.MCAD 304020000 1 74 16143 0 .CMD PLOTFORMAT 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 6 0 1 1 NO-TRACE-STRING 0 2 6 0 1 1 NO-TRACE-STRING 0 3 6 0 1 1 NO-TRACE-STRING 0 4 6 0 1 1 NO-TRACE-STRING 0 1 4 0 1 1 NO-TRACE-STRING 0 2 5 0 1 1 NO-TRACE-STRING 0 3 6 0 1 1 NO-TRACE-STRING 0 4 0 0 1 1 NO-TRACE-STRING 0 1 1 0 1 1 NO-TRACE-STRING 0 2 2 0 1 1 NO-TRACE-STRING 0 3 3 0 1 1 NO-TRACE-STRING 0 4 4 0 1 1 NO-TRACE-STRING 0 1 5 0 1 1 NO-TRACE-STRING 0 2 6 0 1 1 NO-TRACE-STRING 0 3 0 0 1 1 NO-TRACE-STRING 0 4 1 0 1 1 NO-TRACE-STRING 0 1 1 30 24 0 0 3 .CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=4 mass length time charge temperature tr=0 vm=0 .CMD SET ORIGIN 0 .CMD SET TOL 0.001000000000000 .CMD SET PRNCOLWIDTH 8 .CMD SET PRNPRECISION 4 .CMD PRINT_SETUP 1.200000 1.218750 1.200000 1.200000 0 .CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 |F |P |D^^|T .CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 colrid=1359499528 .CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=1359499528 .CMD DEFAULT_TEXT_PARPROPS 0 0 0 .CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables .CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants .CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text .CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1 .CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2 .CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3 .CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4 .CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5 .CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6 .CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7 .CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=2 family=Courier points=10 bold=0 italic=0 underline=0 colrid=5 .CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 colrid=-1 .CMD UNITS U=1 .CMD DIMENSIONS_ANALYSIS 0 0 .CMD COLORTAB_ENTRY 0 0 0 .CMD COLORTAB_ENTRY 128 0 0 .CMD COLORTAB_ENTRY 0 128 0 .CMD COLORTAB_ENTRY 128 128 0 .CMD COLORTAB_ENTRY 0 0 128 .CMD COLORTAB_ENTRY 128 0 128 .CMD COLORTAB_ENTRY 0 128 128 .CMD COLORTAB_ENTRY 128 128 128 .CMD COLORTAB_ENTRY 192 192 192 .CMD COLORTAB_ENTRY 255 0 0 .CMD COLORTAB_ENTRY 0 255 0 .CMD COLORTAB_ENTRY 255 255 0 .CMD COLORTAB_ENTRY 0 0 255 .CMD COLORTAB_ENTRY 255 0 255 .CMD COLORTAB_ENTRY 0 255 255 .CMD COLORTAB_ENTRY 255 255 255 .CMD COLORTAB_ENTRY 64 128 128 .TXT 2 1 1 0 0 Cg a29.250000,29.250000,29 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard MICROSTRIP TRANSMISSION LINES} .TXT 0 47 2 0 0 Cg a18.250000,18.250000,18 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard file: mstrip.mcd} .TXT 4 -47 3 0 0 Cg a38.250000,38.250000,38 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Formulas included in this spreadsheet:} .TXT 4 2 4 0 0 Cg a67.250000,67.250000,344 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Effective relative permittivity EEFF() (used internally)\par Effective electrical trace width WE() (used internally)\par \par Microstrip characteristic impedance ZMSTRIP()\par Microstrip propagation delay PMSTRIP()\par Microstrip trace inductance LMSTRIP()\par Microstrip trace capacitance CMSTRIP()} .EQN 17 37 16131 0 0 { 28 32 8768 0 8 457 589}{66} !1!*!!!$$h#e!!>{'m!!!!!!$G!!!#1G#U!?!0LVLVIu!"+u!!!x3|'Q#E!n2y*E3|*B2J,7/sK'2#.[!!!,!A!!!!!&!!!!#%&m"x?+#5!!!0>}!!!!!!!!!!!!!!!!!!!!!!!"!%+y!!!!(_#e!!+u!!!#!1#e#u!!!0>}>ZIq!!!!!!"S!1!!!!!!!!!3/CE\&P'Z3e"1!!+u!!!N!1#e!q!!!!9S!!!!!!+u!!!#!1#e!a!!!!&L!1!/ !!!!'M1P!"&KLVLVLG!!"C!!!##h$'7-$$49"3!!!0Ac!1!!!!!!!!!%!!!!(_#g!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#h!!Aa!!!E!Q+u(O#b"eAa*s!K#H<7(/In"c6k!!#_!A!!!!!!!!!!!!!%!!!!(_#i!!+u!!#U!1)1"3!!!0Ac!!#dLVIq!!!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!!!"!!!!!!!!!A+u!!!N!1.[#%!!!#+x !a#)!]Ae+%>G!d?'@?0c!\6p!a!!!#DH!a!%!!!!Iq#j!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH!q!-!!!!'-)5!-+x@?/8"n6p+%>o!}+xJS._!!!!(_#i!!+u!!#U!1.[!a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#j!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#k!!6k!!!F!Q&KF++0 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(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#j!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#k!!6k!!!F!Q&KEI0c!j6q9Q+y!!!!(_#i!!+u!!#U!1.[!a!!!0!""#!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!1.["C!!!0<9!!!"!!!!!!!!!A+u!!!N!11A"C!!!#.^!A#0",!%IA0j!a+u!!!N!1+u!a!!!0!"!q!% !!!!Iq#k!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH!q!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"#!)!!!!'=)3!#!'CU.X",!%!a!!!#DH!a!%!!!!Iq#j!!+u!!#U!11A!a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#j!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#k!!6k!!!F!Q&K-i5X!gG3 CE+y!!!!(_#i!!+u!!#U!1.[!a!!!0!""#!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!1.["C!!!0<9!!!"!!!!!!!!!A+u!!!N!11A"C!!!#.^!A"j"/6o6K5X!a+u!!!N!1+u!a!!!0!"!q!%!!!!Iq#k!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH!q!)!!!!KU&K!!#e!!!!!!!#!a!! !#DH"#!)!!!!'=)3!,!(91.5"/6o!a!!!#DH!a!%!!!!Iq#j!!+u!!#U!11A!a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#j!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#k!!6k!!!F!Q&K#%63!kDN;e+y!!!!(_#i!!+u!!#U!1.[!a!!!0!""#!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!1.[ "C!!!0<9!!!"!!!!!!!!!A+u!!!N!11A"C!!!#.^!A"s"=9U,g61!a+u!!!N!1+u!a!!!0!"!q!%!!!!Iq#k!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH!q!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"#!)!!!!'=)3!(4.Bc-f">4+!a!!!#DH!a!%!!!!Iq#j!!+u!!#U!11A!a!!!#DH!Q!+!!!!'M1P!!<7LVLV LG#e!!!!!!+u!!!#!1#e!a!!!!&L!1!%!!!!!A#f!!)1!!!?!!4'!!!7!e#mAQ0$"54(!a!!!!&L!1!1!!!!Ke'FLG!!!!!!!*!"!!!!LG!!!"'?3{EJ3e!A4W+u!!!N!1.['=!!!$&U7]4N!2#e!a!!!!!!0OGO"x'R3K${2z2H&Q/i29*G4M:V!'Iq-Y!O!%<7(o!O!&+u-Y!K!%<7(o!k!%<7(o!Y!#G--Y!%!!!!!A#f!!+u!!!H!@LV !a!!!!&L!1!%!!!!!A#f!!)1!!!?!!4'!!!7!oG5!a1s"E4(!a!!!!&L!1!%!!!!(_#j!#6k!!!S"f&S']#x!!+u!!!!!&?+&k@/2:'Z2z--2z2L4n9q3{1a4m7r!&+u-Y!Y!)&K(o!O!#G-(o!u!#G-(o!u!#<7/=!Y!#<7(o!u!%<7!a!!!!&L!1!%!!!!']&JLG+u!!!#!1#e!a!!!!&L!1!$!!!!&+!(!!!!$g-V"bDJG-74!1+u!!!# !1#e!a!!!#DH!q!;!!!!)Q>["E4("c!%!!!!!!!|#G&V4^/_4^-+1X,|(S#e/=!u!%#e(o!Y!%<7(o!k!#<7!a!!!!&L!1!%!!!!']&JLG+u!!!#!1#e!a!!!!&L!1!$!!!!&+!(!!!!$g,F!?G!o>{!1!%!!!!!!!|#G&V2c!}!!+u!!!#!1#e!a!!!#4(LVIu!!!!!A#f!!+u!!!N!1&K"C!!!0<9!!!"!!!!!!!!!A+u!!!N!14'"c!!!#+x!Q".!K?")!&l"-.]&[1E!!!!(_#i!!+u!!#U!14'!a!!!#DH!Q!%!!!!!A#f!!+u!!!#!1#e !a!!!!&L!1!$!!!!&+!(!!!!$g-^"[+yHO9P!Q+u!!!#!1#e#e!!!0>}0>Iq!!!!!!"S!1#e!0Iq!!!3/#K"1WG-.V&O!!!!(_#l!!DG!!!S"q6sLG)2!!+u!!!!!&?+&k@$!%<7!a!!!!&L!1!%!!!!']&JLG+u!!!#!1#e!a!!!!&L!1!$!!!!&+!(!!!!$g.5"]<;-I:>!a+u!!!#!1#e#e!!!0>}6*Iq!!!!!!"S!1#e!0Iq!!!3/#K" 1WG-#!+y!!!!(_#m!!DG!!!S"gDP-i+v!!+u!!!!!&?+&k@1!$+u!a!!!!&L!1!%!!!!']&JLG+u!!!#!1#e#E!!!#1G#U!3!0LVLVIq!!6k!!!%"$&Y+U=+#u+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!19Q"C!!!0<9!!!"!!!!!!!!!A+u!!!N!1<7"C!!!#.^!A"]![DL;e%V!q+u!!!N!1+u!a!!!0!""S!%!!!!Iq#o!!+u !!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH"S!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"c!)!!!!'=)3!'>}(?2N!H9W!a!!!#DH!a!%!!!!Iq#n!!+u!!#U!1<7!a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#n!!<7!!!E!Q)135(_!cIs0?-_!F<;!a!!!#DH!a!%!!!!Iq#n!!+u!!!N!1)1!a!! !#DH!A!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"S!+!!!!'-)4!.4,4w*3!t<:1A0O!Q+u!!!N!1+u!a!!!0!""S!%!!!!(_#h!!<7!!!G"#Iq"c#dLVLV!1!!!!!!!a!!!!&L!1!%!!!!!A#f!!+u!!!#!1#e!Q!!!"G-"3!!!"1E#U)P"71C2c1E!!!!!A#f!!+u!!!N!11A#5!!!$&U,w'U"##e!a!!!!!!0OGO"z4'5i!%!!!!!A#f!!+u !!!H!@LV!a!!!!&L!1!%!!!!(_#g!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#n!!<7!!!E!Q)1>k5>!S.c*s)V"N!$!a!!!#DH!a!%!!!!Iq#n!!+u!!!N!1)1!a!!!!&L!1!%!!!!!A#f!!+u!!!#!1#e!Q!!!"G-"3!!!"1E,7-?#,9T$GAe!!!!!A#f!!+u!!!N!11A#5!!!$&U5Y)E#%#e!a!!!!!!0OGO"z+u)a!%!!!!!A#f!!+u!!!H !@LV!a!!!!&L!1!/!!!!'M1P!"&KLVLVLG!!"C!!!!+{-yDt$!G>!a!!!#DH!A!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"S!+!!!!'-)4!'?(:C,G"tIu=9?}0?-$!A)5!a!!!#DH!a!%!!!!Iq#n!!+u!!#U!1<7!a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#n!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#o!!6k!!!F!Q&K 1Q/r!Q9V4w)5!!!!(_#i!!+u!!#U!19Q!a!!!0!""c!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!19Q"C!!!0<9!!!"!!!!!!!!!A+u!!!N!1<7"C!!!#.^!A#B!~4)F[/g!a+u!!!N!1+u!a!!!0!""S!%!!!!Iq#o!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH"S!)!!!!KU&K!!#e!!!! !!!#!a!!!#DH"c!)!!!!'=)3!'?(*#/h"{DL!a!!!#DH!a!%!!!!Iq#n!!+u!!#U!1<7!a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#n!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#o!!6k!!!F!Q&K5)>G!m.gCe+y!!!!(_#i!!+u!!#U!19Q!a!!!0!""c!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u !!!N!19Q"C!!!0<9!!!"!!!!!!!!!A+u!!!N!1<7"C!!!#.^!A#Q"<#iBSC6!a+u!!!N!1+u!a!!!0!""S!%!!!!Iq#o!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH"S!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"c!)!!!!'=)3!,#lEY(@"9<;!a!!!#DH!a!%!!!!Iq#n!!+u!!#U!1<7!a!!!#DH!Q!%!!!!(_#g !!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#n!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#o!!6k!!!F!Q&K'M8$!XDO4w)5!!!!(_#i!!+u!!#U!19Q!a!!!0!""c!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!19Q"C!!!0<9!!!"!!!!!!!!!A+u!!!N!1<7"C!!!#.^!A"."tIu35A(!Q+u!!!N!1+u!a!!!0!""S!%!!!! Iq#o!!+u!!!N!1)1"c!!!#1G#U!+!0LVLVIr!!!!!!!%!!!!!A#f!!+u!!!N!1!!!Q!!!!!!!!!$!!!!!!"?!&Aa0_!}!&Aa0_!Q  .TXT 3 -39 5 0 0 Cg a38.250000,38.250000,388 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Formulas from: I. J. Bahl and \par Ramesh Garg, "Simple and accurate\par formulas for microstrip with \par finite strip thickness", Proc. \par IEEE, 65, 1977, pp. 1611-1612. \par \par This material is nicely summarized \par in T. C. Edwards, "Foundations of\par Microstrip Circuit Design," John \par Wiley, New York, 1981, reprinted 1987.\par \par (Watch out for Edward's error in \par Equation 3.52b, where he omits a \par ln() function.)} .TXT 34 0 7 0 0 Cg a15.250000,15.250000,15 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Variables used:} .TXT 4 2 8 0 0 Cg a53.250000,53.250000,217 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard h Trace height above ground (in.)\par \par w Trace width (in.)\par \par t Trace thickness (in.)\par \par er Relative permittivity of material between trace\par and ground plane (dimensionless) \par \par x Trace length (in.)} .TXT 38 -2 10 0 0 Cg a43.250000,43.250000,75 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Effective relative permittivity\par as a function of microstrip trace geometry:} .TXT 6 2 11 0 0 Cg a25.250000,25.250000,25 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard For skinny traces (w < h)} .EQN 6 -2 12 0 0 {0:E_skny}NAME({0:h}NAME,{0:w}NAME,{0:er}NAME):({0:er}NAME+1)/(2)+(({0:er}NAME-1)/(2))*(((1+(12*{0:h}NAME)/({0:w}NAME)))^(-.500)+.04*((1-({0:w}NAME)/({0:h}NAME)))^(2)) .TXT 12 2 13 0 0 Cg a23.250000,23.250000,23 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard For wide traces (w > h)} .EQN 4 3 14 0 0 {0:E_wide}NAME({0:h}NAME,{0:w}NAME,{0:er}NAME):({0:er}NAME+1)/(2)+(({0:er}NAME-1)/(2))*((1+(12*{0:h}NAME)/({0:w}NAME)))^(-.500) .TXT 14 -5 15 0 0 Cg a68.250000,68.250000,68 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Composite formula picks skinny or wide model depending on w/h ratio:} .EQN 6 2 16 0 0 {0:E_temp}NAME({0:h}NAME,{0:w}NAME,{0:er}NAME):{0:if}NAME({0:w}NAME>{0:h}NAME,{0:E_wide}NAME({0:h}NAME,{0:w}NAME,{0:er}NAME),{0:E_skny}NAME({0:h}NAME,{0:w}NAME,{0:er}NAME)) .TXT 6 -2 17 0 0 Cg a50.250000,50.250000,50 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Special adjustment to account for trace thickness:} .EQN 6 7 18 0 0 {0:EEFF}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME):{0:E_temp}NAME({0:h}NAME,{0:w}NAME,{0:er}NAME)-(({0:er}NAME-1)*(({0:t}NAME)/({0:h}NAME)))/(4.6*\(({0:w}NAME)/({0:h}NAME))) .TXT 18 -5 19 0 0 Cg a50.250000,50.250000,173 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard When w/h is skinny, you get the average of the PCB permittivity, er, and the permittivity of air.\par When w/h is wide, (the trace is very close to the\par ground plane) you get er.} .TXT 26 -2 21 0 0 Cg a36.250000,36.250000,63 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Effective trace width as a function \par of other parameters (in.):} .TXT 6 2 22 0 0 Cg a28.250000,28.250000,28 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard For skinny traces (2{\f1 p}w < h)} .EQN 6 7 23 0 0 {0:WE_skny}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME):{0:w}NAME+(1.25*{0:t}NAME)/({0:\p}NAME)*(1+{0:ln}NAME((4*{0:\p}NAME*{0:w}NAME)/({0:t}NAME))) .TXT 10 -7 24 0 0 Cg a25.250000,25.250000,25 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard For wide traces (2{\f1 p}w > h)} .EQN 6 7 25 0 0 {0:WE_wide}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME):{0:w}NAME+(1.25*{0:t}NAME)/({0:\p}NAME)*(1+{0:ln}NAME((2*{0:h}NAME)/({0:t}NAME))) .TXT 12 -9 26 0 0 Cg a68.250000,68.250000,68 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Composite formula picks skinny or wide model depending on w/h ratio:} .EQN 6 5 27 0 0 {0:WE}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME):{0:if}NAME({0:w}NAME>({0:h}NAME)/(2*{0:\p}NAME),{0:WE_wide}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME),{0:WE_skny}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME)) .TXT 58 -5 29 0 0 Cg a39.250000,39.250000,62 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard Characteristic impedance as a function \par of trace geometry ({ \f1 W}):} .TXT 6 0 30 0 0 Cg a40.250000,40.250000,78 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Accuracy of better than 2 percent is \par obtained under the following conditions:} .TXT 8 2 31 0 0 Cg a18.250000,18.250000,56 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard 0 < t/h < 0.2\par 0.1 < w/h < 20 \par 0 < er < 16\par } .TXT 12 0 32 0 0 Cg a25.250000,25.250000,25 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard For skinny traces (w < h)} .EQN 6 4 33 0 0 {0:ZMS_skny}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME):60*{0:ln}NAME((8*{0:h}NAME)/({0:WE}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME))+({0:WE}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME))/(4*{0:h}NAME)) .TXT 12 -4 34 0 0 Cg a23.250000,23.250000,23 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard For wide traces (w > h)} .EQN 6 -2 35 0 0 {0:ZMS_wide}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME):(120*{0:\p}NAME)/(({0:WE}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME))/({0:h}NAME)+1.393+.667*{0:ln}NAME(({0:WE}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME))/({0:h}NAME)+1.444)) .TXT 16 0 36 0 0 Cg a68.250000,68.250000,68 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Composite formula picks skinny or wide model depending on w/h ratio:} .EQN 8 1 37 0 0 {0:ZMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME):({0:if}NAME({0:w}NAME>{0:h}NAME,{0:ZMS_wide}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME),{0:ZMS_skny}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME)))/(\({0:EEFF}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME))) .TXT 30 -1 39 0 0 Cg a37.250000,37.250000,37 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Microstrip propagation delay (s/in.):} .EQN 6 9 40 0 0 {0:PMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME):84.72*(10)^(-12)*\({0:EEFF}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME)) .TXT 12 -9 41 0 0 Cg a29.250000,29.250000,29 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Inductance of microstrip (H):} .EQN 6 5 42 0 0 {0:LMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:x}NAME):{0:PMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,1.)*{0:ZMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,1.)*{0:x}NAME .TXT 4 -3 43 0 0 Cg a38.250000,38.250000,76 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard (Use a dummy er value of 1. It doesn't\par matter for inductance calculations.)} .TXT 10 -2 44 0 0 Cg a30.250000,30.250000,30 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Capacitance of microstrip (F):} .EQN 6 9 45 0 0 {0:CMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME,{0:x}NAME):({0:PMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME))/({0:ZMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME,{0:er}NAME))*{0:x}NAME .TXT 58 -9 47 0 0 Cg a67.250000,67.250000,104 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard ___________________________________________________________________ \par Example microstrip wire calculations} .TXT 6 2 48 0 0 Cg a25.250000,25.250000,25 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Height above ground (in.)} .EQN 0 34 49 0 0 {0:H}NAME:.006 .TXT 4 -34 50 0 0 Cg a20.250000,20.250000,20 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Width of trace (in.)} .EQN 0 34 51 0 0 {0:W}NAME:.008 .TXT 4 -34 52 0 0 Cg a24.250000,24.250000,24 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Thickness of trace (in.)} .EQN 0 34 53 0 0 {0:T}NAME:.00137 .TXT 0 14 54 0 0 Cg a16.250000,16.250000,29 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard (1-oz copper plating weight)} .TXT 4 -48 55 0 0 Cg a20.250000,20.250000,20 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Length of wire (in.)} .EQN 0 34 56 0 0 {0:X}NAME:11.000 .TXT 6 -34 57 0 0 Cg a22.250000,22.250000,74 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Relative electric\par permeability (affects \par capacitance, but not \par inductance)} .EQN 0 34 58 0 0 {0:er}NAME:4.5 .TXT 12 -36 59 0 0 Cg a14.500000,14.500000,14 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard Impedance ({\f1 W}):} .EQN 6 9 16132 0 0 {0:ZMSTRIP}NAME({0:H}NAME,{0:W}NAME,{0:T}NAME,{0:er}NAME)={0}?_n_u_l_l_ .TXT 4 -9 61 0 0 Cg a21.250000,21.250000,21 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Total inductance (H):} .EQN 4 9 16133 0 0 {0:LMSTRIP}NAME({0:H}NAME,{0:W}NAME,{0:T}NAME,{0:X}NAME)={0}?_n_u_l_l_ .TXT 4 -9 63 0 0 Cg a18.250000,18.250000,18 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Same result in nH:} .EQN 5 9 16134 0 0 {0:LMSTRIP}NAME({0:H}NAME,{0:W}NAME,{0:T}NAME,{0:X}NAME)*(10)^(9)={0}?_n_u_l_l_ .TXT 4 -9 65 0 0 Cg a23.250000,23.250000,23 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Inductance per in. (H):} .EQN 4 9 16135 0 0 {0:LMSTRIP}NAME({0:H}NAME,{0:W}NAME,{0:T}NAME,1)={0}?_n_u_l_l_ .TXT 8 -9 67 0 0 Cg a22.250000,22.250000,22 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Total capacitance (F):} .EQN 4 9 16136 0 0 {0:CMSTRIP}NAME({0:H}NAME,{0:W}NAME,{0:T}NAME,{0:er}NAME,{0:X}NAME)={0}?_n_u_l_l_ .TXT 4 -9 69 0 0 Cg a18.250000,18.250000,18 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Same result in pF:} .EQN 5 9 16137 0 0 {0:CMSTRIP}NAME({0:H}NAME,{0:W}NAME,{0:T}NAME,{0:er}NAME,{0:X}NAME)*(10)^(12)={0}?_n_u_l_l_ .TXT 4 -9 71 0 0 Cg a24.250000,24.250000,24 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Capacitance per in. (F):} .EQN 4 9 16138 0 0 {0:CMSTRIP}NAME({0:H}NAME,{0:W}NAME,{0:T}NAME,{0:er}NAME,1)={0}?_n_u_l_l_ .TXT 8 -9 74 0 0 Cg a17.250000,17.250000,17 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Tolerance effects} .EQN 5 4 75 0 0 {0:ZMSTRIP_TOL}NAME({0:h}NAME,{0:htol}NAME,{0:w}NAME,{0:wtol}NAME,{0:t}NAME,{0:er}NAME,{0:ertol}NAME):({3,1}ö{0:ZMSTRIP}NAME({0:h}NAME-{0:htol}NAME,{0:w}NAME+{0:wtol}NAME,{0:t}NAME,{0:er}NAME+{0:ertol}NAME)ö{0:ZMSTRIP}NAME({0:h}NAME,{0:w}NAME,{0:t}NAME, {0:er}NAME)ö{0:ZMSTRIP}NAME({0:h}NAME+{0:htol}NAME,{0:w}NAME-{0:wtol}NAME,{0:t}NAME,{0:er}NAME-{0:ertol}NAME)) .EQN 9 0 16141 0 0 {0:\a}NAME:{0:ZMSTRIP_TOL}NAME(.007,.002,.011,.002,.0022,4.5,.1) .EQN 6 0 16142 0 0 {0:\a}NAME={0}?_n_u_l_l_ .EQN 19 0 16140 0 0 {0:REFL}NAME({0:x}NAME,{0:z}NAME):({3,1}ö({0:z}NAME-({0:x}NAME)[(2))/({0:z}NAME+({0:x}NAME)[(2))ö({0:z}NAME-({0:x}NAME)[(1))/({0:z}NAME+({0:x}NAME)[(1))ö({0:z}NAME-({0:x}NAME)[(0))/({0:z}NAME+({0:x}NAME)[(0))) .EQN 19 -1 16143 0 0 {0:REFL}NAME({0:\a}NAME,50)={0}?_n_u_l_l_