Why did right-angle bends in
the wires cause such a
problem? As explained in
this article, wires used in resistors,
capacitors, inductors, antennas, and
ground connections affect AC and DC
When the current is AC (at any
frequency), new things begin to
appear (the numbers in this next
section are summarized in Table 1).
A perfect wire should conduct a
signal without adding noise, attenuation, or distortion. Whatever is electrically happening at one end of the wire
should be happening at the other end
exactly in the same form, no
matter what the current, voltage, frequency, surroundings, or temperature.
However, this isn’t the case. For example, the effect of the wire on a signal
depends on the frequency of the
current that the wire is conducting.
The higher the frequency, the more
the effect of the wire on the signal.
When the current is DC (ƒ = 0,
that is, the frequency is 0 Hz), the
behavior of the wire is most nearly the
perfect behavior described above. The
shape does not matter, what is near or
around the wire does not matter, and
the current flows in the whole wire.
But the temperature matters. For
example, six feet of No. 12 wire at
room temperature ( 20°C) has a resistance of about 9. 5 mΩ (0.0095Ω). At
30°C (hot day), the same wire has a
resistance of 9. 87 mΩ.
• Resistance — With AC, there are two
kinds of resistance. The first is the
ordinary well-known stuff that turns
electric power into heat. The second
is radiation resistance which turns
alternating current into electromagnetic waves. That means that a
wire becomes an antenna, which is
certainly not an ideal conductor.
No. 12 copper wire has a resistance at
30 MHz of 400 mΩ, compared to 9. 5
mΩ at DC. Even if the wire connects
to a perfect ground at one end, the
other end is not a good ground.
And there will be about 2. 2 μH of
inductance, as well.
• Skin Effect — As the frequency
increases, current moves out from the
center of the wire, and concentrates
at the surface so that, at high frequencies, all the current flows in a thin
“skin” at the surface of the wire. To an
RF (Radio Frequency) current, a wire
looks like a thin tube or pipe.
RF currents could be considered
“anti-social;” each RF current element
tries to get as far away from every
other element as possible. Since the
current flows entirely on the surface of
the wire, the inside of the wire might
as well not be there. At 30 MHz, the
effective conducting thickness of a
copper wire is a surface skin about 0.5
mils (0.0005 inch) thick. So, a tube of
copper half a mil thick and 80. 8 mils
in diameter is just as good at 30 MHz
as a solid No. 12 wire.
Now the result of this skin effect
anti-social behavior is that six feet of
Conductor Type and Length at 20°C DC Resistance
at 30 MHz
at 30 MHz
No. 12 Copper, six feet long 0.0095 ohms 0.40 ohms 2. 72 μH
of No. 12 Copper, 0.00318 ohms 0.18 ohms
six feet long
No. 6 Copper, six feet long 0.00237 ohms 0.20 ohms 2.0 μH
No. 30 Copper, six feet long 0.619 ohms 3. 4 ohms 3. 48 μH
Copper Foil, six feet
long, one inch wide, 0.0095 ohms 0.11 ohms 2.0 μH
five mils thick
Copper Foil, six feet
long, two inches 0.00475 ohms 0.06 ohms 1.75 μH
wide, five mils thick
TABLE 1. Resistance, Inductance, and Reactance.
56 February 2008
(depends on wire
• Proximity Effect — If more surface
area decreases the resistance, it would
be reasonable to use more than one
wire. Consider the result with three
twisted No. 12 conductors six feet long.
It would seem that the resistance
should be one-third of that produced
with one No. 12 conductor (0.4Ω).
Instead, the RF resistance is now at least
0.18Ω (instead of one-third of 0.4Ω or
0.133Ω)! It could be a lot more; it
depends very much on the condition of
the wire surface. The inductance with
this arrangement will be higher, too.
The proximity effect is very similar
to the skin effect in that it can also be
visualized as an anti-social tendency.
The RF current will stay on the top
surface of the wire so, with twisted
wires, the current flows from one conductor to another, and that is a high-resistance path. Incidentally, this is
why copper braid has a high RF resistance — up to 1Ω per foot at 20 MHz.
To avoid the proximity effect with
twisted wires, use one wire of approximately the same size in circular mils
as twisted wires. No. 6 wire has more
than three times the cross-sectional
area of No. 12 wire. Six feet of No.
6 wire will produce 0.2Ω of RF
resistance (only half of the resistance
of one No. 12 wire), and about 2.0 μH
of inductance at 30 MHz.
Now consider the proximity
effect in a coil. RF resistance is lower if
the space between turns is equal to
twice the wire diameter. Then, the RF
resistance increases by only about
5%, whereas if the turns are tightly
pressed against each other, the
resistance increases by about 33%,
avoiding the wire surface that is
pressed against another wire surface.
This is true if the current is flowing in
the same direction in the closely
spaced wires; if the current in
adjacent turns were somehow flowing
in opposite directions, the resistance
increase would be much greater.