# Evaluate an antenna gain

Discussion in 'Homework Help' started by PsySc0rpi0n, Jul 4, 2017.

1. ### PsySc0rpi0n Thread Starter Well-Known Member

Mar 4, 2014
1,433
9
Hello everyone.

I have a problem that asks me to evaluate the gain of a lossless antenna. The information we have is the following:

U(θ,Φ) = B_0 * cos³(θ)
with 0 <= θ < π/2 and 0 <= θ < 2π
B_0
is a constant value.

I have already evaluated B_0 = 20/π by means of P_rad generic formula.
I already evaluated the Antenna Directivity, D = 8 ⇒ 9.031dB

I have 2 formulas to evaluate the Gain but none suits the information I have from the problem. They are:

$image=https://latex.codecogs.com/gif.latex?G%3D%5Cfrac%7B4%5Ccdot%20%5Cpi%20%5Ccdot%20U%28%5Ctheta%20%2C%20%5Cphi%20%29%7D%7BP_%7Brad%7D%7D&hash=f878ce3f80e279bafb27e618b0fc421a$

and using the antenna efficiency and reflection coefficient by:

$image=https://latex.codecogs.com/gif.latex?%5CGamma%20%3D%20%5Cfrac%7BZ_%7BL%7D%20-%20Z_%7B0%7D%7D%7BZ_%7BL%7D%20+%20Z_%7B0%7D%7D&hash=ac736451f8db50bbdc8435fab8ac7a3b$

e = 1 - |Γ|²

and

G = e * D

This said, how can I evaluate the antenna gain?

Last edited: Jul 4, 2017
2. ### PsySc0rpi0n Thread Starter Well-Known Member

Mar 4, 2014
1,433
9
What is wrong with the "tex" tags?

Well, problem fixed but something is wrong with the tex tags

3. ### RBR1317 Active Member

Nov 13, 2010
417
81
Tried doing one of the formula in tex:

$G=\frac{4\pi\cdot U(\theta,\phi)}{P_{rad}$

It seems to work OK. This is the code used: