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Rotated Math Font Arial Narrow| TextRegion docRegion7shpBoxDI /99l9l CharacterMapRangeMap,BBROAD BAND IMPEDANCE TRANSFORMATION BETWEEN RESISTIVE TERMINATIONS by means of structures of lowpass filter form. The structure here described is made up of lumped reactive elements in the form of a ladder network giving Tchebyshev impedance match between resistive terminations and can readily be designed in semi-lumped element form for use at microwave frequencies. It is a very useful coupling structure for the RF Design Engineer and was presented in 1964 in tabulated form by George Matthaei 1.  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(u` ?bb b@?@<@?@((((((((((((pp @z3@pp @z3@t`1 UUUUUU?t`1 ((0{Gz?@baaa@@u` @@?@u` ?@P1hD W4lE XW4@ @@?@?@?@?@?Pt`1 ?t`1 ?t`1 ?t`1 ? )u` ? )u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4RL1hD W lEW&PD *Pv @@@?@?@?@?@?Pt`1 ?t`1 ?t`1 ?t`1 ? *u` ? *u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4L11hD WlE8WPD 0*P? @@@?@?@?@?@?Pt`1 333333?t`1 ?t`1 ?t`1 ? +u` ? +u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4L21hD ` WlE!WPD HW @?@?@?@?@?@?Pt`1 ?t`1 ?t`1 ?t`1 ? ,u` ? ,u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4Ln1hD +XelEPXPD `W @@@?@?@?@?@?Pt`1 ?t`1 ?t`1 ?t`1 ? -u` ? -u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4C11hD W.lE$WJPD xW @@@?@?@?@?@?Pt`1 """"""?t`1 ?t`1 ?t`1 ? .u` ? .u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4C21hD WlEXWPD Wc @?@?@?@?@?@?Pt`1 ?t`1 ?t`1 ?t`1 ? /u` ? /u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4Cn1hD  WlE*WPD  W, @?@?@?@?@?@?Pt`1 ?t`1 ?t`1 ?t`1 ? 0u` ? 0u` ?Pbb bL@aaa@@u` u` @?@u` ?u` @?@?u` ?u` ?@@?u` u` ?@@u` u` T4Rg1hD @ WlEH-WPD ( W @RQ?@p= ף?@@@?@?@?P@RQ?@p= ף?@@@?1 %%&())**++,,--..//00u` ?1 %%&())**++,,--..//00u` ?Pbb b;GG GG GGG"$H*%H2&H:'HB(HJ)HR*HZ+Hb,Hj-Hr.Hz/H0HzrjbZRJB:2*" #$% &'()hD @WRDeD W4D WUUUUUU?*?2FT( 0wPGTQypHT {BHTH L|BHT >~RHTX <RGT& pHT' TBHT' BHT( BHTxoXRGThoXjpHToXBHToXlBHT oXBHT* ԕRGToXpHTH% BHT, BHT*Q0BHToXZRGTXpHTX BHT X8BHT X:dHT XJRGTXfpHT oXBHToXhBHT p/oXdHTX޴RGT X~pHTXBHT`XBHT XdHT#XRHTp WBHT0WBHT(WBHTWBHTWBHT(WRHTWJRHTWRHTXRHT XRHTWnRHTW7RHTWRGT/WPU p&Wd4D H+P^Page-1Black fillWhite fillBlue fillRed fillGreen fill-Cyan fillYellow fillGMagenta fillGray fill10% Gray fillWhite line30% Gray fillLong dashed lineBlue dark fillCyan dark fillGreen dark fillMagenta dark fillRed dark fillYellow dark fill50% Gray fill70% Gray fill90% Gray fill1pxl line3pxl line9pxl lineHairlineShort dashed lineArial centeredArial top leftArial topTimes centeredTimes topTimes top leftEE NormalResistorInductorInductor.110Inductor.16;CapacitorCapacitor.26Capacitor.3133t3f3V3G3;303!33333333333x3h3X3G343$3333333333r3d3U3G3<3-33 3* g( Y>h@(^X>h@( Y>h@(^X>h@HT P4dD(PD8PTQ&D PTT P%DA'D?J(`TX+Ptz$T &P`u D&Plu!D((Ptu)D8(P|u'T x)Pb>p oX2D%X@'@Daaa BRDMATCH.mcd( (- ))'255,0,0* *- ++",-  -- .!@NormalTimes New Roman /@Dkkk"Roald C.Maximo Rev: Feb.1998("0-"1)/{*"2-"3+"4- "5-"6!@NormalTimes New Roman 7@Ds+ roald@mandic.com.br(*8-9+":- ;-tree1 p?1 >@@1d?f.a@A1?@B1t@A2.8@C1@A@D1t@C10@E1@C8@F@Dp,$;p8p#Enter: Lower frequency limit ( Hz )(#@G-#@H)@F0,0,128*#@I-#@J+"@K- #@L-#@M!@NormalTimes New Roman @N3@DDRa#X@O1 p@P1 @O@Q1d@Pf.b@R1@P@S1t@R5.2@T1@R@U1t@T10@V1@T8@W@DpL'[pXp$Enter: Upper frequency limit ( Hz ) (##$@X-#@Y)@W0,0,128@Z-@[)@W@X@Z@X*$@\-$@]+"@^- $@_-$@`!@NormalTimes New Roman @a3@DJaX@b1 p@c1 @b@d1d@cR.L@e1@c30@f@DKy[XpEnter: Load resistance ( W )(@g-@h)@f0,0,128@i-@j)@fSymbol0,0,128@g@k-@l)@f0,0,128@i@k@g*@m-@n+"@o- @p-@q!@NormalTimes New Roman @r3@Dj0|x,@s1 p@t1 @s@u1d@tN@v1@t4@w@DHlY{Hx-3Enter: Number of reactive elements ( must be even )(3@x-3@y)@w0,0,128*3@z-3@{+"@|- 3@}-3@~!@NormalTimes New Roman @3@Djx @1 p@1 @@1d@R.G@1@75@@Dk{x!pEnter: Source resistance ( W )(@-@)@0,0,128@-@)@Symbol0,0,128@@-@)@0,0,128@@@*@-@+"@- @-@!@NormalTimes New Roman @@DU)EE@S***********************************************************************************(S@-S@)@0,0,255*S@-S@+"@- S@-S@!@NormalTimes New Roman @@D$Preliminary parameters calculations:($*$@-$@+"@- $@-$@!@NormalTimes New Roman @3@D\@1 p@1 @@1d@w@1@@1t@2@1@@1@@@1d@f.b@1@f.a@1@@1d@f.b@1@f.a@3@D@1 p@1 @@1d@\w.a@1@@1t@1@1@@1d@w@1@2@3@D[2@1 p@1 @@1d@\w.b@1@@1t@1@1@@1d@w@1@2@3@D@1 p@1 @@1d@r@1@@1d@R.G@1@R.L@3@DX%@1 p@1 @@1d@f.m@1@@1@@@1d@f.a@1@f.b@1@2@3@Dm@,0@1 p@1 @@1d@\w.m@1@@1@@@1d@\w.a@1@\w.b@1@2@3@DA@0 @1 p@1 @@1d@A@1@@1@@@1@@@1d@\w.b@1@2@1@@1d@\w.a@1@2@1@2@3@D_H 8 @1 p@1 @@1d@\w.0@1{@@1@@1@@@1@@@1d@\w.a@1@2@1@@1d@\w.b@1@2@1@2@3@DC` @1 p@1 @@1d@\e@1@@1@@@1p@@@1@@1d@r@1@1@1@2@1@@1@@@1t@4@1@rA1@A1@AA1dAcoshA1pAA1AA1@AA1dANA1A2A1AA 1dAacoshA 1pAA 1A A 1@A A 1dA \w.0A1A 2A1A AA1A2A3@DhDuxA1 pA1 AA1dAaA1AA1@AA1tA2A1AA1dAasinhA1pAA1{AA1AA1tA1A1A\eA1ANA @D@0#0#@yParameter a will be used to locate the poles and zeros of a conventional Tchebyshev low pass filter2 with N/2 elements (e yA!- A")A A#-A$)A yA!A%-YA&)A A#A'-A()A ]A%A)-A*)A A'A)A#*yA+-yA,+"A-- yA.-yA/!@NormalTimes New Roman A0@D5Poles and Zeros on the l plane:(A1-A2)A0z0,0,0A3-A4)A0zSymbol0,0,0A1A5-A6)A0z0,0,0A3A5A1*A7-A8+"A9- A:-A;!@NormalTimes New Roman A<3@D(J5 A=1 pA>1 A=A?1dA>nA@1A>AA1dA@NAB1A@2AC3@Dp AD1 pAE1 ADAF1dAEmAG1AEAH1tAG1AI1AGnAJ3@Da8*(6AK1 pAL1 AKAM1@ALAN1dAM\lpAO1AMmAP1ALAQ1@APAR1K@AQAS1ARAT1dASsinhAU1pASAV1AUaAW1AQAX1dAWsinAY1pAWAZ1AYA[1@AZA\1dA[\pA]1pA[A^1A]A_1@A^A`1tA_2Aa1A_mAb1A^1Ac1AZAd1tAc2Ae1AcnAf1APAg1@AfAh1tAg1jAi1AgAj1dAicoshAk1pAiAl1AkaAm1AfAn1dAmcosAo1pAmAp1AoAq1@ApAr1dAq\pAs1pAqAt1AsAu1@AtAv1tAu2Aw1AumAx1At1Ay1ApAz1tAy2A{1AynA|@D!407K  poles(A}-A~)A|~ *A-A+"A- A-A!@NormalTimes New Roman A3@DIp)` A1 pA1 AA1@AA1dA\lzA1AmA1AA1tA1jA1AA1dAcosA1pAA1AA1@AA1dA\pA1pAA1AA1@AA1tA2A1AmA1A1A1AA1tA2A1AnA@DQd` %  zeros(A-A)A~ *A-A+"A- A-A!@NormalTimes New Roman A3@D7ZA1 pA1AA1@AA1@AA1@AA1tA2A1KAA1A2A1AA1dA _n_u_l_l_A1A _n_u_l_l_A1 AA1@AA1dAImA1pAA1AA1dA\lpA1AmA1AA1dAImA1pAA1AA1dA\lzA1AmA1AA1@AA1@AA1tA1A1KAA1A1A1AA1dA _n_u_l_l_A1A _n_u_l_l_A1 AA1@AA1dAReA1pAA1AA1dA\lpA1AmA1AA1dAReA1pAA1AA1dA\lzA1AmAd2_graph_format graphData  axisFormatLL%poles and zeros on the "lambda"plane.trace2D     A@DXXX( *<*<@These poles and zeros shall now be mapped to get the corresponding poles and zeros of the impedance transforming network. Note that this process will double the number of reactive elements.(*A-A+"A- A-A!@NormalTimes New Roman A@D)#Poles and Zeros on the " p" plane:(#A-#A)Az0,0,0*#A-#A+"A- #A-#A!@NormalTimes New Roman A3@DH'+A1 pA1 AA1dAmA1AA1tA1A1AnA3@D<A1 pA1 AA1dAkA1AA1tA1A1ANA3@D'A1 pA1 AA1@AA1dAiA1AmA1AA1dAmA1AnA3@Db*,A1 pA1 AA1@AA1dA\spA1AmA1AA1dAReB1pAB1BB1dB\lpB1BmB3@D-B1 pB1 BB1@BB1dB\wpB 1BmB 1BB 1dB ImB 1pB B 1B B1dB \lpB1B mB3@D.B1 pB1 BB1@BB1dB\szB1BmB1BB1dBReB1pBB1BB1dB\lzB1BmB3@DW#/B1 pB1 BB1@BB 1dB\wzB!1BmB"1BB#1dB"ImB$1pB"B%1B$B&1dB%\lzB'1B%mB(3@D<x!  B)1 pB*1 B)B+1@B*B,1dB+\qpB-1B+mB.1B*B/1I@B.B01@B/B11@B0B21dB1\pB31B12B41B0B51@B4B61tB51B71B52B81B4B91dB8atanB:1pB8B;1B:B<1@B;B=1dB<AB>1B\spB@1B>mBA1B;BB1@BABC1dBB\w.0BD1BB2BE1BABF1dBEABG1BEBH1dBG\wpBI1BGmBJ1)B/BK1@BJBL1@BKBM1dBLABN1BLBO1dBN\spBP1BNmBQ1BKBR1@BQBS1dBR\w.0BT1BR2BU1BQBV1dBUABW1BUBX1dBW\wpBY1BWmBZ1BJ0B[1}B.B\1pB[B]1B\B^1dB]\pB_1B]B`1@B_Ba1dB`1Bb1B`2Bc1B_Bd1dBcatanBe1pBcBf1BeBg1@BfBh1dBgABi1BgBj1dBi\spBk1BimBl1BfBm1@BlBn1dBm\w.0Bo1Bm2Bp1BlBq1dBpABr1BpBs1dBr\wpBt1BrmBu3@D8(Bv1 pBw1 BvBx1@BwBy1dBx\qzBz1BxmB{1BwB|1dB{\pB}1B{2B~3@D^)1B1 pB1 BB1@BB1dBppB1BmB1BB1@BB1p@BB1BB1@BB1p@BB1BB1@BB1dB\w.0B1B2B1BB1dBAB1BB1dB\wpB1BmB1B2B1BB1p@BB1BB1dBAB1BB1dB\spB1BmB1B2B1BB1tB1B1B4B1pBB1BB1@BB1dBcosB1pBB1BB1dB\qpB1BmB1BB1tB1jB1BB1dBsinB1pBB1BB1dB\qpB1BmB3@DNB1 pB1 BB1@BB1dBpzB1BmB1BB1tB1jB1{BB1BB1@BB1dB\w.0B1B2B1BB1dBAB1BB1dB\wzB1BmB3@DS 62B1 pB1 BB1@BB1eBppB1pBB1BB1dBiB1BmB1BB1@BB1dBppB1BmB3@D 5B1 pB1 BB1@BB1eBpzB1pBB1BB1dBiB1BmB1BB1@BB1dBpzB1BmB3@D7  B1 pB1BB1@BB1@BB1@BB1fB 1.507575B1KBB1B 1.507575B1BB1dB _n_u_l_l_B1B _n_u_l_l_B1 BB1@BB1dBImB1pBB1BB1dBppB1BkB1BB1dBImB1pBB1BB1dBpzB1BkB1BB1@BB1@BB1tB.1B1KBB1B 0.697722B1BB1dB _n_u_l_l_B1B _n_u_l_l_B1 BB1@BB1dBReC1pBC1CC1dCppC1CkC1BC1dCReC1pCC1CC1dCpzC 1CkC  LLpoles and zeros on the "p"plane     C 3@DX*<8C 1 pC 1 C C1dC ORIGINC1C 1C3@D(*n<78C1 pC1 CC1dCmC1CC1tC1C1CC1dCNC1C1C3@D(Rrd9` C1 pC1 CC1dC\wC1CC1 @CC1tC.1C 1C.11C!1C5C"@DX|XK/./.@With the calculated values it's now possible to create the numerator and denominator Hurwitz polynomials for the rational function that defines G (w)(C#-C$)C"C%-C&)C"SymbolC#C'-C()C"C%C)-C*)C"SymbolC'C+-C,)C"C)C+C%*C--C.+"C/- C0-C1!@NormalTimes New Roman C23@DX|C31 pC41 C3C51@C4C61dC5PC71pC5C81C7\wC91!C4C:1dC9mC;1pC9C<1C;C=1dC<\wC>1CppC@1C>mCA3@D{%CB1 pCC1 CBCD1@CCCE1dCDQCF1pCDCG1CF\wCH1!CCCI1dCHmCJ1pCHCK1CJCL1dCK\wCM1CKCN1dCMpzCO1CMmCP@D+.;8} 7The reflection coefficient function G(w) is then simply('$7CQ-$CR)CPCS-CT)CPSymbolCQCU-CV)CPSymbolCSCW-CX)CPCUCWCS*7CY-7CZ+"C[- 7C\-7C]!@NormalTimes New Roman C^@D,;8 and(*C_-C`+"Ca- Cb-Cc!@NormalTimes New Roman Cd3@D`)P@ Ce1 pCf1,CeCg1@CfCh1dCg\GCi1pCgCj1Ci\wCk1CfCl1@CkCm1dClQCn1pClCo1Cn\wCp1CkCq1dCpPCr1pCpCs1Cr\wCt3@D)sP!@ Cu1 pCv1,CuCw1@CvCx1dCwZCy1pCwCz1Cy\wC{1CvC|1@C{C}1@C|C~1dC}PC1pC}C1C\wC1C|C1dCQC1pCC1C\wC1C{C1@CC1dCPC1pCC1C\wC1CC1dCQC1pCC1C\wC@Dt' 2Numerator and denominator polynomial coefficients:(2*2C-2C+"C- 2C-2C!@NormalTimes New Roman C3@DC C1 pC1 CC1@CC1dCNumC1pCC1C\wC1CC1@CC1dCPC1pCC1C\wC1CC1dCQC1pCC1C\wC3@DU C1 pC1 CC1@CC1dCDenC1pCC1C\wC1CC1@CC1dCPC1pCC1C\wC1CC1dCQC1pCC1C\wC3@D f/YC1 pC1 CC1dCmC1CC1tC1C1CC1dCNC1C1C3@D *4C1 pC1 CC1@CC1dCAC1CmC1CC1tC2C1%CC1@CC1tC0C1C1C1CC1dCxC1CC1@CC1dCNumC1pCC1pCC1CC1dCexpC1pCC1CC1@CC1tC2jC1C\pC1CxC1CC1dCcosC1pCC1CC1@CC1@CC1dCmC1C2C1C\pC1CxC3@Dhp|C1 pC1 CC1@CC1dCBC1CmC1CC1tC2C1%CC1@CC1tC0C1C1C1CC1dCxC1CC1@CC1dCDenC1pCC1pCC1CC1dCexpC1pCC1CC1@CC1tC2jC1C\pC1CxC1CC1dCcosC1pCD1CD1@DD1@DD1dDmD1D2D1D\pD1DxD3@D U1D(N D1 pD 1 DD 1@D D 1eD BD 1D D 1dD ND1D 1D1D 0D3@D1(O D1 pD1 DD1@DD1eDBD1DD1dDND1D2D1D0D3@DH8(P D1 pD1 DD1dDkD1DD1@DD1@DD 1dDceilD!1pDD"1D!D#1dD"ND$1D"2D%1D1D&1D1D'3@D1( D(1 pD)1 D(D*1@D)D+1eD*viD,1D*kD-1D)D.1@D-D/1tD.2D01D.kD11D-1D23@D61( D31 pD41 D3D51@D4D61dD5\iD71D5kD81pD4D91D8D:1tD92D;1D9kD<3@D JUi2X D=1 pD>1 D=D?1@D>D@1dD?VDA1D?kDB1D>DC1dDBADD1pDBDE1DDDF1dDEiDG1DEkDH3@DJiX DI1 pDJ1 DIDK1@DJDL1dDKUDM1DKkDN1DJDO1dDNBDP1pDNDQ1DPDR1dDQ\iDS1DQkDT3@D J\0X DU1 pDV1 DUDW1dDVMDX1DVDY1dDXaugmentDZ1pDXD[1 DZD\1dD[VD]1D[UD^@D   c3c3@The rational function can now be decomposed by the method of successive division and inversion 3 to extract the normalized element values g. This process, described in a prior worksheet 2, is here automated by the Mathcad program bellow (*). (_D_-_D`)D^Da-Db)D^]D_Dc-Dd)D^DaDe-+Df)D^DcDg-Dh)D^kTimes New Roman0,0,0DeDi-/Dj)D^DgDk-Dl)D^]DiDm-4Dn)D^DkDo-Dp)D^mTimes New Roman0,0,0DmDq-Dr)D^DoDqDa*Ds-Dt+"Du- Dv-Dw!@NormalTimes New Roman Dx3@D8veo Dy1 pDz1 DyD{1dDzORIGIND|1Dz1D}3@D 8 DD~1 pD1 D~D1@DD1dDGD1pDD1DMD1DD1@DD1@DD1H@DD1dDnD1DD1dDlengthD1pDD14DD1dDMD1D1D1HDD1@DD1dDgD1D1D1DD1@DD1dDMD1 DD1dDnD1D1D1DD1dDMD1 DD1@DD1dDnD1D1D1D2D1DD1@DD1@DD1@DD1@DD1@DD1H@DD1dDPD1DD14@DD1dDMD1D2D1DD1dDgD1DkD1DD1H@DD1@DD1dDVD1D\kD1DD1I@DD1@DD1dDPD1DnD1,DD1dD\kD1D1D1}DD1DD1dDPD1DD1dD\kD1D1D1HDD1dD\kD1DD1dDnD1D1D1HDD1dDUD1DD14@DD1dDMD1D1D1DVD1DD1H@DD1@DD1dDV1D1D\kD1DD1I@DD1@DD1p@DD14DD1dDMD1D2D1DnD1,DD1dD\kD1D1D1}DD1DD1p@DD14DD1dDMD1D2D1DD1dD\kD1D1D1HDD1dD\kD1DD1dDnD1D1D1HDD1dDMD1DD1dDaugmentD1pDD1 DD1dDV1D1DUD1HDD1@DD1dDgD1DD1dDkD1D1D1DD1@DD1dDMD1 DD1dDnD1D1E1DE1dEME1 EE1@EE1dEnE1E1E1E2E1HDE1dEkE 1EE 1tE 1E 1E E 1dE NE 1E 1E1DgE3@Dp E1 pE1 EE1dEgE1EE1dEGE1pEE1EME3@Dn   q E1 pE1EE1dEgE1EE1+@ESerial_DisplayNodeFE1E _n_u_l_l_E@D   ss@vThe final values can be readily obtained by scaling the normalized elements for actual frequency and impedance level.:(v*vE-vE +"E!- vE"-vE#!@NormalTimes New Roman E$3@D ;  E%1 pE&1 E%E'1dE&iE(1E&E)1tE(1E*1E(nE+3@Dh  { E,1 pE-1 E,E.1@E-E/1dE.XlE01E.iE11E-E21dE1R.LE31E1E41dE3gE51E3E61@E5E71tE62E81E6iE91E51E:3@D $  E;1 pE<1 E;E=1@E1dE=XcE?1E=iE@1E1F1F@1F>NFA1EFB1dFAzFC1FANFD3@D( ~ ( FE1 pFF1FEFG1@FFFH1@FGFI1@FHFJ1@FIFK1tFJ1.5FL1FJR.GFM1KFIFN1FMR.GFO1FHFP1dFOR.GFQ1FO _n_u_l_l_FR1 FGFS1@FRFT1dFSReFU1pFSFV1pFUFW1FVFX1dFWZFY1pFWFZ1FYfF[1FRF\1dF[ImF]1pF[F^1F]F_1dF^ZF`1pF^Fa1F`fFb1FFFc1@FbFd1@FcFe1@FdFf1tFe1.4Fg1Fef.bFh1Fd10Fi1FcFj1dFif.aFk1Fif.bFl1FbfFm \\$Impedance as seen from the generator     Fn3@D * Fo1 pFp1 FoFq1dFpL.AdcFr1FpFs1K@FrFt1Fs10Fu1FrFv1dFulogFw1pFuFx1FwFy1@FxFz1p@FyF{1FzF|1dF{rF}1F{1F~1Fy2F1FxF1tF4F1FrF@D t !<== attenuation at zero frequency(!*!F-!F+"F- !F-!F!@NormalTimes New Roman F3@DpAhX F1 pF1 FF1dF\G.maxF1FF1tF1F1FF1dFcoshF1pFF1FF1dFnF1FaF3@DJa+X F1 pF1 FF1dFL.ArF1FF1K@FF1F10F1FF1dFlogF1pFF1FF1tF1F1F\eF3@DDwu'` F1 pF1 FF1@FF1dF\GF1pFF1FfF1{FF1FF1@FF1dFR.GF1FF1dFZF1pFF1FfF1FF1dFR.GF1FF1dFZF1pFF1FfF3@DL@i` F1 pF1 FF1@FF1dFP.LF1pFF1FfF1FF1tF10F1FF1dFlogF1pFF1FF1tF1F1FF1p@FF1FF1dF\GF1pFF1FfF1F2F3@Dphp F1 pF1FF1@FF1@FF1@FF1fF0.91308F1FF1dF 5.557534F1FF1dF10F1KFF1F4F1FF1dF\G.maxF1F _n_u_l_l_F1FF1dF\GF1pFF1FfF1FF1@FF1@FF1BFF1dF 7.279927F1FF1dF10F1F8F1F10F1FF1dFf.aF1Ff.bF1FfF \ frequency\reflection coefficient     F3@DZh F1 pF1FF1@FF1@FF1@FF1tF0F1KFF1F3F1FF1dFL.ArF1FL.AdcF1FF1dFP.LF1pFF1FfF1FF1@FF1@FG1BFG1dG 7.279927G1GG1dG10G1G8G1F0G1FG1dGf.aG1Gf.bG 1FfG  \ frequency\dB attenuationpower delivered to the load     G 3@Db*G 1 pG 1G G1dG L.ArG1G G1+@G@FG1G _n_u_l_l_cJG@Dxx8dB(*G-G+"G- G-G!@NormalTimes New Roman G@D%%3<== passband ripple or maximum passband attenuation(3*3G-3G+"G- 3G-3G!@NormalTimes New Roman G3@Dc1G1 pG 1GG!1dG L.AdcG"1G G#1+@G"@FG$1G" _n_u_l_l_bJG%@Dxx0dB(*G&-G'+"G(- G)-G*!@NormalTimes New Roman G+@D&<== d.c. or zero frequency attenuation(&*&G,-&G-+"G.- &G/-&G0!@NormalTimes New Roman G13@Dg6G21 pG31G2G41dG3\G.maxG51G3G61+@G5@FG71G5 _n_u_l_l_cJG8@D +<== maximum passband reflection coefficient(+*+G9-+G:+"G;- +G<-+G=!@NormalTimes New Roman G>@D    @(*) The author feels indebted to Steven Finch of Mathsoft for his kind assistance in the implementation of this Mathcad program.(G?-G@)G>nTimes New Roman0,0,0*GA-GB+"GC- GD-GE!@NormalTimes New Roman GF@DJ BB References:( GG- GH)GF}* GI- GJ+"GK-  GL- GM!@NormalTimes New Roman GN@D4 /, , @(1) G.L.Mattthaei: Tables of Chebyshev Impedance Transforming Networks of lowpass Filter Form; Proceedings of IEEE, August 1964(GO-GP)GN~GQ-GR)GN|GOGS-mGT)GN~GQGSGO*GU-GV+"GW- GX-GY!@NormalTimes New Roman GZ@D+" 0# # @{(2) R.C.Maximo: LPFSYNTH.mcd MathSoft; Mathcad Applications Files (http://www.mathsoft.com/appsindex.html), Feb. 1998 (z{G[-G\)GZ~G]-G^)GZ|G[G_- G`)GZlTimes New Roman0,0,0G]Ga-kGb)GZ~G_Gc-Gd)GZ|GaGcG[*{Ge-{Gf+"Gg- {Gh-{Gi!@NormalTimes New Roman Gj@D,;8@a(3) E. A. Guillemin: Communications Networks, Vol. II; John Wiley & Sons, Twelfth Printing 1956. (`aGk-Gl)Gj~Gm-Gn)Gj|GkGo-Gp)Gj~GmGq- Gr)Gj|GoGs-MGt)Gj~GqGu-Gv)GjGsGuGk*aGw-aGx+"Gy- aGz-aG{!@NormalTimes New Roman