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top="3.75" width="183.75" height="18" align-x="162" 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"> <f family="Arial" charset="0" size="16"> <inlineAttr line-through="false"> <c val="#000080">Miller Opamp Design</c> </inlineAttr> </f> </text> </region> <region region-id="3958" left="336" top="20.25" width="169.5" height="24" align-x="336" align-y="30" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Chris Haji-Michael www.sunshadow.co.uk/chris.htm</c> </inlineAttr> </f> </text> </region> <region region-id="3610" left="6" top="50.25" width="495" height="96" align-x="6" align-y="60" 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"> <c val="#000080">This sheet is used to design a low speed Miller Operational Amplifier, using the technique explained by </c> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Willy Sansen in his book "Analog Design Essentials" chapters 1 and 6, main slide 0629.</c> </inlineAttr> </f> <c val="#000080">PMOS input devices are chosen as these normally have better matching and lower noise. There is a good explanation of why this is generally better in </c> <c val="#000080">Analog integrated Circuit Design, Johns, Martin, page 232</c> <c val="#000080">Cc in the following schematic is replaced with Cc and Rc in series.</c> <c val="#000080">Design Inputs yellow; BSIM inputs blue; outputs green</c> </text> </region> <region region-id="2571" left="6" top="168" width="302.25" height="196.5" align-x="6" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="300.75" display-height="195"/> </picture> <rendering item-idref="3"/> </region> <region region-id="3799" left="450" top="158.25" width="44.25" height="33.75" align-x="469.5" align-y="174" 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" 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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"> <c val="#000080">The starting point of the analysis focuses on this graph, which shows the EKV model and gives i the inversion coefficient for Vgs-Vt.</c> <c val="#000080">The EKV model allows a single equation to be used for both the striong inversion and weak inversion operating zones on the FET.<sp count="2"/> </c> <c val="#000080">This model allows Vgs-Vt (Vgt) to be negative and typically vary from -0.2 to 0.5V. 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<region region-id="2347" left="6" top="857.25" width="497.25" height="39.75" align-x="6" align-y="870" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 2.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>From U0 and the other BSIM mobility parameters, calculate the mobility for the NMOS and the PMOS devices as this changes with Vgt.<sp count="2"/>The equations for this are from </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">W Liu "Mosfet Models for Spice Simulation", page 249</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080">.<sp count="2"/>Assume MOBMOD=1 which is the default.</c> </inlineAttr> </text> </region> <region region-id="2894" left="6" top="906" width="261" height="53.25" align-x="44.25" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">Vgt</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="n">U0</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="n">UA</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Vgt</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="n">VTH0</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">TOX</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="n">UB</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Vgt</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="n">VTH0</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">TOX</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="2965" left="6" top="972" width="261" height="53.25" align-x="44.25" 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/math30"> <ml:function> <ml:id xml:space="preserve" subscript="p">μ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">Vgt</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="p">U0</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="p">UA</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Vgt</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="p">VTH0</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">TOX</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="p">UB</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Vgt</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="p">VTH0</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">TOX</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="3953" left="210" top="1032" width="288" height="207.75" align-x="210" align-y="1032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="30"/> <rendering item-idref="31"/> </region> <region region-id="3956" left="60" top="1040.25" width="105.75" height="33.75" align-x="101.25" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">V</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>118.76854619825605</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="2"/> <unitReference unit="second" power-numerator="-1"/> <unitReference unit="volt" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="3957" left="36" top="1124.25" width="156" height="60" align-x="44.25" align-y="1134" 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"> <c val="#000080">This shows how the mobility changes with Vgt for both the NMOS and PMOS</c> <c val="#000080">It is 50% higher for the NMOS</c> </text> </region> <region region-id="2512" left="6" top="1253.25" width="497.25" height="51.75" align-x="16.5" align-y="1266" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 3.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>Calculate FT (frequency at which gain equals 1) for transistor M6 to get the gain-bandwidth.<sp count="2"/>From this we can calculate L (Gate Length) and we use this same L for most of the transistors.<sp count="2"/>The EKV model is used here, as this is what Samson uses, refer slides:</c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080"> 0138, 0140, 0165, 0627.</c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false"> <c val="#000080"> <sp count="2"/>The gate length needs to be at least twice the minimum. </c> </inlineAttr> </f> </text> </region> <region region-id="2997" left="6" top="1320" width="121.5" height="30" align-x="39.75" align-y="1338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="n">NFACTOR</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="b">k</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:id xml:space="preserve">q</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="3781" left="138" top="1328.25" width="21" height="12" align-x="138" align-y="1338" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0138</c> </inlineAttr> </f> </text> </region> <region region-id="3844" left="342" top="1328.25" width="21" height="12" align-x="342" align-y="1338" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0138</c> </inlineAttr> </f> </text> </region> <region region-id="3302" left="204" top="1311.75" width="127.5" height="42" align-x="234.75" align-y="1350" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">i</ml:id> <ml:boundVars> <ml:id xml:space="preserve">Vgt</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Vgt</ml:id> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="2822" left="6" top="1368" width="113.25" height="37.5" align-x="49.5" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0140</c> </inlineAttr> </f> </text> </region> <region region-id="2835" left="222" top="1376.25" width="114" height="27.75" align-x="239.25" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="T">F</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> <ml:id xml:space="preserve">γ</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve">GBW</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="3783" left="348" top="1382.25" width="21" height="12" align-x="348" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0627</c> </inlineAttr> </f> </text> </region> <region region-id="3785" left="258" top="1442.25" width="21" height="12" align-x="258" align-y="1452" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0165</c> </inlineAttr> </f> </text> </region> <region region-id="3251" left="6" top="1423.5" width="238.5" height="48.75" align-x="58.5" align-y="1458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:boundVars> <ml:id xml:space="preserve">Vgt</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="b">k</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:id xml:space="preserve">q</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="3966" left="312" top="1461" width="75" height="15" align-x="344.25" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">V</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.053048626321532087</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="volt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="38"/> </region> <region region-id="3963" left="414" top="1461" width="72" height="12.75" align-x="447.75" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>14.386192368979446</ml:real> </result> </ml:eval> </math> <rendering item-idref="39"/> </region> <region region-id="3961" left="306" top="1485" width="105" height="15" align-x="361.5" align-y="1494" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.82425772662247587</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="3960" left="426" top="1485" width="65.25" height="15" align-x="441.75" align-y="1494" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="T">F</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">MHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>480</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megahertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="3010" left="6" top="1512" width="300" height="192.75" align-x="6" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="42"/> <rendering item-idref="43"/> </region> <region region-id="3443" left="336" top="1538.25" width="163.5" height="36" align-x="344.25" 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"> <c val="#000080">This graph shows how the length of the gate influences the FT (the frequency at which the gain is 1)</c> </text> </region> <region region-id="3832" left="48" top="1716" width="249.75" height="183.75" align-x="48" align-y="1716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="44"/> <rendering item-idref="45"/> </region> <region region-id="3452" left="336" top="1742.25" width="164.25" height="36" align-x="336" align-y="1752" 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"> <c val="#000080">We also get this strange graph that shows how the required gate length changes with Vgt.</c> </text> </region> <region region-id="2765" left="6" top="1913.25" width="497.25" height="27.75" align-x="6" align-y="1926" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 4. </c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> Use the following equations to calculate the widths and currents of M6 and M5, which are dependent on CL.</c> </inlineAttr> </text> </region> <region region-id="2268" left="6" top="1956" width="37.5" height="30" align-x="21.75" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">C</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L">C</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="2520" left="72" top="1956" width="50.25" height="30" align-x="95.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="gs6">C</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L">C</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="3978" left="138" top="1964.25" width="21" height="12" align-x="138" align-y="1974" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0621</c> </inlineAttr> </f> </text> </region> <region region-id="2522" left="222" top="1956" width="51" height="30" align-x="242.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="ox">C</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ox">ε</ml:id> <ml:id xml:space="preserve">TOX</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="3496" left="318" top="1958.25" width="128.25" height="30" align-x="338.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="6">W</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="gs6">C</ml:id> <ml:apply> <ml:div/> <ml:real>3</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve" subscript="ox">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="3977" left="462" top="1964.25" width="21" height="12" align-x="462" align-y="1974" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0161</c> </inlineAttr> </f> </text> </region> <region region-id="2542" left="6" top="2010" width="184.5" height="32.25" align-x="31.5" align-y="2028" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DSt6">I</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="ox">C</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="6">W</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="3976" left="438" top="2018.25" width="21" height="12" align-x="438" align-y="2028" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0138</c> </inlineAttr> </f> </text> </region> <region region-id="3044" left="252" top="2013.75" width="166.5" height="26.25" align-x="275.25" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DS6">I</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="DSt6">I</ml:id> <ml:parens> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="3056" left="324" top="2067" width="74.25" height="15" align-x="348" align-y="2076" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DSt6">I</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μA</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>8.19921776583062</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="microampere"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering 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background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve">GM</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="DS6">I</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="3979" left="120" top="2072.25" width="21" height="12" align-x="120" align-y="2082" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0141</c> </inlineAttr> </f> </text> </region> <region region-id="3841" left="228" top="2072.25" width="74.25" height="27.75" align-x="248.25" align-y="2088" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mA</ml:id> <ml:id xml:space="preserve">V</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.30215638135011963</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="milliampere"/> <unitReference unit="volt" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="55"/> </region> <region region-id="3606" left="324" top="2097" width="76.5" height="15" align-x="345.75" align-y="2106" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DS6">I</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μA</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>31.098923267609134</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="microampere"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="56"/> </region> <region region-id="3607" left="420" top="2097" width="72.75" height="15" align-x="438.75" align-y="2106" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="6">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>29.278026014607821</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="57"/> </region> <region region-id="2612" left="6" top="2141.25" width="498.75" height="75.75" align-x="6" align-y="2154" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 5.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>We need the Early voltage for M6 so that we can calculate the output resistance to get the voltage gain.<sp count="2"/>From this we can convert Cc to the equivalent input capacitance from the Miller equation.<sp count="2"/> </c> </inlineAttr> <c val="#000080">W Liu "Mosfet Models for Spice Simulation", equations A-62, A-78.</c> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>The equivalent Early voltage is VA and this converts to the ro6 by the slope at the point of operation. The output impedance is halved as M5 needs to be considered and is assumed to be equal to rout of M6.<sp count="2"/>Also a 1/2 adjustment is made for ro, as we are working near VTH0 and ro is reduced.</c> </inlineAttr> </text> </region> <region region-id="2605" left="6" top="2232" width="71.25" height="32.25" align-x="30" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="sat6">ε</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="n" subscript-size="small">VSAT</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="3181" left="120" top="2241" width="103.5" height="15" align-x="144.75" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">VA6</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="sat6">ε</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="3182" left="264" top="2232" width="137.25" height="32.25" align-x="284.25" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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</ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="3183" left="6" top="2282.25" width="77.25" height="27.75" align-x="40.5" align-y="2298" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vgain6</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ro6</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="3700" left="120" top="2289" width="120.75" height="15" align-x="140.25" align-y="2298" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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<unitedValue> <ml:real>205982.005436567</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="3847" left="426" top="2289" width="70.5" height="12.75" align-x="449.25" align-y="2298" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">VA6</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">V</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>11.978637163160089</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="volt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> 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line-through="false"> <c val="#000080">0165</c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">and 065 for FT</c> </inlineAttr> </f> </text> </region> <region region-id="3427" left="6" top="2514" width="121.5" height="30" align-x="39.75" align-y="2532" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="GSTtp">V</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="p">NFACTOR</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="b">k</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:id xml:space="preserve">q</ml:id> </ml:apply> </ml:apply> </ml:define> </math> 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<ml:div/> <ml:id xml:space="preserve">mA</ml:id> <ml:id xml:space="preserve">V</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.3593764414246379</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="milliampere"/> <unitReference unit="volt" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="82"/> </region> <region region-id="3974" left="420" top="2607" width="72.75" height="15" align-x="438.75" align-y="2616" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result 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The output resistance is the Early voltage divided by the current.<sp count="2"/>This is halved because both there are two FETS and the gain is halved again as we are working near VTH0 and the output resistance is slightly lower at this point.</c> </inlineAttr> </text> </region> <region region-id="3330" left="6" top="2706" width="71.25" height="32.25" align-x="30" align-y="2724" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="sat1">ε</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="p" subscript-size="small">VSAT</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="p">μ</ml:id> <ml:id xml:space="preserve">Vgt1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> 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<ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">VA1</ml:id> <ml:id xml:space="preserve" subscript="p">VTH0</ml:id> </ml:apply> <ml:id xml:space="preserve">Vgt1</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="DS1">I</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="3333" left="6" top="2756.25" width="77.25" height="27.75" align-x="40.5" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vgain1</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="m1">g</ml:id> <ml:apply> <ml:div/> 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<ml:real>27.050546577511241</ml:real> </result> </ml:eval> </math> <rendering item-idref="93"/> </region> <region region-id="3936" left="6" top="2831.25" width="495.75" height="39.75" align-x="6" align-y="2844" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 8.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>Calculate the compensation components Rc and Cc.<sp count="2"/>This is calculated to </c> </inlineAttr> <c val="#000080">5.74, </c> <c val="#000080">5.75, </c> <c val="#000080">5.76</c> <c val="#000080"> <inlineAttr font-weight="normal"> according to </inlineAttr> </c> <c val="#000080">Analog </c> <c val="#000080">integrated Circuit Design, Johns, Martin, page 243.</c> <inlineAttr font-weight="normal"> <c val="#000080"> 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<ml:mult style="auto-select"/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">V</ml:id> </ml:apply> </ml:globalDefine> </math> <rendering item-idref="109"/> </region> <region region-id="3764" left="6" top="3041.25" width="496.5" height="15.75" align-x="6" align-y="3054" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Summary of circuit values</c> </inlineAttr> </f> </text> </region> <region region-id="3470" left="6" top="3069" width="105" height="15" align-x="61.5" align-y="3078" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.82425772662247587</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="110"/> </region> <region region-id="4024" left="156" top="3069" width="63.75" height="15" align-x="170.25" align-y="3078" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p">L</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> 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</unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="112"/> </region> <region region-id="4020" left="396" top="3069" width="76.5" height="15" align-x="417.75" align-y="3078" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DS6">I</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μA</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>31.098923267609134</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="microampere"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="113"/> </region> <region region-id="3494" left="6" top="3093" width="72.75" height="15" align-x="24.75" align-y="3102" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="6">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>29.278026014607821</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="114"/> </region> <region region-id="4025" left="156" top="3093" width="72.75" height="15" align-x="174.75" align-y="3102" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>36.275978501946064</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="115"/> </region> <region region-id="4023" left="276" top="3093" width="74.25" height="12.75" align-x="291.75" align-y="3102" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Rc</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kohm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8.8254520879262941</ml:real> </result> </ml:eval> </math> <rendering item-idref="116"/> </region> <region region-id="4021" left="396" top="3093" width="78" height="12.75" align-x="435.75" align-y="3102" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Gain_dB</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>83.961714298062873</ml:real> </result> </ml:eval> </math> <rendering item-idref="117"/> </region> <region region-id="3712" left="6" top="3117" width="72.75" height="15" align-x="24.75" align-y="3126" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="4">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>14.639013007303911</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="118"/> </region> <region region-id="3511" left="6" top="3140.25" width="84.75" height="36" align-x="10.5" align-y="3150" 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"> <c val="#000080">Ln is the length of all devices except M1 and M2</c> </text> </region> <region region-id="4026" left="150" top="3140.25" width="84.75" height="24" align-x="150" align-y="3150" 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"> <c val="#000080">Lp is the length of M1 and M2</c> </text> </region> <region region-id="4027" left="150" top="3170.25" width="76.5" height="24" align-x="156.75" align-y="3180" 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"> <c val="#000080">W1 is the width</c> <c val="#000080">of M1 and M2</c> </text> </region> <region region-id="3724" left="6" top="3182.25" width="80.25" height="24" align-x="12.75" align-y="3192" 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"> <c val="#000080">W6 is the width of</c> <c val="#000080">M6, M5 and M7.</c> </text> </region> <region region-id="3725" left="12" top="3212.25" width="70.5" height="24" align-x="18.75" align-y="3222" 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"> <c val="#000080">W4 is the width </c> <c val="#000080">of M3 and M4</c> </text> </region> <region region-id="3766" left="6" top="3257.25" width="495" height="15.75" align-x="6" align-y="3270" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Simulation</c> </inlineAttr> </f> </text> </region> <region region-id="3967" left="6" top="3278.25" width="495.75" height="60" align-x="6" align-y="3288" 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"> <inlineAttr font-weight="normal"> <c val="#000080">The amplifier is simulated using ADS with BSIM3 parameters available from the BSIM3 website at Berkeley (and used in the calculations).<sp count="2"/>The current reference is set to 31uA.<sp count="2"/>The output range goes to within 300mV of the rails.</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080"> This is a very good amplifier for this current and such a large output capacitance</c> </inlineAttr> </text> </region> <region region-id="4086" left="108" top="3354" width="302.25" height="196.5" align-x="108" align-y="3354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="119" display-width="300.75" display-height="195"/> </picture> <rendering item-idref="120"/> </region> <region region-id="4089" left="54" top="3564" width="378.75" height="208.5" align-x="54" align-y="3564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="121"/> <rendering item-idref="122"/> </region> <region region-id="4166" left="24" top="3792" width="474.75" height="327" align-x="24" align-y="3792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="123"/> <rendering item-idref="124"/> </region> <region region-id="4055" left="6" top="4130.25" width="495.75" height="60" align-x="6" align-y="4140" 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"> <inlineAttr font-weight="normal"> <c val="#000080">The gain from the first stage is simulated 27.6dB, calculated 27.051dB</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080">The gain from the second stage is simulated 36dB, calculated 14.93dB</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080">The gm6 is simulated 0.254mA/V, calculated 0.302mA/V.</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080">I think there is something wrong with the sims!!!<sp count="3"/> </c> </inlineAttr> </text> </region> <region region-id="4048" left="402" top="4179" width="87.75" height="12.75" align-x="451.5" align-y="4188" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vgain1_dB</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>27.050546577511241</ml:real> </result> </ml:eval> </math> <rendering item-idref="125"/> </region> <region region-id="4046" left="6" top="4206" width="421.5" height="324.75" align-x="6" align-y="4206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="126"/> <rendering item-idref="127"/> </region> <region region-id="4050" left="402" top="4197" width="83.25" height="12.75" align-x="451.5" align-y="4206" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vgain6_dB</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>14.930310571520188</ml:real> </result> </ml:eval> </math> <rendering item-idref="128"/> </region> <region region-id="4053" left="408" top="4214.25" width="74.25" height="27.75" align-x="428.25" align-y="4230" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mA</ml:id> <ml:id xml:space="preserve">V</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.30215638135011963</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="milliampere"/> <unitReference unit="volt" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="129"/> </region> <region region-id="4084" left="6" top="4550.25" width="497.25" height="24" align-x="6" align-y="4560" 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"> <inlineAttr font-weight="normal"> <c val="#000080">The unity gain frequency is simulated 100MHz, calculated 20MHz. 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top="3.75" width="183.75" height="18" align-x="162" 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"> <f family="Arial" charset="0" size="16"> <inlineAttr line-through="false"> <c val="#000080">Miller Opamp Design</c> </inlineAttr> </f> </text> </region> <region region-id="3958" left="336" top="20.25" width="169.5" height="24" align-x="336" align-y="30" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Chris Haji-Michael www.sunshadow.co.uk/chris.htm</c> </inlineAttr> </f> </text> </region> <region region-id="3610" left="6" top="50.25" width="495" height="96" align-x="6" align-y="60" 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"> <c val="#000080">This sheet is used to design a low speed Miller Operational Amplifier, using the technique explained by </c> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Willy Sansen in his book "Analog Design Essentials" chapters 1 and 6, main slide 0629.</c> </inlineAttr> </f> <c val="#000080">PMOS input devices are chosen as these normally have better matching and lower noise. There is a good explanation of why this is generally better in </c> <c val="#000080">Analog integrated Circuit Design, Johns, Martin, page 232</c> <c val="#000080">Cc in the following schematic is replaced with Cc and Rc in series.</c> <c val="#000080">Design Inputs yellow; BSIM inputs blue; outputs green</c> </text> </region> <region region-id="2571" left="6" top="168" width="302.25" height="196.5" align-x="6" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="300.75" display-height="195"/> </picture> <rendering item-idref="3"/> </region> <region region-id="3799" left="450" top="158.25" width="44.25" height="33.75" align-x="469.5" align-y="174" 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" 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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"> <c val="#000080">The starting point of the analysis focuses on this graph, which shows the EKV model and gives i the inversion coefficient for Vgs-Vt.</c> <c val="#000080">The EKV model allows a single equation to be used for both the striong inversion and weak inversion operating zones on the FET.<sp count="2"/> </c> <c val="#000080">This model allows Vgs-Vt (Vgt) to be negative and typically vary from -0.2 to 0.5V. 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<region region-id="2347" left="6" top="857.25" width="497.25" height="39.75" align-x="6" align-y="870" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 2.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>From U0 and the other BSIM mobility parameters, calculate the mobility for the NMOS and the PMOS devices as this changes with Vgt.<sp count="2"/>The equations for this are from </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">W Liu "Mosfet Models for Spice Simulation", page 249</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080">.<sp count="2"/>Assume MOBMOD=1 which is the default.</c> </inlineAttr> </text> </region> <region region-id="2894" left="6" 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</ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="3953" left="210" top="1032" width="288" height="207.75" align-x="210" align-y="1032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="30"/> <rendering item-idref="31"/> </region> <region region-id="3956" left="60" top="1040.25" width="105.75" height="33.75" align-x="101.25" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">cm</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">V</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>118.76854619825605</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="centimeter" power-numerator="2"/> <unitReference unit="second" power-numerator="-1"/> <unitReference unit="volt" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="3957" left="36" top="1124.25" width="156" height="60" align-x="44.25" align-y="1134" 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"> <c val="#000080">This shows how the mobility changes with Vgt for both the NMOS and PMOS</c> <c val="#000080">It is 50% higher for the NMOS</c> </text> </region> <region region-id="2512" left="6" top="1253.25" width="497.25" height="51.75" align-x="16.5" align-y="1266" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 3.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>Calculate FT (frequency at which gain equals 1) for transistor M6 to get the gain-bandwidth.<sp count="2"/>From this we can calculate L (Gate Length) and we use this same L for most of the transistors.<sp count="2"/>The EKV model is used here, as this is what Samson uses, refer slides:</c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080"> 0138, 0140, 0165, 0627.</c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" 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</ml:apply> <ml:id xml:space="preserve">GBW</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="3783" left="348" top="1382.25" width="21" height="12" align-x="348" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0627</c> </inlineAttr> </f> </text> </region> <region region-id="3785" left="258" top="1442.25" width="21" height="12" align-x="258" align-y="1452" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0165</c> </inlineAttr> </f> </text> </region> <region region-id="3251" left="6" top="1423.5" width="238.5" height="48.75" align-x="58.5" align-y="1458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:boundVars> <ml:id xml:space="preserve">Vgt</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="b">k</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:id xml:space="preserve">q</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="3966" left="312" top="1461" width="75" height="15" align-x="344.25" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">V</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.053048626321532087</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="volt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="38"/> </region> <region region-id="3963" left="414" top="1461" width="72" height="12.75" align-x="447.75" align-y="1470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>14.386192368979446</ml:real> </result> </ml:eval> </math> <rendering item-idref="39"/> </region> <region region-id="3961" left="306" top="1485" width="105" height="15" align-x="361.5" align-y="1494" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.82425772662247587</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="3960" left="426" top="1485" width="65.25" height="15" align-x="441.75" align-y="1494" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="T">F</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">MHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>480</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megahertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="3010" left="6" top="1512" width="300" height="192.75" align-x="6" align-y="1512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="42"/> <rendering item-idref="43"/> </region> <region region-id="3443" left="336" top="1538.25" width="163.5" height="36" align-x="344.25" 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"> <c val="#000080">This graph shows how the length of the gate influences the FT (the frequency at which the gain is 1)</c> </text> </region> <region region-id="3832" left="48" top="1716" width="249.75" height="183.75" align-x="48" align-y="1716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="44"/> <rendering item-idref="45"/> </region> <region region-id="3452" left="336" top="1742.25" width="164.25" height="36" align-x="336" align-y="1752" 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"> <c val="#000080">We also get this strange graph that shows how the required gate length changes with Vgt.</c> </text> </region> <region region-id="2765" left="6" top="1913.25" width="497.25" height="27.75" align-x="6" align-y="1926" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 4. </c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> Use the following equations to calculate the widths and currents of M6 and M5, which are dependent on CL.</c> </inlineAttr> </text> </region> <region region-id="2268" left="6" top="1956" width="37.5" height="30" align-x="21.75" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">C</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L">C</ml:id> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="2520" left="72" top="1956" width="50.25" height="30" align-x="95.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="gs6">C</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="L">C</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve">α</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="3978" left="138" top="1964.25" width="21" height="12" align-x="138" align-y="1974" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0621</c> </inlineAttr> </f> </text> </region> <region region-id="2522" left="222" top="1956" width="51" height="30" align-x="242.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="ox">C</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ox">ε</ml:id> <ml:id xml:space="preserve">TOX</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="3496" left="318" top="1958.25" width="128.25" height="30" align-x="338.25" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="6">W</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="gs6">C</ml:id> <ml:apply> <ml:div/> <ml:real>3</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve" subscript="ox">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="3977" left="462" top="1964.25" width="21" height="12" align-x="462" align-y="1974" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0161</c> </inlineAttr> </f> </text> </region> <region region-id="2542" left="6" top="2010" width="184.5" height="32.25" align-x="31.5" align-y="2028" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DSt6">I</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="ox">C</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="6">W</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="3976" left="438" top="2018.25" width="21" height="12" align-x="438" align-y="2028" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0138</c> </inlineAttr> </f> </text> </region> <region region-id="3044" left="252" top="2013.75" width="166.5" height="26.25" align-x="275.25" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DS6">I</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="DSt6">I</ml:id> <ml:parens> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">i</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="3056" left="324" top="2067" width="74.25" height="15" align-x="348" align-y="2076" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DSt6">I</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μA</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>8.19921776583062</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="microampere"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="52"/> </region> <region region-id="3190" left="420" top="2067" width="62.25" height="15" align-x="434.25" align-y="2076" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">C</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.33333333333333337</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="53"/> </region> <region region-id="3048" left="6" top="2064" width="101.25" height="32.25" align-x="27.75" align-y="2082" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:id xml:space="preserve">GM</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="DS6">I</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="GSTtn">V</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="3979" left="120" top="2072.25" width="21" height="12" align-x="120" align-y="2082" 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"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">0141</c> </inlineAttr> </f> </text> </region> <region region-id="3841" left="228" top="2072.25" width="74.25" height="27.75" align-x="248.25" align-y="2088" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mA</ml:id> <ml:id xml:space="preserve">V</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.30215638135011963</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="milliampere"/> <unitReference unit="volt" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="55"/> </region> <region region-id="3606" left="324" top="2097" width="76.5" height="15" align-x="345.75" align-y="2106" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="DS6">I</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μA</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>31.098923267609134</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="microampere"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="56"/> </region> <region region-id="3607" left="420" top="2097" width="72.75" height="15" align-x="438.75" align-y="2106" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="6">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>29.278026014607821</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="57"/> </region> <region region-id="2612" left="6" top="2141.25" width="498.75" height="75.75" align-x="6" align-y="2154" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 5.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>We need the Early voltage for M6 so that we can calculate the output resistance to get the voltage gain.<sp count="2"/>From this we can convert Cc to the equivalent input capacitance from the Miller equation.<sp count="2"/> </c> </inlineAttr> <c val="#000080">W Liu "Mosfet Models for Spice Simulation", equations A-62, A-78.</c> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>The equivalent Early voltage is VA and this converts to the ro6 by the slope at the point of operation. The output impedance is halved as M5 needs to be considered and is assumed to be equal to rout of M6.<sp count="2"/>Also a 1/2 adjustment is made for ro, as we are working near VTH0 and ro is reduced.</c> </inlineAttr> </text> </region> <region region-id="2605" left="6" top="2232" width="71.25" height="32.25" align-x="30" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="sat6">ε</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="n" subscript-size="small">VSAT</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="n">μ</ml:id> <ml:id xml:space="preserve">Vgt6</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="3181" left="120" top="2241" width="103.5" height="15" align-x="144.75" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">VA6</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="sat6">ε</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="n">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">Vgt6</ml:id> <ml:id xml:space="preserve" subscript="T">F</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="3182" left="264" top="2232" width="137.25" height="32.25" align-x="284.25" align-y="2250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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</ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="3183" left="6" top="2282.25" width="77.25" height="27.75" align-x="40.5" align-y="2298" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vgain6</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ro6</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="3700" left="120" top="2289" width="120.75" height="15" align-x="140.25" align-y="2298" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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<unitedValue> <ml:real>205982.005436567</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="3847" left="426" top="2289" width="70.5" height="12.75" align-x="449.25" align-y="2298" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">VA6</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">V</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>11.978637163160089</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="volt"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> 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align-x="469.5" align-y="2346" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vgain6_dB</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>14.930310571520188</ml:real> </result> </ml:eval> </math> <rendering item-idref="69"/> </region> <region region-id="2718" left="6" top="2375.25" width="496.5" height="27.75" align-x="6" align-y="2388" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 6. </c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> Now scale M1 and M2.<sp count="2"/>Keep Vgt1 low to 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line-through="false"> <c val="#000080">0165</c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">and 065 for FT</c> </inlineAttr> </f> </text> </region> <region region-id="3427" left="6" top="2514" width="121.5" height="30" align-x="39.75" align-y="2532" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="GSTtp">V</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="p">NFACTOR</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="b">k</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> <ml:id xml:space="preserve">q</ml:id> </ml:apply> </ml:apply> </ml:define> </math> 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The output resistance is the Early voltage divided by the current.<sp count="2"/>This is halved because both there are two FETS and the gain is halved again as we are working near VTH0 and the output resistance is slightly lower at this point.</c> </inlineAttr> </text> </region> <region region-id="3330" left="6" top="2706" width="71.25" height="32.25" align-x="30" align-y="2724" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="sat1">ε</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="narrow-dot"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="p" subscript-size="small">VSAT</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="p">μ</ml:id> <ml:id xml:space="preserve">Vgt1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="84"/> </region> <region region-id="3331" left="120" top="2715" width="62.25" height="15" align-x="144.75" align-y="2724" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">VA1</ml:id> <ml:apply> <ml:mult style="narrow-dot"/> <ml:id xml:space="preserve" subscript="sat1">ε</ml:id> <ml:id xml:space="preserve" subscript="p">L</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="85"/> </region> <region region-id="3332" left="264" top="2706" width="140.25" height="47.25" align-x="284.25" align-y="2724" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ro1</ml:id> <ml:apply> <ml:mult style="auto-select"/> 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<ml:real>27.050546577511241</ml:real> </result> </ml:eval> </math> <rendering item-idref="93"/> </region> <region region-id="3936" left="6" top="2831.25" width="495.75" height="39.75" align-x="6" align-y="2844" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">STEP 8.</c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="2"/>Calculate the compensation components Rc and Cc.<sp count="2"/>This is calculated to </c> </inlineAttr> <c val="#000080">5.74, </c> <c val="#000080">5.75, </c> <c val="#000080">5.76</c> <c val="#000080"> <inlineAttr font-weight="normal"> according to </inlineAttr> </c> <c val="#000080">Analog </c> <c val="#000080">integrated Circuit Design, Johns, Martin, page 243.</c> <inlineAttr font-weight="normal"> <c val="#000080"> 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xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="4156" left="426" top="2955" width="74.25" height="12.75" align-x="441.75" align-y="2964" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Rc</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kohm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8.8254520879262941</ml:real> </result> </ml:eval> </math> <rendering item-idref="101"/> </region> <region region-id="3890" left="6" top="2975.25" width="497.25" height="15.75" align-x="6" align-y="2988" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Design Requirements</c> </inlineAttr> </f> </text> </region> <region region-id="3951" left="66" top="2997" width="39" height="15" align-x="81.75" align-y="3006" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="L">C</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1</ml:real> <ml:id xml:space="preserve">pF</ml:id> </ml:apply> </ml:globalDefine> </math> <rendering item-idref="102"/> </region> <region region-id="3950" left="114" top="2997" width="63" height="12.75" align-x="141" align-y="3006" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:globalDefine 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background-color="#ffff80" tag=""> <math optimize="false" disable-calc="false"> <ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>3</ml:real> </ml:globalDefine> </math> <rendering item-idref="105"/> </region> <region region-id="3945" left="282" top="2997" width="23.25" height="12.75" align-x="293.25" align-y="3006" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <math optimize="false" disable-calc="false"> <ml:globalDefine xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">β</ml:id> <ml:real>3</ml:real> </ml:globalDefine> </math> <rendering item-idref="106"/> </region> <region region-id="3946" left="318" top="2997" width="23.25" height="12.75" align-x="329.25" align-y="3006" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <math optimize="false" disable-calc="false"> <ml:globalDefine 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>36.275978501946064</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="115"/> </region> <region region-id="4023" left="276" top="3093" width="74.25" height="12.75" align-x="291.75" align-y="3102" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Rc</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kohm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8.8254520879262941</ml:real> </result> </ml:eval> </math> <rendering item-idref="116"/> </region> <region region-id="4021" left="396" top="3093" width="78" height="12.75" align-x="435.75" align-y="3102" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Gain_dB</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>83.961714298062873</ml:real> </result> </ml:eval> </math> <rendering item-idref="117"/> </region> <region region-id="3712" left="6" top="3117" width="72.75" height="15" align-x="24.75" align-y="3126" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="4">W</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">μm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>14.639013007303911</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="micron"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="118"/> </region> <region region-id="3511" left="6" top="3140.25" width="84.75" height="36" align-x="10.5" align-y="3150" 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"> <c val="#000080">Ln is the length of all devices except M1 and M2</c> </text> </region> <region region-id="4026" left="150" top="3140.25" width="84.75" height="24" align-x="150" align-y="3150" 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"> <c val="#000080">Lp is the length of M1 and M2</c> </text> </region> <region region-id="4027" left="150" top="3170.25" width="76.5" height="24" align-x="156.75" align-y="3180" 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"> <c val="#000080">W1 is the width</c> <c val="#000080">of M1 and M2</c> </text> </region> <region region-id="3724" left="6" top="3182.25" width="80.25" height="24" align-x="12.75" align-y="3192" 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"> <c val="#000080">W6 is the width of</c> <c val="#000080">M6, M5 and M7.</c> </text> </region> <region region-id="3725" left="12" top="3212.25" width="70.5" height="24" align-x="18.75" align-y="3222" 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"> <c val="#000080">W4 is the width </c> <c val="#000080">of M3 and M4</c> </text> </region> <region region-id="3766" left="6" top="3257.25" width="495" height="15.75" align-x="6" align-y="3270" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Simulation</c> </inlineAttr> </f> </text> </region> <region region-id="3967" left="6" top="3278.25" width="495.75" height="60" align-x="6" align-y="3288" 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"> <inlineAttr font-weight="normal"> <c val="#000080">The amplifier is simulated using ADS with BSIM3 parameters available from the BSIM3 website at Berkeley (and used in the calculations).<sp count="2"/>The current reference is set to 31uA.<sp count="2"/>The output range goes to within 300mV of the rails.</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080"> This is a very good amplifier for this current and such a large output capacitance</c> </inlineAttr> </text> </region> <region region-id="4086" left="108" top="3354" width="302.25" height="196.5" align-x="108" align-y="3354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="119" display-width="300.75" display-height="195"/> </picture> <rendering item-idref="120"/> </region> <region region-id="4089" left="54" top="3564" width="378.75" height="208.5" align-x="54" align-y="3564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="121"/> <rendering item-idref="122"/> </region> <region region-id="4166" left="24" top="3792" width="474.75" height="327" align-x="24" align-y="3792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="123"/> <rendering item-idref="124"/> </region> <region region-id="4055" left="6" top="4130.25" width="495.75" height="60" align-x="6" align-y="4140" 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"> <inlineAttr font-weight="normal"> <c val="#000080">The gain from the first stage is simulated 27.6dB, calculated 27.051dB</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080">The gain from the second stage is simulated 36dB, calculated 14.93dB</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080">The gm6 is simulated 0.254mA/V, calculated 0.302mA/V.</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080">I think there is something wrong with the sims!!!<sp count="3"/> </c> </inlineAttr> </text> </region> <region region-id="4048" left="402" top="4179" width="87.75" height="12.75" align-x="451.5" align-y="4188" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vgain1_dB</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>27.050546577511241</ml:real> </result> </ml:eval> </math> <rendering item-idref="125"/> </region> <region region-id="4046" left="6" 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show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="m6">g</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">mA</ml:id> <ml:id xml:space="preserve">V</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.30215638135011963</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="milliampere"/> <unitReference unit="volt" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="129"/> </region> <region region-id="4084" left="6" top="4550.25" width="497.25" height="24" align-x="6" align-y="4560" 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"> <inlineAttr font-weight="normal"> <c val="#000080">The unity gain frequency is simulated 100MHz, calculated 20MHz. 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