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Air Line Coax from Brass/Copper Tubing

A project log for The Rise and Fall of Pulses

A project in which I try to go faster and faster

Ted YapoTed Yapo 09/07/2019 at 23:100 Comments

You know you want to make some air-line coax for an impedance reference from brass hobby tubing. But, what sizes to use? I threw together a quick python script to find the characteristic impedance and cutoff frequencies for all the combinations.

The script uses all the available sizes (metric and inch) of K&S brass tubing. Some sizes are also available in copper, and any of them could be silver plated, although this probably isn't necessary for short sections.

I haven't built any coax this way yet, but now I know which sizes to select.

Calculations

The characteristic impedance of coax is given by:

where D is the inner diameter of the outer conductor, and d is the outer diameter of the inner conductor. The diameter units cancel.

Cutoff Frequency

At lower frequencies, waves travel in coax in the so-called transverse electromagnetic mode (TEM), where the electric and magnetic fields are both perpendicular to the direction of travel (i.e. the coax). Above a certain frequency, called the cutoff, higher-order modes can also exist on the cable. These propagate at different speeds, and generally ruin your day.

The cutoff frequency for coax is given by:

with D and d in inches.

In both cases, the code uses Er = 1.00058986, the value for air.

Code

The python code calculates the characteristic impedance and cutoff frequency for all the combinations of K&R tubing sizes:

#!/usr/bin/env python3

import numpy as np
from fractions import Fraction

# (name, OD, ID) inches

US_idx = np.linspace(1, 21, 21)
US_tubing = map(lambda x: (str(Fraction(int(x), 32))+'"',
                              x/32, x/32 - 0.028), US_idx)

mm_idx1 = [1, 1.5, 2, 3, 3.5, 4, 4.5, 5]
mm_idx2 = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]

mm_tubing1 = map(lambda x: (str(x) + '/0.225 mm', x/25.4, (x-2*0.225)/25.4), mm_idx1)
mm_tubing2 = map(lambda x: (str(x) + '/0.45 mm', x/25.4, (x-2*0.45)/25.4), mm_idx2)

tubing = list(US_tubing) + list( mm_tubing1) + list(mm_tubing2)

Er = 1.00058986

table = []

print('       Inner        Outer   Cutoff     Z0')
print('                             (GHz)   (Ohm)')
print('--------------------------------------------')
for outer in tubing:
    for inner in tubing:
        if inner[1] >= outer[2]:
            continue
        Z0 = 138 * np.log10(outer[2]/inner[1])/np.sqrt(Er)
        fc = 7.51393 / ((inner[1] + outer[2])*np.sqrt(Er))
        table.append((inner[0], outer[0], fc, Z0))

for i in sorted(table, key=lambda x: x[3]):
    print('{:>12s}  {:>12s}  {:5.1f}  {:6.2f}'.format(i[0], i[1], i[2], i[3]))

Table

Here are the results. For the really low-Z combinations, although the tubing would fit based on the nominal sizes, it would probably short out due to manufacturing tolerances.

       Inner        Outer   Cutoff     Z0
                             (GHz)   (Ohm)
--------------------------------------------
   8/0.45 mm        11/32"   11.9    0.15
        5/8"        21/32"    6.0    0.31
      19/32"          5/8"    6.3    0.33
       9/16"        19/32"    6.7    0.35
      17/32"         9/16"    7.0    0.37
        1/2"        17/32"    7.5    0.39
      15/32"          1/2"    8.0    0.41
       7/16"        15/32"    8.6    0.44
      13/32"         7/16"    9.2    0.48
  12/0.45 mm    13/0.45 mm    7.9    0.50
        3/8"        13/32"   10.0    0.52
  11/0.45 mm    12/0.45 mm    8.6    0.54
      11/32"          3/8"   10.9    0.56
  10/0.45 mm    11/0.45 mm    9.5    0.60
       5/16"        11/32"   12.0    0.62
4.5/0.225 mm    5/0.225 mm   21.1    0.66
   9/0.45 mm    10/0.45 mm   10.5    0.66
       9/32"         5/16"   13.3    0.69
  4/0.225 mm  4.5/0.225 mm   23.7    0.74
   4/0.45 mm  4.5/0.225 mm   23.7    0.74
   8/0.45 mm     9/0.45 mm   11.9    0.74
  4/0.225 mm         3/16"   23.7    0.76
   4/0.45 mm         3/16"   23.7    0.76
        1/4"         9/32"   14.9    0.77
3.5/0.225 mm    4/0.225 mm   27.1    0.85
   7/0.45 mm     8/0.45 mm   13.5    0.85
       7/32"          1/4"   17.0    0.88
      15/32"    13/0.45 mm    7.9    0.97
  3/0.225 mm  3.5/0.225 mm   31.5    0.99
   3/0.45 mm  3.5/0.225 mm   31.5    0.99
   6/0.45 mm     7/0.45 mm   15.8    0.99
       3/16"         7/32"   19.9    1.03
  11/0.45 mm        15/32"    8.6    1.05
  5/0.225 mm     6/0.45 mm   18.9    1.19
   5/0.45 mm     6/0.45 mm   18.9    1.19
       5/32"  4.5/0.225 mm   23.8    1.21
       5/16"     9/0.45 mm   11.9    1.21
       5/32"         3/16"   23.8    1.23
  4/0.225 mm     5/0.45 mm   23.6    1.48
   4/0.45 mm     5/0.45 mm   23.6    1.48
        1/8"         5/32"   29.7    1.54
   7/0.45 mm         5/16"   13.4    1.91
       5/32"     5/0.45 mm   23.6    1.95
1.5/0.225 mm    2/0.225 mm   62.6    1.96
  3/0.225 mm     4/0.45 mm   31.3    1.96
   3/0.45 mm     4/0.45 mm   31.3    1.96
       3/32"          1/8"   39.4    2.04
  10/0.45 mm         7/16"    9.4    2.36
      11/32"    10/0.45 mm   10.7    2.48
  13/0.45 mm         9/16"    7.2    2.60
  1/0.225 mm  1.5/0.225 mm   93.1    2.92
  2/0.225 mm     3/0.45 mm   46.5    2.92
   2/0.45 mm     3/0.45 mm   46.5    2.92
       1/16"         3/32"   58.6    3.04
      19/32"        21/32"    6.1    3.38
        3/8"    11/0.45 mm    9.7    3.51
       9/16"          5/8"    6.5    3.57
      17/32"        19/32"    6.8    3.77
  12/0.45 mm        17/32"    7.7    3.79
   9/0.45 mm        13/32"   10.3    3.91
        1/2"         9/16"    7.3    4.00
       3/32"    3/0.225 mm   38.7    4.10
       3/16"     6/0.45 mm   19.3    4.10
   6/0.45 mm         9/32"   15.3    4.17
      15/32"        17/32"    7.7    4.26
      13/32"    12/0.45 mm    8.9    4.37
4.5/0.225 mm         7/32"   20.4    4.43
       7/16"          1/2"    8.3    4.55
      13/32"        15/32"    8.9    4.88
  3/0.225 mm         5/32"   30.5    4.93
   3/0.45 mm         5/32"   30.5    4.93
       7/16"    13/0.45 mm    8.2    5.10
  11/0.45 mm          1/2"    8.3    5.16
        3/8"         7/16"    9.6    5.27
       7/32"     7/0.45 mm   16.4    5.59
  11/0.45 mm    13/0.45 mm    8.3    5.71
  1/0.225 mm     2/0.45 mm   90.9    5.71
      11/32"        13/32"   10.4    5.73
   8/0.45 mm          3/8"   11.3    5.80
       1/32"         1/16"  114.2    5.93
  13/0.45 mm        19/32"    7.0    6.00
  10/0.45 mm    12/0.45 mm    9.0    6.25
       5/16"          3/8"   11.4    6.27
1.5/0.225 mm         3/32"   60.2    6.43
       9/16"        21/32"    6.3    6.62
        1/8"    4/0.225 mm   28.4    6.69
        1/4"     8/0.45 mm   14.2    6.69
  10/0.45 mm        15/32"    9.0    6.76
   9/0.45 mm    11/0.45 mm   10.0    6.91
       9/32"        11/32"   12.6    6.93
      17/32"          5/8"    6.7    6.99
  5/0.225 mm          1/4"   17.9    7.20
   5/0.45 mm          1/4"   17.9    7.20
  12/0.45 mm         9/16"    7.5    7.39
        1/2"        19/32"    7.0    7.40
4.5/0.225 mm     6/0.45 mm   19.9    7.50
       9/32"     9/0.45 mm   12.5    7.53
  4/0.225 mm    5/0.225 mm   22.3    7.72
   4/0.45 mm    5/0.225 mm   22.3    7.72
   8/0.45 mm    10/0.45 mm   11.2    7.72
        1/4"         5/16"   14.1    7.75
      15/32"         9/16"    7.5    7.86
   7/0.45 mm        11/32"   12.7    8.15
       5/32"    5/0.225 mm   22.4    8.19
       5/16"    10/0.45 mm   11.2    8.19
       7/16"        17/32"    8.0    8.39
   9/0.45 mm         7/16"    9.8    8.67
      11/32"    11/0.45 mm   10.1    8.73
3.5/0.225 mm  4.5/0.225 mm   25.3    8.74
   7/0.45 mm     9/0.45 mm   12.6    8.74
3.5/0.225 mm         3/16"   25.3    8.76
       7/32"         9/32"   15.9    8.77
      13/32"          1/2"    8.6    8.99
  11/0.45 mm        17/32"    8.0    9.00
        3/8"    12/0.45 mm    9.3    9.17
  13/0.45 mm          5/8"    6.8    9.22
3.5/0.225 mm     5/0.45 mm   25.1    9.48
      13/32"    13/0.45 mm    8.5    9.54
        3/8"        15/32"    9.2    9.68
      17/32"        21/32"    6.5   10.05
  3/0.225 mm    4/0.225 mm   29.1   10.09
   3/0.45 mm    4/0.225 mm   29.1   10.09
   6/0.45 mm     8/0.45 mm   14.6   10.09
       3/16"          1/4"   18.3   10.12
      11/32"         7/16"   10.0   10.49
        1/2"          5/8"    6.8   10.62
  12/0.45 mm        19/32"    7.2   10.80
  10/0.45 mm          1/2"    8.7   10.87
   8/0.45 mm        13/32"   10.8   10.97
   6/0.45 mm         5/16"   14.4   11.14
      15/32"        19/32"    7.3   11.27
  10/0.45 mm    13/0.45 mm    8.6   11.42
       5/16"        13/32"   10.9   11.44
  4/0.225 mm         7/32"   21.6   11.48
   4/0.45 mm         7/32"   21.6   11.48
  5/0.225 mm     7/0.45 mm   17.2   11.91
   5/0.45 mm     7/0.45 mm   17.2   11.91
       5/32"         7/32"   21.6   11.95
       7/16"         9/16"    7.7   12.00
  13/0.45 mm        21/32"    6.6   12.28
  2/0.225 mm          1/8"   42.7   12.50
   2/0.45 mm          1/8"   42.7   12.50
   9/0.45 mm    12/0.45 mm    9.5   12.57
       9/32"          3/8"   12.0   12.59
  11/0.45 mm         9/16"    7.8   12.61
      13/32"        17/32"    8.3   12.83
   9/0.45 mm        15/32"    9.4   13.08
4.5/0.225 mm          1/4"   18.8   13.52
        1/2"        21/32"    6.7   13.68
        3/8"          1/2"    8.9   13.78
   7/0.45 mm          3/8"   12.1   13.80
   8/0.45 mm    11/0.45 mm   10.5   13.97
        1/4"        11/32"   13.3   13.99
  12/0.45 mm          5/8"    7.0   14.02
        3/8"    13/0.45 mm    8.8   14.34
      11/32"    12/0.45 mm    9.6   14.38
       5/16"    11/0.45 mm   10.6   14.44
      15/32"          5/8"    7.0   14.49
       9/32"    10/0.45 mm   11.7   14.50
  2/0.225 mm    3/0.225 mm   41.9   14.56
   2/0.45 mm    3/0.225 mm   41.9   14.56
  4/0.225 mm     6/0.45 mm   21.0   14.56
   4/0.45 mm     6/0.45 mm   21.0   14.56
        1/8"  4.5/0.225 mm   26.4   14.58
        1/4"     9/0.45 mm   13.2   14.58
        1/8"         3/16"   26.4   14.60
       7/32"     8/0.45 mm   15.1   14.69
  10/0.45 mm        17/32"    8.4   14.71
       3/32"  3.5/0.225 mm   35.1   14.83
       3/16"     7/0.45 mm   17.6   14.83
      11/32"        15/32"    9.6   14.89
       5/32"     6/0.45 mm   21.0   15.03
  5/0.225 mm         9/32"   16.7   15.09
   5/0.45 mm         9/32"   16.7   15.09
        1/8"     5/0.45 mm   26.2   15.32
       7/16"        19/32"    7.5   15.40
3.5/0.225 mm    5/0.225 mm   23.7   15.72
   7/0.45 mm    10/0.45 mm   11.9   15.72
   8/0.45 mm         7/16"   10.4   15.73
       7/32"         5/16"   14.9   15.75
       3/32"     4/0.45 mm   34.8   15.80
  11/0.45 mm        19/32"    7.5   16.01
       5/16"         7/16"   10.4   16.20
      13/32"         9/16"    8.0   16.44
       1/32"  1.5/0.225 mm  103.5   16.76
       1/16"     3/0.45 mm   51.7   16.76
  12/0.45 mm        21/32"    6.8   17.08
   9/0.45 mm          1/2"    9.1   17.18
   6/0.45 mm        11/32"   13.6   17.39
      15/32"        21/32"    6.8   17.55
        3/8"        17/32"    8.6   17.62
   9/0.45 mm    13/0.45 mm    9.0   17.73
       9/32"        13/32"   11.4   17.75
  3/0.225 mm  4.5/0.225 mm   27.1   17.98
   3/0.45 mm  4.5/0.225 mm   27.1   17.98
   6/0.45 mm     9/0.45 mm   13.5   17.98
  3/0.225 mm         3/16"   27.1   18.00
   3/0.45 mm         3/16"   27.1   18.00
       3/16"         9/32"   17.0   18.01
4.5/0.225 mm     7/0.45 mm   18.0   18.23
  10/0.45 mm         9/16"    8.1   18.32
       7/16"          5/8"    7.3   18.62
  3/0.225 mm     5/0.45 mm   26.9   18.72
   3/0.45 mm     5/0.45 mm   26.9   18.72
       3/32"         5/32"   33.8   18.77
   7/0.45 mm        13/32"   11.5   18.97
      11/32"          1/2"    9.2   19.00
  11/0.45 mm          5/8"    7.3   19.23
3.5/0.225 mm         7/32"   22.9   19.48
      11/32"    13/0.45 mm    9.2   19.55
       1/32"     2/0.45 mm  100.8   19.55
   8/0.45 mm    12/0.45 mm   10.0   19.62
        1/4"          3/8"   12.6   19.64
      13/32"        19/32"    7.7   19.84
       5/16"    12/0.45 mm   10.0   20.09
   8/0.45 mm        15/32"    9.9   20.13
1.5/0.225 mm     3/0.45 mm   53.0   20.16
  4/0.225 mm          1/4"   19.8   20.57
   4/0.45 mm          1/4"   19.8   20.57
       5/16"        15/32"   10.0   20.60
       9/32"    11/0.45 mm   11.1   20.75
  5/0.225 mm     8/0.45 mm   15.8   21.01
   5/0.45 mm     8/0.45 mm   15.8   21.01
   9/0.45 mm        17/32"    8.8   21.02
       5/32"          1/4"   19.9   21.04
        3/8"         9/16"    8.3   21.23
4.5/0.225 mm         9/32"   17.5   21.41
        1/8"    5/0.225 mm   24.7   21.56
        1/4"    10/0.45 mm   12.3   21.56
       7/16"        21/32"    7.0   21.68
  10/0.45 mm        19/32"    7.8   21.72
   7/0.45 mm    11/0.45 mm   11.2   21.97
       7/32"        11/32"   14.1   21.99
  5/0.225 mm         5/16"   15.6   22.07
   5/0.45 mm         5/16"   15.6   22.07
  11/0.45 mm        21/32"    7.1   22.29
       9/32"         7/16"   10.9   22.51
3.5/0.225 mm     6/0.45 mm   22.2   22.56
       7/32"     9/0.45 mm   14.0   22.58
      11/32"        17/32"    8.9   22.84
   6/0.45 mm          3/8"   12.9   23.04
      13/32"          5/8"    7.5   23.06
   7/0.45 mm         7/16"   11.0   23.73
       3/32"    4/0.225 mm   32.2   23.93
       3/16"     8/0.45 mm   16.1   23.93
   8/0.45 mm          1/2"    9.5   24.24
   9/0.45 mm         9/16"    8.5   24.63
        3/8"        19/32"    8.0   24.64
       5/16"          1/2"    9.6   24.71
   8/0.45 mm    13/0.45 mm    9.5   24.79
        1/4"        13/32"   12.0   24.81
  10/0.45 mm          5/8"    7.6   24.94
  3/0.225 mm    5/0.225 mm   25.3   24.96
   3/0.45 mm    5/0.225 mm   25.3   24.96
   6/0.45 mm    10/0.45 mm   12.6   24.96
       3/16"         5/16"   15.9   24.98
       5/16"    13/0.45 mm    9.5   25.26
  2/0.225 mm  3.5/0.225 mm   37.8   25.28
   2/0.45 mm  3.5/0.225 mm   37.8   25.28
  4/0.225 mm     7/0.45 mm   18.9   25.28
   4/0.45 mm     7/0.45 mm   18.9   25.28
        1/8"         7/32"   23.8   25.32
       5/32"     7/0.45 mm   18.9   25.75
      13/32"        21/32"    7.3   26.12
  1/0.225 mm    2/0.225 mm   74.8   26.26
  2/0.225 mm     4/0.45 mm   37.4   26.26
   2/0.45 mm     4/0.45 mm   37.4   26.26
       1/16"          1/8"   47.1   26.34
       9/32"    12/0.45 mm   10.5   26.40
      11/32"         9/16"    8.6   26.45
       9/32"        15/32"   10.4   26.92
4.5/0.225 mm     8/0.45 mm   16.4   27.32
   7/0.45 mm    12/0.45 mm   10.5   27.62
       7/32"          3/8"   13.3   27.64
        1/4"    11/0.45 mm   11.6   27.81
        3/8"          5/8"    7.7   27.86
  10/0.45 mm        21/32"    7.4   28.00
   9/0.45 mm        19/32"    8.2   28.04
   8/0.45 mm        17/32"    9.2   28.08
   7/0.45 mm        15/32"   10.5   28.13
   6/0.45 mm        13/32"   12.2   28.21
  5/0.225 mm        11/32"   14.7   28.31
   5/0.45 mm        11/32"   14.7   28.31
4.5/0.225 mm         5/16"   16.3   28.38
       1/16"    3/0.225 mm   46.1   28.40
        1/8"     6/0.45 mm   23.1   28.40
  4/0.225 mm         9/32"   18.3   28.46
   4/0.45 mm         9/32"   18.3   28.46
       5/16"        17/32"    9.2   28.55
3.5/0.225 mm          1/4"   20.9   28.57
  3/0.225 mm         7/32"   24.3   28.72
   3/0.45 mm         7/32"   24.3   28.72
  5/0.225 mm     9/0.45 mm   14.6   28.90
   5/0.45 mm     9/0.45 mm   14.6   28.90
       5/32"         9/32"   18.3   28.93
  2/0.225 mm         5/32"   36.3   29.23
   2/0.45 mm         5/32"   36.3   29.23
       7/32"    10/0.45 mm   13.0   29.56
        1/4"         7/16"   11.4   29.57
1.5/0.225 mm          1/8"   48.1   29.73
      11/32"        19/32"    8.3   29.85
  1/0.225 mm         3/32"   71.5   30.73
        3/8"        21/32"    7.5   30.92
       9/32"          1/2"   10.0   31.02
   6/0.45 mm    11/0.45 mm   11.9   31.20
       3/16"        11/32"   14.9   31.23
   9/0.45 mm          5/8"    7.9   31.26
       9/32"    13/0.45 mm    9.9   31.57
   8/0.45 mm         9/16"    8.8   31.69
1.5/0.225 mm    3/0.225 mm   47.1   31.79
  3/0.225 mm     6/0.45 mm   23.6   31.79
   3/0.45 mm     6/0.45 mm   23.6   31.79
       3/32"  4.5/0.225 mm   29.7   31.82
       3/16"     9/0.45 mm   14.8   31.82
       3/32"         3/16"   29.7   31.84
       5/16"         9/16"    8.9   32.16
   7/0.45 mm          1/2"   10.0   32.24
       3/32"     5/0.45 mm   29.4   32.56
   7/0.45 mm    13/0.45 mm   10.0   32.79
       7/32"        13/32"   12.6   32.81
   6/0.45 mm         7/16"   11.6   32.96
      11/32"          5/8"    8.0   33.07
3.5/0.225 mm     7/0.45 mm   19.9   33.28
        1/4"    12/0.45 mm   10.9   33.46
  5/0.225 mm          3/8"   13.8   33.96
   5/0.45 mm          3/8"   13.8   33.96
        1/4"        15/32"   10.9   33.97
   9/0.45 mm        21/32"    7.6   34.31
  2/0.225 mm    4/0.225 mm   34.4   34.38
   2/0.45 mm    4/0.225 mm   34.4   34.38
  4/0.225 mm     8/0.45 mm   17.2   34.38
   4/0.45 mm     8/0.45 mm   17.2   34.38
        1/8"          1/4"   21.6   34.41
4.5/0.225 mm        11/32"   15.2   34.62
       5/32"     8/0.45 mm   17.2   34.85
       9/32"        17/32"    9.6   34.86
   8/0.45 mm        19/32"    8.5   35.09
4.5/0.225 mm     9/0.45 mm   15.1   35.22
  4/0.225 mm         5/16"   17.0   35.44
   4/0.45 mm         5/16"   17.0   35.44
       5/16"        19/32"    8.6   35.56
       7/32"    11/0.45 mm   12.2   35.81
  5/0.225 mm    10/0.45 mm   13.5   35.88
   5/0.45 mm    10/0.45 mm   13.5   35.88
       5/32"         5/16"   17.0   35.91
   7/0.45 mm        17/32"    9.6   36.08
      11/32"        21/32"    7.7   36.13
3.5/0.225 mm         9/32"   19.2   36.46
   6/0.45 mm    12/0.45 mm   11.2   36.86
       3/16"          3/8"   14.1   36.88
   6/0.45 mm        15/32"   11.1   37.37
       7/32"         7/16"   12.0   37.57
  3/0.225 mm          1/4"   22.1   37.81
   3/0.45 mm          1/4"   22.1   37.81
        1/4"          1/2"   10.4   38.08
   8/0.45 mm          5/8"    8.2   38.31
       9/32"         9/16"    9.2   38.47
        1/4"    13/0.45 mm   10.3   38.63
       5/16"          5/8"    8.3   38.78
       3/32"    5/0.225 mm   27.5   38.80
       3/16"    10/0.45 mm   13.8   38.80
       1/16"  3.5/0.225 mm   41.1   39.12
        1/8"     7/0.45 mm   20.6   39.12
  5/0.225 mm        13/32"   13.1   39.13
   5/0.45 mm        13/32"   13.1   39.13
   7/0.45 mm         9/16"    9.3   39.69
       1/32"    2/0.225 mm   81.4   40.10
       1/16"     4/0.45 mm   40.7   40.10
4.5/0.225 mm          3/8"   14.3   40.28
   8/0.45 mm        21/32"    8.0   41.37
       7/32"    12/0.45 mm   11.5   41.46
   6/0.45 mm          1/2"   10.6   41.47
  4/0.225 mm        11/32"   15.9   41.68
   4/0.45 mm        11/32"   15.9   41.68
       5/16"        21/32"    8.0   41.84
       9/32"        19/32"    8.9   41.88
        1/4"        17/32"   10.0   41.92
       7/32"        15/32"   11.4   41.97
   6/0.45 mm    13/0.45 mm   10.5   42.03
       3/16"        13/32"   13.3   42.05
  5/0.225 mm    11/0.45 mm   12.6   42.13
   5/0.45 mm    11/0.45 mm   12.6   42.13
       5/32"        11/32"   15.9   42.15
4.5/0.225 mm    10/0.45 mm   14.0   42.19
  2/0.225 mm  4.5/0.225 mm   31.5   42.27
   2/0.45 mm  4.5/0.225 mm   31.5   42.27
  4/0.225 mm     9/0.45 mm   15.8   42.27
   4/0.45 mm     9/0.45 mm   15.8   42.27
  2/0.225 mm         3/16"   31.5   42.29
   2/0.45 mm         3/16"   31.5   42.29
        1/8"         9/32"   19.9   42.30
3.5/0.225 mm     8/0.45 mm   18.0   42.38
1.5/0.225 mm  3.5/0.225 mm   41.9   42.52
  3/0.225 mm     7/0.45 mm   21.0   42.52
   3/0.45 mm     7/0.45 mm   21.0   42.52
       3/32"         7/32"   26.4   42.56
       5/32"     9/0.45 mm   15.8   42.74
  2/0.225 mm     5/0.45 mm   31.3   43.01
   2/0.45 mm     5/0.45 mm   31.3   43.01
       1/16"         5/32"   39.4   43.07
   7/0.45 mm        19/32"    8.9   43.09
3.5/0.225 mm         5/16"   17.8   43.44
1.5/0.225 mm     4/0.45 mm   41.5   43.49
  5/0.225 mm         7/16"   12.4   43.89
   5/0.45 mm         7/16"   12.4   43.89
  1/0.225 mm     3/0.45 mm   61.5   44.45
       1/32"         3/32"   77.4   44.57
       3/16"    11/0.45 mm   12.8   45.04
       9/32"          5/8"    8.6   45.10
   6/0.45 mm        17/32"   10.2   45.31
4.5/0.225 mm        13/32"   13.5   45.44
        1/4"         9/16"    9.6   45.53
       3/32"     6/0.45 mm   25.5   45.63
  3/0.225 mm         9/32"   20.2   45.70
   3/0.45 mm         9/32"   20.2   45.70
       7/32"          1/2"   10.9   46.08
   7/0.45 mm          5/8"    8.6   46.31
1.5/0.225 mm         5/32"   40.1   46.46
       7/32"    13/0.45 mm   10.8   46.63
       3/16"         7/16"   12.6   46.80
  4/0.225 mm          3/8"   14.9   47.33
   4/0.45 mm          3/8"   14.9   47.33
  5/0.225 mm    12/0.45 mm   11.9   47.78
   5/0.45 mm    12/0.45 mm   11.9   47.78
       5/32"          3/8"   14.9   47.80
       9/32"        21/32"    8.3   48.15
       1/16"    4/0.225 mm   37.1   48.22
        1/8"     8/0.45 mm   18.6   48.22
  5/0.225 mm        15/32"   11.8   48.29
   5/0.45 mm        15/32"   11.8   48.29
4.5/0.225 mm    11/0.45 mm   13.1   48.44
   6/0.45 mm         9/16"    9.7   48.92
        1/4"        19/32"    9.2   48.93
  2/0.225 mm    5/0.225 mm   29.1   49.25
   2/0.45 mm    5/0.225 mm   29.1   49.25
  4/0.225 mm    10/0.45 mm   14.6   49.25
   4/0.45 mm    10/0.45 mm   14.6   49.25
        1/8"         5/16"   18.3   49.28
   7/0.45 mm        21/32"    8.3   49.37
3.5/0.225 mm        11/32"   16.6   49.68
       5/32"    10/0.45 mm   14.6   49.72
       7/32"        17/32"   10.4   49.92
4.5/0.225 mm         7/16"   12.8   50.20
3.5/0.225 mm     9/0.45 mm   16.4   50.27
       3/16"    12/0.45 mm   12.0   50.70
       3/16"        15/32"   12.0   51.21
1.5/0.225 mm    4/0.225 mm   37.8   51.62
  3/0.225 mm     8/0.45 mm   18.9   51.62
   3/0.45 mm     8/0.45 mm   18.9   51.62
       3/32"          1/4"   23.8   51.65
        1/4"          5/8"    8.9   52.15
   6/0.45 mm        19/32"    9.4   52.33
  5/0.225 mm          1/2"   11.2   52.40
   5/0.45 mm          1/2"   11.2   52.40
  4/0.225 mm        13/32"   14.0   52.50
   4/0.45 mm        13/32"   14.0   52.50
  3/0.225 mm         5/16"   18.7   52.67
   3/0.45 mm         5/16"   18.7   52.67
  5/0.225 mm    13/0.45 mm   11.2   52.95
   5/0.45 mm    13/0.45 mm   11.2   52.95
       5/32"        13/32"   14.1   52.97
  2/0.225 mm         7/32"   27.9   53.01
   2/0.45 mm         7/32"   27.9   53.01
       7/32"         9/16"   10.0   53.53
  1/0.225 mm          1/8"   55.1   54.03
4.5/0.225 mm    12/0.45 mm   12.2   54.10
4.5/0.225 mm        15/32"   12.2   54.61
        1/4"        21/32"    8.6   55.21
       3/16"          1/2"   11.4   55.31
3.5/0.225 mm          3/8"   15.5   55.33
  4/0.225 mm    11/0.45 mm   13.5   55.50
   4/0.45 mm    11/0.45 mm   13.5   55.50
        1/8"        11/32"   17.0   55.52
   6/0.45 mm          5/8"    9.0   55.55
       3/16"    13/0.45 mm   11.3   55.87
       5/32"    11/0.45 mm   13.6   55.97
  1/0.225 mm    3/0.225 mm   53.7   56.09
  2/0.225 mm     6/0.45 mm   26.9   56.09
   2/0.45 mm     6/0.45 mm   26.9   56.09
       1/16"  4.5/0.225 mm   33.8   56.11
        1/8"     9/0.45 mm   16.9   56.11
       1/16"         3/16"   33.8   56.13
  5/0.225 mm        17/32"   10.7   56.24
   5/0.45 mm        17/32"   10.7   56.24
       3/32"     7/0.45 mm   22.5   56.36
       1/16"     5/0.45 mm   33.5   56.85
       7/32"        19/32"    9.6   56.93
3.5/0.225 mm    10/0.45 mm   15.1   57.25
  4/0.225 mm         7/16"   13.2   57.26
   4/0.45 mm         7/16"   13.2   57.26
       5/32"         7/16"   13.3   57.73
       1/32"     3/0.45 mm   65.9   58.29
   6/0.45 mm        21/32"    8.7   58.61
4.5/0.225 mm          1/2"   11.6   58.71
  3/0.225 mm        11/32"   17.3   58.92
   3/0.45 mm        11/32"   17.3   58.92
       3/16"        17/32"   10.9   59.15
4.5/0.225 mm    13/0.45 mm   11.5   59.26
1.5/0.225 mm  4.5/0.225 mm   34.4   59.51
  3/0.225 mm     9/0.45 mm   17.2   59.51
   3/0.45 mm     9/0.45 mm   17.2   59.51
1.5/0.225 mm         3/16"   34.4   59.53
       3/32"         9/32"   21.6   59.54
  5/0.225 mm         9/16"   10.3   59.85
   5/0.45 mm         9/16"   10.3   59.85
       7/32"          5/8"    9.2   60.15
1.5/0.225 mm     5/0.45 mm   34.1   60.25
3.5/0.225 mm        13/32"   14.6   60.50
  4/0.225 mm    12/0.45 mm   12.6   61.15
   4/0.45 mm    12/0.45 mm   12.6   61.15
        1/8"          3/8"   15.9   61.17
       5/32"    12/0.45 mm   12.7   61.62
  4/0.225 mm        15/32"   12.6   61.66
   4/0.45 mm        15/32"   12.6   61.66
  2/0.225 mm          1/4"   25.0   62.10
   2/0.45 mm          1/4"   25.0   62.10
       5/32"        15/32"   12.6   62.13
4.5/0.225 mm        17/32"   11.0   62.55
       3/16"         9/16"   10.4   62.76
       1/16"    5/0.225 mm   31.1   63.09
        1/8"    10/0.45 mm   15.5   63.09
       7/32"        21/32"    8.9   63.21
  5/0.225 mm        19/32"    9.9   63.25
   5/0.45 mm        19/32"    9.9   63.25
3.5/0.225 mm    11/0.45 mm   14.0   63.50
  3/0.225 mm          3/8"   16.2   64.57
   3/0.45 mm          3/8"   16.2   64.57
3.5/0.225 mm         7/16"   13.7   65.26
       3/32"     8/0.45 mm   20.1   65.46
  4/0.225 mm          1/2"   11.9   65.77
   4/0.45 mm          1/2"   11.9   65.77
4.5/0.225 mm         9/16"   10.6   66.16
       3/16"        19/32"   10.0   66.17
       5/32"          1/2"   12.0   66.24
  4/0.225 mm    13/0.45 mm   11.9   66.32
   4/0.45 mm    13/0.45 mm   11.9   66.32
        1/8"        13/32"   14.9   66.34
  5/0.225 mm          5/8"    9.5   66.47
   5/0.45 mm          5/8"    9.5   66.47
1.5/0.225 mm    5/0.225 mm   31.5   66.49
  3/0.225 mm    10/0.45 mm   15.8   66.49
   3/0.45 mm    10/0.45 mm   15.8   66.49
       3/32"         5/16"   19.9   66.51
       5/32"    13/0.45 mm   11.9   66.79
  1/0.225 mm  3.5/0.225 mm   47.1   66.81
  2/0.225 mm     7/0.45 mm   23.6   66.81
   2/0.45 mm     7/0.45 mm   23.6   66.81
       1/16"         7/32"   29.7   66.85
  1/0.225 mm     4/0.45 mm   46.5   67.79
       1/32"          1/8"   58.6   67.87
3.5/0.225 mm    12/0.45 mm   13.1   69.15
        1/8"    11/0.45 mm   14.4   69.34
       3/16"          5/8"    9.6   69.39
  5/0.225 mm        21/32"    9.1   69.53
   5/0.45 mm        21/32"    9.1   69.53
4.5/0.225 mm        19/32"   10.1   69.57
  4/0.225 mm        17/32"   11.4   69.61
   4/0.45 mm        17/32"   11.4   69.61
3.5/0.225 mm        15/32"   13.0   69.66
  3/0.225 mm        13/32"   15.1   69.74
   3/0.45 mm        13/32"   15.1   69.74
       1/32"    3/0.225 mm   57.1   69.93
       1/16"     6/0.45 mm   28.5   69.93
  2/0.225 mm         9/32"   22.6   69.99
   2/0.45 mm         9/32"   22.6   69.99
       5/32"        17/32"   11.4   70.08
1.5/0.225 mm         7/32"   30.1   70.25
  1/0.225 mm         5/32"   44.8   70.76
        1/8"         7/16"   14.1   71.10
       3/16"        21/32"    9.2   72.45
  3/0.225 mm    11/0.45 mm   14.6   72.73
   3/0.45 mm    11/0.45 mm   14.6   72.73
       3/32"        11/32"   18.3   72.76
4.5/0.225 mm          5/8"    9.7   72.79
  4/0.225 mm         9/16"   10.9   73.22
   4/0.45 mm         9/16"   10.9   73.22
1.5/0.225 mm     6/0.45 mm   28.9   73.32
       3/32"     9/0.45 mm   18.2   73.35
       5/32"         9/16"   10.9   73.69
3.5/0.225 mm          1/2"   12.3   73.77
3.5/0.225 mm    13/0.45 mm   12.2   74.32
  3/0.225 mm         7/16"   14.2   74.49
   3/0.45 mm         7/16"   14.2   74.49
        1/8"    12/0.45 mm   13.4   74.99
        1/8"        15/32"   13.3   75.50
4.5/0.225 mm        21/32"    9.3   75.84
  1/0.225 mm    4/0.225 mm   41.9   75.91
  2/0.225 mm     8/0.45 mm   21.0   75.91
   2/0.45 mm     8/0.45 mm   21.0   75.91
       1/16"          1/4"   26.4   75.94
  4/0.225 mm        19/32"   10.4   76.62
   4/0.45 mm        19/32"   10.4   76.62
  2/0.225 mm         5/16"   20.7   76.97
   2/0.45 mm         5/16"   20.7   76.97
       5/32"        19/32"   10.4   77.09
3.5/0.225 mm        17/32"   11.7   77.61
  3/0.225 mm    12/0.45 mm   13.5   78.39
   3/0.45 mm    12/0.45 mm   13.5   78.39
       3/32"          3/8"   17.0   78.41
  3/0.225 mm        15/32"   13.4   78.90
   3/0.45 mm        15/32"   13.4   78.90
1.5/0.225 mm          1/4"   26.7   79.34
        1/8"          1/2"   12.6   79.61
  4/0.225 mm          5/8"   10.0   79.84
   4/0.45 mm          5/8"   10.0   79.84
        1/8"    13/0.45 mm   12.5   80.16
       5/32"          5/8"   10.0   80.31
       3/32"    10/0.45 mm   16.6   80.32
       1/32"  3.5/0.225 mm   49.6   80.65
       1/16"     7/0.45 mm   24.8   80.65
3.5/0.225 mm         9/16"   11.2   81.22
       1/32"     4/0.45 mm   49.0   81.63
  4/0.225 mm        21/32"    9.6   82.90
   4/0.45 mm        21/32"    9.6   82.90
  3/0.225 mm          1/2"   12.7   83.00
   3/0.45 mm          1/2"   12.7   83.00
  2/0.225 mm        11/32"   19.0   83.21
   2/0.45 mm        11/32"   19.0   83.21
       5/32"        21/32"    9.6   83.37
        1/8"        17/32"   12.0   83.45
  3/0.225 mm    13/0.45 mm   12.6   83.56
   3/0.45 mm    13/0.45 mm   12.6   83.56
       3/32"        13/32"   15.9   83.58
  1/0.225 mm  4.5/0.225 mm   37.8   83.80
  2/0.225 mm     9/0.45 mm   18.9   83.80
   2/0.45 mm     9/0.45 mm   18.9   83.80
  1/0.225 mm         3/16"   37.8   83.82
       1/16"         9/32"   23.8   83.83
1.5/0.225 mm     7/0.45 mm   25.1   84.05
  1/0.225 mm     5/0.45 mm   37.4   84.54
       1/32"         5/32"   47.1   84.60
3.5/0.225 mm        19/32"   10.7   84.62
       3/32"    11/0.45 mm   15.3   86.57
  3/0.225 mm        17/32"   12.1   86.84
   3/0.45 mm        17/32"   12.1   86.84
        1/8"         9/16"   11.4   87.06
1.5/0.225 mm         9/32"   24.1   87.23
3.5/0.225 mm          5/8"   10.2   87.84
       3/32"         7/16"   14.9   88.33
  2/0.225 mm          3/8"   17.6   88.86
   2/0.45 mm          3/8"   17.6   88.86
       1/32"    4/0.225 mm   43.9   89.75
       1/16"     8/0.45 mm   22.0   89.75
  3/0.225 mm         9/16"   11.5   90.45
   3/0.45 mm         9/16"   11.5   90.45
        1/8"        19/32"   10.9   90.46
  1/0.225 mm    5/0.225 mm   34.4   90.78
  2/0.225 mm    10/0.45 mm   17.2   90.78
   2/0.45 mm    10/0.45 mm   17.2   90.78
       1/16"         5/16"   21.6   90.81
3.5/0.225 mm        21/32"    9.8   90.90
       3/32"    12/0.45 mm   14.2   92.23
       3/32"        15/32"   14.1   92.74
1.5/0.225 mm     8/0.45 mm   22.2   93.15
        1/8"          5/8"   10.4   93.68
  3/0.225 mm        19/32"   11.0   93.86
   3/0.45 mm        19/32"   11.0   93.86
  2/0.225 mm        13/32"   16.4   94.03
   2/0.45 mm        13/32"   16.4   94.03
1.5/0.225 mm         5/16"   21.9   94.20
  1/0.225 mm         7/32"   32.6   94.54
        1/8"        21/32"   10.0   96.74
       3/32"          1/2"   13.3   96.84
  2/0.225 mm    11/0.45 mm   15.8   97.03
   2/0.45 mm    11/0.45 mm   15.8   97.03
       1/16"        11/32"   19.9   97.05
  3/0.225 mm          5/8"   10.5   97.08
   3/0.45 mm          5/8"   10.5   97.08
       3/32"    13/0.45 mm   13.2   97.40
  1/0.225 mm     6/0.45 mm   31.3   97.62
       1/32"  4.5/0.225 mm   39.4   97.64
       1/16"     9/0.45 mm   19.7   97.64
       1/32"         3/16"   39.4   97.66
       1/32"     5/0.45 mm   39.0   98.38
  2/0.225 mm         7/16"   15.4   98.79
   2/0.45 mm         7/16"   15.4   98.79
  3/0.225 mm        21/32"   10.1  100.14
   3/0.45 mm        21/32"   10.1  100.14
1.5/0.225 mm        11/32"   20.0  100.45
       3/32"        17/32"   12.6  100.68
1.5/0.225 mm     9/0.45 mm   19.9  101.04
  2/0.225 mm    12/0.45 mm   14.6  102.68
   2/0.45 mm    12/0.45 mm   14.6  102.68
       1/16"          3/8"   18.3  102.70
  2/0.225 mm        15/32"   14.5  103.19
   2/0.45 mm        15/32"   14.5  103.19
  1/0.225 mm          1/4"   28.7  103.63
       3/32"         9/16"   12.0  104.29
       1/32"    5/0.225 mm   35.7  104.62
       1/16"    10/0.45 mm   17.9  104.62
1.5/0.225 mm          3/8"   18.5  106.10
  2/0.225 mm          1/2"   13.6  107.30
   2/0.45 mm          1/2"   13.6  107.30
       3/32"        19/32"   11.4  107.70
  2/0.225 mm    13/0.45 mm   13.5  107.85
   2/0.45 mm    13/0.45 mm   13.5  107.85
       1/16"        13/32"   17.0  107.87
1.5/0.225 mm    10/0.45 mm   18.0  108.02
  1/0.225 mm     7/0.45 mm   26.9  108.34
       1/32"         7/32"   33.8  108.38
       1/16"    11/0.45 mm   16.3  110.87
       3/32"          5/8"   10.9  110.92
  2/0.225 mm        17/32"   12.9  111.14
   2/0.45 mm        17/32"   12.9  111.14
1.5/0.225 mm        13/32"   17.2  111.27
       1/32"     6/0.45 mm   32.4  111.46
  1/0.225 mm         9/32"   25.7  111.52
       1/16"         7/16"   15.9  112.63
       3/32"        21/32"   10.4  113.98
1.5/0.225 mm    11/0.45 mm   16.4  114.26
  2/0.225 mm         9/16"   12.2  114.75
   2/0.45 mm         9/16"   12.2  114.75
1.5/0.225 mm         7/16"   16.0  116.02
       1/16"    12/0.45 mm   15.0  116.52
       1/16"        15/32"   14.9  117.03
  1/0.225 mm     8/0.45 mm   23.6  117.44
       1/32"          1/4"   29.7  117.47
  2/0.225 mm        19/32"   11.7  118.15
   2/0.45 mm        19/32"   11.7  118.15
  1/0.225 mm         5/16"   23.2  118.50
1.5/0.225 mm    12/0.45 mm   15.1  119.92
1.5/0.225 mm        15/32"   15.0  120.43
       1/16"          1/2"   14.1  121.14
  2/0.225 mm          5/8"   11.1  121.37
   2/0.45 mm          5/8"   11.1  121.37
       1/16"    13/0.45 mm   13.9  121.69
       1/32"     7/0.45 mm   27.7  122.18
  2/0.225 mm        21/32"   10.6  124.43
   2/0.45 mm        21/32"   10.6  124.43
1.5/0.225 mm          1/2"   14.1  124.53
  1/0.225 mm        11/32"   21.2  124.74
       1/16"        17/32"   13.3  124.98
1.5/0.225 mm    13/0.45 mm   14.0  125.09
  1/0.225 mm     9/0.45 mm   21.0  125.33
       1/32"         9/32"   26.4  125.36
1.5/0.225 mm        17/32"   13.4  128.37
       1/16"         9/16"   12.6  128.59
  1/0.225 mm          3/8"   19.4  130.39
       1/32"     8/0.45 mm   24.2  131.28
1.5/0.225 mm         9/16"   12.7  131.98
       1/16"        19/32"   12.0  131.99
  1/0.225 mm    10/0.45 mm   18.9  132.31
       1/32"         5/16"   23.8  132.34
       1/16"          5/8"   11.4  135.21
1.5/0.225 mm        19/32"   12.0  135.39
  1/0.225 mm        13/32"   18.0  135.56
       1/16"        21/32"   10.9  138.27
  1/0.225 mm    11/0.45 mm   17.2  138.56
       1/32"        11/32"   21.6  138.58
1.5/0.225 mm          5/8"   11.4  138.61
       1/32"     9/0.45 mm   21.5  139.17
  1/0.225 mm         7/16"   16.7  140.32
1.5/0.225 mm        21/32"   10.9  141.67
  1/0.225 mm    12/0.45 mm   15.8  144.21
       1/32"          3/8"   19.9  144.23
  1/0.225 mm        15/32"   15.6  144.72
       1/32"    10/0.45 mm   19.3  146.15
  1/0.225 mm          1/2"   14.7  148.83
  1/0.225 mm    13/0.45 mm   14.6  149.38
       1/32"        13/32"   18.3  149.40
       1/32"    11/0.45 mm   17.5  152.40
  1/0.225 mm        17/32"   13.8  152.67
       1/32"         7/16"   17.0  154.16
  1/0.225 mm         9/16"   13.1  156.28
       1/32"    12/0.45 mm   16.0  158.05
       1/32"        15/32"   15.9  158.56
  1/0.225 mm        19/32"   12.4  159.68
       1/32"          1/2"   14.9  162.67
  1/0.225 mm          5/8"   11.8  162.90
       1/32"    13/0.45 mm   14.8  163.22
  1/0.225 mm        21/32"   11.3  165.96
       1/32"        17/32"   14.1  166.51
       1/32"         9/16"   13.3  170.12
       1/32"        19/32"   12.6  173.52
       1/32"          5/8"   12.0  176.74
       1/32"        21/32"   11.4  179.80

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