# Re: Coax Attenuation

```On Sat, Jul 07, 2001 at 10:05:36AM -0700, william washburn wrote:
> Folks,
>
> I wasn't going to post this concept, but since there
> seems to be some discussion today about coax attenuation,
> I think I will anyway.
>
> I tried last week to develop (since I couldn't find one)
> a formula for calculating the attenuation of a known
> length of cable given the attenuation per 100 ft.
>
> For example, given an attenuation of 3dB per 100 feet,
> what is the attenuation of 50 feet of said cable in dB?

The attenuation in dB = (attenuation/100ft) X (length in ft)/100, or
for 50 ft, 3 X 50 / 100 = 1.5 dB.

>
> Given 10 watts into 100 ft of this 3dB line, the ratio
> of input power to output power is 10/5 or 2 (3dB).
>
> For 50 ft, the power loss is half what it was before or
> 2.5W lost rather than 5W lost.  The I/O power ratio of
> 50ft is 10/7.5 or 1.25dB.

This is not correct.  Suppose the cable length was doubled to 200 ft.
If 2.5 W is lost for each 50 ft, that would imply that all of the 10
watts would be lost, whereas in reality half of the input power (5
watts) is lost in the first 100 ft and half of the remaining power (2.5
watts) is lost in the second 100 ft and 2.5 watts is delivered at the
output.

For a 100 ft cable, the power attenuated in the first 50 ft would be
2.93 watts.  The input to the second 50 feet would therefore be
10.00-2.93=7.07 watts and the power attenuated in that section would be
2.07 watts, resulting in an output power of 5 watts at the end of the
100 ft cable.

>
> The scaling must be done with power ratios, not dB.  I have
> seen, however, articles saying to halve the 3dB factor which
> gives 1.5dB not 1.25dB.

Loss in dB = 10 log (PWRout/PWRin)

> This may seem a small difference, but for critical calculations
> it becomes important.

Of course, this is why the calculation must be done correctly.  To be
more precise, a loss of half the power is 3.0103 dB, not 3.00 dB.

73,
Bob, N7XY

--
Bob Nielsen, N7XY                          nielsen@oz.net
Bainbridge Island, WA                      http://www.oz.net/~nielsen
IOTA NA-065, USI WA-028S
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