Mathcad Professional 14.0 <description/> <author>M Carroll</author> <company>Parametric Technology Corporation</company> <keywords/> <revisedBy> M Carroll</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>E0F9435A-6A36-4180-B4C9-8E05E6E283A8</documentID> <versionID>72610CEF-A5CB-48AE-9688-A76514E2D67D</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="14" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 2"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="bold" font-style="italic" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 3"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Paragraph"> <blockAttr margin-left="0" margin-right="0" text-indent="21" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="false" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="error"> <compatibility multiple-assignment="MC12" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="538" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="44" left="48" top="26.25" width="90" height="12" align-x="70.5" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Component Values</b> </p> </text> </region> <region region-id="1" left="48" top="51" width="47.25" height="16.5" align-x="63" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="f">L</ml:id> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:id xml:space="preserve">μH</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="2" left="132" top="51" width="51" height="16.5" align-x="147.75" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="f">C</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">μF</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="202" left="258" top="51" width="57" height="16.5" align-x="283.5" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="out">R</ml:id> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:id xml:space="preserve">kΩ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="4" left="48" top="75" width="47.25" height="16.5" align-x="66" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Lf">r</ml:id> <ml:apply> <ml:mult/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="5" left="132" top="75" width="52.5" height="16.5" align-x="150.75" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="Cf">r</ml:id> <ml:apply> <ml:mult/> <ml:real>0.01</ml:real> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="46" left="48" top="104.25" width="53.25" height="12" align-x="69" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Frequency</b> <sp/> </p> </text> </region> <region region-id="65" left="48" top="122.25" width="82.5" height="12" align-x="62.25" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">number of decades</p> </text> </region> <region region-id="76" left="192" top="123" width="23.25" height="12.75" align-x="203.25" align-y="132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">n</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="68" left="48" top="140.25" width="123" height="12" align-x="62.25" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">number of points per decade</p> </text> </region> <region region-id="69" left="192" top="141" width="27.75" height="12.75" align-x="203.25" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">p</ml:id> <ml:real>20</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="78" left="48" top="158.25" width="54" height="12" align-x="59.25" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">matrix count</p> </text> </region> <region region-id="79" left="192" top="159" width="44.25" height="12.75" align-x="203.25" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">q</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="84" left="48" top="212.25" width="72" height="12" align-x="67.5" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">frequency matrix</p> </text> </region> <region region-id="82" left="192" top="186" width="73.5" height="45" align-x="206.25" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">q</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:apply> <ml:vectorize/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">q</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="365" left="48" top="248.25" width="183" height="12" align-x="75" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>FILTER RESPONSE WITHOUT DAMPER</b> </p> </text> </region> <region 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</ml:apply> <ml:id xml:space="preserve" subscript="f">L</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="87" left="180" top="285" width="96.75" height="27" align-x="202.5" align-y="300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="L">X</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.0012566370614359172</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="12"/> </region> <region region-id="151" left="48" top="316.5" width="88.5" height="35.25" align-x="64.5" align-y="336" 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="L">θ</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.71996210430958352</ml:real> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="154" left="48" top="363" width="67.5" height="16.5" align-x="65.25" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="L">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="Lf">r</ml:id> <ml:apply> <ml:mult/> <ml:imag symbol="j">1</ml:imag> <ml:id xml:space="preserve" subscript="L">X</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="95" left="48" top="398.25" width="45.75" height="12" align-x="66.75" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Capacitor</b> </p> </text> </region> <region region-id="538" left="618" top="399" width="12" height="12.75" align-x="623.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Da</ml:id> </math> <rendering item-idref="16"/> </region> <region region-id="155" left="48" top="416.25" width="63.75" height="31.5" align-x="67.5" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="C">X</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">f</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="f">C</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="156" left="186" top="423" width="74.25" height="21" align-x="209.25" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="C">X</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>159.15494309189535</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="161" left="48" top="454.5" width="95.25" height="35.25" align-x="65.25" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="C">θ</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">atan</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="C">X</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lf">r</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>180</ml:real> <ml:id 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<ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:apply> <ml:vectorize/> <ml:apply> <ml:absval/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="2">Z</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="L">Z</ml:id> <ml:id xml:space="preserve" subscript="2">Z</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="136" left="234" top="789" width="89.25" height="27" align-x="252.75" align-y="804" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="f">g</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="f">θ</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-0.036007146350144126</ml:real> </result> </ml:eval> </math> <rendering item-idref="34"/> </region> <region region-id="317" left="36" top="890.25" width="162.75" height="12" align-x="63" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>FILTER RESPONSE WITH DAMPER</b> </p> </text> </region> <region region-id="402" left="36" top="914.25" width="87.75" height="12" align-x="53.25" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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