AAARG! I hate it when this happens. My table of wire impedances has an
error. The formula had a decimal point error. Plus the strap inductance
calculations has the same decimal point error. I found it while trying
to verify some of Polyphaser's numbers. The conclusions don't change
much from before, only a little more surprising since the frequencies
are lower than before. Here is a revised table and I'll repeat the
conclusions with the proper numbers.
------------------
Some interesting conclusions can be drawn from this data. For example,
at 3.3 Hz the impedance of a #4 wire due to its inductance is the same
as its skin resistance, but the DC resistance still dominates. At 112
Hz the impedance due to inductance is equal to the total DC
resistance(skin plus DC resistance). That means for any frequency above
112 Hz, the impedance of the wire is due primarily to its inductance,
not its DC resistance or skin resistance. As a matter of fact, above
about 2 kHz, the DC resistance and skin resistances are insignificant
for this wire, even though they are continually increasing. Since all
these parameters are linear with length, this conclusion is the same
regardless of the length of the wire. For a #2 wire, this same point
happens at 73 HZ instead of 112 Hz.
Calculated data:
#4 wire, 10 ft length, L = 4.13 uH (straight wire in free space)
Note: A wire in the ground will appear as a higher inductance than shown
here, because of the decreased velocity factor of the medium.
Z(L) represents impedance calculated from inductance only.
Freq Z(L) DC res Skin res
3.3 Hz 8.9e-5 2.49e-3 8.9e-5
93 Hz 2.49e-3 2.49e-3 4.7e-4
112 Hz 3e-3 2.49e-3 5.16e-4
1 kHz 0.027 2.49e-3 1.15e-3
10 kHz 0.269 2.49e-3 4.88e-3
100 kHz 2.69 2.49e-3 1.54e-2
1 MHz 26.9 2.49e-3 4.88e-2
I didn't have a spreadsheet already made up to calculate the skin
resistance of a strap, but I do have one to calculate its inductance.
Since the inductance is the predominate parameter, it's probable all you
will need anyway. The calculations are for a strap thickness of 0.05
inches, and a length of 10 ft. Since the thickness doesn't effect the
inductance very much, it wasn't included as a variable parameter.
Compare these numbers to a #4 wire, same length, which was 4.13 uH.
Strap width Inductance uH
0.5 in 3.96
1 in 3.59
2 in 3.2
3 in 2.97
4 in 2.8
5 in 2.66
6 in 2.56
The formula for the wire inductance and strap inductance came from the
Polyphaser book, Grounds for Lightning & EMP Protection.
Jerry, K4SAV
K4SAV wrote:
>All this grounding talk has got me thinking again.
>
>Most of us know that the impedance of a wire is increased by its skin
>resistance, and that a wire with more skin area (such as a strap) will
>provide a lower impedance. But how much lower? I decided to break out my
>spread sheet I made for calculating these things and take a look. The
>data is tabulated below.
>
>Some interesting conclusions can be drawn from this data. For example,
>at 330 HZ the impedance of a #4 wire due to its inductance is the same
>as its skin resistance, but the DC resistance still dominates. At 1660
>Hz the impedance due to inductance is equal to the total DC resistance
>(skin plus DC resistance). That means for any frequency above 1660 Hz,
>the impedance of the wire is due primarily to its inductance, not its DC
>resistance or skin resistance. As a matter of fact, above about 20 KHz,
>the DC resistance and skin resistances are insignificant for this wire,
>even though they are continually increasing. Since all these parameters
>are linear with length, this conclusion is the same regardless of the
>length of the wire. For a #2 wire, this same point happens at 1100 HZ
>instead of 1660 Hz.
>
>Note that when applying these conclusions to other things besides ground
>wires, there is a difference between impedance due to inductance and
>impedance due to resistance.
>
>---------------------
>Calculated data:
>#4 wire, 10 ft length, L = 0.43 uH (straight wire in free space)
>Note: A wire in the ground will appear as a higher inductance than shown
>here, because of the decreased velocity factor of the medium.
>Z(L) represents impedance calculated from inductance only.
>
>Freq Z(L) DC res Skin res
>330 Hz 8.86e-4 2.49e-3 8.86e-4
>920 Hz 2.47e-3 2.49e-3 1.48e-3
>1660 Hz 4.46e-3 2.49e-3 1.99e-3
>10 kHz 2.69e-2 2.49e-3 4.88e-3
>100 kHz 0.269 2.49e-3 1.54e-2
>1 MHz 2.69 2.49e-3 4.88e-2
>
>
>I didn't have a spreadsheet already made up to calculate the skin
>resistance of a strap, but I do have one to calculate its inductance.
>Since the inductance is the predominate parameter, it's probable all you
>will need anyway. The calculations are for a strap thickness of 0.05
>inches, and a length of 10 ft. Since the thickness doesn't effect the
>inductance very much, it wasn't included as a variable parameter.
>Compare these numbers to a #4 wire, same length, which was 0.43 uH.
>
>Strap width Inductance uH
> 0.5 in 0.40
> 1 in 0.36
> 2 in 0.32
> 3 in 0.30
> 4 in 0.28
> 5 in 0.27
> 6 in 0.26
>
>The formula for the wire inductance and strap inductance came from the
>Polyphaser book, Grounds for Lightning & EMP Protection.
>
>One other note of significance: None of these calculations include
>resonant effects. For wires that are long compared to the frequencies
>being considered, resonance effects can increase the impedance by a huge
>amount compared to an impedance value calculated from wire inductance.
>
>Jerry, K4SAV
>_______________________________________________
>
>
>
>_______________________________________________
>TowerTalk mailing list
>TowerTalk@contesting.com
>http://lists.contesting.com/mailman/listinfo/towertalk
>
>
>
_______________________________________________
_______________________________________________
TowerTalk mailing list
TowerTalk@contesting.com
http://lists.contesting.com/mailman/listinfo/towertalk
|