PWM

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Amplitude slicing PWM. - Phase interleaving PWM. Spectral ... Amplitude Slicing and Phase Interleaving. 11/15 ... Number of averages for PSD: Oversampling of ...
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) •

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Efficient signal generation - Power electronics - Audio - Communications

Introduction Carrier-based PWM • •

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Simple implementation Basis for most PWM modulators

Introduction Multilevel carrier-based PWM • •

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Less distortion Lower switching voltage

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

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State of the Art Black, 1953 - Double Fourier series

Song, 2003 - Combination of pulse spectra

Hausmair, 2013 - Partial Fourier series

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 Many carrier configurations  Extension to multilevel  Single tone input signal  Arbitrary input signals  Many carrier configurations  Not well suited for multilevel

 Arbitrary input signals  Extension to multilevel  Specific carrier configuration

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

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System Model

(b) Binary PWM element

(a) Multilevel PWM model

Parameters: 7/15

(c) Piecewise-linear carrier

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

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Multilevel PWM Schemes Amplitude slicing

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Multilevel PWM Schemes Amplitude slicing

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Multilevel PWM Schemes Amplitude slicing

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Multilevel PWM Schemes Amplitude slicing

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Multilevel PWM Schemes Amplitude slicing

Phase interleaving

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Multilevel PWM Schemes Amplitude slicing

Phase interleaving

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Multilevel PWM Schemes Amplitude slicing

Phase interleaving

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Multilevel PWM Schemes Amplitude slicing

Phase interleaving

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Multilevel PWM Schemes Amplitude slicing Parameters:

Phase interleaving Parameters:

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Unified Description for M-Level Amplitude Slicing and Phase Interleaving Fourier series

Harmonic amplitude distortion

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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

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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

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Amplitude distortion:

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

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