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TextStyle>@ Arial 128,0,128Serial_ParPropDefaultW?Normalÿÿÿÿÿÿÿÿ€font_style_listO font_stylePóÿÿÿôÿÿÿ  VariablesArial@Póÿÿÿôÿÿÿ  ConstantsArial@Póÿÿÿôÿÿÿ TextArial@Póÿÿÿôÿÿÿ ÿÿÿÿGreek VariablesSymbol@Póÿÿÿôÿÿÿ ÿÿÿÿUser^1Arial@Póÿÿÿôÿÿÿ ÿÿÿÿUser^2 Courier New@Póÿÿÿóÿÿÿ ÿÿÿÿUser^3System@Póÿÿÿôÿÿÿ ÿÿÿÿÿUser^4Script@Póÿÿÿôÿÿÿ ÿÿÿÿÿUser^5Roman@Póÿÿÿôÿÿÿ ÿÿÿÿÿUser^6Modern@Póÿÿÿôÿÿÿ ÿÿÿÿUser^7Times New Roman@Póÿÿÿôÿÿÿ SymbolsSymbol@Póÿÿÿ ÿÿÿÿCurrent Selection FontArial@Póÿÿÿ ÿÿÿÿUndefined Font@Póÿÿÿ : :HeaderArial@Póÿÿÿ : :FooterArial@Póÿÿÿôÿÿÿ Rotated Math FontArial3 TextRegion* docRegionGshpBoxUÈœÈpÔÔ CharacterMap-RangeMap; Group Delay for Butterworth BPF  ChrPropMap7  RangeElem<  ChrPropData8 RangeData=} ParPropMap9 <  ParPropData:@W,ÿÿÿÿÿÿÿÿÿÿÿÿEmbedMap1 <LinkMap/ < LinkData0ÿÿÿÿ@NormalArial€€ *@U;p{HHhh@h@-A@Group Delay Variation: Filters can introduce distortion by delaying the spectral components a modulated RF waveform. If the low frequency spectral components of a waveform arrive at the output of a filter before the high frequency components, this can cause "intersymbol interference" in a digital communication system.7@<8y<*89@<@:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1</@<@0ÿÿÿÿ@NormalArial€€ *@U“aÉ J]Y6Y6-@ÌButterworth Filter Group Delay:: Group delay, , for the Butterworth class of filters maybe calculated using the following formula (see Receiving System Design by Steve Erst, Artech House, 1984, pg. 159):7»Ì<8y<8<8? @@t=2?@@¤=\p@@@@Žp€<@A@@ˆÇ€@@@B@@d@AF.max@C@@¤@AF.min@D@@Žp€9@E@@‰Ç€@D@F@@t@E1@G@@¤@EJ@H@@É€8@I@@d@H\k@J@@û€@H@K@@{@@J@L@@Ê€@K@M@@d@L\a@N@@¤@L\k@O@@‰Ç€@J@P@@ü@@O@Q@@Žp@@P@R@@ý€@Q@S@@d@R\a@T@@¤@R\k@U@@´@P2@V@@ü€@O@W@@Žp@@V@X@@ˆÇ€@W@Y@@d@X\c@Z@@ý€@X@[@@d@Z\w@\@@¤@Z\k@]@@´@V2@^*@U`+‚;`8RX""-where79@_<@`:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1@a</@b<@c0ÿÿÿÿ@NormalArial€€ @d*@U¨+Ï—¨8TÐ'l'l-@ì = Upper -3 dB frequency (Hz)  = Lower -3 dB frequency (Hz) F = Frequency of computation (Hz) n = Number of resonators for the bandpass case or the number of reactances for the lowpass case J = 0 for lowpass and 1 for bandpass filters7Áì@e<@f8@d?@g<@h8@d@e@i<@j8@d?@g@k<@l8@d@i@m<@n8@d}0,0,0@k@oExample: For a bandpass filter with the following parameters:7 >A< A8AyA<5A8AAAA9>A<>A:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1A </>A!<>A"0ÿÿÿÿ@NormalArial€€ A#*@U€»ÈË€ÈHHH- Center Freq:7 A$< A%8A#s9 A&< A':@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1A(</ A)< A*0ÿÿÿÿ@NormalArial€€ A+@B@U»YÐȃA,@@ pA-@@ Á€A,A.@@dA-f.oA/@@Ê€A-A0@@tA/400A1@@¤A/MHzA2*@U€ÓÌã€àÜLL- No. of Poles:7 A3< A48A2s9 A5< A6:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1A7</ A8< A90ÿÿÿÿ@NormalArial€€ A:@B@UÓ*åàÝA;@@ pA<@@ Á€A;A=@@dA<NA>@@´A<2A?@B@UÓÆåŸàèA@@@ pAA@@ Á€A@AB@@dAAnAC@@€AAAD@@tAC1AE@@¤ACNAF*@U€óë€ßHkk-3dB BW (% of fo):7AG<AH8AFs9AI<AJ:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1AK</AL<AM0ÿÿÿÿ@NormalArial€€ AN@B@UóC2àAO@@ pAP@@ Á€AOAQ@@dAP%BWAR@@´AP4AS*@U€Û+€(ãH[[- 3dB BW (MHz):7 AT< AU8ASs9 AV< AW:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1AX</ AY< AZ0ÿÿÿÿ@NormalArial€€ A[@B@Ue8&(âA\@@ pA]@@ Á€A\A^@@dA]BWA_@@û€A]A`@@Ê@A_Aa@@dA`%BWAb@@¤A`f.oAc@@´A_100Ad@B@Uá-­(êAe@@ pAf@@ŒÁ€AeAg@@dAfBWAh@@–Ä€AfAi@@+@AhSerial_DisplayNodeXAj@@¤AhMHzAk*@UC`SPï0PP-9Group Delay and Selectivity can be determined as follows.7999Al<9Am:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1An</9Ao<9Ap0ÿÿÿÿ@NormalArial€€ Aq*@UkX{x©0@@- Freq index:7 Ar< As8Aqs9 At< Au:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1Av</ Aw< Ax0ÿÿÿÿ@NormalArial€€ Ay@B@UÈkò}ÓxµAz@@ pA{@@ Á€AzA|@@dA{IA}@@´A{100A~@B@Uk¼}›x¸A@@ pA€@@ Á€AA@@dA€iA‚@@€A€Aƒ@@tA‚0A„@@¤A‚IA…*@U‹c›˜ª0KK- Frequencies:7 A†< A‡8A…s9 Aˆ< A‰:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1AŠ</ A‹< AŒ0ÿÿÿÿ@NormalArial€€ A@B@UÈF¨ߘ³AŽ@@ pA@@ Á€AŽA@@ý@AA‘@@dA\DfA’@@¤AiA“@@Ê€AA”@@Ê@A“A•@@û@A”A–@@tA•1A—@@´A•2A˜@@Žp€A”A™@@ˆÇ€A˜Aš@@dA™iA›@@û€A™Aœ@@dA›IA@@´A›2Až@@¤A“MHzAŸ@B@U‹Ò Ÿ˜ºA @@ pA¡@@ Á€A A¢@@ý@A¡A£@@dA¢fA¤@@¤A¢iA¥@@‰Ç€A¡A¦@@dA¥f.oA§@@ý€A¥A¨@@dA§\DfA©@@¤A§iAª*@UÃvÓоH^^-Lower 3dB Freq:7A«<A¬8Aªs9A­<A®:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1A¯</A°<A±0ÿÿÿÿ@NormalArial€€ A²@B@UȹbàíЭA³@@ pA´@@ Á€A³Aµ@@dA´F.minA¶@@Ê€A´A·@@Žp@A¶A¸@@ˆÇ€A·A¹@@tA¸1Aº@@Ê€A¸A»@@û@AºA¼@@dA»%BWA½@@´A»100A¾@@û€AºA¿@@tA¾1AÀ@@´A¾2AÁ@@¤A¶f.oAÂ@B@UÃïØ´Ð»AÃ@@ pAÄ@@ŒÁ€AÃAÅ@@dAÄF.minAÆ@@–Ä€AÄAÇ@@+@AÆ@XAÈ@@¤AÆMHzAÉ*@Uów¿@__-Upper 3dB Freq:7AÊ<AË8AÉs9AÌ<AÍ:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1AÎ</AÏ<AÐ0ÿÿÿÿ@NormalArial€€ AÑ@B@UÈéeï¯AÒ@@ pAÓ@@ Á€AÒAÔ@@dAÓF.maxAÕ@@Ê€AÓAÖ@@Žp@AÕA×@@‰Ç€AÖAØ@@tA×1AÙ@@Ê€A×AÚ@@û@AÙAÛ@@dAÚ%BWAÜ@@´AÚ100AÝ@@û€AÙAÞ@@tAÝ1Aß@@´AÝ2Aà@@¤AÕf.oAá@B@Uóñ¶¼Aâ@@ pAã@@ŒÁ€AâAä@@dAãF.maxAå@@–Ä€AãAæ@@+@Aå@XAç@@¤AåMHzAè*@U3nC@Á@VV-% Freq Offset:7Aé<Aê8Aès9Aë<Aì:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1Aí</Aî<Aï0ÿÿÿÿ@NormalArial€€ Að@B@UÀ&›SÒ@½Añ@@ pAò@@ Á€AñAó@@ý@AòAô@@dAóxAõ@@¤AóiAö@@Ê€AòA÷@@û@AöAø@@tA÷1Aù@@ˆÇ€A÷Aú@@dAùF.maxAû@@¤AùF.minAü@@Žp€AöAý@@ˆÇ€AüAþ@@ý@AýAÿ@@dAþfB@@¤AþiB@@û€AýB@@Ê@BB@@dBF.maxB@@¤BF.minB@@ý€BB@@dBfB@@¤BiB*@UkT{xÂH<<- J for BPF:7 B < B 8Bs9 B < B :@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1B </ B< B0ÿÿÿÿ@NormalArial€€ B@B@UÀkß}ÎxÃB@@ pB@@ Á€BB@@dBJB@@´B1B@B@U ‘'¸·¨÷B@@ pB@@ Á€BB@@ý@BB@@dB\qB@@¤BnB@@Ê€BB@@û@BB@@ˆÇ@BB@@‰Ç@BB@@Ê@BB @@tB2B!@@¤BnB"@@¤BNB#@@´B1B$@@¤BNB%@@Žp€BB&@@û€B%B'@@dB&\pB(@@´B&2B)@B@U@›°W¨ÒB*@@ pB+@@ Á€B*B,@@ý@B+B-@@dB,\sB.@@¤B,nB/@@΀B+B0@@dB/cosB1@@Žp€B/B2@@ý€B1B3@@dB2\qB4@@¤B2nB5@B@U°›ý°È¨ÓB6@@ pB7@@ Á€B6B8@@ý@B7B9@@dB8\wB:@@¤B8nB;@@΀B7B<@@dB;sinB=@@Žp€B;B>@@ý€B=B?@@dB>\qB@@@¤B>nBA*@UÛcëèÍ@KK- Group Delay:7 BB< BC8BAs9 BD< BE:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1BF</ BG< BH0ÿÿÿÿ@NormalArial€€ BI@B@U É÷·èöBJ@@ pBK@@ Á€BJBL@@ý@BKBM@@dBL\tgBN@@¤BLiBO@@Ê€BKBP@@Ê@BOBQ@@û@BPBR@@tBQ1BS@@Ê€BQBT@@Ê@BSBU@@tBT2BV@@¤BT\pBW@@Žp€BSBX@@ˆÇ€BWBY@@dBXF.maxBZ@@¤BXF.minB[@@Žp€BPB\@@‰Ç€B[B]@@tB\1B^@@¤B\JB_@@@ù€BOB`@@ŸÁ@B_Ba@@tB`1Bb@@¤B`NBc@@ŸÁ€B_Bd@@dBcnBe@@û€BcBf@@{@BeBg@@ý€BfBh@@dBg\sBi@@¤BgnBj@@‰Ç€BeBk@@ü@BjBl@@Žp@BkBm@@ý€BlBn@@dBm\sBo@@¤BmnBp@@´Bk2Bq@@ü€BjBr@@Žp@BqBs@@ˆÇ€BrBt@@ý@BsBu@@dBtxBv@@¤BtiBw@@ý€BsBx@@dBw\wBy@@¤BwnBz@@´Bq2B{*@U+W;8Õ`??- Selectivity:7 B|< B}8B{s9 B~< B:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1B€</ B< B‚0ÿÿÿÿ@NormalArial€€ Bƒ@B@U b]»8õB„@@ pB…@@ Á€B„B†@@ý@B…B‡@@dB†A1Bˆ@@¤B†iB‰@@Ê€B…BŠ@@•K@B‰B‹@@´BŠ10BŒ@@΀B‰B@@dBŒlogBŽ@@Žp€BŒB@@‰Ç€BŽB@@tB1B‘@@ü€BB’@@Žp@B‘B“@@û€B’B”@@ý@B“B•@@dB”\DfB–@@¤B”iB—@@Žp€B“B˜@@û€B—B™@@dB˜BWBš@@´B˜2B›@@Ê€B‘Bœ@@tB›2B@@¤B›NBž@E@U°@¸°ABŸ@B@UÈN"È?B @@ pB¡@@Á€B B¢@@ŸÁ@B¡B£@@ŸÁ@B¢B¤@@ŸÁ@B£B¥@@vB¤33.954B¦@@¶B¤2.951B§@@ŸÁ€B£B¨@@dB§ _n_u_l_l_B©@@¤B§ _n_u_l_l_Bª@@û€B¢B«@@ý@BªB¬@@dB«\tgB­@@¤B«iB®@@¤BªnsB¯@@ŸÁ€B¡B°@@ŸÁ@B¯B±@@ŸÁ@B°B²@@vB±425B³@@¶B±375B´@@ŸÁ€B°Bµ@@dB´ _n_u_l_l_B¶@@¤B´ _n_u_l_l_B·@@û€B¯B¸@@ý@B·B¹@@dB¸fBº@@¤B¸iB»@@¤B·MHzB¼ @# )NFrequency (MHz))N Delay (ns) Group Delay&&&&&&&&& & & & & &&&B½@B@U8N’8ñB¾@@ pB¿@@Á€B¾BÀ@@ŸÁ@B¿BÁ@@ŸÁ@BÀBÂ@@ŸÁ@BÁBÃ@@vBÂ0BÄ@@•K€BÂBÅ@@´BÄ21BÆ@@ŸÁ€BÁBÇ@@dBÆ _n_u_l_l_BÈ@@¤BÆ _n_u_l_l_BÉ@@ý€BÀBÊ@@dBÉA1BË@@¤BÉiBÌ@@ŸÁ€B¿BÍ@@ŸÁ@BÌBÎ@@ŸÁ@BÍBÏ@@vBÎ425BÐ@@¶BÎ375BÑ@@ŸÁ€BÍBÒ@@dBÑ _n_u_l_l_BÓ@@¤BÑ _n_u_l_l_BÔ@@û€BÌBÕ@@ý@BÔBÖ@@dBÕfB×@@¤BÕiBØ@@¤BÔMHzBÙ @# )NFrequency (MHz))Selectivity (dB)Frequency Response&&&&&&&&& & & & & &&&BÚ*@U³XÃÀz@HH- Define units:7 9 BÛ< BÜ:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1BÝ</ BÞ< Bß0ÿÿÿÿ@NormalArial€€ Bà@B@U¬ÐŲÀ{Bá@@ pBâ@@Á€BáBã@@dBâMHzBä@@ü€BâBå@@tBä10Bæ@@´Bä6Bç@B@Uð¬-ÅÀ|Bè@@ pBé@@Á€BèBê@@dBénsBë@@ü€BéBì@@tBë10Bí@@•K€BëBî@@´Bí9Bï*@UëÅ øòhµ0µ0-7Dave Peterson Senior Technical Staff Engineer ITT-A/CD7797Bð<7Bñ:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1Bò</7Bó<7Bô0ÿÿÿÿ@NormalArial€€