# Isotropic antenna Transmit and Receive power

• SPYazdani
In summary, the conversation discusses the task of plotting and comparing the path loss for the free-space and plane-Earth models at a frequency of 800MHz over a distance range of 1m to 40km. It also explains the concept of Lp, the minimum signal level required at the receiving antenna, and how it relates to the distance between antennas and the wavelength of the transmitted signal. The conversation ends with the speaker thanking the other person for helping them solve their problem.
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 $P_T$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 $P_T$

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

marcusl said:
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

You're welcome!

and I don't know what the last equation means.

As a scientist, it is important to always double check your equations and make sure they make sense. In this case, the last equation you derived (Ae 4\pi = \lambda^2) does not make sense and may be a result of a mistake in your algebra.

To find P_T, you will need to use the given information and equations for the free space and plane Earth models. For the free space model, you can use the equation P_R = P_T/L_P and substitute in the given values for G_T, G_R, and L_P. Then, you can solve for P_T. Similarly, for the plane Earth model, you can use the given equation P_R = P_TG_TG_R(h_Th_R/R^2)^2 and solve for P_T. Once you have P_T for both models, you can plot the path loss (in dB) for the free space and plane Earth models at 800MHz vs distance on a logarithmic scale.

It is also important to note that the height of the antennas (10m) will affect the path loss calculations and should be taken into account. It may be helpful to review the equations and make sure you have all the necessary information before attempting to solve the problem.

or how to proceed with the problem.

Hello, it seems like you are on the right track with your attempt at finding P_T. However, there is no need to find P_T in order to solve this problem. Instead, you can use the given information about the antennas' height and frequency to calculate the wavelength (λ) and then use that to find L_P for both the free space and plane Earth models. Once you have L_P, you can easily plot and compare the path loss (in dB) for the two models at various distances on a logarithmic scale. I hope this helps. Good luck with your homework!

## 1. What is an isotropic antenna?

An isotropic antenna is a theoretical antenna that radiates and receives electromagnetic waves equally in all directions. It is considered to be the most basic and ideal antenna type.

## 2. How does an isotropic antenna work?

An isotropic antenna works by converting electrical energy into electromagnetic waves, which are then transmitted in all directions evenly. Similarly, when receiving signals, it captures electromagnetic waves from all directions and converts them into electrical energy.

## 3. What is transmit power in relation to an isotropic antenna?

Transmit power refers to the amount of power that is being sent out by an isotropic antenna. It is measured in watts and determines the strength and range of the transmitted signal.

## 4. How is receive power different from transmit power for an isotropic antenna?

Receive power refers to the amount of power that is being captured by an isotropic antenna from incoming electromagnetic waves. It is also measured in watts and determines the sensitivity and efficiency of the antenna in picking up signals.

## 5. How can the transmit and receive power of an isotropic antenna be improved?

The transmit and receive power of an isotropic antenna can be improved by using a larger antenna size and increasing the input power. Additionally, using a directional antenna or adding a reflector can also improve the efficiency of the antenna in transmitting and receiving signals.

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