## Isotropic antenna Transmit and Receive power

1. The problem statement, all variables and given/known data
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

2. Relevant 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 $f=800MHz$.

3. 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 $P_T$by 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 $P_T$
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 Recognitions: Science Advisor What is Lp? How does it relate to what you are asked for?

 Quote by marcusl 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

Recognitions: