.MCAD 310000000 \  docDocument MmcObject[uu d2_graph_format graphData% axisFormat)D)Ltrace2D&&&&&&&&& & & & & &&& )1 1 ) 1 1 0 3 &&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING &1 1 NO-TRACE-STRING &1 1 NO-TRACE-STRING &1 1 NO-TRACE-STRING &1 1 NO-TRACE-STRING &1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING&1 1 NO-TRACE-STRING dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii  shpRectVmcDocumentObjectState\ mcPageModelK_I?_I?].?].?mcHeaderFooterI@I  CHeaderFooterJ@J@J@J MbP?MbP? TextState? TextStyle>@ MS Sans Serif0,0,128Serial_ParPropDefaultW?Normalfont_style_listO font_styleP  VariablesMS Serif@P  ConstantsMS Serif@P Text MS Sans Serif@P Greek VariablesSymbol@P User^1 MS Sans Serif@P User^2Courier@P User^3System@P User^4Script@P User^5Roman@P User^6Modern@P User^7MS Serif@P SymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderArial@P FooterArial@P Rotated Math FontMS Serif TextRegion* docRegionGshpBoxU0 ce0 133X3X CharacterMap-RangeMap;ASkin Depth and AC impedance of copper track This sheet is derived from equations given in the VLSI Handbook, CRC Press, section 7.4. The skin depth becomes more important with the small dimensions of an IC process. Most RF current flows within 2 skin depths.  ChrPropMap7<,  RangeElem<,  ChrPropData8 RangeData=lArial0,0,128 < 8l Arial0,0,128 <8l Arial0,0,128  ParPropMap9< ParPropData:@W/EmbedMap1<LinkMap/<LinkData0@Normal MS Sans Serif *@UpkspxN  -7Chris Haji-Michael http://www.sunshadow.co.uk/chris.htm77<8l Arial0,0,128<78l Arial0,0,1289$7<:@W/<$:@W/1</7<70@Normal MS Sans Serif *@UP-8First calculate the skin depth at different frequencies.78!<8"8 l Arial0,0,12898#<8$:@W?1%</8&<8'0@Normal MS Sans Serif (*@Umm m -Copper =1.673 Aluminium = 2.6557)<*8(Arial9+<,:@W?1-</.</0@Normal MS Sans Serif 0eqRegionB@UaB1tree@ p2@@ 13@@d2 Conductivity4@@25@@t416@@47@@@68@@@79@@t81.673:@@8;@@t:10<@@K:=@@<6>@@7ohm?@@6cm@@@B@US >@A@@ p@B@@ @A@C@@d@B\mm@D@@@B@E@@@@D@F@@t@E10@G@@K@E@H@@@G6@I@@@Dm@J@B@U &D@K@@ p@L@@ @K@M@@@@L@N@@d@M\m@O@@@M0@P@@@L@Q@@@@P@R@@p@@Q@S@@@R@T@@t@S4@U@@@S\p@V@@@Q@W@@t@V10@X@@K@V@Y@@@X7@Z@@@P@[@@d@Zhenry@\@@@Zm@]@B@U%@^@@ p@_@@ @^@`@@@@_@a@@d@`\d@b@@p@`@c@@@bfreq@d@@@_@e@@t@d1@f@@{@d@g@@@f@h@@@@g@i@@@@h@j@@d@i\p@k@@@ifreq@l@@@h@m@@d@l\m@n@@@l0@o@@@g Conductivity@p@B@U u7X@q@@ p@r@@@q@s@@@@r@t@@d@s\d@u@@p@s@v@@@u@w@@t@v1@x@@@vGHz@y@@@r@z@@+@@ySerial_DisplayNodeX@{@@@y\mm@|@B@U@8(,@8@}@@ p@~@@@}@@@@@~@@@@@@@@@@@@@B@@@@t@2.059@@@@@@@t@10@@@K@@@@@5@@@@@@@t@6.51@@@@@@@t@10@@@K@@@@@7@@@@@@@@@@@@@@@@@@@@@@@@@d@\d@@@p@@@@@freq@@@@m@@@@~@@@@@@@@@@@@@@@@@@t@10@@@@GHz@@@@@@@d@10@@@@MHz@@@@@@@@@@@@@@@@@freq@ , )GHz)OumSkin Depth vs Frequency&&&&&&&&& & & & & &&&@*@Uatp:-4Minimum track thickess (h) at different frequencies.74@<4@8@l Arial0,0,12894@<4@:@W?1@</4@<4@0@Normal MS Sans Serif @@B@UAG@@@ p@@@ @@@@@@@@@d@h@@@p@@@@@freq@@@@@@@@@@@@d@\p@@@@@@@d@\d@@@p@@@@@freq@@@@2@@B@Uw9V@@@ p@@@@@@@@@@@@d@h@@@p@@@@@@@@t@1@@@@GHz@@@@@@@+@@@X@@@@\mm@@B@U[@@@ p@@@@@@@@@@@@@@@@@@@@@@@@@@@t@100@@@@\mm@@@@@@@t@0.1@@@@\mm@@@@@@@@@@@@@@@@@@@@d@h@@@p@@@@@freq@@@@@@@@@@@@@@@@@@@@@@t@10@@@@GHz@@@@@@@d@10@@@@MHz@@@@@@@@@@@@@@@@@freq@ , )GHz)OumMinimum Thickness vs Frequency&&&&&&&&& & & & & &&&@@B@U:a@@@ p@@@@@@@@@@@@d@h@@@p@@@@@@@@t@1@@@@MHz@@@@@@@+@@@X@@@@\mm@*@U{KcPP-@mThis graph shows the minimum track thickness at different frequencies that should be aimed for in the design.7m9m@  Root EntryF[jq@Ole CompObjqOlePres000p  FMicrosoft Visio DrawingVISIO 4.0 ShapesVisio.Drawing.69q%76   o - "-$7l7l7 "-- - "-%7l- - "-%Rl- - "-%R4- - "-%RR4- - "-%R-  Arial-"System- . -!wv- -- . -!h"- -- . -!l3w-Oh+'08HT`lxChrisVisioDocument:'VisioInformation"SummaryInformation(Visio (TM) Drawing :'Rs& d !fffMMM333?q0?T d Arial)-3Times New Roman)-":5T?? 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