- #1

SPYazdani

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## 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: [itex]P_R=\frac{P_T G_T G_R}{L_P}[/itex]

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

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

## The Attempt at a Solution

Isotropic antennae have [itex]G_T=G_R=1[/itex]. So That simplifies [itex]P_R=\frac{P_T G_T G_R}{L_P}[/itex] = [itex]P_R=\frac{P_T}{L_P}[/itex]

[itex]L_P=(\frac{R4\pi}{\lambda})^2[/itex].

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 [itex]P_T[/itex]. I tried deriving an equation for [itex]P_T[/itex]by substituting [itex]L_P=(\frac{R4\pi}{\lambda})^2[/itex] into [itex]P_R=\frac{P_T}{L_P}[/itex] but that lead me nowhere. At least I don't know what the answer means.

Here's what happened.

[itex]P_R=\frac{P_T}{R^24\pi}A_e[/itex]

[itex]P_R=\frac{P_T}{L_P}[/itex]

[itex]L_P=(\frac{R4\pi}{\lambda})^2[/itex]

[itex]\frac{P_T}{R^24\pi}A_e=\frac{P_T}{(\frac{R4\pi}{λ})^2}[/itex]

Then a bunch of cancellation on both sides and finally

[itex]Ae 4\pi = \lambda^2[/itex]

Help! I don't know how to find [itex]P_T[/itex]