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is-visible="false" ruler-unit="cm"/> <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="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1455" 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="7" left="6" top="6.75" width="266.25" height="14.25" align-x="24.75" align-y="18" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">Cathodyne or Concertina Phase Splitter (CPS) Derivations</inlineAttr> </u> </f> </p> </text> </region> <region region-id="431" left="6" top="30.75" width="83.25" height="14.25" align-x="15" align-y="42" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">Fix-biased version</inlineAttr> </u> </f> </p> </text> </region> <region region-id="1376" left="12" top="54" width="287.25" height="190.5" align-x="12" align-y="54" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <png item-idref="2" display-width="285.75" display-height="189"/> <rendering item-idref="3"/> </region> <region region-id="950" left="324" top="213" width="174.75" height="11.25" align-x="330" 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="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit">Fig. 10.1a<sp count="2"/>Basic CPS circuit with fixed bias</p> </text> </region> <region region-id="1377" left="24" top="264" width="412.5" height="213.75" align-x="24" align-y="264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <png item-idref="4" display-width="411" display-height="212.25"/> <rendering item-idref="5"/> </region> <region region-id="949" left="156" top="489" width="163.5" height="11.25" align-x="156" align-y="498" 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="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit">Fig. 10.7a Equivalent circuit of Fig. 10.1a</p> </text> </region> <region region-id="947" left="66" top="516" width="241.5" height="129.75" align-x="66" align-y="516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <png item-idref="6" display-width="240" display-height="128.25"/> <rendering item-idref="7"/> </region> <region region-id="948" left="366" top="609" width="93" height="33.75" align-x="371.25" align-y="618" 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" 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RB</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>1093042.9843964847</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="453" left="6" top="968.25" width="92.25" height="33.75" align-x="23.25" align-y="990" 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/math20"> <ml:id xml:space="preserve" subscript="g">R</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">RA</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">RB</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="454" left="108" top="975" width="93.75" height="22.5" align-x="124.5" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="g">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>731333.2</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="909" left="234" top="981" width="147" height="16.5" align-x="340.5" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="cc">V</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">I</ml:id> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="a">V</ml:id> </ml:apply> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="g">V</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>82.73</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="volt"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="27"/> </region> <region region-id="910" left="234" top="1005" width="129" height="16.5" align-x="318" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="cc">V</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">I</ml:id> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="g">V</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>167.27</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="volt"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="28"/> </region> <region region-id="1112" left="6" top="1032.75" width="233.25" height="14.25" align-x="6" align-y="1044" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">1. CPS used as un-balanced to balanced converter </inlineAttr> </u> </f> </p> </text> </region> <region region-id="732" left="6" top="1062.75" width="46.5" height="14.25" align-x="15" align-y="1074" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">1.1 Gains </inlineAttr> </u> </f> </p> </text> </region> <region region-id="734" left="6" top="1086.75" width="85.5" height="17.25" align-x="12" align-y="1098" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">1.1.1 Idle gains G</inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false"> <sub>0</sub> </inlineAttr> </f> </p> </text> </region> <region region-id="884" left="6" top="1113" width="63" height="13.5" align-x="19.5" align-y="1122" 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">cathode gain G<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>c</sub> </inlineAttr> </f> </p> </text> </region> <region region-id="675" left="6" top="1138.5" width="126.75" height="35.25" align-x="29.25" align-y="1158" 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/math20"> <ml:id xml:space="preserve" subscript="0.c">G</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">µ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">R</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="a">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="677" left="240" top="1143" width="96.75" height="22.5" align-x="262.5" align-y="1158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.c">G</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.93129346314325456</ml:real> </result> </ml:eval> </math> <rendering item-idref="30"/> </region> <region region-id="886" left="6" top="1185" width="55.5" height="13.5" align-x="16.5" align-y="1194" 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">anode gain G<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>a</sub> </inlineAttr> </f> </p> </text> </region> <region region-id="680" left="6" top="1204.5" width="132" height="35.25" align-x="29.25" align-y="1224" 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/math20"> <ml:id xml:space="preserve" subscript="0.a">G</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="a">R</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="a">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="682" left="240" top="1209" width="102" height="22.5" align-x="262.5" align-y="1224" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.a">G</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>-0.93129346314325456</ml:real> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="889" left="6" top="1251" width="267" height="13.5" align-x="15" align-y="1260" 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">equal loads R lead to the general idle gain equation G<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>0</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> and G</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>0.bal</sub> </inlineAttr> </f> </p> </text> </region> <region region-id="696" left="6" top="1281" width="52.5" height="16.5" align-x="45" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="a">R</ml:id> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </math> <rendering item-idref="33"/> </region> <region region-id="698" left="78" top="1281" width="10.5" height="11.25" align-x="78" align-y="1290" 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">=></p> </text> </region> <region region-id="711" left="240" top="1274.25" width="165" height="31.5" align-x="326.25" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:absval/> <ml:id xml:space="preserve" subscript="0.a">G</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0.c">G</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">G</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">µ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">R</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="914" left="6" top="1311" width="80.25" height="16.5" align-x="35.25" align-y="1320" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="o.bal">v</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" 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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">=></p> </text> </region> <region region-id="1385" left="240" top="1352.25" width="132.75" height="31.5" align-x="303" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="0">G</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="39"/> </region> <region region-id="892" left="6" top="1383" width="98.25" height="13.5" align-x="12" align-y="1392" 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">Idle balanced gain G<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>0.bal</sub> </inlineAttr> </f> <sp/> </p> </text> </region> <region region-id="730" left="6" top="1413" width="30" height="16.5" align-x="18" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve" subscript="a">R</ml:id> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="729" left="60" top="1413" width="10.5" height="11.25" align-x="60" align-y="1422" 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">=></p> </text> </region> <region region-id="728" left="90" top="1406.25" width="99" height="31.5" align-x="120.75" align-y="1422" 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/math20"> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="727" left="240" top="1407" width="87.75" height="22.5" align-x="270" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8625869262865091</ml:real> </result> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="737" left="6" top="1452.75" width="324" height="17.25" align-x="15" align-y="1464" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">1.1.2 Gains G</inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false"> <sub>bal</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">(R</inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false"> <sub>L</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">) with o/p loaded and balanced o/p resistance R</inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false"> <sub>o.bal</sub> </inlineAttr> </f> </p> </text> </region> <region region-id="822" left="6" top="1479" width="432" height="13.5" align-x="21" align-y="1488" 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">balanced o/p load = R<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>L </sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">, hence, the</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> additional loads to the existing R</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>a</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> and R</inlineAttr> </f> <inlineAttr line-through="false"> <sub> <f family="Times New Roman" charset="0">c</f> </sub> </inlineAttr> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> is the paralleling of 0.5*R</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>L</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> each</inlineAttr> </f> </p> </text> </region> <region region-id="750" left="6" top="1503" width="59.25" height="22.5" align-x="23.25" align-y="1518" 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/math20"> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>10</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="749" left="96" top="1509" width="10.5" height="11.25" align-x="96" align-y="1518" 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">=></p> </text> </region> <region region-id="748" left="132" top="1498.5" width="45.75" height="31.5" align-x="156" align-y="1518" 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/math20"> <ml:id xml:space="preserve" subscript="L.a">R</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="747" left="240" top="1509" width="49.5" height="16.5" align-x="264" align-y="1518" 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/math20"> <ml:id xml:space="preserve" subscript="L.c">R</ml:id> <ml:id xml:space="preserve" subscript="L.a">R</ml:id> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="917" left="6" top="1539" width="496.5" height="38.25" align-x="18" align-y="1548" 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">Output load dependent gain:</p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">any decrease or increase of the anode and cathode resistors from R to eg. R<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>new</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> = </inlineAttr> </f>R||(0.5*R<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>L</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">) automatically leads to a changed G</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>0.bal </sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">via the new G</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>0.</sub> </inlineAttr> </f> <sub> <inlineAttr line-through="false"> <f family="Times New Roman" charset="0">a.new</f> </inlineAttr> </sub> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> = G</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>0.</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>c.new</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> = G</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>0.</sub> </inlineAttr> </f> <sub> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">new</inlineAttr> </f> </sub> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">, thus changing the balanced output resistance too.</inlineAttr> </f> </p> </text> </region> <region region-id="920" left="6" top="1592.25" width="128.25" height="37.5" align-x="53.25" align-y="1614" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="new">R</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="921" left="240" top="1599" width="110.25" height="22.5" align-x="286.5" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="new">R</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>3750</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="47"/> </region> <region region-id="756" left="6" top="1677" width="10.5" height="11.25" align-x="6" align-y="1686" 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">=></p> </text> </region> <region region-id="754" left="36" top="1645.5" width="183" height="77.25" align-x="83.25" align-y="1686" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="bal1">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="755" left="240" top="1671" width="104.25" height="22.5" align-x="286.5" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="bal1">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8156182212581344</ml:real> </result> </ml:eval> </math> <rendering item-idref="49"/> </region> <region region-id="895" left="6" top="1749" width="10.5" height="11.25" align-x="6" align-y="1758" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">=></p> </text> </region> <region region-id="896" left="30" top="1746.75" width="124.5" height="30" align-x="123" align-y="1758" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:limit/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="bal1">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:lambda> <ml:id xml:space="preserve">∞</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">G</ml:id> <ml:real font="0">0.bal</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="50"/> </region> <region region-id="898" left="180" top="1749" width="70.5" height="11.25" align-x="189" align-y="1758" 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">q.e.d see next line</p> </text> </region> <region region-id="784" left="6" top="1784.25" width="489" height="34.5" align-x="462" align-y="1800" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:limit/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="bal1">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:lambda> <ml:id xml:space="preserve">∞</ml:id> </ml:apply> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>.77500000000000000000e21</ml:real> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">Ω</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">S</ml:id> <ml:apply> <ml:plus/> <ml:real>3587962962962962963.</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>.41250000000000000000e21</ml:real> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">S</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:symResult> </ml:symEval> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8625869262865091</ml:real> </result> </ml:eval> <resultFormat> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </resultFormat> </math> <rendering item-idref="51"/> </region> <region region-id="808" left="6" top="1851" width="153" height="13.5" align-x="21" align-y="1860" 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">Simplification of the G<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>bal</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> (R</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>L</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">) equation</inlineAttr> </f> </p> </text> </region> <region region-id="844" left="6" top="1881" width="10.5" height="11.25" align-x="6" align-y="1890" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">=></p> </text> </region> <region region-id="843" left="36" top="1874.25" width="150.75" height="37.5" align-x="78.75" align-y="1890" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="new">R</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="845" left="288" top="1875" width="99.75" height="22.5" align-x="330" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8156182212581347</ml:real> </result> </ml:eval> </math> <rendering item-idref="53"/> </region> <region region-id="814" left="6" top="1944.75" width="211.5" height="17.25" align-x="16.5" align-y="1956" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">1.2 Output resistance</inlineAttr> </u> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr underline="false" line-through="false"> R</inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr underline="false" line-through="false"> <sub>o.bal</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <inlineAttr underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">of balanced output</inlineAttr> </u> </f> </p> </text> </region> <region region-id="923" left="6" top="1977" width="207" height="11.25" align-x="24" align-y="1986" 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">Equivalent circuit of the balanced amp situation:</p> </text> </region> <region region-id="1455" left="30" top="2028" width="228.75" height="116.25" align-x="30" align-y="2028" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <png item-idref="54" display-width="227.25" display-height="114.75"/> <rendering item-idref="55"/> </region> <region region-id="759" left="276" top="2109" width="210" height="22.5" align-x="281.25" align-y="2118" 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="center" list-style-type="inherit" tabs="inherit">Fig. 10.10<sp count="2"/>Equivalent circuit of the balanced situation </p> </text> </region> <region region-id="929" left="6" top="2158.5" width="129.75" height="35.25" align-x="35.25" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="o.bal">v</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="i">v</ml:id> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="o.bal">R</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="56"/> </region> <region region-id="930" left="186" top="2158.5" width="78" height="35.25" align-x="218.25" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o.bal">v</ml:id> <ml:id xml:space="preserve" subscript="i">v</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="57"/> </region> <region region-id="931" left="282" top="2169" width="10.5" height="11.25" align-x="282" align-y="2178" 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">=></p> </text> </region> <region region-id="933" left="312" top="2158.5" width="134.25" height="35.25" align-x="356.25" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="o.bal">R</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="58"/> </region> <region region-id="769" left="30" top="2212.5" width="147.75" height="35.25" align-x="66" align-y="2232" 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/math20"> <ml:id xml:space="preserve" subscript="o.bal1">R</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="771" left="312" top="2217" width="112.5" height="22.5" align-x="347.25" align-y="2232" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="o.bal1">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.69262865090354</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="60"/> </region> <region region-id="786" left="6" top="2229" width="10.5" height="11.25" align-x="6" align-y="2238" 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">=></p> </text> </region> <region region-id="772" left="30" top="2260.5" width="125.25" height="35.25" align-x="66" align-y="2280" 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/math20"> <ml:id xml:space="preserve" subscript="o.bal2">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="773" left="312" top="2265" width="112.5" height="22.5" align-x="347.25" align-y="2280" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="o.bal2">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.6926286509028</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="62"/> </region> <region region-id="842" left="6" top="2319" width="206.25" height="13.5" align-x="6" align-y="2328" 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">Simplification of the R<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>o.</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>bal </sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">equation</inlineAttr> </f> </p> </text> </region> <region region-id="1378" left="222" top="2299.5" width="237.75" height="106.5" align-x="382.5" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:parens> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.69262865090423</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="835" left="6" top="2415" width="10.5" height="11.25" align-x="6" align-y="2424" 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="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">=></p> </text> </region> <region region-id="838" left="30" top="2404.5" width="99.75" height="35.25" align-x="61.5" align-y="2424" 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/math20"> <ml:id xml:space="preserve" subscript="o.bal">R</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">µ</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="64"/> </region> <region region-id="858" left="228" top="2409" width="108" height="22.5" align-x="258.75" align-y="2424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="o.bal">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.692628650904</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> <region region-id="848" left="6" top="2514.75" width="162" height="14.25" align-x="30" align-y="2526" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">1.3 Input and Output Capacitances </inlineAttr> </u> </f> </p> </text> </region> <region region-id="850" left="6" top="2541" width="414" height="27" align-x="9" align-y="2550" 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"> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">C</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>a</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> and C</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>o.</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>bal</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> plus t</inlineAttr> </f>rimming of C<sub>o.c</sub> will <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">lead to frequency dependent G</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>bal</sub> </inlineAttr> </f> <inlineAttr line-through="false"> <f family="Times New Roman" charset="0">(f)</f> </inlineAttr> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub> <sp/> </sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">and o/p impedance Z</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>o.bal</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">(f) as follows:</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub> <sp/> </sub> </inlineAttr> </f> </p> </text> </region> <region region-id="899" left="6" top="2565" width="91.5" height="18.75" align-x="15" align-y="2580" 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/math20"> <ml:id xml:space="preserve">f</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:mult style="auto-select"/> <ml:real>10</ml:real> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>20</ml:real> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:sequence> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>5</ml:real> </ml:apply> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="66"/> </region> <region region-id="900" left="6" top="2601" width="76.5" height="22.5" align-x="30" align-y="2616" 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/math20"> <ml:id xml:space="preserve" subscript="g.c">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>3.1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-12</ml:real> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="67"/> </region> <region region-id="901" left="156" top="2601" width="76.5" height="22.5" align-x="180" align-y="2616" 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/math20"> <ml:id xml:space="preserve" subscript="g.a">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>1.4</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-12</ml:real> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="68"/> </region> <region region-id="902" left="294" top="2601" width="75.75" height="22.5" align-x="317.25" align-y="2616" 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/math20"> <ml:id xml:space="preserve" subscript="a.c">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>3.0</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-12</ml:real> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="859" left="6" top="2631" width="56.25" height="16.5" align-x="37.5" align-y="2640" 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/math20"> <ml:id xml:space="preserve" subscript="o.bal">C</ml:id> <ml:id xml:space="preserve" subscript="a.c">C</ml:id> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="852" left="6" top="2684.25" width="163.5" height="37.5" align-x="48" align-y="2706" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="o.bal">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="o.bal">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">2</ml:imag> <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="o.bal">C</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="860" left="24" top="2736" width="357.75" height="157.5" align-x="24" align-y="2736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="72"/> <rendering item-idref="73"/> </region> <region region-id="952" left="120" top="2883" width="192.75" height="11.25" align-x="126" align-y="2892" 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="center" list-style-type="inherit" tabs="inherit">Fig. 10.11<sp count="2"/>Output impedance vs. frequency</p> </text> </region> <region 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subscript="a">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="g.c">C</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="c">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="76"/> </region> <region region-id="870" left="234" top="3009" width="90" height="22.5" align-x="247.5" align-y="3024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="i">C</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>2.9567245119305852E-12</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="farad"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="77"/> </region> <region region-id="872" left="6" top="3044.25" width="114.75" height="37.5" align-x="30.75" align-y="3066" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="i">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="g">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">2</ml:imag> <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="i">C</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="78"/> </region> <region region-id="874" left="30" top="3096" width="332.25" height="159.75" align-x="30" align-y="3096" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="79"/> <rendering item-idref="80"/> </region> <region region-id="955" left="126" top="3249" width="212.25" height="11.25" align-x="132" align-y="3258" 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="center" list-style-type="inherit" tabs="inherit">Fig. 10.12<sp count="2"/>Input impedance vs. frequency</p> </text> </region> <region region-id="878" left="6" top="3297" width="135" height="22.5" align-x="23.25" align-y="3312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:real>1.5</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:sequence> <ml:apply> <ml:mult style="default"/> <ml:real>100</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="879" left="48" top="3348" width="327" height="161.25" align-x="48" align-y="3348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="82"/> <rendering item-idref="83"/> </region> <region region-id="959" left="90" top="3501" width="274.5" height="22.5" align-x="96" align-y="3510" 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="center" list-style-type="inherit" tabs="inherit">Fig. 10.13<sp count="2"/>Gain of the un-balanced to balanced converter PCS vs. 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xml:space="preserve">f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">2</ml:imag> <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="4">C</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="97"/> </region> <region region-id="1047" left="30" top="3938.25" width="186" height="46.5" align-x="84.75" align-y="3954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> 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style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="100"/> </region> <region region-id="1110" left="258" top="4022.25" width="186" height="46.5" align-x="312.75" align-y="4038" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="bal4">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="4">Z</ml:id> <ml:id xml:space="preserve">f</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="101"/> </region> <region region-id="1065" left="18" top="4074" width="370.5" height="205.5" align-x="18" align-y="4074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="102"/> <rendering item-idref="103"/> </region> <region region-id="1013" left="90" top="4257" width="276" height="22.5" align-x="90" align-y="4266" 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="center" list-style-type="inherit" tabs="inherit">Fig. 10.15<sp count="2"/>Balanced gain vs. frequency with equal additional capacitances parellel to the anode and cathode load resistors R</p> </text> </region> <region region-id="1066" left="18" top="4299" width="34.5" height="12.75" align-x="28.5" align-y="4308" 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/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>1</ml:real> <ml:real>5</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="104"/> </region> <region region-id="1071" left="108" top="4293" width="52.5" height="18.75" align-x="117" align-y="4308" 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/math20"> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>20</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="105"/> </region> <region region-id="1101" left="210" top="4299" width="56.25" height="131.25" align-x="246.75" align-y="4320" 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/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="p">C</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:sequence> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:real>10</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-12</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-9</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:real>10</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-9</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:real>33</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-9</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:real>100</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-9</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">F</ml:id> </ml:apply> </ml:sequence> </ml:define> </math> <rendering item-idref="106"/> </region> <region region-id="1104" left="12" top="4436.25" width="108.75" height="33.75" align-x="28.5" align-y="4458" 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/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:imag symbol="j">2</ml:imag> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">f</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="p">C</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>-1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="107"/> </region> <region region-id="1105" left="204" top="4442.25" width="149.25" height="48" align-x="232.5" align-y="4458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> 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z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="109"/> <rendering item-idref="110"/> </region> <region region-id="1107" left="66" top="4653" width="313.5" height="22.5" align-x="72" align-y="4662" 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="center" list-style-type="inherit" tabs="inherit">Fig. 10.15<sp count="2"/>Balanced gain at a f = 20kHz vs. various equal additional capacitances parallel to the anode and cathode load resistors R </p> </text> </region> <region region-id="1113" left="6" top="4692.75" width="384.75" height="14.25" align-x="6" align-y="4704" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">2. CPS used as un-balanced to un-balanced converter via anode OR cathode output </inlineAttr> </u> </f> </p> </text> </region> <region region-id="1121" left="6" top="4716.75" width="60.75" height="14.25" align-x="11.25" align-y="4728" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">2.1 Idle gains</inlineAttr> </f> </p> </text> </region> <region region-id="1132" left="6" top="4749" width="80.25" height="11.25" align-x="10.5" align-y="4758" 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">via the anode alone:</p> </text> </region> <region region-id="1125" left="108" top="4738.5" width="132" height="35.25" align-x="131.25" align-y="4758" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.a">G</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="a">R</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="a">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="111"/> </region> <region region-id="1144" left="384" top="4743" width="102" height="22.5" align-x="406.5" align-y="4758" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.a">G</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>-0.93129346314325456</ml:real> </result> </ml:eval> </math> <rendering item-idref="112"/> </region> <region region-id="1133" left="6" top="4797" width="87.75" height="11.25" align-x="10.5" align-y="4806" 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">via the cathode alone:</p> </text> </region> <region region-id="1126" left="108" top="4786.5" width="126.75" height="35.25" align-x="131.25" align-y="4806" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.c">G</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">µ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">R</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="a">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="1145" left="384" top="4791" width="96.75" height="22.5" align-x="406.5" align-y="4806" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.c">G</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.93129346314325456</ml:real> </result> </ml:eval> </math> <rendering item-idref="114"/> </region> <region region-id="1123" left="6" top="4830.75" width="326.25" height="14.25" align-x="6" align-y="4842" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">2.2 Output resistances (between respective output and ground!)</inlineAttr> </f> </p> </text> </region> <region region-id="1135" left="6" top="4881" width="80.25" height="11.25" align-x="10.5" align-y="4890" 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">via the anode alone:</p> </text> </region> <region region-id="1137" left="108" top="4870.5" width="119.25" height="35.25" align-x="132" align-y="4890" 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/math20"> <ml:id xml:space="preserve" subscript="o.a">R</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">R</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="a">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="1146" left="384" top="4875" width="96" height="22.5" align-x="407.25" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="o.a">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>14549.374130737135</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="116"/> </region> <region region-id="1136" left="6" top="4929" width="87.75" height="11.25" align-x="10.5" align-y="4938" 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">via the cathode alone:</p> </text> </region> <region region-id="1142" left="108" top="4918.5" width="54" height="31.5" align-x="121.5" align-y="4938" 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/math20"> <ml:id xml:space="preserve" subscript="c">r</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="a">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="1143" left="210" top="4918.5" width="64.5" height="35.25" align-x="234" align-y="4938" 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/math20"> <ml:id xml:space="preserve" subscript="o.c">R</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="c">R</ml:id> <ml:id xml:space="preserve" subscript="c">r</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="c">r</ml:id> <ml:id xml:space="preserve" subscript="c">R</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="118"/> </region> <region region-id="1147" left="384" top="4923" width="100.5" height="22.5" align-x="407.25" align-y="4938" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="o.c">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>579.97218358831708</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="119"/> </region> <region region-id="1149" left="6" top="4962.75" width="264.75" height="14.25" align-x="6" align-y="4974" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">2.3 Output loaded gains (outputs separately loaded!)</inlineAttr> </f> </p> </text> </region> <region region-id="1151" left="6" top="4983" width="61.5" height="22.5" align-x="30" align-y="4998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.a">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="120"/> </region> <region region-id="1152" left="114" top="4983" width="61.5" height="22.5" align-x="138" align-y="4998" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.c">R</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="default"/> <ml:real>5</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="121"/> </region> <region region-id="1155" left="6" top="5020.5" width="120.75" height="35.25" align-x="48" align-y="5040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve" subscript="a">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="L.a">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="0.a">G</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L.a">R</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="L.a">R</ml:id> <ml:id xml:space="preserve" subscript="o.a">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="122"/> </region> <region region-id="1156" left="384" top="5025" width="116.25" height="22.5" align-x="425.25" align-y="5040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="a">G</ml:id> <ml:id xml:space="preserve" subscript="L.a">R</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>-0.23819009675583383</ml:real> </result> </ml:eval> </math> <rendering item-idref="123"/> </region> <region region-id="1160" left="390" top="5067" width="111" height="22.5" align-x="431.25" align-y="5082" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="c">G</ml:id> <ml:id xml:space="preserve" subscript="L.c">R</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.88548003173763545</ml:real> </result> </ml:eval> </math> <rendering item-idref="124"/> </region> <region region-id="1158" left="6" top="5068.5" width="120.75" height="35.25" align-x="48" align-y="5088" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve" subscript="c">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="L.c">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="0.c">G</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L.c">R</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="L.c">R</ml:id> <ml:id xml:space="preserve" subscript="o.c">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="1167" left="6" top="5358.75" width="333" height="14.25" align-x="7.5" align-y="5370" 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"> <f family="Times New Roman" charset="0" size="12"> <u> <inlineAttr line-through="false">3. Derivation of the balanced equations and proof of the above given ones</inlineAttr> </u> </f> </p> </text> </region> <region region-id="1288" left="24" top="5388" width="216" height="205.5" align-x="24" align-y="5388" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <png item-idref="126" display-width="214.5" display-height="204"/> <rendering item-idref="127"/> </region> <region region-id="1276" left="264" top="5571" width="181.5" height="11.25" align-x="270" align-y="5580" 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">Fig. 10.16<sp count="2"/>Un-balanced to balanced concerter</p> </text> </region> <region region-id="1380" left="12" top="5604" width="309.75" height="189" align-x="12" align-y="5604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <png item-idref="128" display-width="308.25" display-height="187.5"/> <rendering item-idref="129"/> </region> <region region-id="1381" left="354" top="5787" width="162" height="11.25" align-x="360" align-y="5796" 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">Fig. 10.17<sp count="2"/>Equivalent circuit of Fig. 10.16</p> </text> </region> <region region-id="1294" left="6" top="5820.75" width="150" height="14.25" align-x="11.25" align-y="5832" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">3.1 Relevant derivation equations</inlineAttr> </f> </p> </text> </region> <region region-id="1280" left="6" top="5853" width="32.25" height="11.25" align-x="14.25" align-y="5862" 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">node A:</p> </text> </region> <region region-id="1172" left="72" top="5853" width="75.75" height="16.5" align-x="126" align-y="5862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">i</ml:id> <ml:id xml:space="preserve" subscript="2">i</ml:id> </ml:apply> <ml:id xml:space="preserve" font="1" subscript="3">i</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="o.a">i</ml:id> </ml:apply> </math> <rendering item-idref="130"/> </region> <region region-id="1281" left="6" top="5877" width="30.75" height="11.25" align-x="6" align-y="5886" 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">node C:</p> </text> </region> <region region-id="1174" left="72" 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</ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="152"/> </region> <region region-id="1259" left="6" top="6285" width="54" height="18.75" align-x="18" align-y="6300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>15</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="153"/> </region> <region region-id="1260" left="102" top="6285" width="59.25" height="22.5" align-x="119.25" align-y="6300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>10</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="154"/> </region> <region region-id="1273" left="228" top="6280.5" width="221.25" height="35.25" align-x="391.5" align-y="6300" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="m">g</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8156182212581349</ml:real> </result> </ml:eval> </math> <rendering item-idref="155"/> </region> <region region-id="1229" left="6" top="6340.5" width="186" height="35.25" align-x="54.75" align-y="6360" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="diff1">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="156"/> </region> <region region-id="1231" left="252" top="6351" width="105.75" height="22.5" align-x="300" align-y="6366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="diff1">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8156182212581344</ml:real> </result> </ml:eval> </math> <rendering item-idref="157"/> </region> <region region-id="1251" left="12" top="6405" width="10.5" height="11.25" align-x="12" align-y="6414" 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">=></p> </text> </region> <region region-id="1252" left="42" top="6398.25" width="161.25" height="46.5" align-x="87" align-y="6414" 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/math20"> <ml:function> <ml:id xml:space="preserve" subscript="diff">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="158"/> </region> <region region-id="1236" left="252" top="6399" width="102" height="22.5" align-x="296.25" align-y="6414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="diff">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8156182212581347</ml:real> </result> </ml:eval> </math> <rendering item-idref="159"/> </region> <region region-id="1305" left="36" top="6471" width="10.5" height="11.25" align-x="36" align-y="6480" 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">=></p> </text> </region> <region region-id="1306" left="72" top="6471" width="93.75" height="16.5" align-x="120" align-y="6480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="diff">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="160"/> </region> <region region-id="1307" left="258" top="6468.75" width="24" height="14.25" align-x="258" align-y="6480" 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"> <f family="Times New Roman" charset="0" size="12"> <b> <inlineAttr line-through="false">q.e.d</inlineAttr> </b> </f> </p> </text> </region> <region region-id="1320" left="6" top="6519" width="69.75" height="13.5" align-x="12.75" align-y="6528" 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">with R<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>L</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> = infinite:</inlineAttr> </f> </p> </text> </region> <region region-id="1321" left="102" top="6512.25" width="95.25" height="46.5" align-x="135" align-y="6528" 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/math20"> <ml:id xml:space="preserve" subscript="0.diff">G</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="161"/> </region> <region region-id="1323" left="264" top="6513" width="90" height="22.5" align-x="296.25" align-y="6528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0.diff">G</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.8625869262865089</ml:real> </result> </ml:eval> </math> <rendering item-idref="162"/> </region> <region region-id="1329" left="36" top="6573" width="10.5" height="11.25" align-x="36" align-y="6582" 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">=></p> </text> </region> <region region-id="1328" left="102" top="6573" width="68.25" height="16.5" align-x="137.25" align-y="6582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="0.diff">G</ml:id> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> </ml:apply> </math> <rendering item-idref="163"/> </region> <region region-id="1327" left="258" top="6570.75" width="24" height="14.25" align-x="258" align-y="6582" 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"> <f family="Times New Roman" charset="0" size="12"> <b> <inlineAttr line-through="false">q.e.d</inlineAttr> </b> </f> </p> </text> </region> <region region-id="1386" left="6" top="6714.75" width="419.25" height="14.25" align-x="6" align-y="6726" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">3.3 Derivation of the differential (= balanced) output resistance (see Fig. 10.17)</inlineAttr> </f> </p> </text> </region> <region region-id="1388" left="6" top="6738.75" width="117" height="14.25" align-x="15" align-y="6750" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">3.3.1 Equations approach</inlineAttr> </f> </p> </text> </region> <region region-id="1299" left="6" top="6777" width="75.75" height="16.5" align-x="26.25" align-y="6786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="o.a">i</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">i</ml:id> <ml:id xml:space="preserve" subscript="2">i</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="3">i</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="164"/> </region> <region region-id="1300" left="120" top="6777" width="63.75" height="16.5" align-x="153" align-y="6786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="2">i</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="165"/> </region> <region region-id="1336" left="216" top="6766.5" width="56.25" height="35.25" align-x="229.5" align-y="6786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="2">i</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="166"/> </region> <region region-id="1337" left="306" top="6777" width="51" height="16.5" align-x="319.5" align-y="6786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="3">i</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:id xml:space="preserve" subscript="g.c">v</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="167"/> </region> <region region-id="1338" left="408" top="6766.5" width="41.25" height="31.5" align-x="421.5" align-y="6786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="1">i</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="R.a">v</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="168"/> </region> <region region-id="1339" left="6" top="6808.5" width="313.5" height="35.25" align-x="143.25" align-y="6828" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="o.a">i</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="R.a">v</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:id xml:space="preserve" subscript="g.c">v</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:id xml:space="preserve" subscript="i">v</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="169"/> </region> <region region-id="1358" left="6" top="6867" width="56.25" height="13.5" align-x="12.75" align-y="6876" 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">with v<f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>i</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> = 0<sp count="2"/>=></inlineAttr> </f> </p> </text> </region> <region region-id="1359" left="90" top="6856.5" width="139.5" height="35.25" align-x="110.25" align-y="6876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="o.a">i</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </math> <rendering item-idref="170"/> </region> <region region-id="1310" left="6" top="6904.5" width="333.75" height="54" align-x="262.5" align-y="6924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:equal/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve" subscript="o.diff">R</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="o.a">i</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="o.c">i</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="o.diff">v</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="171"/> </region> <region region-id="1312" left="6" top="6962.25" width="114" height="50.25" align-x="43.5" align-y="6978" 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/math20"> <ml:id xml:space="preserve" subscript="o.diff1">R</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="m">g</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="172"/> </region> <region region-id="1314" left="276" top="6969" width="114" height="22.5" align-x="312.75" align-y="6984" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="o.diff1">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.69262865090406</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="173"/> </region> <region region-id="1350" left="18" top="7035" width="10.5" height="11.25" align-x="18" align-y="7044" 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">=></p> </text> </region> <region region-id="1348" left="66" top="7024.5" width="102" height="35.25" align-x="99.75" align-y="7044" 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/math20"> <ml:id xml:space="preserve" subscript="o.diff">R</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="174"/> </region> <region region-id="1352" left="276" top="7029" width="110.25" height="22.5" align-x="309" align-y="7044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="o.diff">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.692628650904</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="175"/> </region> <region region-id="1353" left="90" top="7071" width="10.5" height="11.25" align-x="90" align-y="7080" 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">=></p> </text> </region> <region region-id="1354" left="126" top="7071" width="68.25" height="16.5" align-x="161.25" align-y="7080" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="o.diff">R</ml:id> <ml:id xml:space="preserve" subscript="o.bal">R</ml:id> </ml:apply> </math> <rendering item-idref="176"/> </region> <region region-id="1355" left="270" top="7068.75" width="24" height="14.25" align-x="270" align-y="7080" 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"> <f family="Times New Roman" charset="0" size="12"> <b> <inlineAttr line-through="false">q.e.d</inlineAttr> </b> </f> </p> </text> </region> <region region-id="1390" left="6" top="7116.75" width="114.75" height="14.25" align-x="15" align-y="7128" 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"> <f family="Times New Roman" charset="0" size="12"> <inlineAttr line-through="false">3.3.2 '0.5-times' approch</inlineAttr> </f> </p> </text> </region> <region region-id="1392" left="6" top="7149" width="384" height="13.5" align-x="9.75" align-y="7158" 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">At the gain <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">G</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>b</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>al.L</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> = 0.5*</inlineAttr> </f>G<sub>bal.nL</sub> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> the output resistance R</inlineAttr> </f> <inlineAttr line-through="false"> <sub> <f family="Times New Roman" charset="0">o.bal</f> </sub> </inlineAttr> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> equals the load resistance R</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sub>L</sub> </inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false">. Hence,</inlineAttr> </f> <f family="Times New Roman" charset="0"> <inlineAttr line-through="false"> <sp/> </inlineAttr> </f> </p> </text> </region> <region region-id="1403" left="6" top="7198.5" width="66" height="35.25" align-x="23.25" align-y="7218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0.5</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve" subscript="bal">G</ml:id> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0.bal">G</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="177"/> </region> <region region-id="1405" left="102" top="7209" width="10.5" height="11.25" align-x="102" align-y="7218" 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">=></p> </text> </region> <region region-id="1402" left="150" top="7168.5" width="114.75" height="95.25" align-x="167.25" align-y="7218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0.5</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>0.5</ml:real> <ml:id xml:space="preserve" subscript="L">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="178"/> </region> <region region-id="1412" left="6" top="7275" width="10.5" height="11.25" align-x="6" align-y="7284" 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">=></p> </text> </region> <region region-id="1415" left="24" top="7264.5" width="85.5" height="35.25" align-x="41.25" align-y="7284" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L">R</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="a">r</ml:id> </ml:apply> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="a">r</ml:id> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>2</ml:real> <ml:id xml:space="preserve">µ</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="179"/> </region> <region region-id="1432" left="150" top="7275" width="10.5" height="11.25" align-x="150" align-y="7284" 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">=></p> </text> </region> <region region-id="1433" left="168" top="7269" width="93.75" height="22.5" align-x="184.5" align-y="7284" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>258.692628650904</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="180"/> </region> <region region-id="1423" left="12" top="7311" width="19.5" height="11.25" align-x="18.75" align-y="7320" 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">with </p> </text> </region> <region region-id="1424" left="48" top="7311" width="50.25" height="16.5" align-x="79.5" align-y="7320" show-border="false" show-highlight="false" 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