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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$@@tJ#10J%@@J#J&@@dJ%logJ'@@pJ%J(@@J'J)@@tJ(1J*@@J(J+@@p@J*J,@@J+J-@@dJ,f.sJ.@@J,f.cJ/@@J*J0@@tJ/2J1@@J/nJ2@B@U)8J3@@ pJ4@@J3J5@@dJ4AatfsJ6@@J4J7@@+@J6@XJ8@@J6dBJ9*@U*8?-Stopband Attenuation79J:<J;:@W?1J<</J=<J>0@ NormalTimes New Roman J?@E@U @( .J@*@U)<8C-->Function 2: Holds Ripple Constant and chooses n to meet Atten7>9>JA<>JB:@W?1JC</>JD<>JE0@ NormalTimes New Roman JF@B@U0<>f IH(/JG@@ pJH@@ 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__@@d_cascp_@@_Rs_@@__@@p@__@@,__@@@__@@d_LCtype_@@_m_@@Z_R_@@p__@@,__@@@__@@d_sp_@@_m_@@Z_s_@@I_S_@@@__@@d_casc_@@__@@d_augment_@@p__@@ __@@d_cascp_@@_Rp_@@__@@p@__@@,__@@@__@@d_LCtype_@@_m_@@Z_R_@@p__@@,__@@@__@@d_sp_@@_m_@@Z_p_@@_R_@@d_cascp_@@_casc_@@_Q_@@d_m_@@__@@t_1_@@__@@d_length_@@p__@@_LC_@@_G_@@d_val_@@__@@d_augment_@@p__@@ __@@d_casc_@@_Zp_@@_F_@@@__@@d_val_@@__@@d_replace_@@p__@@ __@@ @__@@ @__@@d_val_@@__@@d_picture_@@p__@@__@@d_LC_@@_i_@@_62`@@_`@@t`54`@@``@@t`50`@@`i`@@_`@@d`i`@@``@@t`1` @@`` @@d` length` @@p` ` @@` LC` @@_Eval`@B@U0^Fy8`@@ p`@@ ``@@d`Z.S`@@`R.S`@B@Uz8`@@ p`@@ ``@@d`Z.L`@@`R.S`@D@UK h8Create Circuit Create CircuitOw`@B@U0(w8`@@ p`@@``@@d`Z.S`@@``@@+@`@X`@@`k\W` @B@U;PHx8`!@@ p`"@@`!`#@@d`"Z.L`$@@`"`%@@+@`$@X`&@@`$k\W`'*@U`x-33-@@_______________________________________ Butterworth Coefficients7('@`(<'`)8`'~`*<`+8`'`(`,<`-8`'`*`,`(9@`.<@`/:@W1`0</@`1<@`20@ Heading 1Arial`3@B@U0O?.`4@@ p`5@@ `4`6@@d`5n`7@@`52`8@B@U0.`9@@ p`:@@?`9`;@@@`:`<@@d`;if`=@@p`;`>@@ `=`?@@ @`>`@@@(@`?`A@@@`@`B@@d`Aceil`C@@p`A`D@@`C`E@@d`Dn`F@@`D2`G@@`@`H@@d`Gn`I@@`G2`J@@`?`K@@p@`J`L@@`K`M@@d`Lss`N@@`L1`O@@A`J`P@@@`O`Q@@t`P1`R@@`P`S@@@`R`T@@d`Sn`U@@`S1`V@@`R2`W@@`O`X@@d`Wk`Y@@p`W`Z@@`Y`[@@@`Z`\@@@`[`]@@d`\ss`^@@`\2`_@@`[``@@@`_`a@@t``2`b@@```c@@d`bcos`d@@p`b`e@@`d`f@@@`e`g@@d`fk`h@@`f\p`i@@`en`j@@`_ss`k@@`Z1`l@@A`>`m@@@`l`n@@t`m1`o@@`m`p@@d`on`q@@`o2`r@@`l`s@@d`rk`t@@p`r`u@@`t`v@@@`u`w@@@`v`x@@d`wss`y@@`w2`z@@`v`{@@@`z`|@@t`{2`}@@`{`~@@d`}cos`@@p`}`@@``@@@``@@p@``@@``@@@``@@t`2`@@`k`@@`1`@@`\p`@@``@@t`2`@@`n`@@`zss`@@`u1`@@`:`@E@U@ .`*@U S8-33-2_______________________________________ Functions 7('2`<'`8`~`<`8```< `8````92`<2`:@W1`</2`<2`0@ Heading 1Arial`@B@U0\h.`@@ p`@@ ``@@@``@@d`butter`@@p``@@ ``@@ @``@@ @``@@ @``@@d`Atten`@@`Ripple`@@`f.p`@@`f.s`@@`R.S`@@``@@@``@@@``@@@``@@@``@@@``@@@``@@@``@@@``@@@``@@@``@@d`n`@@`1`@@``@@d`f.c`@@``@@d`f.s`@@``@@p@``@@``@@@``@@t`10`@@``@@d`Atten`@@`10`@@`1`@@``@@t`1`@@``@@t`2`@@`n`@@``@@d`Aatfp`@@``@@t`10`@@``@@d`log`@@p``@@``@@t`1`@@``@@p@``@@``@@d`f.p`@@`f.c`@@``@@t`2`@@`n`@@``@@d`Aatfs`@@``@@t`10`@@``@@d`log`@@p``@@``@@t`1`@@``@@p@``@@``@@d`f.s`@@`f.c`@@``@@t`2`@@`n`@@``@@@``@@@``@@@``@@@``@@d`n`@@``@@d`n`@@`1`@@``@@d`f.c`@@``@@d`f.s`@@``@@p@``@@``@@@``@@t`10`@@``@@d`Attena@@`10a@@`1a@@`a@@ta1a@@aa@@ta2a@@ana@@`a@@daAatfpa @@aa @@ta 10a @@a a @@da loga @@pa a@@a a@@ta1a@@aa@@p@aa@@aa@@daf.pa@@af.ca@@aa@@ta2a@@ana@@`a@@daAatfsa@@aa@@ta10a@@aa@@daloga@@paa@@aa @@ta1a!@@aa"@@p@a!a#@@a"a$@@da#f.sa%@@a#f.ca&@@a!a'@@ta&2a(@@a&na)@@`a*@@p@a)a+@@.a*a,@@da+Aatfsa-@@a+Attena.@@pa)a/@@(a.a0@@da/Aatfpa1@@a/Ripplea2@@`a3@@@a2a4@@@a3a5@@da4ga6@@a4ka7@@a3a8@@da7sina9@@pa7a:@@a9a;@@@a:a<@@@a;a=@@@a@@ta=2a?@@a=ka@@@a<1aA@@a;aB@@taA2aC@@aAnaD@@a:\paE@@a2aF@@daEkaG@@aEaH@@taG1aI@@aGnaJ@@`aK@@daJnumLaL@@aJaM@@daLifaN@@paLaO@@ aNaP@@ @aOaQ@@(@aPaR@@@aQaS@@daRceilaT@@paRaU@@aTaV@@daUnaW@@aU2aX@@aQaY@@daXnaZ@@aX2a[@@aPa\@@@a[a]@@da\na^@@a\1a_@@a[2a`@@aOaa@@da`nab@@a`2ac@@`ad@@dacnumCae@@acaf@@daeifag@@paeah@@ agai@@ @ahaj@@(@aiak@@@ajal@@dakceilam@@pakan@@amao@@dannap@@an2aq@@ajar@@daqnas@@aq2at@@aiau@@@atav@@daunaw@@au1ax@@at2ay@@ahaz@@dayna{@@ay2a|@@`a}@@@a|a~@@@a}a@@da~La@@a~iLa@@a}a@@@aa@@daR.Sa@@aa@@@aa@@ta2a@@a\pa@@af.ca@@aa@@daga@@aa@@ta2a@@aiLa@@a|a@@daiLa@@aa@@ta1a@@anumLa@@`a@@@aa@@@aa@@eaCa@@aiCa@@aa@@@aa@@ta1a@@aa@@@aa@@@aa@@ta2a@@a\pa@@af.ca@@aR.Sa@@aa@@daga@@aa@@@aa@@ta2a@@aiCa@@a1a@@aa@@daiCa@@aa@@ta1a@@anumCa@@p`a@@0aa@@0Aaa@@@aa@@aa@@daCa@@aFa@@aa@@daLa@@aHa@E@U@8a*@U-33-0_______________________________________ Example 7('0a<'a8a~a<a8aaa<a8aaaa90a<0a:@W1a</0a<0a0@ Heading 1Ariala@B@U0=.a@@ pa@@ aa@@daxa@@aa@@dabuttera@@paa@@ aa@@ @aa@@ @aa@@ @aa@@daAttena@@aRipplea@@af.pa@@af.sa@@aR.Sa@B@U0g,? .a@@ pa@@ aa@@daLa@@aa@@@aa@@daxa@@a1a@@aHa@B@U-(.a@@ pa@@aa@@@aa@@daLa@@aa@@+@a@Xa@@aHa@B@U04fL@@.a@@ pa@@ aa@@daCa@@aa@@@aa@@daxa@@a2a@@aFa@B@U-E@.a@@ pa@@aa@@@aa@@daCa@@aa@@+@a@Xa@@anFa*@UhE.33-@J_______________________________________ Butterworth LC Filter Coefficients7('Ja<'a8a~a<a8aaa<"a8aaaa9Ja@L%C:\John\template\Template07_06_02.mcd%.\..\..\template\Template07_06_02.mcd#toc33-@F_______________________________________ S Parameter Frequency Response7('Fb?<'b@8b;nArialbA<bB8b;b?bC<bD8b;bAbCb?9((FbE<(bF:@WbG<bH:@W?bEbGbG1bI<bJ23bK4/''FbL<'bM0bN<bO0bLbNbN@ NormalTimes New Roman bP*@UQ9`.-D S-parameter is an abbreviation for scattering parameters. S-parameters are a measure of the power gain of a network. The term scattering comes from the concept of a cue ball scattering other balls as it transfers power to them. Sij is the measure of power gain from port j to port i. Specifically, the square root of power gain. For example, S21, the most useful S-parameter, is the measure of the ratio of output power to the available input power. This is an important sentence. This sentence is used to perform hand calculations. The output power is easy to explain, it is VOrms2/RL. The available input power is trickier to explain. Available input power is the maximum power that can be delivered from a source. For a source impedance of RS, and a source voltage of VSrms; the available input power is (VSrms/2)2/RS. Why, because maximum power is delivered is to a resistance of RS. Thus a voltage division of two for the voltage, when delivering maximum available power. Thus the power gain of a network, S21, is found by dividing the two powers 2*Vo/VS*sqrt(RS/RL). Here S-parameters for the network are calculated by finding the ABCD matrix for each element of the network, then multiplying all the matrices to get an ABCD matrix for the system.7@bQ<bR8bPbS<bT8bP_bQbU@@ c=c?@@dc>ABCDc@@@c>Z.0cA@@c:cB@@@cAcC@@@cBcD@@@cCcE@@@cDcF@@@cEcG@@dcFAcH@@cFcI@@dcHABCDcJ@@ cHcK@@tcJ1cL@@cJ1cM@@cEcN@@dcMBcO@@cMcP@@dcOABCDcQ@@ cOcR@@tcQ1cS@@cQ2cT@@cDcU@@dcTCcV@@cTcW@@dcVABCDcX@@ cVcY@@tcX2cZ@@cX1c[@@cCc\@@dc[Dc]@@c[c^@@dc]ABCDc_@@ c]c`@@tc_2ca@@c_2cb@@IcBcc@@p@cbcd@@ccce@@@cdcf@@tce1cg@@pcech@@cgci@@@chcj@@@cick@@dcjAcl@@cjcm@@@clcn@@dcmBco@@cm\Wcp@@clZ.0cq@@cicr@@dcqCcs@@cqct@@dcsZ.0cu@@cs\Wcv@@chDcw@@pcdcx@@0cwcy@@0Acxcz@@0Acyc{@@0Aczc|@@@c{c}@@c{c~@@@c}c@@@c~c@@K@cc@@cAc@@cc@@@cc@@dcBc@@c\Wc@@cZ.0c@@c~c@@dcCc@@cc@@dcZ.0c@@c\Wc@@c}Dc@@czc@@tc2c@@pcc@@cc@@@cc@@dcAc@@cDc@@cc@@dcBc@@cCc@@cy2c@@cxc@@@cc@@@cc@@dcAc@@cc@@@cc@@dcBc@@c\Wc@@cZ.0c@@cc@@dcCc@@cc@@dcZ.0c@@c\Wc@@cDc@@8cbc@@p@cc@@cc@@@cc@@@cc@@dcAc@@cc@@@cc@@dcBc@@c\Wc@@cZ.0c@@cc@@dcCc@@cc@@dcZ.0c@@c\Wc@@cDc@@c0c@@IcAc@@p@cc@@0cc@@0Acc@@0Acc@@0Acc@@@cc@@c1c@@cc@@tc10c@@c8c@@c0c@@c1c@@,cc@@p@cc@@cc@@@cc@@@cc@@dcAc@@cc@@@cc@@dcBc@@c\Wc@@cZ.0c@@cc@@dcCc@@cc@@dcZ.0c@@c\Wc@@cDc@@c0c*@U!J! !.99-A This scattering parameter conversion routine (to convert to arbitrary source and load impedances) is given "Applied RF Techniques I" lecture notes, but is incorrect. A correct version of the routine is found on page 31 of "Microwave Amplifiers and Oscillators," by Christian Gentili.79c<c:@W?1c</c<c0@ NormalTimes New Roman c@B@U0H!" `!.c@@ pc@@ cc@@@cc@@dcS.convc@@pcc@@ cc@@ @cc@@ @cc@@ @cc@@dcSc@@c Z.Sbeginc@@cZ.Sendc@@c Z.Lbeginc@@cZ.Lendc@@cc@@@cc@@@cc@@@cc@@@cc@@@cc@@dc\G.Sc@@cc@@@cc@@dcZ.Sendc@@c Z.Sbeginc@@cc@@dcZ.Sendc@@c Z.Sbeginc@@cc@@dc\G.Lc@@cc@@@cc@@dcZ.Lendd@@c Z.Lbegind@@cd@@ddZ.Lendd@@d Z.Lbegind@@cd@@ddDd@@dd@@@dd@@p@dd @@dd @@td 1d @@d d @@dd \G.Sd @@d d@@dd Sd@@ d d@@td1d@@d1d@@pdd@@dd@@td1d@@dd@@dd\G.Ld@@dd@@ddSd@@ dd@@td2d@@d2d@@dd@@@dd@@@dd@@dd\G.Sd @@d\G.Ld!@@dd"@@dd!Sd#@@ d!d$@@td#1d%@@d#2d&@@dd'@@dd&Sd(@@ d&d)@@td(2d*@@d(1d+@@cd,@@dd+A.1d-@@d+d.@@@d-d/@@@d.d0@@td/1d1@@d/d2@@dd1\G.Sd3@@{d.d4@@d3d5@@td41d6@@d4\G.Sd7@@{d-d8@@d7d9@@td81d:@@d8d;@@p@d:d<@@{d;d=@@d<\G.Sd>@@d:2d?@@cd@@@dd?A.2dA@@d?dB@@@dAdC@@@dBdD@@tdC1dE@@dCdF@@ddE\G.LdG@@{dBdH@@dGdI@@tdH1dJ@@dH\G.LdK@@{dAdL@@dKdM@@tdL1dN@@dLdO@@p@dNdP@@{dOdQ@@dP\G.LdR@@dN2dS@@pcdT@@0dSdU@@0AdTdV@@0AdUdW@@0AdVdX@@@dWdY@@dWdZ@@@dYd[@@@dZd\@@dd[A.2d]@@dZA.2d^@@dYd_@@@d^d`@@@d_da@@p@d`db@@dadc@@tdb1dd@@dbde@@ddd\G.Sdf@@dddg@@ddfSdh@@ dfdi@@tdh1dj@@dh1dk@@pd`dl@@dkdm@@@dldn@@ddmSdo@@ dmdp@@tdo2dq@@do2dr@@dlds@@ddr\G.Ldt@@d_du@@@dtdv@@ddu\G.Sdw@@dudx@@ddwSdy@@ dwdz@@tdy1d{@@dy2d|@@dtd}@@dd|Sd~@@ d|d@@td~2d@@d~1d@@d^Dd@@dVd@@@dd@@@dd@@ddA.2d@@dA.1d@@dd@@@dd@@@dd@@ddSd@@ dd@@td1d@@d2d@@pdd@@dd@@td1d@@dd@@p@dd@@{dd@@d\G.Sd@@d2d@@dDd@@dUd@@@dd@@@dd@@@dd@@ddA.1d@@dA.2d@@dd@@ddSd@@ dd@@td2d@@d1d@@dd@@@dd@@td1d@@dd@@p@dd@@{dd@@d\G.Ld@@d2d@@dDd@@dTd@@@dd@@@dd@@ddA.1d@@dA.1d@@dd@@@dd@@@dd@@p@dd@@dd@@td1d@@dd@@dd\G.Ld@@dd@@ddSd@@ dd@@td2d@@d2d@@pdd@@dd@@@dd@@ddSd@@ dd@@td1d@@d1d@@dd@@dd\G.Sd@@dd@@@dd@@dd\G.Ld@@dd@@ddSd@@ dd@@td1d@@d2d@@dd@@ddSd@@ dd@@td2d@@d1d@@dDd@B@U0""^".d@@ pd@@ dd@@@dd@@ddS.50d@@pdd@@d\wd@@dd@@ddABCD2Sd@@pdd@@ dd@@@dd@@ddABCDd@@pdd@@d\wd@@dZ.0d*@U""".&&-@OS-parameters of ideal matching network with actual load and source impedances. 7O9Od@@e<kHze?@@e;e@@@de?f.starteA@@e?kHzeB@@e:eC@@deB _n_u_l_l_eD@@eB _n_u_l_l_eE@@e9eF@@@eEeG@@deFfeH@@eFieI@@eEkHzeJ  )_Frequency (kHz))^Amplitude (dB20)S11 vs. Frequency&&&&&&&&& & & & & &&&eK@B@U`#$`#7eL@@ peM@@eLeN@@@eMeO@@@eNeP@@@eOeQ@@teP0eR@@ePeS@@K@eReT@@eSAtteneU@@KeReV@@eU10eW@@eOeX@@K@eWeY@@eXAtteneZ@@KeWe[@@eZRipplee\@@eNe]@@te\20e^@@e\e_@@de^loge`@@pe^ea@@{e`eb@@eaec@@@ebed@@decSee@@pecef@@eeeg@@def\weh@@efiei@@ ebej@@tei1ek@@ei2el@@eMem@@@elen@@@emeo@@@enep@@deof.stopeq@@eokHzer@@enes@@derf.startet@@erkHzeu@@emev@@@euew@@devf.pex@@evkHzey@@euez@@deyf.se{@@eykHze|@@ele}@@@e|e~@@de}fe@@e}ie@@e|kHze  )_frequency (kHz))^S12 vs. Frequency&&&&&&&&& & & & & &&&e@B@U`#$`#7e@@ pe@@ee@@@ee@@@ee@@@ee@@te0e@@ee@@K@ee@@eRipplee@@e3e@@ee@@K@ee@@eAttene@@Kee@@eRipplee@@ee@@te20e@@ee@@deloge@@pee@@{ee@@ee@@@ee@@deSe@@pee@@ee@@de\we@@eie@@ ee@@te1e@@e2e@@ee@@@ee@@@ee@@@ee@@@ee@@def.pe@@e2e@@ekHze@@ee@@te0e@@ekHze@@ee@@@ee@@def.pe@@ekHze@@ee@@def.se@@ekHze@@ee@@@ee@@defe@@eie@@ekHze  )^frequency (kHz))^S12 vs. Frequency&&&&&&&&& & & & & &&&e@B@U $U$ $/e@@ pe@@ee@@@ee@@@ee@@@ee@@Bee@@K@ee@@e3.163e@@ee@@te10e@@Kee@@e3e@@Kee@@e10e@@ee@@de _n_u_l_l_e@@e _n_u_l_l_e@@ee@@te20e@@ee@@deloge@@pee@@{ee@@ee@@@ee@@deSe@@pee@@ee@@de\we@@eie@@ ee@@te2e@@e1e@@ee@@@ee@@@ee@@@ee@@def.stope@@eMHze@@ee@@def.starte@@eMHze@@ee@@de _n_u_l_l_e@@e _n_u_l_l_e@@ee@@@ee@@defe@@eie@@eMHze  )O) S21 vs. Frequency&&&&&&&&& & & & & &&&e@B@Up $$p $7e@@ pe@@ee@@@ee@@@ee@@@ee@@Bee@@K@ee@@e4.905e@@ee@@te10e@@Kee@@e8e@@Kee@@e31.379e@@ee@@de _n_u_l_l_e@@e _n_u_l_l_f@@ef@@tf20f@@ff@@dflogf@@pff@@{ff@@ff@@@ff@@dfSf @@pff @@f f @@df \wf @@f if @@ ff@@tf 2f@@f 2f@@ef@@@ff@@@ff@@@ff@@dff.stopf@@fMHzf@@ff@@dff.startf@@fMHzf@@ff@@df _n_u_l_l_f@@f _n_u_l_l_f@@ff@@@ff@@dfff@@fif @@fMHzf!  )O) S22 vs. Frequency&&&&&&&&& & & & & &&&f"*@U%3%%.33-3_______________________________________ References 7('3f#<'f$8f"~f%<f&8f"f#f'< f(8f"f%f'f#93f)<3f*:@W1f+</3f,<3f-0@ NormalTimes New Roman f.*@U8%%H%.LL-A[1]Microwave Electronic Circuit Technology, by Yoshihiro Konishi, Marcel Dekker Publishing, New York, 1998, Filter Design Equations: pp 199- 2]Passive and Active Filters, Theory and Implementations, by Wai-Kai Chen, John Wiley & Sons, New York, 1986, pp. 177-1847*f/<*f08f.kArial0,0,255f1*@U%%%8f?@Hf@@HfA@L%C:\John\template\Template07_06_02.mcd%.\..\..\template\Template07_06_02.mcd#toc33-@F_______________________________________ Copyright and Trademark Notice7('FfB<'fC8f>nArialfD<fE8f>fBfF<fG8f>fDfFfB9((FfH<(fI:@WfJ<fK:@WfHfJfJ1fL<fM23fN4/''FfO<'fP0fQ<fR0fOfQfQ@ NormalTimes New Roman fS*@U%E&%.-B) All software and other materials included in this document are protected by copyright, and are owned or controlled by Circuit Sage. The routines are protected by copyright as a collective work and/or compilation, pursuant to federal copyright laws, international conventions, and other copyright laws. Any reproduction, modification, publication, transmission, transfer, sale, distribution, performance, display or exploitation of any of the routines, whether in whole or in part, without the express written permission of Circuit Sage is prohibited.7)9)fT<fU:@WfV<fW:@W?fTfX<fY:@WfVfXfX1fZ</)f[<)f\0@ NormalTimes New Roman 0