Understanding the PWM Nonlinearity: Single-Sided Modulation
This paper provides a new look at the mechanisms underlying pulse width modulation (PWM). A simple approach to analyze the behavior of a single-sided pulse width modulator is presented. By using elementary methods, the pulse-width-modulated waveform is written as the sum of two sawtooth functions an...
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| Veröffentlicht in: | IEEE transactions on power electronics 2012-04, Vol.27 (4), p.2116-2128 |
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| container_title | IEEE transactions on power electronics |
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| creator | Mouton, H. Putzeys, B. |
| description | This paper provides a new look at the mechanisms underlying pulse width modulation (PWM). A simple approach to analyze the behavior of a single-sided pulse width modulator is presented. By using elementary methods, the pulse-width-modulated waveform is written as the sum of two sawtooth functions and the original modulating waveform. Simply applying the well-known Fourier series expansion of the sawtooth function, an equivalent model of the pulse width modulator, which shows that it is in essence a sequence of phase modulators, is derived. This model provides a clear understanding of the nonlinearities involved in the PWM process. It is shown how the superposition of modulating waveforms in the time-domain translates into the convolution of the sidebands in the frequency domain. Finally, the interaction of the pulse width modulator and a sample-and-hold register is studied and a general expression for the Fourier transform of a regular-sampled PWM waveform is derived. The analysis applies to periodic as well as aperiodic modulating waveforms. |
| doi_str_mv | 10.1109/TPEL.2011.2169283 |
| format | Article |
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A simple approach to analyze the behavior of a single-sided pulse width modulator is presented. By using elementary methods, the pulse-width-modulated waveform is written as the sum of two sawtooth functions and the original modulating waveform. Simply applying the well-known Fourier series expansion of the sawtooth function, an equivalent model of the pulse width modulator, which shows that it is in essence a sequence of phase modulators, is derived. This model provides a clear understanding of the nonlinearities involved in the PWM process. It is shown how the superposition of modulating waveforms in the time-domain translates into the convolution of the sidebands in the frequency domain. Finally, the interaction of the pulse width modulator and a sample-and-hold register is studied and a general expression for the Fourier transform of a regular-sampled PWM waveform is derived. The analysis applies to periodic as well as aperiodic modulating waveforms.</description><identifier>ISSN: 0885-8993</identifier><identifier>EISSN: 1941-0107</identifier><identifier>DOI: 10.1109/TPEL.2011.2169283</identifier><identifier>CODEN: ITPEE8</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Amplitude modulation ; Applied sciences ; Carrier-based pulse width modulation (PWM) strategies ; Carson's rule ; Circuit properties ; Circuits of signal characteristics conditioning (including delay circuits) ; closed-form solutions ; digital simulation ; double Fourier integral ; Electric, optical and optoelectronic circuits ; Electronic circuits ; Electronics ; Exact sciences and technology ; Fourier series ; Fourier transforms ; Frequencies ; Harmonic analysis ; Mathematical model ; Pulse width modulation ; pulse width modulation (PWM) ; regular sampling ; Waveform analysis</subject><ispartof>IEEE transactions on power electronics, 2012-04, Vol.27 (4), p.2116-2128</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Apr 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c322t-62797c2fac920a9e8adc95cafe368dc34e338798df88aeba7094dcd3a84b226e3</citedby><cites>FETCH-LOGICAL-c322t-62797c2fac920a9e8adc95cafe368dc34e338798df88aeba7094dcd3a84b226e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6026253$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6026253$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=25721745$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Mouton, H.</creatorcontrib><creatorcontrib>Putzeys, B.</creatorcontrib><title>Understanding the PWM Nonlinearity: Single-Sided Modulation</title><title>IEEE transactions on power electronics</title><addtitle>TPEL</addtitle><description>This paper provides a new look at the mechanisms underlying pulse width modulation (PWM). A simple approach to analyze the behavior of a single-sided pulse width modulator is presented. By using elementary methods, the pulse-width-modulated waveform is written as the sum of two sawtooth functions and the original modulating waveform. Simply applying the well-known Fourier series expansion of the sawtooth function, an equivalent model of the pulse width modulator, which shows that it is in essence a sequence of phase modulators, is derived. This model provides a clear understanding of the nonlinearities involved in the PWM process. It is shown how the superposition of modulating waveforms in the time-domain translates into the convolution of the sidebands in the frequency domain. Finally, the interaction of the pulse width modulator and a sample-and-hold register is studied and a general expression for the Fourier transform of a regular-sampled PWM waveform is derived. The analysis applies to periodic as well as aperiodic modulating waveforms.</description><subject>Amplitude modulation</subject><subject>Applied sciences</subject><subject>Carrier-based pulse width modulation (PWM) strategies</subject><subject>Carson's rule</subject><subject>Circuit properties</subject><subject>Circuits of signal characteristics conditioning (including delay circuits)</subject><subject>closed-form solutions</subject><subject>digital simulation</subject><subject>double Fourier integral</subject><subject>Electric, optical and optoelectronic circuits</subject><subject>Electronic circuits</subject><subject>Electronics</subject><subject>Exact sciences and technology</subject><subject>Fourier series</subject><subject>Fourier transforms</subject><subject>Frequencies</subject><subject>Harmonic analysis</subject><subject>Mathematical model</subject><subject>Pulse width modulation</subject><subject>pulse width modulation (PWM)</subject><subject>regular sampling</subject><subject>Waveform analysis</subject><issn>0885-8993</issn><issn>1941-0107</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kEtLAzEUhYMoWB8_QNwMgsupyc3MJNGViC9otdAWlyFN7mjKmKnJdNF_75SWru7ifOdc-Ai5YnTIGFV3s8nzaAiUsSGwSoHkR2TAVMFyyqg4JgMqZZlLpfgpOUtpSSkrSsoG5GEeHMbUmeB8-M66H8wmX-Psow2ND2ii7zb32bSPGsyn3qHLxq1bN6bzbbggJ7VpEl7u7zmZvzzPnt7y0efr-9PjKLccoMsrEEpYqI1VQI1CaZxVpTU18ko6ywvkXAolXS2lwYURVBXOOm5ksQCokJ-Tm93uKrZ_a0ydXrbrGPqXWkFVUCaF7CG2g2xsU4pY61X0vyZuNKN6q0hvFemtIr1X1Hdu98MmWdPU0QTr06EIpQAmirLnrnecR8RDXFGooOT8H5nibss</recordid><startdate>20120401</startdate><enddate>20120401</enddate><creator>Mouton, H.</creator><creator>Putzeys, B.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20120401</creationdate><title>Understanding the PWM Nonlinearity: Single-Sided Modulation</title><author>Mouton, H. ; Putzeys, B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-62797c2fac920a9e8adc95cafe368dc34e338798df88aeba7094dcd3a84b226e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Amplitude modulation</topic><topic>Applied sciences</topic><topic>Carrier-based pulse width modulation (PWM) strategies</topic><topic>Carson's rule</topic><topic>Circuit properties</topic><topic>Circuits of signal characteristics conditioning (including delay circuits)</topic><topic>closed-form solutions</topic><topic>digital simulation</topic><topic>double Fourier integral</topic><topic>Electric, optical and optoelectronic circuits</topic><topic>Electronic circuits</topic><topic>Electronics</topic><topic>Exact sciences and technology</topic><topic>Fourier series</topic><topic>Fourier transforms</topic><topic>Frequencies</topic><topic>Harmonic analysis</topic><topic>Mathematical model</topic><topic>Pulse width modulation</topic><topic>pulse width modulation (PWM)</topic><topic>regular sampling</topic><topic>Waveform analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mouton, H.</creatorcontrib><creatorcontrib>Putzeys, B.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998–Present</collection><collection>IEEE Xplore</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on power electronics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Mouton, H.</au><au>Putzeys, B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Understanding the PWM Nonlinearity: Single-Sided Modulation</atitle><jtitle>IEEE transactions on power electronics</jtitle><stitle>TPEL</stitle><date>2012-04-01</date><risdate>2012</risdate><volume>27</volume><issue>4</issue><spage>2116</spage><epage>2128</epage><pages>2116-2128</pages><issn>0885-8993</issn><eissn>1941-0107</eissn><coden>ITPEE8</coden><abstract>This paper provides a new look at the mechanisms underlying pulse width modulation (PWM). A simple approach to analyze the behavior of a single-sided pulse width modulator is presented. By using elementary methods, the pulse-width-modulated waveform is written as the sum of two sawtooth functions and the original modulating waveform. Simply applying the well-known Fourier series expansion of the sawtooth function, an equivalent model of the pulse width modulator, which shows that it is in essence a sequence of phase modulators, is derived. This model provides a clear understanding of the nonlinearities involved in the PWM process. It is shown how the superposition of modulating waveforms in the time-domain translates into the convolution of the sidebands in the frequency domain. Finally, the interaction of the pulse width modulator and a sample-and-hold register is studied and a general expression for the Fourier transform of a regular-sampled PWM waveform is derived. The analysis applies to periodic as well as aperiodic modulating waveforms.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TPEL.2011.2169283</doi><tpages>13</tpages></addata></record> |
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| source | IEEE Xplore |
| subjects | Amplitude modulation Applied sciences Carrier-based pulse width modulation (PWM) strategies Carson's rule Circuit properties Circuits of signal characteristics conditioning (including delay circuits) closed-form solutions digital simulation double Fourier integral Electric, optical and optoelectronic circuits Electronic circuits Electronics Exact sciences and technology Fourier series Fourier transforms Frequencies Harmonic analysis Mathematical model Pulse width modulation pulse width modulation (PWM) regular sampling Waveform analysis |
| title | Understanding the PWM Nonlinearity: Single-Sided Modulation |
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