Isotropic antenna Transmit and Receive power

[SPYazdani]

Homework Statement

Plot and compare the path loss (dB) for the free-space and plane-Earth models at 800MHz vs distance on a logarithmic scale for distances from 1m to 40Km. Assume that the antennas are isotropic and have a height of 10m

Homework Equations

Free space: P_R=\frac{P_T G_T G_R}{L_P}

Plane Earth: P_R=P_TG_TG_R(\frac{h_Th_R}{R^2})^2

Two isotropic antennas separated by a distance R\epsilon[1m,40km] at frequency f=800MHz.

The Attempt at a Solution

Isotropic antennae have G_T=G_R=1. So That simplifies P_R=\frac{P_T G_T G_R}{L_P} = P_R=\frac{P_T}{L_P}
L_P=(\frac{R4\pi}{\lambda})^2.

I'm solving the question for 1m for the free space model, then once I have that, plotting it is easy in Excel.

I'm stuck on finding P_T. I tried deriving an equation for P_Tby substituting L_P=(\frac{R4\pi}{\lambda})^2 into P_R=\frac{P_T}{L_P} but that lead me nowhere. At least I don't know what the answer means.

Here's what happened.

P_R=\frac{P_T}{R^24\pi}A_e
P_R=\frac{P_T}{L_P}
L_P=(\frac{R4\pi}{\lambda})^2
\frac{P_T}{R^24\pi}A_e=\frac{P_T}{(\frac{R4\pi}{λ})^2}
Then a bunch of cancellation on both sides and finally
Ae 4\pi = \lambda^2

Help! I don't know how to find P_T

 

[marcusl]

What is Lp? How does it relate to what you are asked for?

 

[SPYazdani]

What is Lp? How does it relate to what you are asked for?

For reliable communication, Lp is the minimum signal level required at the receiving antenna. It's a ratio of \frac{P_T (mW)}{P_R(mW)}. The distance R = \frac{\lambda\sqrt{L_P}}{4\pi}. Rearranging and solving for L_P = (\frac{4R\pi}{\lambda})^2 implies the loss is related to the distance separated by the antennas as well as the wavelength of the transmitted signal.

Thanks for pointing that out. I can now solve my problem :D

 

[marcusl]

You're welcome!