.MCAD 304020000 1 74 16139 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=3 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 1.197917 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=1257786104 .CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=1257786104 .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 a28.250000,28.250000,27 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard INDUCTANCE OF CIRCULAR LOOP} .TXT 0 51 16137 0 0 Cg a19.250000,19.250000,19 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard file: circular.mcd} .TXT 6 -51 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 a46.250000,46.250000,210 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Inductance of circular wire loop LCIRC()\par Impedance magnitude of inductor at\par one frequency XLF()\par Impedance magnitude of inductor as\par seen by rising edge XLR()} .EQN 10 35 16139 0 0 { 26 33 11040 0 8 457 589}{66} !1!*!!!$5Z.[!!<7*3!!!!!!$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!k!!+u!!!N!1#e!q!!!!9S!!!!!!+u!!!#!1#e!a!!!!&L!1!( !!!!Ku&L!!!!!!!!!!+u!!!N!1&K"C!!!0<9!!!"!!!!!!!!!A+u!!!N!1)1#%!!!#+x!a!M!0DQ(O![!#(!*._#U!%!!!!!!!|#G&V-OH34}*G1WH225"22E"$!$6k/=!u!&+u-Y!O!%<7/=!k!%<7(/!u!$6k(/!k!!+u!!!#!1#e!a!!!#4(LVIu!!!!!A#f!!+u!!!#!1#e!Q!!!"G-"3!!!"1E$w&O"X>|)q+y!!!!!A#f!!+u!!!N!1.['M!!!$&U0O$P!b&K!a!!!!!!0OGO"y*<4M*H 3K$y&R524M.{3KK$4+<7(o!Y!%<7/=!O!%<7*S!K!(9Q(o!Y!%<7(/!O!&+u/=!u!!+u!!!#!1#e!a!!!#4(LVIu!!!!!A#f!!G-!!!G"#Iq$'#dLVLV!!!)!!!!A1:?$$!0)"4+!!!!(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#k!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#l!#+u!!!F!R!!;%17"]4,!Q>0!r!+BC.w"p)6'm>]!t); 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!0<9!!!"!!!!!!!!!A+u!!!N!14'#E!!!#.^!q!s!l?&/M-p"X6o?M:M!kIz0_-c"S+u!!!N!1+u!a!!!0!""#!%!!!!Iq#l!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH"#!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"3!/!!!!'=)6!&?!=y:P!k.d1!-Y"XG1;E:Q!j1J!a!!!#DH!a!%!!!!Iq#k!!+u!!#U!14' !a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A.[!1!!!!!!!!&O!!!!(_#k!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#l!!G-!!!F!Q.[1!-O"XG19Q:P!i?&0_->"X<;6k9U!!!!(_#i!!+u!!#U!11A!a!!!0!""3!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!11A"C!!!0<9!!!"!!!!!!!!!A+u!!!N!14'#E!!!#.^!q!{ !i!*/}-4"X._5):E!h#n.K-%"S+u!!!N!1+u!a!!!0!""#!%!!!!Iq#l!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH"#!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"3!/!!!!'=)6!%Iu3E:?!g6t-9,|"W._1Q:3!fG6!a!!!#DH!a!%!!!!Iq#k!!+u!!#U!14'!a!!!#DH!Q!%!!!!(_#g!!6k!!#_!A.[!1!!!!!! !!&O!!!!(_#k!!6k!!#_!A!!!1!!!!!!!!&O!!!!(_#l!!G-!!!F!Q.[+u,u"VAe0O:*!f<@)a,o"UG1/m9U!!!!(_#i!!+u!!#U!11A!a!!!0!""3!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!11A"C!!!0<9!!!"!!!!!!!!!A+u!!!N!14'#E!!!#.^!q!O!f40'},n"U._/m9r!f40%i,p"S+u!!!N!1+u!a!! !0!""#!%!!!!Iq#l!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH"#!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"3!G!!!!'=)B!%)5BC:P!l?&4w-m"[<;>[;4!k9Z?--`"_)5[39!jDM?]-F".+y6;3:!gDM@/+y!!!!(_#i!!+u!!#U!16k!a!!!0!""S!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N!16k"C!!!0<9!!!"!!!!!!!!!A+u!!!N!19Q'm!!!#.^$'"0".4+1!3=!f!'@o,X".DK)a3F!c.aBC,."/6o "S3Q!p<6m"c._!!!!(_#i!!+u!!#U!16k!a!!!0!""S!%!!!!(_#h!!+u!!!N!1&K"C!!!0<9!q!"!!!!!!!!!A+u!!!N !16k"C!!!0<9!!!"!!!!!!!!!A+u!!!N!19Q"C!!!#.^!A#\!ODK.[,z!a+u!!!N!1+u!a!!!0!""C!%!!!!Iq#n!!+u!!!N!1)1!a!!!#DH!A!)!!!!KU&P!!#e!!!!!!!#!a!!!#DH"C!)!!!!KU&K!!#e!!!!!!!#!a!!!#DH"S!)!!!!'=)3!!1F%i.:")DJ!a!!!#DH!a!%!!!!Iq#m!!+u!!#U!19Q!a!!!#DH!Q!+!!!!'M1P!!<7 LVLVLG#e!!!!!!+u!!!#!1#e!a!!!#DH!!!$!!!!!!#dLVLV!1!!!!!!!a!!!!&L!1!%!!!!(_#e!!)1!!!!!!4."34."34."B6r!!+u  .TXT 4 -37 5 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 7 0 0 Cg a31.250000,31.250000,59 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard d Diameter of wire (in.)\par \par x Diameter of wire loop (in.)} .TXT 30 -2 8 0 0 Cg a28.250000,28.250000,28 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Inductance of wire loop (H):} .EQN 4 14 9 0 0 {0:LCIRC}NAME({0:d}NAME,{0:x}NAME):1.56*(10)^(-8)*{0:x}NAME*({0:ln}NAME((8*{0:x}NAME)/({0:d}NAME))-2) .TXT 10 -12 10 0 0 Cg a42.250000,42.250000,111 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard A loop of 24-gauge wire the size of the \par loop between your thumb and forefinger has \par about 100 nH of inductance.} .EQN 2 47 16131 0 0 {0:LCIRC}NAME(.01,1.3)={0}?_n_u_l_l_ .TXT 6 -47 11 0 0 Cg a44.250000,44.250000,129 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Changing the wire diameter from AWG 24 \par to AWG 14 makes little difference. The log \par function is rather insensitive to wire size.} .EQN 1 47 16132 0 0 {0:LCIRC}NAME(.1,1.3)={0}?_n_u_l_l_ .TXT 29 -49 12 0 0 Cg a51.500000,51.500000,51 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard Impedance magnitude of inductor at frequency f ({\f1 W}):} .TXT 4 2 13 0 0 Cg a20.250000,20.250000,42 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard l Inductance (H) \par \par f Frequency (Hz)} .EQN 8 22 14 0 0 {0:XLF}NAME({0:l}NAME,{0:f}NAME):2*{0:\p}NAME*{0:f}NAME*{0:l}NAME .TXT 4 -22 15 0 0 Cg a32.250000,32.250000,57 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard The impedance, at 100 MHz, of a \par 100-nH inductor is 62 {\f1 W}.} .EQN 6 22 16135 0 0 {0:XLF}NAME(100*(10)^(-9),(10)^(8))={0}?_n_u_l_l_ .TXT 4 -24 17 0 0 Cg a59.500000,59.500000,59 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard Impedance magnitude of inductor as seen by rising edge ({\f1 W}):} .TXT 4 2 18 0 0 Cg a27.250000,27.250000,51 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard l Inductance (H) \par \par tr 10-90% rise time (s)\par } .EQN 10 23 19 0 0 {0:XLT}NAME({0:l}NAME,{0:tr}NAME):({0:\p}NAME*{0:l}NAME)/({0:tr}NAME) .TXT 8 -23 20 0 0 Cg a45.250000,45.250000,75 {\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0 \fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 \pard The impedance, as seen by a 5-ns rising edge,\par of a 100-nH inductor is 62 {\f1 W}.} .EQN 7 23 16136 0 0 {0:XLT}NAME(100*(10)^(-9),5*(10)^(-9))={0}?_n_u_l_l_