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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

SLIDE 1

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

SLIDE 2

Pulse Width Modulation (PWM)

Introduction

Efficient signal generation
Power electronics
Audio
Communications

1/15

SLIDE 3

Carrier-based PWM

Introduction

Simple implementation
Basis for most PWM modulators

2/15

SLIDE 4

Multilevel carrier-based PWM

Introduction

Less distortion
Lower switching voltage

3/15

SLIDE 5

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

Problem Statement

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SLIDE 6

Black, 1953

Double Fourier series

Song, 2003

Combination of pulse spectra

Hausmair, 2013

Partial Fourier series

State of the Art

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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

SLIDE 7

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

Contributions

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SLIDE 8

System Model

(a) Multilevel PWM model (b) Binary PWM element (c) Piecewise-linear carrier Parameters:

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SLIDE 9

System representation by 2-dimensional function

Analysis of System Model

Implicit mathematical description Periodicity in time-dimension

Fourier series expansion in time-dimension is possible.

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SLIDE 10

Fourier series

Analytical Description

Fourier coefficients Parameters

Duty cycle Pulse center

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SLIDE 11

Multilevel PWM Schemes

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SLIDE 12

Amplitude slicing

Multilevel PWM Schemes

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SLIDE 13

Amplitude slicing

Multilevel PWM Schemes

10/15

SLIDE 14

Amplitude slicing

Multilevel PWM Schemes

10/15

SLIDE 15

Amplitude slicing

Multilevel PWM Schemes

10/15

SLIDE 16

Amplitude slicing

Multilevel PWM Schemes

Phase interleaving

10/15

SLIDE 17

Amplitude slicing

Multilevel PWM Schemes

Phase interleaving

10/15

SLIDE 18

Amplitude slicing

Multilevel PWM Schemes

Phase interleaving

10/15

SLIDE 19

Amplitude slicing

Multilevel PWM Schemes

Phase interleaving

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SLIDE 20

Amplitude slicing

Multilevel PWM Schemes

Phase interleaving

Parameters: Parameters:

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SLIDE 21

Fourier series

Unified Description for M-Level

Harmonic amplitude distortion

Amplitude Slicing and Phase Interleaving

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SLIDE 22

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

Spectral Analysis

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SLIDE 23

Multitone input signal

Spectral Analysis

Oversampling of simulation: Number of averages for PSD: Oversampling of PWM:

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SLIDE 24

Spectral Analysis

Comparison of number of levels

Amplitude distortion:

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SLIDE 25

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

Summary

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