.MCAD 304020000 1 74 16137 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 1.197917 1.200000 1.200000 0
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.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
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.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 a40.250000,40.250000,40
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard DC RESISTANCE OF 
COPPER WIRES AND TRACES}
.TXT 0 49 2 0 0
Cg a16.250000,16.250000,16
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard file: resist.mcd}
.TXT 6 -49 3 0 0
Cg a52.250000,52.250000,869
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Conversion formulas 
included in this spreadsheet:\par \par   Diameter to AWG                      
AWG()\par   AWG to diameter                      DIAMETER()\par   
Thickness to copper plating weight   CPW()\par   Copper plating weight 
to thickness   THICKNESS()\par \par             \par Resistance 
formulas included in this spreadsheet:\par \par   DC resistance of 
round wires\par     From diameter                   RROUND()\par     
From AWG wire size              RROUND_AWG()\par     At room 
temperature only        RROUND_RT()\par \par   DC resistance of 
printed circuit board traces\par     From trace thickness and width  
RTRACE()\par     Using copper plating weight     RTRACE_CPW()\par     
At room temperature only        RTRACE_RT() \par                              
                       \par   DC resistance of power or ground planes        
\par     Using thickness and via diameter RPLANE()\par     Using 
copper plating weight     RPLANE_CPW()}
.TXT 50 0 4 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:}
.EQN 3 46 16129 0 0
{0:\r}NAME:6.787*(10)^(-7)
.TXT 1 -44 6 0 0
Cg a29.000000,29.000000,29
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard {\f1 r}  Bulk resistivity of copper}
.TXT 4 3 7 0 0
Cg a61.250000,61.250000,378
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard This coefficient is 
slightly different from the bulk\par resistivity of pure copper 
(6.58E+07) owing to the \par annealing process used in making wire, 
and chemical \par imperfections in the  copper used for making 
practical wires.\par                      \par In practice, the 
resistance of two wires making up a twisted \par pair may often be 
matched as well as 10%, but almost \par never as well as 1%.}
.TXT 18 -3 8 0 0
Cg a35.750000,35.750000,36
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard {\f1 d}{\f1 r} Thermal coefficient of resistance}
.EQN 0 44 9 0 0
{0:\d\r}NAME:.0039
.TXT 4 -41 10 0 0
Cg a65.250000,65.250000,329
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard If the resistance of a copper wire is R at room\par temperature, 
then at a temperature 1\\248C higher it will \par be R(1 + {\f1 d}{\f1 r}
).  This coefficient applies to standard annealed \par copper wires.  
The coefficient for pure copper in its bulk state varies slightly.\par 
\par Over a temperature range 0-70\\248C the resistance of copper \par 
wires varies 28%.}
.TXT 18 -3 12 0 0
Cg a59.250000,59.250000,234
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard x    Length of wire 
(in.)\par      (or separation between contact points on ground plane)
\par \par d    Diameter of wire (in.)\par      (or diameter of contact 
point on ground plane)\par \par AWG  American wire gauge (English 
units)\par \par temp Temperature (\\248C)}
.TXT 20 0 13 0 0
Cg a56.250000,56.250000,203
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard w    Width of printed 
circuit board trace (in.)\par \par t    Thickness of printed circuit 
board trace (in.)\par \par cpw  Thickness of printed circuit board 
traces, in units\par      of copper plating weight (oz/ft\\253)   }
.TXT 18 -2 14 0 0
Cg a36.250000,36.250000,66
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Conversions between 
American \par Wire Gauge (AWG) and diameter (in.):}
.EQN 2 37 15 0 0
{0:DIAMETER}NAME({0:awg}NAME):(10)^(-(({0:awg}NAME+10)/(20)))
.EQN 7 0 16130 0 0
{0:AWG}NAME({0:d}NAME):-10-20*{0:log}NAME({0:d}NAME)
.TXT 5 -37 17 0 0
Cg a31.500000,31.500000,52
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard General formula for \par resistance of a round wire ({\f1 W}):}
.EQN 8 21 16131 0 0
{0:RROUND}NAME({0:d}NAME,{0:x}NAME,{0:temp}NAME):(4*{0:\r}NAME*{0:x}NAME)/({0:\p}NAME*({0:d}NAME)^(2))*(1+({0:temp}NAME-20)*{0:\d\r}NAME)
.TXT 10 -21 19 0 0
Cg a37.250000,37.250000,74
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a round wire specified \par by AWG size instead of 
diameter ({\f1 W}):}
.EQN 8 9 20 0 0
{0:RROUND_AWG}NAME({0:awg}NAME,{0:x}NAME,{0:temp}NAME):{0:RROUND}NAME({0:DIAMETER}NAME({0:awg}NAME),{0:x}NAME,{0:temp}NAME)
.TXT 6 -9 21 0 0
Cg a27.250000,27.250000,53
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a round wire \par at room temperature  ({\f1 W}):}
.EQN 7 20 16132 0 0
{0:RROUND_RT}NAME({0:d}NAME,{0:x}NAME):{0:RROUND}NAME({0:d}NAME,{0:x}NAME,20)
.TXT 12 -20 24 0 0
Cg a30.250000,30.250000,76
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard Conversion between 
thickness, \par t (in.) and copper plating \par weight, cpw (oz):}
.EQN 2 37 16133 0 0
{0:CPW}NAME({0:t}NAME):({0:t}NAME)/(.00137)
.EQN 7 0 16135 0 0
{0:THICKNESS}NAME({0:cpw}NAME):.00137*{0:cpw}NAME
.TXT 7 -37 27 0 0
Cg a18.500000,18.500000,35
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a \par circuit trace ({\f1 W}):}
.EQN 7 18 16136 0 0
{0:RTRACE}NAME({0:w}NAME,{0:t}NAME,{0:x}NAME,{0:temp}NAME):({0:x}NAME*{0:\r}NAME)/({0:w}NAME*{0:t}NAME)*(1+({0:temp}NAME-20)*{0:\d\r}NAME)
.TXT 9 -18 29 0 0
Cg a43.500000,43.500000,76
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a trace specified \par by plating weight instead 
of thickness ({\f1 W}):}
.EQN 8 9 30 0 0
{0:RTRACE_CPW}NAME({0:w}NAME,{0:cpw}NAME,{0:x}NAME,{0:temp}NAME):{0:RTRACE}NAME({0:w}NAME,{0:THICKNESS}NAME({0:cpw}NAME),{0:x}NAME,{0:temp}NAME)
.TXT 6 -9 31 0 0
Cg a30.250000,30.250000,55
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a circuit trace \par at room temperature ({\f1 W}):}
.EQN 7 18 16137 0 0
{0:RTRACE_RT}NAME({0:w}NAME,{0:t}NAME,{0:x}NAME):{0:RTRACE}NAME({0:w}NAME,{0:t}NAME,{0:x}NAME,20)
.TXT 50 -18 34 0 0
Cg a43.500000,43.500000,43
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a power or ground plane  ({\f1 W}):}
.TXT 4 0 35 0 0
Cg a64.250000,64.250000,900
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard When using long, 
skinny traces or wires, the approximations \par above work extremely 
well.  Each formula assumes a uniform \par distribution of current 
throughout the conducting body, for \par which resistance is directly 
proportional to length.  \par \par Currents circulating in a large 
ground or power plane are \par not uniform.  Consequently, the 
resistance measured between \par two points on a ground or power plane 
is not directly \par proportional to the separation between 
measurement points.\par \par The following equation models the 
resistance between two \par contact points on a ground plane.  This 
model assumes each\par contact point touches the ground plane over 
some finite \par area.  The approximate diameter of the contact point 
determines \par the overall resistance.\par \par If the contact points 
lie near any edge of the plane, the \par resistance between them may 
go up by a factor of 2.   \par The resistance near corners may rise 
even higher.}
.TXT 33 2 36 0 0
Cg a52.250000,52.250000,239
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}}\plain\cf1\fs20 \pard d1    Diameter of 1st 
contact point (in.)\par d2    Diameter of 2nd contact point (in.)\par 
t     Thickness of plane (in.)\par cpw   Thickness of plane, copper 
plating weight (oz)\par x     Separation between contact points (in.)
\par temp  Temperature (\\248C)}
.TXT 13 -2 37 0 0
Cg a42.500000,42.500000,42
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a power or ground plane ({\f1 W}):}
.EQN 6 0 38 0 0
{0:RPLANE}NAME({0:d1}NAME,{0:d2}NAME,{0:t}NAME,{0:x}NAME,{0:temp}NAME):({0:\r}NAME)/(2*{0:\p}NAME*{0:t}NAME)*({0:ln}NAME((2*{0:x}NAME)/({0:d1}NAME))+{0:ln}NAME((2*{0:x}NAME)/({0:d2}NAME)))*(1+({0:temp}NAME-20)*{0:\d\r}NAME)
.TXT 14 0 39 0 0
Cg a48.250000,48.250000,92
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Courier;}{\f1\fcharset2\fnil Symbol;}}\plain\cf1\fs20 
\pard Resistance of a power or ground plane specified \par by plating 
weight instead of thickness ({\f1 W}):}
.EQN 8 0 40 0 0
{0:RPLANE_CPW}NAME({0:d1}NAME,{0:d2}NAME,{0:cpw}NAME,{0:x}NAME,{0:temp}NAME):{0:RPLANE}NAME({0:d1}NAME,{0:d2}NAME,{0:THICKNESS}NAME({0:cpw}NAME),{0:x}NAME,{0:temp}NAME)