What is the formula for calculating G_T in line-of-sight antennas?

[bos1234]

Homework Statement

In terrestrial microwave link, line-of-sight transmission limits the separation of transmitters and receivers to about 40km. If a 100mW transmitter at 4GHz is used with transmitting and receiving antennas of 0.5m^2 effective area, what is the received power level in dBm?

Homework Equations

I think this is the equation to use
$$P_{r}=P_{T}+G_{R}+G_{T}-L_{P}$$

P_t is given and G_R and L_P can be found. However, I am having trouble finding G_T?

 

[skeptic2]

Is not the G_T related to the spread angle of the microwave beam. If all the P_T is concentrated in a beam instead of a sphere, the gain should be approximately equal to the reciprocal of cross section of the beam versus the area of the a sphere at the same radius.

 

[bos1234]

thanks for the reply. I've attached a copy of my working out. I stated in my original post that L_p was found, however, it is only the free space loss of two isotropic antennas

 

[skeptic2]

I think I follow your arithmetic but I'm not always sure why you are doing what you're doing.
1. 100 x 10^3 (100 mW) = -10 dBW not dB. However the answer is supposed to be in dBm.

2. Farther down you have L_P = (4 * pi * R / x)^2 What is x or is that lambda?

3. Above that you have G_T = (4 * pi * (R_RX)^2) / (pi * (R_TX)^2) How did you get that formula?

4. Are you assuming there is no spread in the antenna pattern over 40 km?

 

[bos1234]

Hi
1. Sorry its dbW. I will change to dbm later this is not a issue

2.free space loss formula. Sorry about the writing. So I can find this out by substituting the appropriate values i.e. R is the distance between the 2 antennas and lamda can be caluclated since frequency and speed of light are known

3.This formula I sort of made up. There was a similar question posted by me in this thread
https://www.physicsforums.com/showthread.php?t=441793

I treated the satellite as the receiver, and the Earth as the transmitter. So numerator is the suraface area of the receiver whilst denominator is the cross-sectional area of the transmitter.

4. Yes I'm assuming no spread

Am I on the right track or not? I think the problem is with G_t and G_r?

 

[skeptic2]

3. I thought the formula might be related to the free space loss formula but then it would be 16 * pi^2 * R^2... This is what confused me.

4. From the information given I don't know how to calculate G_T and G_R. There is a formula, though I don't know it, that relates parabolic antenna diameter in wavelengths to beam spread. That's what I thought this problem was about. If I remember correctly in order to get a 1 deg spread, the antenna has to be about 10 wavelengths in diameter. Once you have the formula, then the loss would amount to what part of the cross sectional area of the transmitted beam does the receive antenna intercept at the distance given.