network CAD computer aided design CCDF complementary cumulative distribution function CW continuous wave DiVA dynamic I(V) analyser DMI drain modulation index DPCH dedicated physical channel DUT device under test EVM error vector magnitude FDD frequency division duplex FP field-plate GaAs gallium arsenide GaN gallium nitride GSM global system for mobile communication HEMT high electron mobility transistor MLP multi-level perceptron IF intermediate frequency IMD intermodulation distortion IM3L 3rd-order lower intermodulation distortion IMR intermodulation ratio IP3 3rd-order intercept point LDMOS laterally diffused metal oxide semiconductor LTE long term evolution MESFET metal semiconductor field effect transistor MTA microwave transition analyser OFDM orthogonal frequency division multiplexing PA power amplifier PAE power added efficiency PAR peak-to-average ratio QPSK quadrature phase shift keying RF radio frequency UMTS universal mobile telecommunications system VNA vector network analyser VSA vector signal analyser W-CDMA wideband code division multiple access viii List of Symbols a1 incident power wave at port-1 dBm a2 incident power wave at port-2 dBm b1 reflected power wave from port-1 dBm b2 reflected power wave from port-2 dBm β propagation coefficient C capacitance F Cgs intrinsic gate-source capacitance F Cds intrinsic drain-source capacitance F Cgd intrinsic gate-drain capacitance F C/I3 3rd-order carrier-to-intermodulation ratio dBc ∆f carrier spacing Hz ∆IMD IMD asymmetry dB εr dielectric constant e00 directivity e11 port-1 match e10 coupler tracking e01e10 reflection tracking e22 port-2 match fc centre frequency Hz fenv maximum baseband frequency Hz fSR series resonant frequency Hz Γ reflection coefficient ΓL load reflection coefficient G conductance S Gm transconductance S Gds channel conductance S nd Gm2, k2gm 2-order derivative of drain-source current S/V rd Gm3, k3gm 3-order derivative of drain-source current S/V² th hn time-domain n -order Volterra kernel th Hn frequency-domain n -order transfer function st H1 1-order linear transfer function Ids intrinsic incremental drain current A nd i2NL 2-order nonlinear current source A rd i3NL 3-order nonlinear current source A IDS,DC self-biased DC drain current A Imax channel saturation current A In excitation vector (voltage-controlled current source) IP3 3rd-order intercept point dBm k2g, k3g conductance nonlinearity coefficients k2c, k3c capacitance nonlinearity coefficients A transmission line length m ix LS capacitor’s parasitic inductance H M number of phase states Pin input power W Pout output power W P1dB 1 dB compression point dBm Q quality factor Qgs gate-source charge C Qgd gate-drain charge C Qg gate depletion charge C R resistance Ω t time sec TF, TFXYZ, transimpedance transfer function TFXYZW vg gate nodal voltage V vd drain nodal voltage V vs source nodal voltage V vgs incremental gate-source voltage V vds incremental drain-source voltage V vgd incremental gate-drain voltage V VBR gate-drain breakdown voltage V Vin input signal amplitude V VGS0 extrinsic gate-source bias voltage V VDS0 extrinsic drain-source bias voltage V VGS extrinsic gate-source voltage V VDS extrinsic drain-source voltage V Vk knee voltage V Vpi pinch-off voltage V Vt threshold voltage V vx(t) input signal amplitude vpeak(∆f ) peak baseband drain bias voltage V ω angular frequency Hz x(t) input excitation XL inductive reactance Ω XC capacitive reactance Ω y(t) output system response yNL(t) nonlinear output response yML(t) memoryless output response yQM(t) quasi-memoryless output response z(t) linear output response Z0 characteristic impedance Ω ZL load impedance Ω x Abstract Growing demand for higher data rates and ever increasing users on the 3G network is forcing rapid system enhancements to meet the stringent linearity specifications. The implications of microwave power transistor semiconductor technology and design strategies, implemented in basestation power amplifiers (PAs), have become the core focus of research. This thesis offers relevant practical application of computer-aided design (CAD) based modelling and measurement techniques to tackle linearity enhancement issues