Near field path loss with attenuation

[theTimes]

Homework Statement

I have a 2 wireless cards with a power output of 0dBm, two 5dBi gain antennas, and a 30dB attenuator connected to each antenna. I need to figure out what the path loss will be in this scenario, so I can therefore determine the maximum distance possible between the antennas before they can no longer receive each other's signal.

Homework Equations

I know path loss in dB:

L = 20 log_10(4 * π *d / λ)

this one I can use to find the max distance once I know L, but I don't know how to find the path loss due to the attenuation in the first place.

The Attempt at a Solution

I know attenuation is:

= 10 * log_10(power out/ power in)

so

30 dB = 10 * log(power out/ odBm)

How can I find power out from here?

And how could I use that in the path loss equation?


Thank you for the help.

 

[KataKoniK]

To determine the path loss in this scenario, you will need to use both the path loss equation and the attenuation equation. First, let's find the power output of the wireless cards with the given information.

From the attenuation equation, we can rearrange it to solve for power out:

power out = power in * 10^(attenuation/10)

Substituting the given values, we get:

power out = 0dBm * 10^(30/10) = 1000mW

Now, we can use this value of power out in the path loss equation to find the path loss due to the attenuation:

L_attenuation = 20*log10(4*π*d/λ) = 20*log10(4*π*d/λ) = 20*log10(4*π*d/λ) - 20*log10(1000mW) = 20*log10(4*π*d/λ) - 60dB

Next, we can calculate the path loss due to the antennas using the gain of 5dBi:

L_antennas = 20*log10(4*π*d/λ) + 5dBi = 20*log10(4*π*d/λ) + 7dB

Finally, we can calculate the total path loss by adding the two values:

L_total = L_attenuation + L_antennas = 20*log10(4*π*d/λ) - 60dB + 20*log10(4*π*d/λ) + 7dB = 20*log10(4*π*d/λ) - 53dB

Now, we can use this value of path loss in the original equation to find the maximum distance between the antennas:

L_total = 20*log10(4*π*d/λ) - 53dB

Solving for d, we get:

d = 10^(L_total/20 - 53/20)*λ/4*π = 10^(L_total/20 - 2.65)*λ/4*π

Therefore, the maximum distance between the antennas is:

d = 10^(L_total/20 - 2.65)*λ/4*π

I hope this helps! Let me know if you have any further questions. Good luck with your calculations.