Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2005 Gallium Arsenide Mesfet Small-Signal Modeling Using Backpropagation & RBF Neural Networks Diego Langoni Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING GALLIUM ARSENIDE MESFET SMALL-SIGNAL MODELING USING BACKPROPAGATION & RBF NEURAL NETWORKS By DIEGO LANGONI A Thesis submitted to the Electrical and Computer Engineering Department in partial fulfillment of the requirements for the degree of Master of Science Degree Awarded: Fall Semester, 2005 The members of the Committee approve the Thesis of Diego Langoni defended on October 19, 2005. _______________________________ Mark H. Weatherspoon Professor Directing Thesis _______________________________ Simon Y. Foo Committee Member _______________________________ Anke Meyer-Basese Committee Member Approved: _______________________________ Leonard J. Tung, Chair, Electrical and Computer Engineering Department _______________________________ Jim P. Zheng, Graduate Coordinator, Electrical and Computer Engineering Department The Office of Graduate Studies has verified and approved the above named committee members. ii To my family, friends, and Abby… iii ACKNOWLEDGEMENTS I would like to thank Dr. Mark Weatherspoon, my advisor, for his infinite patience and help with finishing my thesis work, and also for providing the MESFET measured data used in my thesis work. To Dr. Simon Foo for his insight on Neural Networks theory which was very helpful in my particular field of work. I would also like to thank Dr. Anke Meyer-Baese for reviewing my work. On another note, I would like to thank my parents for helping me financially whenever money seemed to be running short, to the Florida State University College of Engineering ECE Department for allowing me to work as a teaching assistant and grader in order to pay for my masters education, to Mr. Hector Martinez and Mr. Geoffrey Wall, with whom I started this research, and last but certainly not least, to Abigail Kent for her help and support pulling through at the end of my work. iv TABLE OF CONTENTS List of Tables ............................................................................................ iv List of Figures ............................................................................................ v List of Abbreviations........................................................................................ ix Abstract ............................................................................................ x 1. INTRODUCTION....................................................................................... 1 1.0 Introduction....................................................................................... 1 1.1 Problem Setup ................................................................................... 2 1.2 Summary of Objectives ..................................................................... 2 2. NEURAL NETWORKS THEORY ............................................................. 3 2.0 Introduction....................................................................................... 3 2.1 Backpropagation Networks................................................................ 7 2.1.0 Backpropagation Training......................................................... 8 2.1.1 Faster Training Algorithms ....................................................... 10 2.1.2 Backpropagation Simulation ..................................................... 12 2.2 Radial Basis Function Networks........................................................ 13 2.2.0 RBF Training............................................................................ 14 2.2.1 RBF Simulation ........................................................................ 15 2.3 Summary........................................................................................... 15 3. TWO-PORT NETWORK THEORY........................................................... 17 3.0 Introduction....................................................................................... 17 3.1 N-Port Networks................................................................................ 17 3.2 Impedance (Z) and Admittance (Y) Matrices ..................................... 18 3.3 The Scattering (S) Matrix .................................................................. 20 3.4 Summary........................................................................................... 22 4. MESFET THEORY .................................................................................... 24 4.0 Introduction....................................................................................... 24 4.1 Regions of Operation......................................................................... 26 4.2 MESFET Small-Signal Model ........................................................... 27 4.3 Summary........................................................................................... 31 i 5. SMALL-SIGNAL MODELING USING NEURAL NETWORKS .............. 32 5.0 Introduction....................................................................................... 32 5.1 MESFET Characteristics ................................................................... 32 5.2 ANN Architectures............................................................................ 33 5.3 Backpropagation vs. RBF .................................................................. 35 5.4 Summary........................................................................................... 37 6. SMALL-SIGNAL MODELING RESULTS ................................................ 38 6.0 Introduction....................................................................................... 38 6.1 Normal Training ANN Model Results ............................................... 38 6.2 Stressed Training ANN Model Results .............................................. 49 6.2.0 Backpropagation Network Model Results ................................. 49 6.2.1 RBF Network Model Results .................................................... 50 6.2.2 Network Comparison: Backpropagation vs. RBF ..................... 63 6.3 Summary........................................................................................... 74 7. CONCLUSIONS......................................................................................... 75 7.0 Introduction....................................................................................... 75 7.1 Work Summary ................................................................................. 75 7.2 Specific Technical Contributions ....................................................... 76 7.3 Future Work ...................................................................................... 77 APPENDICES ............................................................................................ 78 A. PARAMETER CONVERSION TABLE............................................ 78 B. BACKPROPAGATION ACTIVATION FUNCTIONS..................... 79 B.1 Log-Sigmoid Function ................................................................ 79 B.2 Tan-Sigmoid Function................................................................. 80 B.3 Linear Function........................................................................... 80 C. PARTIAL DERIVATIVES OF ACTIVATION FUNCTIONS .......... 82 C.1 Log-Sigmoid Function ................................................................ 82 C.2 Tan-Sigmoid Function................................................................. 82 C.3 Linear Function........................................................................... 83 D. INPUT-OUTPUT COMPLEXITY OF MESFET ECPs ..................... 84 E. SAMPLE NETWORK SIMULATION RUNS................................... 90 E.1 Backpropagation Simulations ...................................................... 90 ii E.2 RBF Simulations ......................................................................... 97 REFERENCES ............................................................................................ 105 BIOGRAPHICAL SKETCH ........................................................................... 107 iii LIST OF TABLES 5.1: Network Training Schemes ..................................................................... 36 6.1: Average Relative Error Comparison Between Backpropagation and RBF Networks Under “Normal” Training Conditions ....................... 49 6.2: Network Performance Comparison: Backpropagation vs. RBF ............... 64 7.1: Results Summary Under Different Design Constraints (Backpropagation vs. RBF) ..................................................................... 76 A.1: Two-Port Parameter Conversion Table .................................................... 78 E.1: Matlab Variable Definitions .................................................................... 90 iv LIST OF FIGURES 2.1 Biological Neuron ................................................................................... 4 2.2 Generalized Neuron Model...................................................................... 5 2.3 Multilayer Feed-Forward Network .......................................................... 8 2.4 RBF Neuron Model................................................................................. 14 3.1: Two-Port Device Diagram of Total Voltage and Current ......................... 19