Harald Enzinger, Christian Vogel Telecommunications Research Center - PowerPoint PPT Presentation

Analytical Description of Multilevel Carrier-Based PWM of Arbitrary Bounded Input Signals Harald Enzinger, Christian Vogel Telecommunications Research Center Vienna (FTW), Austria IEEE International Symposium on Circuits and Systems 2014 Melbourne, Australia

Introduction Pulse Width Modulation (PWM) Efficient signal generation • - Power electronics - Audio - Communications 1/15

Introduction Carrier-based PWM Simple implementation • Basis for most PWM modulators • 2/15

Introduction Multilevel carrier-based PWM Less distortion • Lower switching voltage • 3/15

Problem Statement Analytical description of carrier-based PWM - Arbitrary input signal - Arbitrary number of levels - Arbitrary carrier configurations Relevance - Spectral analysis - Comparison of existing modulation schemes - Insight for research on new modulation schemes 4/15

State of the Art  Many carrier configurations Black, 1953  Extension to multilevel - Double Fourier series  Single tone input signal  Arbitrary input signals Song, 2003  Many carrier configurations - Combination of pulse spectra  Not well suited for multilevel Hausmair, 2013  Arbitrary input signals  Extension to multilevel - Partial Fourier series  Specific carrier configuration 5/15

Contributions Generalization of Hausmair 2013 - Arbitrary input signals - Arbitrary number of levels - Arbitrary carrier configurations Application examples - Amplitude slicing PWM - Phase interleaving PWM Spectral analysis - New analytical/numerical approach 6/15

System Model (b) Binary PWM element (a) Multilevel PWM model (c) Piecewise-linear carrier Parameters: 7/15

Analysis of System Model System representation by 2-dimensional function Implicit mathematical description Periodicity in time-dimension Fourier series expansion in time-dimension is possible. 8/15

Analytical Description Fourier series Fourier coefficients Parameters Duty cycle Pulse center 9/15

Multilevel PWM Schemes 10/15

Multilevel PWM Schemes Amplitude slicing 10/15

Multilevel PWM Schemes Amplitude slicing 10/15

Multilevel PWM Schemes Amplitude slicing 10/15

Multilevel PWM Schemes Amplitude slicing 10/15

Multilevel PWM Schemes Amplitude slicing Phase interleaving 10/15

Multilevel PWM Schemes Amplitude slicing Phase interleaving 10/15

Multilevel PWM Schemes Amplitude slicing Phase interleaving 10/15

Multilevel PWM Schemes Amplitude slicing Phase interleaving 10/15

Multilevel PWM Schemes Amplitude slicing Parameters: Phase interleaving Parameters: 10/15

Unified Description for M-Level Amplitude Slicing and Phase Interleaving Fourier series Harmonic amplitude distortion 11/15

Spectral Analysis Conventional numerical approach - Time-domain simulation - FFT analysis of PWM signal  Very high oversampling  No insight into cause of distortion Proposed analytical/numerical approach - Analytical description - FFT analysis for each harmonic  Only moderate oversampling  Insight into the cause of distortion 12/15

Spectral Analysis Multitone input signal Oversampling of PWM: Oversampling of simulation: Number of averages for PSD: 13/15

Spectral Analysis Comparison of number of levels Amplitude distortion: 14/15

Summary Analytical description of carrier-based PWM - Arbitrary input signals - Arbitrary number of levels - Arbitrary carrier configurations Examples - Amplitude slicing - Phase interleaving Spectral analysis - Less computation - More insight 15/15