<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="12" minor="1"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="true"><Hide name="Group Range"/><Hide name="Table Borders"/></View-Properties>
<MapleNet-Properties elisiondigitsbefore="100" labelling="true" indentamount="4" elisiontermsthreshold="10000" ansi="false" errorbreak="1" useclientjvm="true" echo="1" imaginaryunit="I" labelwidth="20" plotdriver="openviz" elisiondigitsafter="100" plotoutput="terminal" rtablesize="10" elisiontermsbefore="100" elisiondigitsthreshold="10000" typesetting="standard" plotdevice="inline" verboseproc="1" showassumed="1" errorcursor="false" longdelim="true" plotoptions="" quiet="false" elisiontermsafter="100" screenwidth="79" preplot="" prettyprint="3" displayprecision="-1" warnlevel="3" screenheight="25" latexwidth="6.0" postplot="" prompt="&gt; " ShowLabels="true"/>
<Styles><Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Code" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[40,120,40]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Page Number" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="16" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
</Annotation-table>
<Task>
</Task><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1324" drawlabel="true">
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<Text-field style="Author" layout="Author"><Font italic="true" size="20">Alan Elbanhawy</Font></Text-field>
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<Text-field style="Text" layout="Author"><Font italic="true">Power industry consultant, email: aelbanhawy@igcorporation.com</Font></Text-field>
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<Text-field style="Text" layout="Normal">Modern scientific papers published all over the world play a major role in disseminating new ideas, concepts and innovations that have propelled the state of the art in technology to amazing heights in the last few decades. These papers, in my opinion, were missing one thing which is being interactive. That is, the ability of the reader to examine the raw data, the mathematical derivations of the formulae used in the paper and the ability to take a individualized look at the intermediate and final results. The Maple<Font superscript="true">TM</Font> document format provides all these features by allowing a single document to contain text, graphics, embedded objects and the best symbolic and numerical engine in the industry. </Text-field>
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<Text-field style="Text" layout="Normal">This paper/worksheet is an attempt to take advantage of all these features and uniquely allow the reader to explore a fresh view of the subject of Metal Oxide Semiconductor Field Effect Transistor (MOSFET) conduction losses while giving him/her the opportunity to take a different look at the results obtained by the author while reading the detailed text of  the paper. Feel free to generate different graphs or examine different packages or silicon by entering your own parameter set. </Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">As the PC makers push for DC-DC converters delivering &gt;150 A at output voltages \342\211\2441V within the next few years, the semiconductor manufacturers are pushing to optimize their MOSFET by improving both the silicon and the packages to provide switching devices suitable for these challenges. In this paper we will address the parasitic resistance attributed to the package alone and in isolation from the silicon on-resistance. </Font>We will show that in most of the traditional packages this resistance has a very strong frequency dependent component.</Text-field>
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<Text-field style="Text" layout="Normal">This means that at a switching frequency of about a few megahertz, this parasitic resistance will constitute a large percentage of the total device on-resistance and hence influences the losses greatly. Based on this observation, we will concentrate on the topology of choice, the synchronous buck converter, and we will derive conduction loss equations that are frequency dependent and calculate actual losses and examine several effects that follow.</Text-field>
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<Text-field style="Heading 1" layout="Heading 1"><Font italic="true">Introduction</Font></Text-field>
<Text-field style="Text" layout="Normal">It is estimated that personal computers (PCs), notebook computers and servers annually use in excess of 500 million synchronous buck DC-DC converters each year. This number alone justifies an in-depth analysis of this very popular topology to enable engineers to refine their design process and save energy and help the environment at the same time. There are several loss mechanisms in this topology but, in this paper, we will concentrate on the conduction loss alone.</Text-field>
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<Text-field style="Text" layout="Normal">Traditionally, the conduction loss, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUGNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUGNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn</Equation>, in power MOSFETs has been calculated from the formula <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIkxGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIkxGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> is the inductor current, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> is the MOSFET's on-resistance plus the package parasitic resistance and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation> is the duty cycle. In this formula, the assumption is that the package parasitic resistance is a constant and is independent of frequency. However, a closer look at the package (see Figure 2) reveals that the bonding wires are thin enough with a diameters of few thousands of an inch that points towards possible skin effect influence on the parasitic resistance.</Text-field>
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<Text-field style="Text" layout="Normal">In this paper we explore the influence of skin effect on power MOSFET's parasitic resistance. Formulae will be derived to express the package parasitic resistance as a function of frequency and power loss will be calculated to demonstrate the percentage error that results if we do not take this effect into account. </Text-field>
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<Text-field style="Heading 1" layout="Heading 1"><Font italic="true">Synchronous Buck Converter</Font></Text-field>
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<Text-field style="Text" layout="Heading 1">Figure 1 depicts a simplified synchronous buck converter. This topology is the workhorse of the PC power conversion industry, which offers an excellent combination of simplicity of operation, ease of control, high conversion efficiency and the all-important low cost.  We will concentrate on the conduction losses in both the <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation> M<Font subscript="true">HS</Font> and M<Font subscript="true">LS</Font> MOSFETs. The frequency effects of the dynamic losses will not be addressed in this paper. The switching current in both of these devices are a rectangular wave that that is represented in Figure 4. </Text-field>
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<Text-field style="Text" layout="Heading 1"><Font bold="true">Figure 1.</Font> Synchronous Buck Converter</Text-field>
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<Text-field style="Heading 3" layout="Heading 3">Principles of operation</Text-field>
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<Text-field style="Text" layout="Normal">Assume the lower MOSFET, M<Font subscript="true">LS</Font>, is initially turned OFF and the top or control MOSFET, M<Font subscript="true">HS</Font>, is turned ON. This applies the input voltage to one end of the inductor, causing the inductor current to ramp up. When M<Font subscript="true">HS</Font> is turned OFF, the current will continue to flow through the inductor but now it flows through M<Font subscript="true">LS </Font><Font encoding="UTF-8">body diode. After a dead time on the order of a few tens of nanoseconds\342\200\224dictated by the PWM controller\342\200\224the MOSFET </Font>M<Font subscript="true">LS</Font> turns ON. This allows all the inductor current to flow through M<Font subscript="true">LS</Font> rather than its body diode since the voltage drop across its on-resistance, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> is lower than the diode voltage drop. </Text-field>
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<Text-field style="Text" layout="Normal">Assuming that the current through the inductor does not reach zero (the Continuous Conduction Mode or CCM), the voltage across the lower MOSFET will simply be <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUScmc2RvdDtGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkgvJSlzdHJldGNoeUdGSC8lKnN5bW1ldHJpY0dGSC8lKGxhcmdlb3BHRkgvJS5tb3ZhYmxlbGltaXRzR0ZILyUnYWNjZW50R0ZILyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVy1GLDYlLUYvNiVRIklGJ0YyRjUtRiM2JS1GLzYlUSJMRidGMkY1RjJGNUY9RkQ=</Equation> during the full OFF period of the top MOSFET where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIkxGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIkxGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> is the inductor current. </Text-field>
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<Text-field style="Text" layout="Normal">At the end of the OFF period of the top MOSFET M<Font subscript="true">HS</Font>, the lower MOSFET, M<Font subscript="true">LS</Font>, will turn OFF, allowing the inductor current to flow in the body diode once more. After the dead time, the top MOSFET will turn ON and the cycle repeats. The average voltage at the output will depend on the average ON time of the top MOSFET if the inductor current is continuous. the output voltage V<Font subscript="true">out</Font> may be calculated from the equation <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation> is the duty cycle and is equal to <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1GIzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUY0NiVRI29uRidGN0Y6RjdGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjdGOi1GIzYkLUYxNiUtRjQ2JVEiVEYnRjdGOi1GIzYlLUY0NiVRIlNGJ0Y3RjpGN0Y6RkIvRjtRJ25vcm1hbEYnLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZYLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRlE=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1GIzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUY0NiVRI29uRidGN0Y6RjdGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjdGOi1GIzYkLUYxNiUtRjQ2JVEiVEYnRjdGOi1GIzYlLUY0NiVRIlNGJ0Y3RjpGN0Y6RkIvRjtRJ25vcm1hbEYnLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZYLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRlE=</Equation> where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI29uRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI29uRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==</Equation> is the on time of the control MOSFET and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> is the duration of one cycle where <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> is the converter switching frequency.</Text-field>
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<Text-field style="Text" layout="Normal">The conduction losses have traditionally been calculated from the equation <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> where all parameters are self explanatory. We will demonstrate that this equation, though useful as a rough estimate, may not be accurate enough for accurate analysis.</Text-field>
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<Text-field style="Text" layout="Normal">The switching currents in M<Font subscript="true">HS</Font> and M<Font subscript="true">LS</Font> are approximately of a rectangular shape. Using Fourier analysis one may break it down to its constituent sinusoidal currents of frequencies <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUklbXN1YkdGJDYlLUYsNiVRImZGJ0YvRjItRiM2JS1GLDYlUSJzRidGL0YyRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjk=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUklbXN1YkdGJDYlLUYsNiVRImZGJ0YvRjItRiM2JS1GLDYlUSJzRidGL0YyRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjk=</Equation> where <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>. Complete analysis is available later on in this worksheet.</Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Package Parasitic Resistance:</Text-field>
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<Text-field style="Text" layout="Normal">Due to the skin effect phenomenon, the bonding wires of the drain, gate and source leads exhibit different parasitic resistance at different frequencies.</Text-field>
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<Text-field style="Text" layout="Normal">The package parasitic resistance is usually between <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEjNjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSJ+RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEtJiMxODE7JiM5Mzc7RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEjNjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSJ+RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEtJiMxODE7JiM5Mzc7RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8=</Equation> for advanced packages to about 2.2 <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEobSYjOTM3O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEobSYjOTM3O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> for the SO8 package and mainly depends on the bonding wires' diameter and length and their physical proximity to each other. This is a very small value that may be ignored in other small signal applications but in modern power circuits, we will show that it represents an appreciable part of the total on-resistance of the switching device, which is the MOSFET for the purposes of this paper. To accurately determine the parasitic resistance it was important to isolate the package from the MOSFET silicon.  To calculate the resistance as a function of frequency, we chose to employ finite element analysis (FEA) techniques.</Text-field>
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<Text-field style="Text" layout="Normal">This has the advantage of allowing us to determine very small resistance values without the need for special test equipment and fixtures.  It also eliminated any error which will be introduced by the test environment.  A harmonic analysis was used to model the magnetic field surrounding the package.  Resistance is then determined by extracting the real part of the characteristic impedance (<Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+</Equation>).</Text-field>
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<Text-field style="Text" layout="Normal">Figure 2 shows both the SO8 and DPAK packages and all their constituents that affect the simulation.  As can clearly be seen this is a fairly complex structure, which cannot readily yield a closed form function describing the parasitics.  The approach we have taken was to fit a curve to the results of the finite element analysis performed at various frequencies. This curve then describes the parasitic resistance as a function of frequency. This is done so we can introduce this function in the loss equations which ultimately allows us to study the effect of  this phenomenon on the predicted losses using DC on-resistance as it is performed today.</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true">Figure 3.</Font> Parasitic Resistance as a function of frequency for SO8 (left) and DPAK (right)</Text-field>
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<Text-field style="Text" layout="Normal">Figure 3 shows this effect clearly. The value of <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI0RTRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI0RTRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==</Equation> goes up by a full order of magnitude by changing the switching frequency from 30 KHz to a mere 10 MHz. This effect is very significant in switching MOSFETs since the device's on-resistance <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> is in the range of a few <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEobSYjOTM3O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEobSYjOTM3O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> to start with. </Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Switching Drain Currents</Text-field>
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<Text-field style="Text" layout="Normal">where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInJGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInJGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> = current rise time, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImZGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImZGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> = current fall time, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3BrRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3BrRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==</Equation> =peak current, and<Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation> = the inductor current at the start of  M<Font subscript="true">HS</Font> on time.</Text-field>
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<Text-field style="Ordered List 1" layout="Ordered List 1">The switching current is shown in Figure 4.  </Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred" bulletsuffix="."><Font bold="true">Figure 4.</Font> Switching Current Waveform</Text-field>
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<Text-field style="Ordered List 1" layout="Ordered List 1" bulletsuffix="." initial="0" bullet="none">Each current cycle may be divided in four distinct regions as follows:</Text-field>
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<Text-field style="Text" layout="Normal"><Font style="Ordered List 1">2. </Font><Equation executable="false" style="Ordered List 1" input-equation="" display="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">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</Equation><Font style="Ordered List 1"> : the time duration of the </Font>M<Font subscript="true">HS</Font><Font style="Ordered List 1"> switched fully on. During this time (the on-time) the inductor current ramps from </Font><Equation executable="false" style="Ordered List 1" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn</Equation><Font style="Ordered List 1"> to </Font><Equation executable="false" style="Ordered List 1" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3BrRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3BrRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==</Equation>.</Text-field>
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<Text-field style="Text" layout="Normal"><Font style="Ordered List 1">3. </Font><Equation executable="false" style="Ordered List 1" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdWJHRiQ2JUYrLUYjNiUtRiw2JVEickYnRi9GMkYvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmhuLUZQNiVGKy1GIzYlLUYsNiVRI29uRidGL0YyRi9GMkZXLUY2Ni1RIy4uRidGOUY7Rj5GQEZCRkRGRkZIRmduL0ZOUSYwLjBlbUYnRk9GWkZqbkZaLUZQNiVGKy1GIzYlLUYsNiVRImZGJ0YvRjJGL0YyRldGOQ==">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</Equation><Font style="Ordered List 1"> : when the </Font>M<Font subscript="true">HS</Font><Font style="Ordered List 1"> is switched off, the MOSFET current starts falling from </Font><Equation executable="false" style="Ordered List 1" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3BrRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3BrRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0Y2USdub3JtYWxGJw==</Equation><Font style="Ordered List 1"> to </Font><Equation executable="false" style="Ordered List 1" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNigtRjU2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YvL0krbXNlbWFudGljc0dGJFElVW5pdEYnLyUlb3BlbkdRKCZsb2JyaztGJy8lJmNsb3NlR1EoJnJvYnJrO0YnRkNGL0Y0Ri8=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNigtRjU2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YvL0krbXNlbWFudGljc0dGJFElVW5pdEYnLyUlb3BlbkdRKCZsb2JyaztGJy8lJmNsb3NlR1EoJnJvYnJrO0YnRkNGL0Y0Ri8=</Equation>.</Text-field>
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<Text-field style="Text" layout="Normal"><Font style="Ordered List 1">4. </Font><Equation executable="false" style="Ordered List 1" input-equation="" display="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">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</Equation><Font style="Ordered List 1"> : </Font>M<Font subscript="true">HS</Font><Font style="Ordered List 1"> continues to be off while </Font>M<Font subscript="true">LS</Font><Font style="Ordered List 1"> is turned on.                          </Font></Text-field>
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<Text-field style="Text" layout="Normal">The first segment, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjSTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjSTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn</Equation>, from <Equation executable="false" style="Ordered List 1" input-equation="" display="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">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</Equation> may be expressed as </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">. </Text-field>
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<Text-field style="Text" layout="Normal">The second segment, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjSTJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjSTJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn</Equation>,  is from <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font italic="true"> </Font> may be expressed as  </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">.</Font></Text-field>
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<Text-field style="Text" layout="Normal">The third segment from <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>  the drain current may be expressed as </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">.</Font></Text-field>
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<Text-field style="Text" layout="Normal">The last segment, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjSTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjSTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn</Equation>,  from <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> and is </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjSTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZN</Equation></Text-field>
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<Text-field style="Text" layout="Normal">.</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">The Fourier series of a periodic function <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==</Equation><Font italic="true"> </Font>with a period of <Font italic="true">2l  </Font>may be expressed in the form:  </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"> where a0 is the averaged current.</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">Now we can calculate the average current <Font italic="true">a0</Font> as well as <Font italic="true">an</Font> and <Font italic="true">bn:</Font></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1643" drawlabel="true" redirect-source="L1430">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1430" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1425" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"> </Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1424" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1427" drawlabel="true" redirect-target="L1638">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1638" drawlabel="true" redirect-source="L1427">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1427" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1421" drawlabel="true" redirect-target="L1644">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1644" drawlabel="true" redirect-source="L1421">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1421" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1715" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L587" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L951" drawlabel="true" redirect-target="L949">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYwLUZQNiYtRiM2Ki1GRzYlUSVzdWJzRidGSkZNLUZQNiQtRiM2LC1JJW1zdWJHRiQ2Ji1GRzYlUSJmRidGSkZNLUYjNiUtRkc2JVEic0YnRkpGTUZKRk0vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRistRiw2LVEiPUYnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZecEYrLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEjMTBGJ0YvLUYjNiUtRmRwNiRRIjZGJ0YvLyUrZXhlY3V0YWJsZUdGNEYvLyUxc3VwZXJzY3JpcHRzaGlmdEdGZm8tRiw2LVEiLEYnRi9GMi9GNkZMRjdGOUY7Rj1GP0ZBL0ZFUSwwLjMzMzMzMzNlbUYnRistRkc2JVEjYW5GJ0ZKRk1GXHFGL0YvRmBxRitGWC1GUDYkLUYjNixGaW5GK0Zqb0YrRmBwRmBxRistRkc2JVEjYm5GJ0ZKRk1GXHFGL0YvRlxxRi9GLy8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRidGYHFGKy1GRzYlUSJuRidGSkZNRitGam9GKy1GZHA2JFEiMUYnRi9GKy1GLDYtUSMuLkYnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJ0ZERistRmRwNiRRIzUwRidGL0ZccUYvRi8tRkc2I1EhRidGZHNGXHFGLw==">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L949" drawlabel="true" redirect-source="L951">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">%;</Text-field>
</Input>
<Output>
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<Text-field style="Text" layout="Normal">By plotting both <Font italic="true">an</Font> and <Font italic="true">bn</Font> as a function of <Font italic="true">n</Font>, we can observe the envelope of the discrete values of both of them. The reason <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzUwRidGOUY5">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzUwRidGOUY5</Equation> was chosen is that the highest frequency we deal with here is 2 MHz and the 50<Font superscript="true">th</Font> harmonic will be 100MHz which is the top value of frequency in our FEA.</Text-field>
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<Text-field style="Text" layout="Normal">In this paper we will only consider the top MOSFET M<Font subscript="true">HS</Font><Font encoding="UTF-8">. This is because in PC applications the duty cycle is relatively small \342\251\275 12% resulting in a very rich harmonic content in the derived Fourier series for the switching current. T</Font>he low side MOSFET M<Font subscript="true">LS</Font><Font encoding="UTF-8"> has a duty cycle \342\251\276 87% resulting in low harmonics and significantly less harmonics.</Font></Text-field>
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<Text-field style="Text" layout="Normal">Now we can express the switching current in the Fourier series, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInRGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInRGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=</Equation>, as:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Now let us verify the above results by plotting the Fourier series representation of the switching current:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">In order to calculate the losses, we must represent the term <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>  equivalently, in the form <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8">,  where the peak amplitude An and the phase \316\246n are</Font></Text-field>
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<Text-field style="Text" layout="Normal"> <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> and <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoJiM5MzQ7bkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSdhcmN0YW5GJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1JJm1mcmFjR0YkNigtRiw2JVEjYm5GJ0YvRjItRiM2JC1GLDYlUSNhbkYnRi9GMkY5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Ziby8lKWJldmVsbGVkR0Y9RjlGOUY5</Equation>.</Text-field>
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<Text-field style="Text" layout="Normal">Since the phase value has no effect on power calculations, only <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjQW5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjQW5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn</Equation> is is needed for our calculation.</Text-field>
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<Text-field style="Text" layout="Normal">The root mean square (RMS) value of the amplitude is <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRI0FuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRi82I1EhRictRiM2JUY6LUkmbXNxcnRHRiQ2Iy1GIzYkLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0ZIRkhGOkZILyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZPLyUpYmV2ZWxsZWRHUSZmYWxzZUYnLUkjbW9HRiQ2LVEiPUYnRkgvJSZmZW5jZUdGVC8lKnNlcGFyYXRvckdGVC8lKXN0cmV0Y2h5R0ZULyUqc3ltbWV0cmljR0ZULyUobGFyZ2VvcEdGVC8lLm1vdmFibGVsaW1pdHNHRlQvJSdhY2NlbnRHRlQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zjby1GQDYjLUYjNiQtRiw2KC1GIzYnLUklbXN1cEdGJDYlLUYvNiVRI2FuRidGMkY1RkIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZWNi1RIitGJ0ZIRllGZW5GZ25GaW5GW29GXW9GX28vRmJvUSwwLjIyMjIyMjJlbUYnL0Zlb0ZbcS1GX3A2JS1GLzYlUSNibkYnRjJGNUZCRmRwRjpGSEZCRkpGTUZQRlJGSC1GVjYtUSIuRidGSEZZRmVuRmduRmluRltvRl1vRl9vL0Zib1EmMC4wZW1GJy9GZW9GZnFGSA==">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</Equation>  </Text-field>
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<Text-field style="Text" layout="Normal">Now the switching current <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3RzRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI3RzRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRicvRjZRJ25vcm1hbEYn</Equation>, may be written as:</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">By plotting </Font><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation><Font style="Text">  we can observe the envelope of the squared discrete current amplitudes.          </Font></Text-field>
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<Text-field style="Text" layout="Normal">The total MOSFET on-resistance, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJURTT05GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=</Equation>,  is made of two basic parameters:</Text-field>
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<Text-field style="Text" layout="Normal"> 1. The silicon on-resistance, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI0RTRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI0RTRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRicvRjZRJ25vcm1hbEYn</Equation>.</Text-field>
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<Text-field style="Text" layout="Normal"> 2. Package parasitic resistance, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIlBGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIlBGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic=</Equation>. </Text-field>
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<Text-field style="Text" layout="Normal">Thus, </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRJURTT05GJ0YyRjVGMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGaW4tRiw2JkYuLUYjNictRi82JVEjRFNGJ0YyRjVGMkY9RkBGNUZDRkYtRko2LVEiK0YnRk1GT0ZRRlNGVUZXRllGZW4vRmhuUSwwLjIyMjIyMjJlbUYnL0Zbb0Znby1GLDYmRi4tRiM2Jy1GLzYlUSJQRidGMkY1RjJGPUZARjVGQ0ZGLUYvNiNRIUYnRj1GTQ==">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</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSNEU0YnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiK0YnL0Y2USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZVLUYsNiVGLi1GLzYlUSJQRidGMkY1RjtGQg==">LCZJOCNtc3ViKG1pKCJSIiksbWkoIkRTIikpRzYiIiIiSTcjbXN1YihtaSgiUiIpLG1pKCJQIikpR0YkRiU=</Equation></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">The following are the Finite Element Analysis data for the SO8, DPAK and D2PAK packages:</Text-field>
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<Text-field style="Text" layout="Normal">where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElZnJlcUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElZnJlcUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> is the frequency in megahertz.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">the raw parasitic resistance data for the SO8 package in m\316\251.</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEnUlBEUEFLRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiYtRiM2NC1JI21uR0YkNiRRJjAuNTI4RidGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZVNiRRJjAuNjY1RidGOUZYLUZVNiRRJjEuNDIxRidGOUZYLUZVNiRRJjIuMzg0RidGOUZYLUZVNiRRJzExLjAwMEYnRjlGWC1GVTYkUScyMi44NThGJ0Y5RlgtRlU2JFEoMTM4Ljc5NkYnRjlGWC1GVTYkUSgyOTguNTExRidGOS8lK2V4ZWN1dGFibGVHRj0vJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNRl9wRmFwRjk=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnUlBEUEFLRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiYtRiM2MS1JI21uR0YkNiRRJjAuNTI4RidGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZVNiRRJjAuNjY1RidGOUZYLUZVNiRRJjEuNDIxRidGOUZYLUZVNiRRJjIuMzg0RidGOUZYLUZVNiRRJzExLjAwMEYnRjlGWC1GVTYkUScyMi44NThGJ0Y5RlgtRlU2JFEoMTM4Ljc5NkYnRjlGWC1GVTYkUSgyOTguNTExRidGOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZN</Equation></Text-field>
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<Text-field style="Text" layout="Normal">the raw parasitic resistance data for the DPAK package <Font encoding="UTF-8">in m\316\251.</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">the raw parasitic resistance data for the D2PAK package <Font encoding="UTF-8">in m\316\251.</Font></Text-field>
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<Text-field style="Text" layout="Normal">Using the <Font bold="true">Curve Fitting Assistant</Font> in Maple, we can fit curves for the parasitic resistance as a function of the frequency, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation><Font encoding="UTF-8">, in megahertz, and the parasitic resistance in m\316\251.</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1660" drawlabel="true" redirect-source="L795">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L795" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L818" drawlabel="true" redirect-target="L1661">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1661" drawlabel="true" redirect-source="L818">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L818" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L797" drawlabel="true" redirect-target="L1662">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L797" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Each formula has a DC term  and several frequency dependent terms. One further point: in this analysis, the minimum skin frequency is approximately 30 KHz for the packages used; below this frequency the skin effect may be considered zero.  Therefore, these equations should be used to calculate the parasitic resistance for the frequency F, where <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>. The DC value of the parasitic resistance is taken directly from the raw data. <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> where <Font italic="true">n</Font> is the harmonic number and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=</Equation> is the DC-DC converter's switching frequency.</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">Now we can write the equation for the packaged MOSFET on-resistance:</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRJURTT05GJ0YyRjVGMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LVEiPUYnL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmluLUYsNiZGLi1GIzYnLUYvNiVRInBGJ0YyRjVGMkY9RkBGNUZDRkYtRko2LVEiK0YnRk1GT0ZRRlNGVUZXRllGZW4vRmhuUSwwLjIyMjIyMjJlbUYnL0Zbb0Znby1GLDYmRi4tRiM2Jy1GLzYlUSNEU0YnRjJGNUYyRj1GQEY1RkNGRkY9RkBGTQ==">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</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LywmSTgjbXN1YihtaSgiUiIpLG1pKCJEUyIpKUc2IiIiIkk3I21zdWIobWkoIlIiKSxtaSgiUCIpKUdGJUYmLCZJNyNtc3ViKG1pKCJSIiksbWkoInAiKSlHRiVGJkYkRiY=</Equation></Text-field>
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<Text-field style="Text" layout="Normal"> where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInBGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInBGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=</Equation> is as before and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI0RTRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRI0RTRidGMkY1RjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRicvRjZRJ25vcm1hbEYn</Equation> is the silicon on-resistance.</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\342\210\264 The equations for </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRJURTT05GJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0Y9">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRJURTT05GJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0Y9</Equation> for all the packages under consideration can be written as:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1493" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Text-field style="Text" layout="Normal"> <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVErUkRTT05EMlBBS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKFJQRDJQQUtGJ0YvRjItRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlYtSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSMxMEYnRjktRiM2JC1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GX28tRmZuNiRRIjNGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIRl5vRmBvLUklbXN1YkdGJDYmLUYsNiVRIlJGJ0YvRjItRiM2Iy1GLDYlUSNEU0YnRi9GMi8lL3N1YnNjcmlwdHNoaWZ0R0Zmby9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZN</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1676" drawlabel="true" redirect-source="L1675">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1675" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="true" labelreference="L1671" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="Maple Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJWJvbGRHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="true" labelreference="L1668" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="Maple Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJWJvbGRHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1677" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L883" drawlabel="true" redirect-target="L1666">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYqLUY2NiYtRiM2Ki1GLDYlUSVzdWJzRidGL0YyLUY2NiQtRiM2KS1JJW1zdWJHRiQ2Ji1GLDYlUSJSRidGL0YyLUYjNiMtRiw2JVEjRFNGJ0YvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGaG4vJSlzdHJldGNoeUdGaG4vJSpzeW1tZXRyaWNHRmhuLyUobGFyZ2VvcEdGaG4vJS5tb3ZhYmxlbGltaXRzR0Zobi8lJ2FjY2VudEdGaG4vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Znby1JI21uR0YkNiRRJTAuMDFGJ0ZaLUZXNi1RIixGJ0ZaRmZuL0ZqbkYxRltvRl1vRl9vRmFvRmNvL0Zmb1EmMC4wZW1GJy9GaW9RLDAuMzMzMzMzM2VtRictRlc2LVEifkYnRlpGZm5GaW5GW29GXW9GX29GYW9GY29GYnAvRmlvRmNwRmZwLUYsNiVRK1JEU09ORDJQQUtGJ0YvRjJGWkZecEY+LUY2NiQtRiM2KUZFRlZGam9GXnBGZnBGZnAtRiw2JVEqUkRTT05EUEFLRidGL0YyRlpGXnBGPi1GNjYkLUYjNilGRUZWRmpvRl5wRmZwRmZwLUYsNiVRKVJEU09OU084RidGL0YyRlpGWi8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRidGXnBGZnAtRiw2JVEiRkYnRi9GMkZWLUZbcDYkUSIwRidGWi1GVzYtUSMuLkYnRlpGZm5GaW5GW29GXW9GX29GYW9GY28vRmZvUSwwLjIyMjIyMjJlbUYnRmlwLUZbcDYkUSQxMDBGJ0ZaRlo=</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1666" drawlabel="true" redirect-source="L883">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">%;</Text-field>
</Input>
<Output>
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<Text-field style="Text" layout="Normal">The above graph shows the parasitic resistance as a function of frequency for all three packages. Notice that the parasitic resistance can go as high as 500 <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEobSYjOTM3O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEobSYjOTM3O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> at 100MHz for bonding wires of only <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUShtJiM5Mzc7RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUShtJiM5Mzc7RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8=</Equation> when measured at DC.</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\342\210\264 the total power dissipation may be written as:</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L1679" drawlabel="true" redirect-source="L1505">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L1505" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1499" drawlabel="true" redirect-target="L698">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">We have replaced </Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZD</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text"> by 50 to facilitate graphing and calculations with reliable accuracy.</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">The traditional conduction loss calculations can be written as follows:</Text-field>
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<Text-field style="Text" layout="Normal">1. Calculate the RMS value of the current, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJVNSTVNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRJVNSTVNGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy9GNlEnbm9ybWFsRic=</Equation>, first:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">2. Calculate the traditional conduction loss, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmUGNyZWZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmUGNyZWZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn</Equation>:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Now we can derive a formula of the error using the traditional value vs. that using the frequency dependent parasitic resistance.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEtUGVyY2VudEVyc284RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSZtZnJhY0dGJDYoLUYjNigtRiw2JVEoUHRvdFNPOEYnRi9GMi1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmVuLUYsNiVRJXN1YnNGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2Ki1JJW1zdWJHRiQ2Ji1GLDYlUSJSRidGL0YyLUYjNiUtRiw2JVEiUEYnRi9GMkYvRjIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkjbW5HRiQ2JFEoMC4wMDIxNkYnRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRltxL0ZORlxxLUYsNiVRJlBjcmVmRidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5RjlGZnFGOS1GIzYnLUYsNiNRIUYnLUYjNiZGZ25Gam5GZnFGOUZqcUZmcUY5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zkci8lKWJldmVsbGVkR0Y9LUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSEZbcUZicS1GZHA2JFEkMTAwRidGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUZmcUY5">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">The percentage error (z-axes) as a function of the switching frequency </Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">and the silicon on-resistance for SO8, DPAK and D2PAK Package</Text-field>
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<Text-field style="Text" layout="Normal">The above graph depicts the percentage error between the calculation using the traditional formula vs. using the formulae derived above with skin effect taken into consideration.</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Please notice that D2PAK will deliver 540% error when operating at 2 MHz and 2 m\316\251 on-resistance. It is also worth noting that at a very low switching frequency, where fs \342\211\244 100 KHz, there is a negligible increase in parasitic resistance due to skin effect.</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSdwbG90M2RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2PC1GOzYmLUYjNi8tSSZtZnJhY0dGJDYoLUYjNiUtRiw2JVEqUHRvdEQyUEFLRidGNEY3LyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUYjNidGKy1GIzYmLUYsNiVRJXN1YnNGJ0Y0RjctRjs2JC1GIzYrLUklbXN1YkdGJDYmLUYsNiVRIlJGJ0Y0RjctRiM2JS1GLDYlUSJQRidGNEY3RjRGNy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSSNtb0dGJDYtUSI9RidGTi8lJmZlbmNlR0ZNLyUqc2VwYXJhdG9yR0ZNLyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmpwLUkjbW5HRiQ2JFEpMC4wMDA5OTVGJ0ZOLUZnbzYtUSJ+RidGTkZqb0ZccEZecEZgcEZicEZkcEZmcC9GaXBRJjAuMGVtRicvRlxxRmVxLUZnbzYtUSIsRidGTkZqby9GXXBGNkZecEZgcEZicEZkcEZmcEZkcS9GXHFRLDAuMzMzMzMzM2VtRidGYXEtRiw2JVEmUGNyZWZGJ0Y0RjdGS0ZORk5GS0ZORitGS0ZOLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zlci8lKWJldmVsbGVkR0ZNLUZnbzYtUScmc2RvdDtGJ0ZORmpvRlxwRl5wRmBwRmJwRmRwRmZwRmRxRmZxLUZecTYkUSQxMDBGJ0ZORmdxLUZENigtRiM2JS1GLDYlUSlQdG90RFBBS0YnRjRGN0ZLRk4tRiM2J0YrLUYjNiZGVC1GOzYkLUYjNistRmZuNiZGaG4tRiM2JEZdb0ZORmBvRmNvRmZvLUZecTYkUSkwLjAwMDUyOEYnRk5GYXFGZ3FGYXFGXXJGS0ZORk5GS0ZORitGS0ZORmByRmNyRmZyRmhyRmpyRl1zRmdxLUZENigtRiM2JS1GLDYlUShQdG90U084RidGNEY3RktGTi1GIzYnRistRiM2JkZULUY7NiQtRiM2K0ZfdEZmby1GXnE2JFEoMC4wMDIxNkYnRk5GYXFGZ3FGYXFGXXJGS0ZORk5GS0ZORitGS0ZORmByRmNyRmZyRmhyRmpyRl1zRktGTkZOLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0ZncUZhcS1GZm42JkZobi1GIzYlLUYsNiVRI0RTRidGNEY3RjRGN0Zgb0Zjb0Zmby1GXnE2JFEmMC4wMDJGJ0ZOLUZnbzYtUSMuLkYnRk5Gam9GXHBGXnBGYHBGYnBGZHBGZnAvRmlwUSwwLjIyMjIyMjJlbUYnRmZxLUZecTYkUSYwLjAxNUYnRk5GZ3FGYXEtRmZuNiYtRiw2JVEiZkYnRjRGNy1GIzYlLUYsNiVRInNGJ0Y0RjdGNEY3RmBvRmNvRmZvLUZecTYkUSQxRTVGJ0ZORmh2LUZecTYkUSQyRTZGJ0ZORmdxRmFxLUYsNiVRJWF4ZXNGJ0Y0RjdGZm8tRiw2JVEmYm94ZWRGJ0Y0RjdGZ3EtRiw2JVEnbGFiZWxzRidGNEY3RmZvLUY7NiYtRiM2LEYrLUkjbXNHRiQ2I1EkUmRzRidGZ3EtRl55NiNRI2ZzRidGYXFGZ3EtRl55NiNRJmVycm9yRidGK0ZLRk5GTi9GaXVRIltGJy9GXHZRIl1GJ0ZLRk5GTkZLRk5GK0ZLRk4=">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</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">%;</Text-field>
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<Output>
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<Text-field style="Text" layout="Normal" alignment="centred">The ratio <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> (z axis) </Text-field>
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<Text-field style="Text" layout="Normal">The above graph shows that in order to have efficient high frequency converters, designers must use advanced packages or they risk having inefficient power conversion leading to unacceptable power losses. </Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Conclusion</Text-field>
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<Text-field style="Text" layout="Normal">1. The package parasitic resistance represents an appreciable part of the MOSFET on-resistance in power applications.</Text-field>
<Text-field style="Text" layout="Normal">2. The package parasitic resistance possesses a very strong frequency dependence due to the skin effect phenomenon.</Text-field>
<Text-field style="Text" layout="Normal">3. A higher fundamental switching frequency will result in higher parasitic resistance and hence higher conduction losses.</Text-field>
<Text-field style="Text" layout="Normal">4. The DC conduction losses calculated above produce an error that can be as large as 500% depending on the package and the fundamental switching frequency.</Text-field>
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<Text-field style="Text" layout="Normal">5. When choosing the switching frequency for a given application, it is mandatory to examine this above mentioned effect to weigh the pros and cons of such a selection.</Text-field>
<Text-field style="Text" layout="Normal">6. New packages have been developed by several manufacturers that address this problem with varying degrees of success. Some are very successful like DirectFet BGA. </Text-field>
<Text-field style="Text" layout="Normal">7. As the DC-DC converters are expected to perform at higher efficiencies, particularly in the notebook field, all loss mechanisms must be placed under the microscope in an attempt to minimize their effect and provide the overall solution that fully utilizes all the advantages made so far in MOSFET design.</Text-field>
<Text-field style="Text" layout="Normal">8. Both with breakthroughs in silicon and in innovative packaging, these new switching devices continue to deliver improvement in performance at very reasonable prices .</Text-field>
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