Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1972 Carrier generation using pulse width modulation Frederick Herbert Raab Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Electrical and Electronics Commons Recommended Citation Raab, Frederick Herbert, "Carrier generation using pulse width modulation " (1972). Retrospective Theses and Dissertations. 5226. https://lib.dr.iastate.edu/rtd/5226 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This dissertation was produced from a microfilm copy of the original document. 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University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 A Xerox Education Company 72-20,000 RAAB, Frederick Herbert, 1946- CARRIER GENERATION USING PULSE WIDTH MODULATION. 1 1 Iowa State University, Ph.D., 1972 ! Engineering, electrical University Microfilms, A XEROKCompany, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFIOffiD EXACTLY AS RECEIVED Carrier génération using pulse width Modulat ion by Frederick Herbert Raab A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements of the Degree of DOCTOR OF PHILOSOPHY Major Subject: Electrical Engineering Approved : Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. For the Najor Department Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1972 PLEASE NOTE: Some pages may have indistinct print. Filmed as received. University Microfilms, A Xerox Education Company ii TABLE OF CONTENTS Page I. INTRODUCTION 1 II. TYPES AND EFFICIENCIES OF AMPLIFIERS 8 A. Conventional Amplifiers 8 B. Switching Amplifiers 17 III. BASIC IMPLEMENTATION 34 IV. BASIC SPECTRAL ANALYSIS 46 V. BASIC SPECTRUM OF A CLASS D RF AMPLIFIER 54 A. Bipolar PV'7>î 55 B. Monopolar PWM 67 C. Saturation Voltage 73 VI. PULSE TIMING DISTORTION 80 A, Pulse Bias Distortion 81 E. Rise/Fall Time Distortion 89 C. Approximations Used 97 D. Combination of Effects 98 VII. SPURIOUS PRODUCTS VÎITH SINUSOIDAL MODULATION 100 A. Voltage Error Products 103 B. Timing Error Products 109 VIII. SPURIOUS PRODUCTS FOR GENERAL CASE 116 IX. DISTORTION REDUCTION BY USE OF FEEDBACK 130 X. COMMENTS AND CONCLUSIONS 144 XI. REFERENCES 147 A, Additional References 149 iii Page XII. ACKNOWLEDGEMENT 149 • XIII. APPENDIX I: OTHER AMPLIFIERS 151 A. Class B 151 B. Conventional Pulse Nidth Modulation 159 C. Other Amplifiers " 173 XIV. APPENDIX II: PROTOTYPE 175 XV. APPENDIX III: SIMULATION 186 XVI., APPENDIX IV: COMMONLY-USED SYMBOLS 211 IV LIST OF ILLUSTRATIONS Page Figure 1.1 Light Dimmer 2 Figure 1.2 Types of Pulse Width Modulation 4 Figure 2.1 Class A Amplifier 9 Figure 2.2 Class B Amplifier 12 Figure 2.3 Class C Amplifier 14 Figure 2.4 Class CD Amplifier 14 Figure 2.5 Efficiencies of Class A, B, and C 16 Amplifiers Figure 2.6 Switching Amplifier 18 Figure 2.7 Class AD Amplifier 20 Figure 2.8 Rise/Fall Times in a Class AD Amplifier 22 Figure 2.9 Saturation Voltages in a Class AD Amplifier 24 Figure 2.10 Efficiency of Class AD and BD Amplifier 25 Figure 2.11 Class BD Amplifier 27 Figure 2.12 Class D RF Amplifier 28 Figure 2.13 Efficiency of a Class D RF Amplifier 32 Figure 3.1 Comparator Pulse Generation for Class AD 35 Figure 3.2 Relationships Between Modulating Signal 35 and Pulse Width Figure 3.3 Waveforms in Class D AM System 36 Figure 3.4 Class D AM Transmitter 38 Figure 3.5 Generation of AM and DSB/SC 39 Figure 3.6 Class D SSB Techniques 41 Figure 3,7 SSB Generation 42 Figure 3.8 Class D SSB Generation Using Kahn*s Method 43 V Page Figure 4.1 Monopolar Pulse f^ (6) 49 Figure 4.2 Decomposition of Bipolar Pulse 50 Figure 4.3 Ramp Waveform 52 Figure 4.4 Triangular Wave AO) 53 Figure 5.1 Modulating Function for DSB/SC 58 Figure 5.2 Spectrum of a Class D RF Amplifier 61 Figure 5.3 Spectrum of a Class D RF Amplifier 62 Figure 5.4 Locus of E(0) and co(0 ) 67 Figure 5.5 Spectrum of a Class D RF Amplifier 58 Figure 5.6 Spectrum of a Class D RF Amplifier 69 Figure 5.7 Waveform with Voltage Error 71 Figure 5.8 Modulation of Even Harmonics for DSB/SC 72 Figure 5.9 Spectrum of a Class D RF Amplifier 74 Figure 5.10 Spectrum of a Class D RF Amplifier 75 Figure 5.11 Saturation Voltage Effects 76 Figure 5.12 Saturation Effect Approximations 77 Figure 5.13 Spurious Products due to non-zero 78 Saturation Voltage Figure 5.14 Circuit Changes to Reduce Saturation 78 Voltage Spurious Products Figure 6.1 Cause of Pulse Bias 81 Figure 6.2 Bias Distortion Waveform 82 Figure 6.3 Modulation Functions for Timing Distortion 86 Figure 6.4 Types of Spurious Products due to Pulse 88 Bias Distortion Figure 6.5 Spectrum of a Class D RF Amplifier 90 vi Page Figure 6.6 Spectrum of a Class D RF Amplifier 91 Figure 6,7 Rise/Fall Time Distortion Waveform 92 Figure 6.8 Spectrum of a Class D RF Amplifier 95 Figure 6.9 Spectrum of a Class D RF Amplifier 96 Figure 6.10 Distortion Curves 98 Figure 6,11 Pulse Deterioration 99 Figure 7,1 Waveforms Used to Find Upper Limits on 102 Spurious Products Figure 7.2 Spurious Products at a Given Frequency 106 Figure 7.3 Maximum Spurious Products for Monopolar 108 DSB/SC Figure 7,4 Maximum Spurious Products for Bipolar 112 DSB/SC with Various Timing Errors Figure 7,5 Maximum Spurious Products for Bipolar AM- 114 Like Signal with Various Timing Errors Figure 8.1 Variation of Spurious Products with Depth 120 of Modulation Figure 8.2 Spectrum of a Class D RF Amplifier 121 Figure 8.3 Spectrum of a Class D RF Amplifier 122 Figure 8.4 Spectrum of a Class D RF Amplifier 123 Figure 8.5 Spectrum of a Class D RF Amplifier 124 Figure 8.6 Spectrum of a Class D RF Amplifier 127 Figure 8.7 Spectrum of a Class D RF Amplifier 128 Figure 9.1 Feedback System I3l Figure 9.2 Feedback System with ct/2'TT =0 138 Figure 9.3 Feedback System with C7/2TT = 0,001 139 Figure 9.4 Feedback System with à/2'rr = 0.01 140 vii Page Figure 9.5 Feedback System vith a/2'rr = 0.1 141 Figure 9.6 Envelope and Phase Feedback System 143 Figure 13,1 Transfer Characteristic for Class B 152 Amplifier Figure 13,2 Waveform in a Class B Amplifier 153 Figure 13,3 Spectrum of a Class B Amplifier 154 Figure 13.4 Spectrum of a Class B Amplifier 156 Figure 13,5 Spectrum of a Class B Amplifier 157 Figure 13.6 Spectrum of a Class B Amplifier 158 Figure 13,7 Spectrum of Conventional PlfM 161 Figure 13.8 Spectrum of a Class AD Amplifier 163 Figure 13.9 Spectrum of a Class AD Amplifier 164 Figure 13.10 Spectrum of a Class AD Amplifier 165 Figure 13,11 Spectrum of a Class BD Amplifier 166 Figure 13,12 Spectrum of a Class AD Amplifier 167 Figure 13.13 Spectrum of a Class AD Amplifier 170 Figure 13.14 Pulse Bias in Class BD Amplifier 171 Figure 13.15 Spectrum of a Class AD Amplifier 172 Figure 14.1 Power Supply 177 Figure 14.2 Audio Amplifier and RF Oscillator 178 Figure 14,3 Reference Generator and Detector 179 Figure 14.4 Clipper and Comparator 180 Figure 14,5 Logic 181 Figure 14.6 Power Amplifier 182 Figure 14.7 Pulse Train and Output Waveform 184 viii Page Figure 14.