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 MIL-HDBK-419A
5.2.2.4 Proximity Effect. When two or more conductors are in close proximity, the current flowing in one
conductor is redistributed because of the magnetic Held produced by the current in the other conductor. This
effect is an extension of skin effect and is called proximity effect. The proximity effect tends to increase the
ac resistance of a conductor to a value greater than that due to simple skin effect.
5.2.3
Resistance Properties vs Impedance Properties.
Although skin effect exists at all frequencies, it becomes more significant as the frequency increases. The
reactance of a conductor also increases with frequency to further increase the conductor impedance above its
dc value. To design an effective ground system one must consider the relative effects of the dc resistance, the
ac resistance, and the inductance upon the total impedance of a ground conductor.
Using Equation 5-1, the dc resistance of round wire conductors can be calculated. The dc resistance per
1000 feet for four standard size copper cables is given in Table 5-3. Table 5-4 gives the dc resistance and (for
60 Hz) the ac resistance, the inductance and the total impedance of various size and length conductors as
determined from Table 5-3 and from Equation 5-12. At a frequency of 1 MHz, these same characteristics for
30-meter (100-foot) lengths are given in Table 5-5 as calculated from Equations 5-3 and 5-12. Note that for
the larger wires (No. 2 AWG or larger) the inductance of the long (> 100 feet! cables determines the magnitude
of the impedance. Also note that for the same length cables there is not as much difference in the impedance
magnitudes of a small and a large cable as there is in the resistance of the two cable sizes. For example, the
ratio of the dc resistance of a 30-meter (100-foot) length of No. 12 AWG copper cable to the dc resistance of a
30 meter (100 feet) of 1/0 AWG copper cable is 0.15880/0.0098 = 16.20. Since the ac resistance at 60 Hz is
approximately the same as the dc resistance, the ratio of the 60 Hz ac resistance of the two cables is also
16.20. At a frequency of 1 MHz the ratio of the ac resistance becomes 1.23/0.307 = 4.01. However, the 60 Hz
impedance ratio is only 0.1605/0.0226 = 7.10 and the 1 MHz impedance ratio is only 382.65/329.49 = 1.16. These
ratios are tabulated in Table 5-6 for comparison. From Tables 5-3 through 5-6 and the above example, the
following conclusions are made:
a . Because of the inductance, the advantages offered by a large cable such as 1/0 AWG are less than
they might appear to be from a comparison of the dc resistance values.
b . The advantage offered by a large cable, e.g., 1/0 AWG, will be somewhat more pronounced for
relatively short conductor lengths than for long conductor runs. This is true because inductance increases more
rapidly with length than does resistance (see Equations 5-1 and 5-9).
c . Because of the lack of dramatic improvement in ac impedance of large cables over smaller cable
sizes for long runs, consideration of materials and labor costs are relatively important and may be the deciding
factor.
d . Since even 1/0 AWG cables exhibit impedances from 22.6
to 115.8
for lengths of 30 meters
(100 feet) and 137 meters (450 feet), respectively, the control of stray currents should be an essential objective
in any signal grounding system.
5-10
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