Exercise dealing with power in dBm (dBmW) & attenuation coefficient in dB/km

Okay, I have a Matlab exercise I've been working on. I've been stuck
on something peripheral to the main problem. It gives two channels,
each with its own attenuation coefficient in dB/km. As well, there are
repeaters with a minimal signal power requirement, given in dBm.
Basically, for this part of the problem, we have to figure out which
channel gets the signal across 100 km with the least cost possible
(the better channel has a more costly repeater).

So I'm stuck on dealing with these units. Unfortunately, neither of my
signals books deals with signal attenuation. I've seen an attenuation
coefficient in electromagnetics class which was measured in np/m. And
you would find out the amplitude the signal is at a point by A = Ao*e^
(-a*x), where a is the attenuation coefficient of the channel (in np/
m), x is the distance from the originating signal which has an
amplitude Ao. Since my unit is dB/km, do I need to do A*10^(-a*x)?

I'm also wondering if the author gave units in dBm and dB/km to make
things easier. Do I need to convert the dBm to Watts then apply the
attenuation formula, then convert it back to dBm or is there an easier
way?

Your help is appreciated!

On 2 Des, 21:48, shawn7...@gmail.com wrote:
> Okay, I have a Matlab exercise I've been working on. I've been stuck
> on something peripheral to the main problem. It gives two channels,
> each with its own attenuation coefficient in dB/km. As well, there are
> repeaters with a minimal signal power requirement, given in dBm.
> Basically, for this part of the problem, we have to figure out which
> channel gets the signal across 100 km with the least cost possible
> (the better channel has a more costly repeater).
>
> So I'm stuck on dealing with these units. Unfortunately, neither of my
> signals books deals with signal attenuation. I've seen an attenuation
> coefficient in electromagnetics class which was measured in np/m. And
> you would find out the amplitude the signal is at a point by A = Ao*e^
> (-a*x), where a is the attenuation coefficient of the channel (in np/
> m), x is the distance from the originating signal which has an
> amplitude Ao. Since my unit is dB/km, do I need to do A*10^(-a*x)?
>
> I'm also wondering if the author gave units in dBm and dB/km to make
> things easier. Do I need to convert the dBm to Watts then apply the
> attenuation formula, then convert it back to dBm or is there an easier
> way?
>
> Your help is appreciated!

The attenuation per km is a factor that has to be accounted for.
In linear scale, you do something like

P_recieved = P_sent * F^length

Convert that to dB and find that the arithmetics becomes

P_dB|recieved = P_dB|sent + length * F_dB

where P_sent and P_recieved are the sent and recieved powers,
length is the length of the channel, and F is the attenuation
factor.

Rune

shawn7...@gmail.com wrote:
> Okay, I have a Matlab exercise I've been working on. I've been stuck
> on something peripheral to the main problem. It gives two channels,
> each with its own attenuation coefficient in dB/km. As well, there are
> repeaters with a minimal signal power requirement, given in dBm.
> Basically, for this part of the problem, we have to figure out which
> channel gets the signal across 100 km with the least cost possible
> (the better channel has a more costly repeater).
>
>

I'm not sure what your questoin is but this might help

http://en.wikipedia.org/wiki/Friis_transmission_equation

Mark