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pDg@@ DfDh@@dDgpinDi@@Dg1Dj@B@U0uO,Dk@@ pDl@@ DkDm@@dDlppmDn@@DlDo@@tDn10Dp@@KDnDq@@Dp6Dr@B@UDs@@ pDt@@ DsDu@@tDt$Dv@@DtdollarDw@B@U"Dx@@ pDy@@ DxDz@@@DyD{@@dDz\D|@@pDzD}@@D|xD~@@DyD@@dD~xD@@D~degD@B@U_H"D@@ pD@@DD@@@DD@@dDcosD@@pDD@@RDD@@tD60D@@D\D@@DD@@+@D@XD@@DD*@Upy"^U-The function 7 D< D8DD<D8D?DDD9D<D:@W1D<D2 3D4D@B@UMD@@ pD@@D\/D<D0@ NormalTimes New Roman D@B@UZ0D@@ pD@@ DD@@@DD@@dD||D@@pDD@@ DD@@dDxD@@DyD@@DD@@@DD@@dDxD@@DyD@@DD@@dDxD@@DyD*@Uh,-Parallel Resistance Operator79D<D:@W1D</D<D0@ NormalTimes New Roman D@B@UD@@ pD@@ DD@@dD\D@@DdegD@B@UT=D@@ pD@@DD@@@DD@@dDasinD@@pDD@@D1D@@DD@@+@D@XD@@D\D*@Upy`U-The variable 7 D< D8DD<D8D?DDD9D<D:@W1D<D2 3D4D@B@UJD@@ pD@@D\/D<D0@ NormalTimes New Roman D@B@U> 'D@@ pD@@DD@@S@DD@@tD1D@@DD@@dD||D@@D3D@@DD@@+@D@XD@@DD*@US2(ZL-@To type this line, select xfy from the evaluation toolbar or (Write a letter, then Shift+Ctrl+k and then two ||, delete the letter in front of || and you got it. But somehow it's funny)79D<D:@W1D</D<D0@ NormalTimes New Roman D@B@U4.E@,D@@ pD@@ DD@@dDbitD@@D1D@B@U3E@"D@@ pD@@D\D@B@UL4]$X %D@@ pD@@ DD@@dDbitsD@@D1D@B@UHChdX %D@@ pD@@ DD@@dDbpsD@@DD@@dDbitsD@@DsecD@B@UD]X%D@@ pD@@ DD@@dDkbpsD@@DD@@@DD@@tD10D@@D3D@@DbpsD@B@UD`]0X%D@@ pE@@ DE@@dEMbpsE@@EE@@@EE@@tE10E@@E6E@@EbpsE@B@UK]X"E@@ pE @@E\E @B@UK4] X"E @@ pE @@ E E @@@E E@@dE \E@@pE E@@ExE@@E E@@dEargE@@pEE@@ExE@B@UHJ]X"E@@ pE@@EE@@Q@EE@@dE\E@@pEE@@EE@@tE1E@@EE@@tE2E@@{EE @@KEE!@@E 1E"@@EE#@@+@E"@XE$@@E"\E%@B@U`upj$E&@@ pE'@@ E&E(@@@E'E)@@dE(*E*@@pE(E+@@E*xE,@@E'E-@@dE,xE.@B@UHbupk$E/@@ pE0@@E/E1@@R@E0E2@@p@E1E3@@E2E4@@tE31E5@@E3E6@@tE52E7@@{E5E8@@KE7E9@@E81E:@@E1*E;@@E0E<@@+@E;@XE=@@E;E>*@Uasp$-(Need to superscript the conjugate symbol7(9(E?<(E@:@W,1EA</(EB<(EC0@ NormalTimes New Roman ED@B@U|a,,EE@@ pEF@@ EEEG@@dEFcupEH@@EFEI@@tEH236.6EJ@@EHmLEK@B@U`|y,EL@@ pEM@@ ELEN@@dEMtspEO@@EMEP@@tEO5EQ@@EOmLER@B@U0|M,ES@@ pET@@ ESEU@@dETpintEV@@ETEW@@tEV  473.176473EX@@EVmLEY@B@UP2,EZ@@ pE[@@ EZE\@@dE[cupsE]@@E[cupE^@B@U`,E_@@ pE`@@ E_Ea@@dE`tbspEb@@E`Ec@@tEb15Ed@@EbmLEe@B@U,Ef@@ pEg@@EfEh@@dEgfl_ozEi@@EgEj@@+@Ei@XEk@@EimLEl@B@U@d,Em@@ pEn@@ EmEo@@dEnquartEp@@EnEq@@tEp  0.946352946Er@@EpLEs@B@U ,Et@@ pEu@@ EtEv@@dEuqtEw@@EuquartEx@B@U?',Ey@@ pEz@@EyE{@@dEzgalE|@@EzE}@@+@E|@XE~@@E|LE@B@UPl,E@@ pE@@EE@@dEpintE@@EE@@+@E@XE@@EcupE*@U9,E@HE@HE@L/http://twt.mpei.ac.ru/ochkov/Units/advice64.htmp&'-@^Temperature Calculations from Valery Ochkov, http://twt.mpei.ac.ru/ochkov/Units/advice64.htm. 7\+^E<+E8EmSymbol0,0,255E<E8EEE@@ pF?@@F>F@@@dF?\DtFA@@F?FB@@+@FA@XFC@@FAFD@B@U,,FE@@ pFF@@FEFG@@dFF\DtFH@@FFFI@@+@FH@XFJ@@FHRFK*@U?,'-.(use this function and unit for displaying F)7,+.FL<+FM8FKFN<FO8FK?FLFP<FQ8FKFNFPFN9.FR<.FS:@W,1FT<FU2+3FV4FW@B@U(/*M$FX@@ pFY@@FX\/.FZ<.F[0@ NormalTimes New Roman F\@B@Uu/$F]@@ pF^@@ F]F_@@@F^F`@@tF_\FFa@@pF_Fb@@FaTFc@@F^Fd@@@FcFe@@dFdTFf@@FdRFg@@Fc459.67Fh@B@U$Fi@@ pFj@@ FiFk@@tFj\FFl@@Fj1Fm@B@UE($Fn@@ pFo@@FnFp@@Q@FoFq@@tFp\FFr@@Fpt.1Fs@@FoFt@@+@Fs@XFu@@Fs\FFv@B@Uh$Fw@@ pFx@@FwFy@@Q@FxFz@@tFy\FF{@@Fyt.2F|@@FxF}@@+@F|@XF~@@F|\FF*@U A,)-.(use this function and unit for displaying C)7,+.F<+F8FF<F8F?FF<F8FFFF9.F<.F:@W,1F<F2+3F4F@B@U( /*L$F@@ pF@@F\/.F<.F0@ NormalTimes New Roman F@B@Uw@00$F@@ pF@@ FF@@@FF@@tF\CF@@pFF@@FTF@@FF@@@FF@@dFTF@@FKF@@F273.15F@B@U#50$F@@ pF@@ FF@@tF\CF@@F1F@B@UCGX)P$F@@ pF@@FF@@Q@FF@@tF\CF@@Ft.1F@@FF@@+@F@XF@@F\CF@B@UhCXP$F@@ pF@@FF@@Q@FF@@tF\CF@@Ft.2F@@FF@@+@F@XF@@F\CF*@UYlh,-"(use this unit for displaying DF)7 "F<F8FF<F8F?FF<F8F@ Times New Roman0,0,255FF<F8FFFF9"F<"F:@W,1F<F23F4F@B@U[mhJ$F@@ pF@@F\/"F<"F0@ NormalTimes New Roman F@B@UkF}4x,F@@ pF@@ FF@@tF\\DFF@@FRF@B@UP+,F@@ pF@@FF@@dF\DtF@@FF@@+@F@XF@@F\\DFF*@U,-"(use this unit for displaying DC)7 "F<F8FF<F8F?FF<F8F@ Times New Roman0,0,255FF<F8FFFF9"F<"F:@W,1F<F23F4F@B@UK$F@@ pF@@F\/"F<"F0@ NormalTimes New Roman F@B@UH5,F@@ pF@@ FF@@tF\\DCF@@FKF@B@UQ+,F@@ pF@@FF@@dF\DtF@@FF@@+@F@XF@@F\\DCF@B@U0WG/F@@ pF@@ FF@@dFdBF@@F1F@D@UJ ,Units UnitsF@C@UK8@M%% F@Tmasslengthtimecharge temperature luminosity substance@Qdii @V@\?@O@P  VariablesTimes New Roman@P  ConstantsTimes New Roman@P TextArial@P Greek VariablesSymbol@P User 1Arial@P User 2 Courier New@P User 3Arial@P User 4Times New Roman@P User 5Times New Roman@P User 6Arial@P User 7Times New Roman@P SymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderArial@P FooterArial@P Rotated Math FontTimes New RomanF@D@UK  ConstantsF*@U5; %%3%3-1_______________________________________ Constants7('1F<'F8FnArialF<F8FFF< G8FFFF9(( 1G<(G:@WG< G:@WGGG1G<G23G4/1G<1G 0@ Normal G @B@UDPUAPG @@ pG @@G G @@dG ORIGING@@G 1G*@UI[X-Origin for Matrices and Vectors79G<G:@W?1G</G<G0@ Normal G@B@UZ<mhG@@ pG@@ GG@@dGjG@@{GG@@KGG@@G1G*@UYkhu-Imaginary Constant79G<G:@W?1G</G <G!0@ Normal G"@B@Uk$G#@@ pG$@@ G#G%@@dG$\e.0G&@@G$G'@@@G&G(@@tG'8.8542G)@@G'G*@@tG)10G+@@KG)G,@@G+12G-@@G&G.@@dG-FG/@@G-mG0*@Uq-Permittivity of Free Space79G1<G2:@W>H1G3</G4<G50@ Normal G6@B@U|&G7@@ pG8@@ G7G9@@dG8\m.0G:@@G8G;@@@G:G<@@@G;G=@@tG<4G>@@G<\pG?@@G;G@@@tG?10GA@@KG?GB@@GA7GC@@G:GD@@dGCHGE@@GCmGF*@U-Permeability of Free Space79GG<GH:@W1GI</GJ<GK0@ Normal GL@B@UGM@@ pGN@@ GMGO@@dGNkGP@@GNGQ@@@GPGR@@tGQ1.383GS@@GQGT@@tGS10GU@@KGSGV@@GU23GW@@GPGX@@@GWGY@@@GXGZ@@dGYvoltG[@@GY2G\@@GXsecG]@@GWG^@@dG]ohmG_@@G]KG`*@Up{-Boltzman's Constant79Ga<Gb:@W?1Gc</Gd<Ge0@ Normal Gf@B@UxGg@@ pGh@@ GgGi@@dGhqGj@@GhGk@@tGj1.602Gl@@GjGm@@@GlGn@@tGm10Go@@KGmGp@@Go19Gq@@GlCGr*@Up-Charge on an electron79Gs<Gt:@W?1Gu</Gv<Gw0@ Normal Gx@B@Ui-Gy@@ pGz@@ GyG{@@dGzv.satG|@@GzG}@@@G|G~@@tG}10G@@G}7G@@G|G@@dGcmG@@GsecG*@U J-Electron velocity saturation79G<G:@W?1G</G<G0@ Normal G@B@UH"0G@@ pG@@ GG@@dGn.iG@@GG@@@GG@@tG1.45G@@GG@@tG10G@@G10G@@GG@@tG1G@@GG@@dGcmG@@G3G*@U!30-'Intrinsic number of carriers in Silicon7'9'G<'G:@W?1G</'G<'G0@ Normal G*@UIm[X]]- Temperature 7 G< G8GgArial0,0,2559 G< G:@W1G</ G< G0@ Normal G@B@U\pIhG@@ pG@@ GG@@dG Temp.maxG@@GG@@@GG@@tG273G@@GKG@@GG@@tG105G@@GKG*@UYkh-!Maximum Operating Die Temperature7!9!G@HH?@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#modelsH@@HHA@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#inputsHB@HHC@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #calculationsHD@HHE@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd#outputsHF@HHG@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #functionsHH@HHI@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #examplesHJ@HHK@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #simulationHL@HHM@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #comparisonHN@HHO@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #referencesHP@HHQ@LC:\John\johnformsect.mcd.\..\..\johnformsect.mcd #copyrightll-@w_______________________________________ Table of Contents I. Introduction IV. Inputs IX. Copyright and Trademark Notice7Y'wHR<'HS8H~HT<HU8HHRHV< HW8HuHTHX<HY8HHVHZ<H[8HuHXH\<H]8HHZH^<H_8HuH\H^HR9UU"wH`<(Ha:@W?Hb<Hc:@W,H`Hd<He:@W?HbHf< Hg:@W?HdHh<"Hi:@W,HfHhHh1Hj</YYwHk<=Hl0Hm< Hn0HkHo<Hp0HmHq<Hr0HoHs<Ht0HqHu<Hv0HsHuHu@ NormalTimes New Roman Hw*@U38Hx@HHy@HHz@L%C:\John\template\Template07_06_02.mcd%.\..\..\template\Template07_06_02.mcd#toc33-4_______________________________________ Introduction7('4H{<'H|8HwnArialH}<H~8HwH{H< H8HwH}HH{9(( 4H<(H:@WH< H:@WHHH1H<H23H4/'' 4H<'H0H< H0HHH@ NormalTimes New Roman H*@U9H8rr-B This routine calculates the required inductances and capacitances for a lowpass LC butterworth filter. It is special in that it also sizes the components to deliver maximum power from a given source resistance to a different load resistance. Reactive portions of the source and load must be remove subtracted the filter network, so it is usually desirable to choose an odd order network for maximum power transfer. Given the lowpass LC coefficients, the network can easily be transformed into a bandpass, highpass, notch filter based on other topologies: gm/C, active RC, etc. A butterworth filter has the following power transfer function, where the order of the filter is given by n:79H<H:@W1H</H<H0@ NormalTimes New Roman H@B@U0A/H@@ pH@@,HH@@dHAH@@HH@@tH10H@@HH@@dHlogH@@pHH@@HH@@tH1H@@HH@@p@HH@@HH@@dHfH@@Hf.cH@@HH@@tH2H@@HnH*@U .H@HH@HH@L-C:\John\Webpage\template\Template07_06_02.mcd".\..\template\Template07_06_02.mcd#toc33-._______________________________________ Inputs7('.H<'H8HnArialH<H8HHH<H8HHHH9((.H<(H:@WH<H:@WHHH1H<H23H4/''.H<'H0H<H0HHH@ NormalTimes New Roman H@B@U0 |W /H@@ pH@@ HH@@dHAttenH@@HH@@tH80H@@HdBH*@U   /-Stop-Band Attenuation7H<H8HmTimes New Roman0,0,2559H<H:@W1H</H<H0@ NormalTimes New Roman H@B@U0y-Z(/H@@ pH@@ HH@@dHRippleH@@HH@@tH1H@@HdBH*@U?,(//-Maximum Passband Ripple7H<H8HmTimes New Roman0,0,2559H<H:@W1H</H<H0@ NormalTimes New Roman H@B@U0,g@C8/H@@ pH@@ HH@@dHf.pH@@HH@@tH1H@@HkHzH*@U)<<8/-Passband corner frequency7H<H8HmTimes New Roman0,0,2559H<H:@W1H</H<H0@ NormalTimes New Roman H@B@U0DkXAP/H@@ pH@@ HH@@dHf.sH@@HH@@tH10H@@HkHzH*@UA;TP//-Stopband corner frequency7H<H8HmTimes New Roman0,0,2559H<H:@W1H</H<H0@ NormalTimes New Roman H@B@U0[mpFh/H@@ pH@@ HH@@dHR.SH@@HH@@tH10H@@Hk\WH*@UYlh/j{{-Source Impedance7H<H8HmTimes New Roman0,0,2559I<I:@W1I</I<I0@ NormalTimes New Roman I@B@U0snG/I@@ pI@@ II@@dIR.LI @@II @@tI 20I @@I k\WI *@Uq/joo-Load Impedance7I <I8I mTimes New Roman0,0,2559I<I:@W1I</I<I0@ NormalTimes New Roman I PageBreakE@U@#.I*@U2-33-@S_______________________________________ Order and -3dB Corner Frequency Estimation 7('SI<'I8I~I<I8III<+I8IIII9SI/I"@@ pI#@@,I"I$@@dI#nI%@@I#I&@@dI%ceilI'@@pI%I(@@I'I)@@@I(I*@@dI)lnI+@@pI)I,@@I+I-@@@I,I.@@tI-10I/@@I-I0@@dI/AttenI1@@I/10I2@@I,1I3@@I(I4@@tI32I5@@I3I6@@dI5lnI7@@pI5I8@@I7I9@@dI8f.sI:@@I8f.cI;*@U//&&-2Required Order of Butterworth Filter for 3dB droop7292I<<2I=:@W?1I></2I?<2I@0@ NormalTimes New Roman IA*@U)<85-->Function 1: Holds Atten Constant and chooses n to meet Ripple7>9>IB<>IC:@W?1ID</>IE<>IF0@ NormalTimes New Roman IG@B@U0D>nIP'/IH@@ pII@@ IHIJ@@dIInf.cIK@@IIIL@@@IKIM@@@ILIN@@@IMIO@@@INIP@@@IOIQ@@dIPnIR@@IP1IS@@IOIT@@dISf.cIU@@ISIV@@dIUf.sIW@@IUIX@@p@IWIY@@IXIZ@@@IYI[@@tIZ10I\@@IZI]@@dI\AttenI^@@I\10I_@@IY1I`@@IWIa@@tI`1Ib@@I`Ic@@tIb2Id@@IbnIe@@INIf@@dIeAatfpIg@@IeIh@@tIg10Ii@@IgIj@@dIilogIk@@pIiIl@@IkIm@@tIl1In@@IlIo@@p@InIp@@IoIq@@dIpf.pIr@@Ipf.cIs@@InIt@@tIs2Iu@@IsnIv@@IMIw@@dIvAatfsIx@@IvIy@@tIx10Iz@@IxI{@@dIzlogI|@@pIzI}@@I|I~@@tI}1I@@I}I@@p@II@@II@@dIf.sI@@If.cI@@II@@tI2I@@InI@@ILI@@@II@@@II@@@II@@@II@@dInI@@II@@dInI@@I1I@@II@@dIf.cI@@II@@dIf.sI@@II@@p@II@@II@@@II@@tI10I@@II@@dIAttenI@@I10I@@I1I@@II@@tI1I@@II@@tI2I@@InI@@II@@dIAatfpI@@II@@tI10I@@II@@dIlogI@@pII@@II@@tI1I@@II@@p@II@@II@@dIf.pI@@If.cI@@II@@tI2I@@InI@@II@@dIAatfsI@@II@@tI10I@@II@@dIlogI@@pII@@II@@tI1I@@II@@p@II@@II@@dIf.sI@@If.cI@@II@@tI2I@@InI@@II@@p@II@@.II@@dIAatfsI@@IAttenI@@pII@@(II@@dIAatfpI@@IRippleI@@pIKI@@0II@@0AII@@@II@@II@@dIf.cI@@IHzI@@In _n_u_l_l_I@B@U0l_?x/I@@ pI@@ II@@dInI@@II@@dInf.cI@@I1I@B@Ul}x#8I@@ pI@@II@@dInI@@II@@+@I@XI@@II*@Ui|x$8?gg-Number of Poles79I<I:@W?1I</I<I0@ NormalTimes New Roman I@B@U0sA/I@@ pI@@ II@@dIf.cI@@II@@@II@@dInf.cI@@I2I@@IHzI@B@U%8I@@ pI@@II@@dIf.cI@@II@@+@I@XI@@IkHzI*@U&8?-3 dB Corner Frequency79I<I:@W?1I</I<I0@ NormalTimes New Roman I@B@U0W!/J@@ pJ@@ JJ@@dJAatfpJ@@JJ@@tJ10J@@JJ@@dJlogJ@@pJJ@@JJ @@tJ1J @@JJ @@p@J J @@J J @@dJ f.pJ@@J f.cJ@@J J@@tJ2J@@JnJ@B@U'8J@@ pJ@@JJ@@dJAatfpJ@@JJ@@+@J@XJ@@JdBJ*@U}(8?ee-Passband Ripple79J<J:@W?1J</J<J0@ NormalTimes New Roman J@B@U0V$/J @@ pJ!@@ J J"@@dJ!AatfsJ#@@J!J$@@tJ#10J%@@J#J&@@dJ%logJ'@@pJ%J(@@J'J)@@tJ(1J*@@J(J+@@p@J*J,@@J+J-@@dJ,f.sJ.@@J,f.cJ/@@J*J0@@tJ/2J1@@J/nJ2@B@U)8J3@@ pJ4@@J3J5@@dJ4AatfsJ6@@J4J7@@+@J6@XJ8@@J6dBJ9*@U*8?-Stopband Attenuation79J:<J;:@W?1J<</J=<J>0@ NormalTimes New Roman J?@E@U @( .J@*@U)<8C-->Function 2: Holds Ripple Constant and chooses n to meet Atten7>9>JA<>JB:@W?1JC</>JD<>JE0@ NormalTimes New Roman JF@B@U0<>f IH(/JG@@ pJH@@ 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