Re: [SI-LIST] : via current carrying capacity

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From: jrbarnes@lexmark.com
Date: Fri Jan 26 2001 - 09:57:55 PST


Sean,
Here is a set of guidelines that I created for our printed-circuit board layout
folks last August. It is based on a literature search & study that I started in
July 1999, when my boss assigned me the development of a controller card using a
Pentium-class processor. I located about 56 print and Internet sources with
information on the ampacity (current-carrying capacity) of printed circuit board
(PCB) traces. From this mass of data I came up with the following equations for
traces made from 0.5 to 3 ounces/square-foot copper:
* For external traces I = 1500*thickness^0.72*width^0.75*deltaT^0.45,
* For internal traces I = 7500*thickness^0.72*width^0.75*deltaT^0.45,
   where:
* I is the permissible current in Amps.
* thickness in inches.
* width in inches.
* deltaT is permissible temperature rise in degrees C

These equations are pretty close to those derived by John McHardy and Mahendra
Gandhi, and by Doug
Brooks, from the Institute of Printed Circuits data (see references at bottom of
 note). I couldn't
find much information for copper heavier than 4 ounces/square-foot, but above
about 3 ounces/square-
foot the exponent for thickness seemed to drop to 0.5-0.6 or so.

The note that I am including was in response for a request "Just tell me how
much current I can
safely run through our standard vias!"

                                              John Barnes Advisory Engineer
                                              Lexmark International

Lonnie,
The short answer to your question:

                     Ampacity (Amps)
            ----------------------------------------
Via/PTH 2-sided Multilayer 2-sided Multilayer
Diameter Via Via PTH PTH
-------- ------- ---------- ------- ----------
0.012" 1.01A 1.01A 1.01A 1.01A
0.018" 1.37A 1.37A 1.37A 1.37A
0.024" 1.70A 1.70A 1.70A 1.70A
0.039" 2.44A 2.44A 2.44A 1.77A <== limited by spokes to
inner planes

When I looked at my notes I remembered some additional factors that I had
forgotten in my off-the-cuff answer at lunch time, which I included in these
calculations. The basic ampacity is a function of the:
* Copper thickness.
* Copper width.
* Permissible temperature rise.
* Whether the copper is on the exterior of the card, so that air can carry heat
away, or on the interior where it is
   thermally insulated in all directions.

Vias also must consider the cross-section between the barrel and the pads/planes
as possible limiting factors. Plated-through-holes for components have thermal
vias where they tie into planes, and the 0.015" wide spokes become the limiting
factors for large holes.

ampacity.wq1 John Barnes 8/28/2000
ampacity of printed circuit board lands, vias, plated-through holes

external I = 1500*thickness^0.72*width^0.75*deltaT^0.45
internal I = 7500*thickness^0.72*width^0.75*deltaT^0.45
I in Amps
thickness in inches
width in inches
deltaT in degrees C

AMPACITY OF TRACES (based on Lexmark ES 43H2362)

ASSUMPTIONS:
Internal 0.5 ounce/ft^2 copper >= 0.00050 inches thick
Internal 1 ounce/ft^2 copper >= 0.00100 inches thick
Internal 2 ounce/ft^2 copper >= 0.00200 inches thick
Internal 3 ounce/ft^2 copper >= 0.00300 inches thick
External 0.5 ounce/ft^2 copper >= 0.00068 inches thick
External 1 ounce/ft^2 copper >= 0.00135 inches thick
External 2 ounce/ft^2 copper >= 0.00270 inches thick
External 3 ounce/ft^2 copper >= 0.00405 inches thick
temperature rise = 10 C

trace 0.5 ounce 0.5 ounce 1 ounce 1 ounce 2 ounce 2 ounce 3 ounce 3
ounce
width external internal external internal external internal external
internal
(inches) (Amps) (Amps) (Amps) (Amps) (Amps) (Amps) (Amps)
(Amps)
-------- --------- --------- -------- -------- -------- -------- -------- --------

   0.001 0.12 0.05 0.20 0.08 0.34 0.14 0.45
0.18
   0.002 0.21 0.08 0.34 0.14 0.57 0.23 0.76
0.31
   0.003 0.28 0.11 0.47 0.19 0.77 0.31 1.03
0.41
   0.004 0.35 0.14 0.58 0.23 0.95 0.38 1.27
0.51
   0.005 0.41 0.17 0.68 0.27 1.12 0.45 1.51
0.61
   0.006 0.48 0.19 0.78 0.32 1.29 0.52 1.73
0.70
   0.007 0.53 0.21 0.88 0.35 1.45 0.58 1.94
0.78
   0.008 0.59 0.24 0.97 0.39 1.60 0.64 2.14
0.86
   0.009 0.64 0.26 1.06 0.43 1.75 0.70 2.34
0.94
   0.010 0.70 0.28 1.15 0.46 1.89 0.76 2.53
1.02
   0.011 0.75 0.30 1.23 0.50 2.03 0.82 2.72
1.10
   0.012 0.80 0.32 1.32 0.53 2.17 0.87 2.90
1.17
   0.013 0.85 0.34 1.40 0.56 2.30 0.93 3.08
1.24
   0.014 0.90 0.36 1.48 0.60 2.43 0.98 3.26
1.31
   0.015 0.94 0.38 1.56 0.63 2.56 1.03 3.43
1.38
   0.016 0.99 0.40 1.63 0.66 2.69 1.08 3.60
1.45
   0.017 1.04 0.42 1.71 0.69 2.82 1.13 3.77
1.52
   0.018 1.08 0.44 1.78 0.72 2.94 1.18 3.93
1.59
   0.019 1.13 0.45 1.86 0.75 3.06 1.23 4.10
1.65
   0.020 1.17 0.47 1.93 0.78 3.18 1.28 4.26
1.72
   0.021 1.22 0.49 2.00 0.81 3.30 1.33 4.42
1.78
   0.022 1.26 0.51 2.07 0.84 3.42 1.38 4.57
1.84
   0.023 1.30 0.52 2.14 0.86 3.53 1.42 4.73
1.90
   0.024 1.34 0.54 2.21 0.89 3.65 1.47 4.88
1.97
   0.025 1.39 0.56 2.28 0.92 3.76 1.51 5.03
2.03
   0.026 1.43 0.57 2.35 0.95 3.87 1.56 5.18
2.09
   0.027 1.47 0.59 2.42 0.97 3.98 1.60 5.33
2.15
   0.028 1.51 0.61 2.48 1.00 4.09 1.65 5.48
2.21
   0.029 1.55 0.62 2.55 1.03 4.20 1.69 5.63
2.27
   0.030 1.59 0.64 2.62 1.05 4.31 1.74 5.77
2.33
   0.035 1.78 0.72 2.94 1.18 4.84 1.95 6.48
2.61
   0.040 1.97 0.79 3.25 1.31 5.35 2.15 7.16
2.88
   0.045 2.15 0.87 3.55 1.43 5.84 2.35 7.82
3.15
   0.050 2.33 0.94 3.84 1.55 6.32 2.55 8.47
3.41
   0.055 2.50 1.01 4.12 1.66 6.79 2.74 9.09
3.66
   0.060 2.67 1.08 4.40 1.77 7.25 2.92 9.71
3.91
   0.065 2.84 1.14 4.67 1.88 7.70 3.10 10.31
4.15
   0.070 3.00 1.21 4.94 1.99 8.14 3.28 10.90
4.39
   0.075 3.16 1.27 5.20 2.10 8.57 3.45 11.48
4.62
   0.080 3.32 1.34 5.46 2.20 8.99 3.62 12.04
4.85
   0.085 3.47 1.40 5.71 2.30 9.41 3.79 12.60
5.08
   0.090 3.62 1.46 5.97 2.40 9.83 3.96 13.16
5.30
   0.095 3.77 1.52 6.21 2.50 10.23 4.12 13.70
5.52
   0.100 3.92 1.58 6.46 2.60 10.63 4.28 14.24
5.74
   0.110 4.21 1.70 6.93 2.79 11.42 4.60 15.29
6.16
   0.120 4.49 1.81 7.40 2.98 12.19 4.91 16.32
6.58
   0.130 4.77 1.92 7.86 3.17 12.95 5.22 17.33
6.98
   0.140 5.04 2.03 8.31 3.35 13.69 5.51 18.33
7.38
   0.150 5.31 2.14 8.75 3.52 14.41 5.81 19.30
7.77
   0.160 5.58 2.25 9.18 3.70 15.13 6.09 20.26
8.16
   0.170 5.83 2.35 9.61 3.87 15.83 6.38 21.20
8.54
   0.180 6.09 2.45 10.03 4.04 16.52 6.66 22.13
8.91
   0.190 6.34 2.55 10.45 4.21 17.21 6.93 23.04
9.28
   0.200 6.59 2.66 10.86 4.37 17.88 7.20 23.95
9.65
   0.210 6.84 2.75 11.26 4.54 18.55 7.47 24.84
10.01
   0.220 7.08 2.85 11.66 4.70 19.21 7.74 25.72
10.36
   0.230 7.32 2.95 12.06 4.86 19.86 8.00 26.59
10.71
   0.240 7.56 3.04 12.45 5.01 20.50 8.26 27.45
11.06
   0.250 7.79 3.14 12.83 5.17 21.14 8.52 28.31
11.40
   0.260 8.02 3.23 13.22 5.32 21.77 8.77 29.15
11.74
   0.270 8.25 3.33 13.60 5.48 22.40 9.02 29.99
12.08
   0.280 8.48 3.42 13.97 5.63 23.02 9.27 30.82
12.42
   0.290 8.71 3.51 14.35 5.78 23.63 9.52 31.64
12.75
   0.300 8.93 3.60 14.72 5.93 24.24 9.76 32.46
13.07

-----------------------------------------------------------
AMPACITY OF VIAS (based on Lexmark ES 43H2362)

ASSUMPTIONS:
Vias plated solid to pads/planes
Vias plated >= 0.001" over 90% of barrel, voids <= 25% circumference
Internal 0.5 ounce/ft^2 copper >= 0.00050 inches thick
Internal 1 ounce/ft^2 copper >= 0.00100 inches thick
Internal 2 ounce/ft^2 copper >= 0.00200 inches thick
Internal 3 ounce/ft^2 copper >= 0.00300 inches thick
External 0.5 ounce/ft^2 copper >= 0.00068 inches thick
External 1 ounce/ft^2 copper >= 0.00135 inches thick
External 2 ounce/ft^2 copper >= 0.00270 inches thick
External 3 ounce/ft^2 copper >= 0.00405 inches thick
Barrel-to-pad/plane ampacity derated 20% for imperfect contact
temperature rise = 10 C

ampacity of external-to-external vias (double-sided cards)

via 0.5 ounce 1 ounce 2 ounce 3 ounce
diameter external external external external
(inches) (Amps) (Amps) (Amps) (Amps)
-------- --------- --------- -------- --------
   0.005 0.52 0.52 0.52 0.52
   0.006 0.60 0.60 0.60 0.60
   0.007 0.67 0.67 0.67 0.67
   0.008 0.74 0.74 0.74 0.74
   0.009 0.81 0.81 0.81 0.81
   0.010 0.88 0.88 0.88 0.88
   0.011 0.94 0.94 0.94 0.94
   0.012 1.01 1.01 1.01 1.01
   0.013 1.07 1.07 1.07 1.07
   0.014 1.13 1.13 1.13 1.13
   0.015 1.19 1.19 1.19 1.19
   0.016 1.25 1.25 1.25 1.25
   0.017 1.31 1.31 1.31 1.31
   0.018 1.37 1.37 1.37 1.37
   0.019 1.42 1.42 1.42 1.42
   0.020 1.48 1.48 1.48 1.48
   0.021 1.53 1.53 1.53 1.53
   0.022 1.59 1.59 1.59 1.59
   0.023 1.64 1.64 1.64 1.64
   0.024 1.70 1.70 1.70 1.70
   0.025 1.75 1.75 1.75 1.75
   0.026 1.80 1.80 1.80 1.80
   0.027 1.85 1.85 1.85 1.85
   0.028 1.90 1.90 1.90 1.90
   0.029 1.95 1.95 1.95 1.95
   0.030 2.00 2.00 2.00 2.00
   0.031 2.05 2.05 2.05 2.05
   0.032 2.10 2.10 2.10 2.10
   0.033 2.15 2.15 2.15 2.15
   0.034 2.20 2.20 2.20 2.20
   0.035 2.25 2.25 2.25 2.25
   0.036 2.30 2.30 2.30 2.30
   0.037 2.35 2.35 2.35 2.35
   0.038 2.39 2.39 2.39 2.39
   0.039 2.44 2.44 2.44 2.44
   0.040 2.49 2.49 2.49 2.49
   0.041 2.53 2.53 2.53 2.53
   0.042 2.58 2.58 2.58 2.58
   0.043 2.63 2.63 2.63 2.63
   0.044 2.67 2.67 2.67 2.67
   0.045 2.72 2.72 2.72 2.72
   0.046 2.76 2.76 2.76 2.76
   0.047 2.81 2.81 2.81 2.81
   0.048 2.85 2.85 2.85 2.85
   0.049 2.90 2.90 2.90 2.90
   0.050 2.94 2.94 2.94 2.94
   0.051 2.98 2.98 2.98 2.98
   0.052 3.03 3.03 3.03 3.03
   0.053 3.07 3.07 3.07 3.07
   0.054 3.12 3.12 3.12 3.12
   0.055 3.16 3.16 3.16 3.16
   0.056 3.20 3.20 3.20 3.20
   0.057 3.24 3.24 3.24 3.24
   0.058 3.29 3.29 3.29 3.29
   0.059 3.33 3.33 3.33 3.33
   0.060 3.37 3.37 3.37 3.37

ampacity of vias external-to-external, external-to-internal,
and internal-to-internal vias (multilayer cards)

via 0.5 ounce 1 ounce 2 ounce 3 ounce
diameter ext/int ext/int ext/int ext/int
(inches) (Amps) (Amps) (Amps) (Amps)
-------- --------- --------- -------- --------
   0.005 0.41 0.52 0.52 0.52
   0.006 0.60 0.60 0.60 0.60
   0.007 0.67 0.67 0.67 0.67
   0.008 0.74 0.74 0.74 0.74
   0.009 0.81 0.81 0.81 0.81
   0.010 0.88 0.88 0.88 0.88
   0.011 0.94 0.94 0.94 0.94
   0.012 1.01 1.01 1.01 1.01
   0.013 1.07 1.07 1.07 1.07
   0.014 1.13 1.13 1.13 1.13
   0.015 1.19 1.19 1.19 1.19
   0.016 1.25 1.25 1.25 1.25
   0.017 1.31 1.31 1.31 1.31
   0.018 1.37 1.37 1.37 1.37
   0.019 1.42 1.42 1.42 1.42
   0.020 1.48 1.48 1.48 1.48
   0.021 1.53 1.53 1.53 1.53
   0.022 1.59 1.59 1.59 1.59
   0.023 1.64 1.64 1.64 1.64
   0.024 1.70 1.70 1.70 1.70
   0.025 1.75 1.75 1.75 1.75
   0.026 1.80 1.80 1.80 1.80
   0.027 1.85 1.85 1.85 1.85
   0.028 1.90 1.90 1.90 1.90
   0.029 1.95 1.95 1.95 1.95
   0.030 2.00 2.00 2.00 2.00
   0.031 2.05 2.05 2.05 2.05
   0.032 2.10 2.10 2.10 2.10
   0.033 2.15 2.15 2.15 2.15
   0.034 2.20 2.20 2.20 2.20
   0.035 2.25 2.25 2.25 2.25
   0.036 2.30 2.30 2.30 2.30
   0.037 2.35 2.35 2.35 2.35
   0.038 2.39 2.39 2.39 2.39
   0.039 2.44 2.44 2.44 2.44
   0.040 2.49 2.49 2.49 2.49
   0.041 2.53 2.53 2.53 2.53
   0.042 2.58 2.58 2.58 2.58
   0.043 2.63 2.63 2.63 2.63
   0.044 2.67 2.67 2.67 2.67
   0.045 2.72 2.72 2.72 2.72
   0.046 2.76 2.76 2.76 2.76
   0.047 2.81 2.81 2.81 2.81
   0.048 2.85 2.85 2.85 2.85
   0.049 2.90 2.90 2.90 2.90
   0.050 2.94 2.94 2.94 2.94
   0.051 2.98 2.98 2.98 2.98
   0.052 3.03 3.03 3.03 3.03
   0.053 3.07 3.07 3.07 3.07
   0.054 3.12 3.12 3.12 3.12
   0.055 3.16 3.16 3.16 3.16
   0.056 3.20 3.20 3.20 3.20
   0.057 3.24 3.24 3.24 3.24
   0.058 3.29 3.29 3.29 3.29
   0.059 3.33 3.33 3.33 3.33
   0.060 3.37 3.37 3.37 3.37

-----------------------------------------------------------
AMPACITY OF PLATED_THROUGH HOLES (based on Lexmark ES 43H2362)

ASSUMPTIONS:
Four 0.015" wide spokes to planes on plated-through holes
Barrels plated >= 0.001" over 90% of barrel, voids <= 25% circumference
Internal 0.5 ounce/ft^2 copper >= 0.00050 inches thick
Internal 1 ounce/ft^2 copper >= 0.00100 inches thick
Internal 2 ounce/ft^2 copper >= 0.00200 inches thick
Internal 3 ounce/ft^2 copper >= 0.00300 inches thick
External 0.5 ounce/ft^2 copper >= 0.00068 inches thick
External 1 ounce/ft^2 copper >= 0.00135 inches thick
External 2 ounce/ft^2 copper >= 0.00270 inches thick
External 3 ounce/ft^2 copper >= 0.00405 inches thick
Barrel-to-pad/plane ampacity derated 20% for imperfect contact
temperature rise = 10 C

ampacity of plated-through holes to external layers (double-sided cards)

PTH 0.5 ounce 1 ounce 2 ounce 3 ounce
diameter external external external external
(inches) (Amps) (Amps) (Amps) (Amps)
-------- --------- --------- -------- --------
   0.005 0.52 0.52 0.52 0.52
   0.006 0.60 0.60 0.60 0.60
   0.007 0.67 0.67 0.67 0.67
   0.008 0.74 0.74 0.74 0.74
   0.009 0.81 0.81 0.81 0.81
   0.010 0.88 0.88 0.88 0.88
   0.011 0.94 0.94 0.94 0.94
   0.012 1.01 1.01 1.01 1.01
   0.013 1.07 1.07 1.07 1.07
   0.014 1.13 1.13 1.13 1.13
   0.015 1.19 1.19 1.19 1.19
   0.016 1.25 1.25 1.25 1.25
   0.017 1.31 1.31 1.31 1.31
   0.018 1.37 1.37 1.37 1.37
   0.019 1.42 1.42 1.42 1.42
   0.020 1.48 1.48 1.48 1.48
   0.021 1.53 1.53 1.53 1.53
   0.022 1.59 1.59 1.59 1.59
   0.023 1.64 1.64 1.64 1.64
   0.024 1.70 1.70 1.70 1.70
   0.025 1.75 1.75 1.75 1.75
   0.026 1.80 1.80 1.80 1.80
   0.027 1.85 1.85 1.85 1.85
   0.028 1.90 1.90 1.90 1.90
   0.029 1.95 1.95 1.95 1.95
   0.030 2.00 2.00 2.00 2.00
   0.031 2.05 2.05 2.05 2.05
   0.032 2.10 2.10 2.10 2.10
   0.033 2.15 2.15 2.15 2.15
   0.034 2.20 2.20 2.20 2.20
   0.035 2.25 2.25 2.25 2.25
   0.036 2.30 2.30 2.30 2.30
   0.037 2.35 2.35 2.35 2.35
   0.038 2.39 2.39 2.39 2.39
   0.039 2.44 2.44 2.44 2.44
   0.040 2.49 2.49 2.49 2.49
   0.041 2.53 2.53 2.53 2.53
   0.042 2.58 2.58 2.58 2.58
   0.043 2.63 2.63 2.63 2.63
   0.044 2.67 2.67 2.67 2.67
   0.045 2.67 2.72 2.72 2.72
   0.046 2.67 2.76 2.76 2.76
   0.047 2.67 2.81 2.81 2.81
   0.048 2.67 2.85 2.85 2.85
   0.049 2.67 2.90 2.90 2.90
   0.050 2.67 2.94 2.94 2.94
   0.051 2.67 2.98 2.98 2.98
   0.052 2.67 3.03 3.03 3.03
   0.053 2.67 3.07 3.07 3.07
   0.054 2.67 3.12 3.12 3.12
   0.055 2.67 3.16 3.16 3.16
   0.056 2.67 3.20 3.20 3.20
   0.057 2.67 3.24 3.24 3.24
   0.058 2.67 3.29 3.29 3.29
   0.059 2.67 3.33 3.33 3.33
   0.060 2.67 3.37 3.37 3.37

ampacity of plated-through holes to external and internal layers
(multilayer cards)

PTH 0.5 ounce 1 ounce 2 ounce 3 ounce
diameter ext/int ext/int ext/int ext/int
(inches) (Amps) (Amps) (Amps) (Amps)
-------- --------- --------- -------- --------
   0.005 0.41 0.52 0.52 0.52
   0.006 0.45 0.60 0.60 0.60
   0.007 0.49 0.67 0.67 0.67
   0.008 0.53 0.74 0.74 0.74
   0.009 0.57 0.81 0.81 0.81
   0.010 0.61 0.88 0.88 0.88
   0.011 0.65 0.94 0.94 0.94
   0.012 0.68 1.01 1.01 1.01
   0.013 0.72 1.07 1.07 1.07
   0.014 0.75 1.13 1.13 1.13
   0.015 0.79 1.19 1.19 1.19
   0.016 0.82 1.25 1.25 1.25
   0.017 0.86 1.31 1.31 1.31
   0.018 0.89 1.37 1.37 1.37
   0.019 0.92 1.42 1.42 1.42
   0.020 0.96 1.48 1.48 1.48
   0.021 0.99 1.53 1.53 1.53
   0.022 1.02 1.59 1.59 1.59
   0.023 1.05 1.64 1.64 1.64
   0.024 1.08 1.70 1.70 1.70
   0.025 1.08 1.75 1.75 1.75
   0.026 1.08 1.77 1.80 1.80
   0.027 1.08 1.77 1.85 1.85
   0.028 1.08 1.77 1.90 1.90
   0.029 1.08 1.77 1.95 1.95
   0.030 1.08 1.77 2.00 2.00
   0.031 1.08 1.77 2.05 2.05
   0.032 1.08 1.77 2.10 2.10
   0.033 1.08 1.77 2.15 2.15
   0.034 1.08 1.77 2.20 2.20
   0.035 1.08 1.77 2.25 2.25
   0.036 1.08 1.77 2.30 2.30
   0.037 1.08 1.77 2.35 2.35
   0.038 1.08 1.77 2.39 2.39
   0.039 1.08 1.77 2.44 2.44
   0.040 1.08 1.77 2.49 2.49
   0.041 1.08 1.77 2.53 2.53
   0.042 1.08 1.77 2.58 2.58
   0.043 1.08 1.77 2.63 2.63
   0.044 1.08 1.77 2.67 2.67
   0.045 1.08 1.77 2.72 2.72
   0.046 1.08 1.77 2.76 2.76
   0.047 1.08 1.77 2.81 2.81
   0.048 1.08 1.77 2.85 2.85
   0.049 1.08 1.77 2.90 2.90
   0.050 1.08 1.77 2.92 2.94
   0.051 1.08 1.77 2.92 2.98
   0.052 1.08 1.77 2.92 3.03
   0.053 1.08 1.77 2.92 3.07
   0.054 1.08 1.77 2.92 3.12
   0.055 1.08 1.77 2.92 3.16
   0.056 1.08 1.77 2.92 3.20
   0.057 1.08 1.77 2.92 3.24
   0.058 1.08 1.77 2.92 3.29
   0.059 1.08 1.77 2.92 3.33
   0.060 1.08 1.77 2.92 3.37

To help the rest of you on the SI-LIST, here are my references:
* Lexmark Electronics Electronic Card/Panel Design Guideline Version 1.1
   Section 7.8.2 Power Wiring
* IPC-2221 Generic Standard on Printed Circuit Board Design
* Printed Circuit Drafting Technical Manual & Catalog 107A (Bishop Graphics,
   1985)
* Electrical Engineering Materials Reference Guide (H. Wayne Beaty, McGraw-
   Hill, 1990)
* The Design & Drafting of Printed Circuits (Darryl Lindsey, McGraw-Hill, 1979)
* Printed Circuits Design (Gerald L. Ginsberg, McGraw-Hill, 1991)
* Electronic Techniques (Robert S. Villanucci, Alexander W. Avtgis, and
   William F. Megow, Prentice-Hall, 1986)
* The Multilayer Printed Circuit Board Handbook (J. A. Scarlett,
   Electrochemical Publications, 1985)
* An Introduction to Printed Circuit Board Technology (J. A. Scarlett,
   Electrochemical Publications, 1984)
* Printed Circuit Boards for Microelectronics 2nd ed (J. A. Scarlett,
   Electrochemical Publications, 1980)
* IBM Design Guide Electronic Packaging ZZ45-4016-1
* Current Carrying Capacity of Flex-Circuit Conductors (Minco Application Aid
   No. 23, 1991)
* Dynacircuits Material Specifications for Printed Circuit Boards Sliderule
   (1985)
* Conductor Width-- Part 1 (Mary Sugden and Mona Johnson, Printed Circuit
   Design, Vol. 14 No. 10, October 1997, p. 38-39)
* Printed Circuit Design and Drafting (Jesse S. Cook III, Tad Institute,
   Cambridge, Mass., 1967)
* Physical Design of Electronic Systems volume IV: Design Process (D. Baker,
   D. C. Koehler, W. O. Fleckenstein, C. E. Roden, R. Sabia, Prentice-Hall,1972)
* Handbook of Materials and Processes for Electronics (Charles A. Harper,
   McGraw-Hill, 1970)
* Measuring Printed Circuits' Current-Carrying Capacity (Walter W. Weick,
   Western Electric Engineer, vol. 5, 1961, pp. 39-41)
* TechNet archive, post by Ralph Hersey on 1 May 1998
* Technet archive, post by Wally Doeling on 19 Dec 1997
* TechNet archive, post by Ralph Hersey on 11 Nov 1997
* TechNet archive, post by Ralph Hersey on 15 Oct 1996
* DesignerCouncil archive, post by Abdulrahmam Lomax on 15 Sep 1998
* DesignerCouncil archive, post by Lisa Williams on 17 Sep 1997
* DesignerCouncil archive, post by Gary Ferrari on 18 Apr 1996
* http://www.aracnet.com/~gpatrick/pcb.html#width
* Technet archive, post by Andrew Magee on 15 Nov 1996
* Mecondor Bus Bars
* Temperature Rise in PCB Traces (Douglas Brooks, Proceedings of the PCB
   Design Conference West, Miller Freeman, 1998)
* Empirical Equation for Sizing Copper PWB Traces (John McHardy, Mahendra
   Gandhi, IPCWorks 1997 technical paper SO6-2-1)
* http://www.rogers-corp.com/nv/m824.htm
* http://www.rogers-corp.com/nv/m823.htm
* http://www.atlee.com/BusBars_DesignCriteriaMain.asp
* http://www.atlee.com/QuickPrint1Bottom.asp
* http://www.atlee.com/QuickPrint2Bottom.asp
* Mini-bus and Q-Pac Bus Bars (Circuit Components)
* Generation of Precision Artwork for Printed Circuit Boards (Preben Lund,
   John Wiley & Sons, 1978)
* Handbook of Electronic Packaging (Charles A. Harper, McGraw-Hill, 1969)
* Handbook of Wiring, Cabling, and Interconnecting for Electronics (Charles
   A. Harper, McGraw-Hill, 1972)
* Handbook of Printed Circuit Design, Manufacture, Components & Assembly
   (Giovanni Leonida, Electrochemical Publications, 1981)
* Printed Circuits Handbook 3rd ed (Clyde F. Coombs, Jr., McGraw-Hill, 1988)
* Multilayer and Flexible Circuits (Clyde F. Coombs, Jr., McGraw-Hill, 1990)
* Wiring and Cable Designer's Handbook (Bernard S. Matisoff, TAB, 1987)
* Novaclad Designing with a New Class of Materials (Sheldahl)
* MIL-STD-275E Military Standard Printed Wiring for Electronic Equipment (1984)
* Main Power Distribution Bus Bars (Eldre)
* Main Power Distribution Bus Bars (Eldre)
* Power Distribution with Noise Control and without Decoupling Capacitors CAP
   BUS (Eldre)
* Printed Circuits and High Currents (Michael E. Friar and Roger H. McClurg,
   Design News, V.23 No.25, December 6, 1968, pages 102-107)
* Fusing Current-- When Traces Melt Without a Trace (Douglas Brooks, Printed
   Circuit Design, December 1998)
* Current-Carrying Capacity of Fine-Line Printed Conductors (A. J. Rainal,
   Bell System Technical Journal, Vol. 60 no. 7, September 1981, p. 1375-1388)
* Wiring and Cable Designer's Handbook (Bernard S. Matisoff, TAB, 1987)
   Figure 6-10 same as Ginsberg Figure 6.3
* Printed Circuit Engineering (Raymon H. Clark, Van Nostrand Reinhold, 1989)
   Figure F-2 same as IPC-2221 external
* Electrical Properties of Printed Wiring Boards (C. W. Jennings
   Sandia Labs SAND75-0663, May 1976)

880*thick^0.7*width^0.75*temp^0.45
* "Planar Transformers Dissipate Up to 150 kW With Copper Trace Windings"
   (Robert G. Tarzwell and David Basista, PCIM, V26 #3, March 2000, 58-64,
   Table 3)

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