Calculation of range for signal with damping

[dolle39]

Homework Statement

Given the transmitting power of 0.1 mW and received noise of -100 dBm. Consider a signal which needs a SNR of 30 dB. Calculate the range for a signal of 0.5 MHz given that the damping for the signal is calculated as:

L = 10 +8.0*f [dB/km] where f is the frequency in MHz

Homework Equations

SNR = "Signal power" / "Noise Power"

S_dBm = 10 log * (P1 / 1mw)

The Attempt at a Solution

I am kinda stuck on how to approach this problem so suggestions are mostly welcome!

 

[collinsmark]

Homework Statement

Given the transmitting power of 0.1 mW and received noise of -100 dBm. Consider a signal which needs a SNR of 30 dB. Calculate the range for a signal of 0.5 MHz given that the damping for the signal is calculated as:

L = 10 +8.0*f [dB/km] where f is the frequency in MHz

Homework Equations

SNR = "Signal power" / "Noise Power"

S_dBm = 10 log * (P1 / 1mw)

The Attempt at a Solution

I am kinda stuck on how to approach this problem so suggestions are mostly welcome!

There's a few things you'll need to do first before putting everything together.

• The noise power is given, and the signal to noise ratio is also given. Calculate the necessary, received signal power (and just keep it in terms of dBm, it will make things easier that way).
• Eventually, you will need to convert 0.1 mW to units of dBm. You might as well do that next.
• Plug in the 0.5 MHz for f and calculate L. Now realize that L, the path loss attenuation figure, is in units of dB/km. [STRIKE]Express L as something like a/d were a is in units of dB and d is in units of km.[/STRIKE] Eventually you'll be solving for d after you put everything together.

Edit: The way I wrote that last part is sort of confusing now that I think about it. L is in units of dB/km. What you'll want to do is come up with an equation that gives attenuation, in dB, for a given distance, like A = Ld where A is the loss in units of dB, and d is the distance in km. You'll still be solving for d though, once everything is put together. That's essentially the same thing as I originally wrote, but I hope worded a little more clearly.