.MCAD 306000000 Z  docDocument<mcObjectI ( dim_formatCmasslengthtimecharge temperature luminosity substanceNumericalFormat@dii shpRectEmcDocumentObjectStateJ mcPageModel:YyI?DD>YyI?}G?mcHeaderFooter9 r.c.maximo9|P ComputeEngine=BuiltInsB SerialAnyvalH@@H @@H@HMbP?@H units_classA TextState0 TextStyle/@ Times New RomanNormal/@ArialHeading 1/@ ArialHeading 2/@ ArialHeading 3 /@ ArialParagraph /@ ArialList /@ ArialIndent /@Times New RomanTitle /@Times New RomanSubtitle font_style_list> font_style?  Variables Arial Narrow?  Constants Arial Narrow? TextArial? Greek VariablesSymbol? User 1Arial? User 2 Courier New? User 3System? User 4Script? User 5Roman? User 6Modern? User 7Times New Roman? SymbolsSymbol? Current Selection FontArial? Undefined Font? HeaderEngrvrsOldEng Bd BT? FooterTimes New Roman? Rotated Math Font Arial Narrowf TextRegion docRegion7shpBoxD 40N  CharacterMapRangeMap,@YShunt Coupled Series Resonators Passive Band-pass Filters SER-BPF.mcd ChrPropMap(N9Y RangeElem-9 ChrPropData) RangeData.lTimes New Roman0,0,0-)nTimes New Roman0,0,0- )lTimes New Roman0,0,0 ParPropMap*Y-Y ParPropData+EmbedMap"-LinkMap Y-YLinkData!@NormalTimes New Roman @D<lKHO \\Roald C. Maximo(-)mTimes New Roman*-+"-  -!!@NormalTimes New Roman "@D(<K(HQ kk July 1998(#-$)"mEngrvrsOldEng BT*%-&+"'- (-)!@NormalTimes New Roman *@D\hR C The series resonators band-pass filter is the exact dual of the shunt resonators band-pass filter with the exception of a mutual complementary asymmetry in the frequency response. The commentaries and restrictions presented in the worksheet "SHNT-BPF "1 apply equally well to this circuits and, for brevity, will not be repeated here. This worksheet intends to demonstrate the implementation of the shunt coupled series resonators band-pass filters by use of K inverters as described by G. Matthaei 2. After calculating the actual elements values for the ideal, non dissipative, filter, we take into account the the finite nature of the resonators Q value to compute and plot the overall insertion loss of the filter chain over the frequency band of interest. The unloaded Q value is supposed to be equal for all the resonators in the filter chain and is considered constant over the operating frequency band. The coupling capacitors are considered ideal since, in practice, their Q is indeed very high. 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Lu` ?bb b@=b@@?@ FS@@?LLLLLLLLLLLLpp @z3@pp @z3@@ FS@@?LLLaaa@@u` @@ί=?@u` ?@PhD @'3 lE X'3@?MFT.ƇPGT4pHT 4HBHT4JBHT 4LdHT4=bGT-3pHTX'3mBHT'3BHT '3dHT`'3ؙbGT(4lpHT8 4؝BHT!4BHT "4dHT@%4AbHT'3CBHT#'3BHT%'3BHT('3YBHT0,'3;BGTP'4ϳpHT`)4;BHT*4yBHT ,4wdHTh.4bGTp'3HpHTP '3xBHTp '3zBHT '3@RHT '3bHTP3BHT35BHT` 3BHT8 3BGT3O@GT3@GT3pHT3BHT3BHT31RHT3RGTP#36pHT0%3fBHT)3hBHT -3~BHT3JbGT` 3pHT.3 BHT 3 BHT ( 3dHTp3bHT8/'3BHT'3BGT`'3pHT'3:BHT'3xBHT`'3BHT'3bGTH3pHT3BHT3DBHT @3ndHT3bGT3b pHT3 BHTH3 BHT3JBHT#3RbGT%3pHT8'3BHT(3BHT )3rdHT+3ZRHT'3LBQ %4@ /"&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 NormalCapacitorCapacitor.6!Capacitor.11CaCapacitor.21ResistorResistor.37kGroundInductorCapacitor.48Inductor.66Capacitor.71Inductor.55ductor.553333333{3o3^3[3J3<303!33333333333x3h3X3G343$3333333333r3d3U3G3<3-33 30 g(!Ce6u@(>铰v@(!Ce6u@(>铰v@HP 4dP & TP *@'4,@W4J-`P$ ڄ !)@4'P X">p /2D +"@q3@D"840 @r1 p@s1 @r@t1d@s\e@u1@s0.1@v@D$30W @jjPassband ripple dB(*@w-@x+"@y- @z-@{!@NormalTimes New Roman @|3@D:0LH @}1 p@~1 @}@1d@~N@1@~4@@D<KHX @ttNumber of resonators(*@-@+"@- @-@!@NormalTimes New Roman @3@DR>i'`@1 p@1 @@1d@R.s@1@50@@DSc`d @qqSource impedance W(@-@)@@-@)@@ Symbol@@@*@-@+"@- @-@!@NormalTimes New Roman @3@Dj<%x@1 p@1 @@1d@R.l@1@50@@Dk{xe @ggLoad impedance W(@-@)@@-@)@@ Symbol@@@*@-@+"@- @-@!@NormalTimes New Roman @3@D|N@1 p@1 @@1d@L@1@@1t@40@1@@1t@10@1K@@1@9@@Dh @Inductance of resonators H(*@-@+"@- @-@!@NormalTimes New Roman @3@DE(~@1 p@1 @@1d@Q.o@1@250@@D^ @||Unloaded resonators Q(*@-@+"@- @-@!@NormalTimes New Roman @@Dj @--------------------------------------------------------------------------------------------------------------------------------------------------------------------(*@-@+"@- @-@!@NormalTimes New Roman @3@DB%@1 p@1 @@1d@Ga@1@@1t@1@1@R.s@3@Dp@1 p@1 @@1d@Gb@1@@1t@1@1@R.l@3@D @1 p@1 @@1@@@1d@g@1@0@1@1@3@DH W@1 p@1 @@1d@\b@1@@1d@ln@1p@@1@@1t@1@1@@1d@tanh@1p@@1@@1d@\e@1@17.37@3@D@mJ@1 p@1 @@1d@i@1@@1t@1@1@N@3@D)^P @i@1 p@1 @@1d@\G@1@@1d@sinh@1p@@1@@1d@\b@1@@1t@2@1@N@3@D)`P@j@1 p@1 @A1@@A1dAaA1AiA1@A1dAsinA1pAA1AA1@AA1p@AA 1AA 1@A A 1tA 2A 1A iA 1A 1A1A\pA1AA1tA2A1ANA3@D#GP@kA1 pA1 AA1@AA1dAbA1AiA1AA1@AA1dA\GA1A2A1AA1@AA1dAsinA1pAA 1AA!1@A A"1dA!iA#1A!\pA$1A NA%1A2A&3@DdD"A'1 pA(1 A'A)1@A(A*1eA)gA+1A)1A,1A(A-1tA,2A.1A,A/1@A.A01dA/aA11A/1A21A.\GA33@DrA41 pA51 A4A61dA5mA71A5A81dA7modA91pA7A:1 A9A;1dA:NA<1A:2A=3@D`\nA>1 pA?1 A>A@1dA?\tAA1A?AB1@AAAC1dAB10AD1ABAE1dAD\eAF1AD10AG1AA1AH3@D8reBAI1 pAJ1 AIAK1dAJiAL1AJAM1tAL2AN1ALNAO3@D0"AP1 pAQ1 APAR1@AQAS1eARgAT1ARAU1dATiAV1AT1AW1AQAX1dAWifAY1pAWAZ1 AYA[1 @AZA\1(@A[A]1dA\mA^1A\0A_1A[1A`1AZAa1p@A`Ab1AaAc1dAbcothAd1pAbAe1AdAf1dAe\bAg1Ae4Ah1A`2Ai3@Dc #Aj1 pAk1 AjAl1@AkAm1eAlgAn1AliAo1AkAp1@AoAq1@ApAr1tAq4As1AqAt1dAsaAu1AsAv1dAuiAw1Au1Ax1ApAy1dAxaAz1AxiA{1AoA|1@A{A}1dA|bA~1A|A1dA~iA1A~1A1A{A1dAgA1AA1dAiA1A1A@D00m <== Prototype elements values(*A-A+"A- A-A!@NormalTimes New Roman A3@D&3k A1 pA1AA1dAgA1AA1+@ASerial_DisplayNodeFA1A _n_u_l_l_A3@D)OP@ A1 pA1 AA1dAf1A1AA1dAFoA1AA1dABWA1A2A3@D)P@ A1 pA1 AA1dAf2A1AA1dAFoA1AA1dABWA1A2A3@D)[P>@ A1 pA1 AA1@AA1dAfA1pAA1ABWA1AA1dABWA1AFoA@Dt @\Here, the correct geometry of the response curve demands two passband dependent corrections:(\*\A-\A+"A- \A-\A!@NormalTimes New Roman A3@DA1 pA1 AA1dAfoA1AA1I@AA1{@AA1AA1dAf1A1Af2A1)AA1@AA1dAfA1pAA1ABWA1A.05A1}AA1AFoA3@D%A1 pA1 AA1dAB.fA1AA1I@AA1@AA1@AA1dAf2A1Af1A1AfoA1)AA1@AA1dAfA1pAA1ABWA1A.05A1}AA1pAA1AA1@AA1dAfoA1Af1A1AA1dAfoA1Af2A3@DJLa"Xp A1 pA1 AA1dA\w.oA1AA1@AA1tA2A1A\pA1AfoA3@DAsXq A1 pA1 AA1dACA1AA1tA1A1AA1@AA1dA\w.oA1A2A1ALA@DLjXu @_<== Capacitance that tunes the resonators with inductance L to the center frequency fo(]:_A-:A)AA-A)AkTimes New RomanAA-"A)AAA-A)AkTimes New RomanAAA*_A-_A+"B- _B-_B!@NormalTimes New Roman B3@DUB1 pB1 BB1dB\kB1BB1tB1B 1BB 1dB NB 1B 1B 3@DB 1 pB1 B B1dBmB1BB1tB1B1BB1dBNB1B1B3@D:B1 pB1 BB1dB\mB1BB1tB1B1BNB3@D0]:B1 pB1 BB1dBiB 1BB!1tB 1B"1B NB#3@D|#B$1 pB%1 B$B&1@B%B'1dB&KB(1B&1B)1{B%B*1B)B+1@B*B,1@B+B-1@B,B.1dB-R.sB/1B-\w.oB01B,LB11B+B.fB21B*B31dB2gB41B21B53@D^!B61 pB71 B6B81@B7B91eB8 KB:1B8B;1dB:iB<1B:1B=1B7B>1@B=B?1@B>B@1dB?\w.oBA1B?LBB1B>B.fBC1{B=BD1BCBE1@BDBF1dBEgBG1BEiBH1BDBI1dBHgBJ1BHBK1dBJiBL1BJ1BM3@D4BN1 pBO1 BNBP1@BOBQ1eBP KBR1BPBS1dBRNBT1BR1BU1{BOBV1BUBW1@BVBX1@BWBY1@BXBZ1dBYR.lB[1BY\w.oB\1BXLB]1BWB.fB^1BVB_1@B^B`1dB_gBa1B_NBb1B^Bc1dBbgBd1BbBe1dBdNBf1Bd1Bg3@D,k1HBh1 pBi1 BhBj1@BiBk1dBjCcBl1Bj1Bm1BiBn1dBmR.sBo1BmBp1dBo\w.oBq1pBoBr1BqBs1@BrBt1dBsKBu1Bs1Bv1{BrBw1BvBx1@BwBy1dBxR.sBz1Bx2B{1BwB|1p@B{B}1B|B~1dB}KB1B}1B1B{2B3@D9ee'PB1 pB1 BB1@BB1eBCcB1BB1dBiB1B1B1BB1tB1B1BB1dB\w.oB1BB1dBKB1BB1dBiB1B1B3@D4sPB1 pB1 BB1@BB1eBCcB1BB1dBNB1B1B1BB1dBR.lB1BB1dB\w.oB1pBB1BB1@BB1dBKB1BB1dBNB1B1B1{BB1BB1@BB1dBR.lB1B2B1BB1p@BB1BB1dBKB1BB1dBNB1B1B1B2B3@D7B1 pB1 BB1@BB1dBCceB1B1B1BB1@BB1tB1B1BB1@BB1@BB1dB\w.oB1B2B1BB1dBCcB1B1B1BB1dBR.sB1B2B1BB1dBCcB1B1B3@DB1 pB1 BB1@BB1eBCceB1BB1dBNB1B1B1BB1@BB1tB1B1BB1@BB1@BB1dB\w.oB1B2B1BB1dBCcB1BB1dBNB1B1B1BB1dBR.lB1B2B1BB1dBCcB1BB1dBNB1B1B3@D,B1 pB1 BB1@BB1dBCtB1BiB1BB1@BB1@BB1K@BB1BCB1BB1dBCcB1BiB1BB1dBCcB1BB1dBiB1B1B1BB1@BB1dBCB1pBB1BB1@BB1dBCcC1BiC1BC1dCCcC1CC1dCiC1C1C1BC1@CC1dCCcC 1CiC 1CC 1dC CcC 1C C 1dC iC1C 1C3@DC1 pC1 CC1@CC1eCCtC1C1C1CC1@CC1@CC1dCCC1CC1dCCceC1C1C1CC1dCCcC1C2C1CC 1@CC!1@C C"1@C!C#1dC"CceC$1C"1C%1C!C&1dC%CcC'1C%2C(1C C)1dC(CC*1C(C+1dC*CceC,1C*1C-1CC.1dC-CC/1C-C01dC/CcC11C/2C23@DC31 pC41 C3C51@C4C61eC5CtC71C5NC81C4C91@C8C:1@C9C;1dC:CC<1C:C=1dC<CcC>1C<NC?1C9C@1dC?CceCA1C?CB1dCANCC1CA1CD1C8CE1@CDCF1@CECG1@CFCH1dCGCcCI1CGNCJ1CFCK1dCJCceCL1CJCM1dCLNCN1CL1CO1CECP1dCOCCQ1COCR1dCQCceCS1CQCT1dCSNCU1CS1CV1CDCW1dCVCCX1CVCY1dCXCcCZ1CXNC[3@D4Le2PC\1 pC]1 C\C^1dC]Ql.aC_1C]C`1@C_Ca1dC`gCb1C`1Cc1C_B.fCd3@D4LmPCe1 pCf1 CeCg1@CfCh1dCgkCi1CgiCj1CfCk1dCjB.fCl1{CjCm1ClCn1@CmCo1dCngCp1CniCq1CmCr1dCqgCs1CqCt1dCsiCu1Cs1Cv3@D4ePCw1 pCx1 CwCy1dCxQl.bCz1CxC{1@CzC|1dC{gC}1C{NC~1CzB.fC3@D`l C1 pC1 CC1dC\iC1CC1tC1C1CC1dCNC1C1C@D 0 And finally, the actual filter elements values:(0*0C-0C+"C- 0C-0C!@NormalTimes New Roman C3@D`n C1 pC1 CC1dC\kC1CC1tC1C1CC1dCNC1C1C3@D`o C1 pC1 CC1dCmC1CC1tC2C1CC1dCNC1C1C3@DX! C1 pC1CC1dCQl.aC1CC1+@C@FC1C _n_u_l_l_C3@D C1 pC1CC1dCQl.bC1CC1+@C@FC1C _n_u_l_l_C@D  <== End resonators loaded Q's (C-C)CC-C)CkTimes New RomanCC-C)CCCC*C-C+"C- C-C!@NormalTimes New Roman C@D4{R@ kk!Coupling capacitors values ( F )(!*!C-!C+"C- !C-!C!@NormalTimes New Roman C@D4`R@ 0Coefficients of coupling between resonator pairs(0*0C-0C+"C- 0C-0C!@NormalTimes New Roman C@D4QR@ aaTuning capacitors values ( F )(*C-C+"C- C-C!@NormalTimes New Roman C3@D ra) C1 pC1CC1@CC1dCCcC1C\kC3@Dr2 C1 pC1CC1@CC1dCkC1C\iC3@DrA C1 pC1CC1@CC1dCCtC1CiC@Di+( YY@sChecking the behavior of the resulting filter network by plotting its response over the frequency band of interest:(s*sC-sC+"C- sC-sC!@NormalTimes New Roman C3@DBTPC1 pC1 CC1dCfC1CC1 @CC1@CC1tC.95C1Cf1C1CC1tC.951C1Cf1C1CC1tC1.05C1Cf2C3@DBTPC1 pC1 CC1@CC1dC\wC1pCC1CfC1CC1@CC1tC2C1C\pC1CfC3@Dj'D -x% D1 pD1 DD1@DD1dDZD1pDD1DfD1DD1@DD1@DD 1@DD 1H@D D 1@D D 1dD BD 1D D1dD ND1D 1D1D D1@DD1@DD1tD1jD1DD1dD\wD1pDD1DfD1DD1dDCcD1DD1dDND1D1D1DD1tD1D1DR.lD 1HD D!1@D D"1dD!ZD#1D!D$1dD#iD%1D#1D&1D D'1@D&D(1@D'D)1@D(D*1tD)1jD+1D)D,1dD+\wD-1pD+D.1D-fD/1D(LD01D'D11tD01D21D0D31@D2D41tD31jD51D3D61dD5\wD71pD5D81D7fD91D2D:1dD9CtD;1D9iD<1D&D=1tD<1D>1DBD@1D>DA1dD@iDB1D@1DC1HDDD1@DCDE1dDDBDF1DDiDG1DCDH1@DGDI1tDH1DJ1DHDK1dDJZDL1DJDM1dDLiDN1DL1DO1DGDP1@DODQ1tDP1jDR1DPDS1dDR\wDT1pDRDU1DTfDV1DODW1dDVCcDX1DViDY1HDDZ1dDYiD[1DYD\1dD[ND]1D[1D^1HDD_1dD^ZD`1D^Da1tD`1Db1D`Dc1dDbBDd1Db1De3@Dfo& Df1 pDg1 DfDh1@DgDi1dDhP.lDj1pDhDk1DjfDl1DgDm1tDl10Dn1DlDo1dDnlogDp1pDnDq1DpDr1tDq1Ds1DqDt1p@DsDu1{DtDv1DuDw1@DvDx1dDwR.sDy1DwDz1dDyZD{1pDyD|1D{fD}1DvD~1dD}R.sD1D}D1dDZD1pDD1DfD1Ds2D3@D g " h %D1 pD1DD1@DD1@DD1@DD1tD0D1KDD1D3D1DD1dD _n_u_l_l_D1KDD1D\eD1DD1dDP.lD1pDD1DfD1DD1@DD1@DD1BDD1dD1.61622D1DD1dD10D1D8D1DD1dD1.387D1DD1dD10D1D8D1DD1dDf1D1Df2D1DfDd2_graph_format graphData&  axisFormat\\#Pass-band ripple of lossless filtertrace2D     D3@Dg " h &D1 pD1DD1@DD1@DD1@DD1tD100D1KDD1D100D1DD1tD0D1DR.sD1 DD1@DD1dDReD1pDD1DD1dDZD1pDD1DfD1DD1dDImD1pDD1DD1dDZD1pDD1DfD1DD1@DD1@DD1BDD1dD1.61622D1DD1dD10D1D8D1DD1dD1.387D1DD1dD10D1D8D1DD1dDFoD1D _n_u_l_l_D1DfD \\"Input impedance of lossless filter     D3@Dr  D1 pD1 DD1dDfD1DD1 @DD1@DD1tD.1D1DFoD1DD1tD.11D1DFoD1DD1tD1.5D1DFoD3@Dr ~  D1 pD1DD1@DD1@DD1dDZD1pDD1DFoD1D\WD1DD1+@D@FD1D\W"JD3@D` j ` (D1 pD1DD1@DD1@DD1@DD1KBDD1DD1dD 9.866922D1DD1dD10D1KDD1D5D1KDD1D 114.564723D1DD1dD _n_u_l_l_E1D _n_u_l_l_E1DE1dEP.lE1pEE1EfE1DE1@EE1@EE1BEE 1dE2.25E 1EE 1dE 10E 1E 8E 1EE1dE 1.5E1E E1dE10E1E7E1EE1dEFoE1E _n_u_l_l_E1EfE* _N(Rel. Input power to lossless filter (dB)     E@D  Insertion loss calculations:(*E-E+"E- E-E!@NormalTimes New Roman E3@Dx   E1 pE1 EE 1dERE!1EE"1@E!E#1@E"E$1dE#\wE%1pE#E&1E%FoE'1E"LE(1E!Q.oE)3@D 7  E*1 pE+1 E*E,1dE+F.1E-1E+E.1dE-floorE/1pE-E01E/E11@E0E21dE1.99E31E1f1E41E0E51tE410E61E46E73@DP  g E81 pE91 E8E:1dE9F.2E;1E9E<1dE;ceilE=1pE;E>1E=E?1@E>E@1dE?1.012EA1E?f2EB1E>EC1tEB10ED1EB6EE3@D ,  ! EF1 pEG1 EFEH1dEGIEI1EGEJ1H@EIEK1dEJ\xEL1EJEM1@ELEN1@EMEO1@ENEP1@EOEQ1@EPER1@EQES1@ERET1@ESEU1H@ETEV1@EUEW1dEV\wEX1EVfEY1EUEZ1@EYE[1@EZE\1tE[2E]1E[\pE^1EZfE_1EYE`1tE_10Ea1E_6Eb1HETEc1@EbEd1dEcBEe1 EcEf1dEefEg1Ee\kEh1EbEi1tEh1Ej1EhEk1@EjEl1tEk1jEm1EkEn1dEm\wEo1EmfEp1EjEq1dEpCcEr1Ep\kEs1HESEt1@EsEu1dEtZEv1 EtEw1dEvfEx1EvmEy1EsEz1@EyE{1@EzE|1@E{E}1tE|1jE~1E|E1dE~\wE1E~fE1E{LE1EzE1tE1E1pEE1EE1@EE1tE1jE1EE1dE\wE1EfE1EE1dECtE1EmE1EyRE1HERE1dE\kE1EE1tE1E1EE1dENE1E1E1HEQE1dEmE1EE1tE1E1ENE1HEPE1@EE1dEME1EfE1EE1@EE1@EE1@EE1@EE1@EE1@EE1H@EE1@EE1dEDE1 EE1tE0E1E0E1EE1dEBE1 EE1dEfE1E1E1HEE1@EE1dEDE1 EE1@EE1dENE1E1E1EE1dENE1E1E1EE1@EE1dEBE1 EE1dEfE1EE1dENE1E1E1ER.lE1HEE1@EE1dEDE1 EE1dEmE1EE1dEmE1E1E1KEE1EE1dEBE1 EE1dEfE1EmE1HEE1@EE1dEDE1 EE1@EE1dEmE1E1E1EmE1KEE1EE1dEBE1 EE1dEfE1EmE1HEE1@EE1dEDE1 EE1dE\iE1E\iE1EE1@EE1@EE1dEBE1 EE1dEfE1EE1dE\iE1E1E1EE1dEZE1 EE1dEfE1E\iE1EE1dEBE1 EE1dEfE1E\iE1HEE1dE\iE1EE1tE1E1ENE1HEE1dEmF1EF1tF1F1FF1dFNF1F1F1EDF1HEOF1@FF1dFVF 1F0F 1F1F 1HENF 1@F F 1dF VF1F mF1F 0F1HEMF1@FF1dFiF1FfF15FF1@FF1p@FF1FF1dFMF1FfF1KFF1F1F1FVF1ELiF1HEIF1dFfF 1FF!1dF F.1F"1F F.2F#@Dh t h 0 Z ZA<== The Mathcad program calculates a matrix iteratively over a frequency band to determine the currents in the various meshes of the network, by Kirchhoff's law, so as to compare the filter input power and the effective power into the load. The input reference voltage is 1 volt.(*F$-F%+"F&- F'-F(!@NormalTimes New Roman F)3@D8 w B F*1 pF+1 F*F,1dF+fF-1F+F.1dF-F.1F/1F-F.2F03@DAHr$X F11 pF21 F1F31@F2F41dF3Z.inF51F3fF61F2F71tF61F81F6F91p@F8F:1F9F;1dF:IF<1F:fF=1F80F>3@DAh F?1 pF@1 F?FA1@F@FB1dFAP.inFC1FAfFD1F@FE1tFD10FF1FDFG1dFFlogFH1pFFFI1FHFJ1tFI1FK1FIFL1p@FKFM1{FLFN1FMFO1@FNFP1dFOR.sFQ1FOFR1dFQZ.inFS1FQfFT1FNFU1dFTR.sFV1FTFW1dFVZ.inFX1FVfFY1FK2FZ3@DA*h F[1 pF\1 F[F]1@F\F^1dF]P.LF_1F]fF`1F\Fa1tF`10Fb1F`Fc1dFblogFd1pFbFe1{FdFf1FeFg1@FfFh1@FgFi1p@FhFj1FiFk1p@FjFl1FkFm1dFlIFn1FlfFo1FjFp1dFoNFq1Fo1Fr1Fh2Fs1FgR.lFt1FfFu1p@FtFv1FuFw1dFvIFx1FvfFy1Ft0Fz3@DJ F{1 pF|1F{F}1@F|F~1@F}F1@F~F1KBFF1F 0.022285F1KFF1F10F1F~F1dF _n_u_l_l_F1F _n_u_l_l_F1 F}F1@FF1dFP.LF1FfF1FF1dFP.inF1FfF1F|F1@FF1@FF1dFF.2F1FF.1F1FF1@FF1dFf1F1FF1tF10F1F6F1FF1dFf2F1FF1tF10F1F6F1FfF \frequency ( MHz )LInsertion loss ( dB )Input Pwr x Load Pwr (dB)     F3@D F1 pF1FF1@FF1@FF1@FF1@FF1tF2F1FR.sF1KFF1F40F1FF1dF _n_u_l_l_F1FR.sF1 FF1@FF1dFReF1pFF1FF1dFZ.inF1FfF1FF1dFImF1pFF1FF1dFZ.inF1FfF1FF1@FF1@FF1fF156F1F144F1FF1@FF1FF1FfF ^^#Input impedance to the lossy filter     F@DH" @$@$@1) R.C. Maximo - Series coupled Shunt Resonators Passive Band-pass Filters Mathsoft site, Math at work, Application Files, SHNT-BPF.mcd(F-F)FlTimes New RomanF-F)FnTimes New RomanFFF*F-F+"F- F-F!@NormalTimes New Roman F@D6@N@ 88@2) Matthaei, Young and Jones - "Microwave Filters, Impedance Matching Networks and Coupling Structures ". 1964, McGraw-Hill(F-F)FlTimes New RomanF-dF)FnTimes New RomanFFF*F-F+"F- F-F!@NormalTimes New Roman