# Homework Help: Directivity of array of antennas

1. Nov 14, 2008

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

I am trying to understand how the total directivity of an array of antennas is calculated.

2. Relevant equations

1. A_e = (D * lambda^2)/(4 * pi)
where:
A_e = effective aperature (or area of antenna)

D = Directivity of one antenna
lambda = wavelength

2. D_t = (4 * pi * A_t) / (lambda^2)
where:
D_t = directivity of array
A_t = effective aperature (of array)
lambda = wavelength

3. The attempt at a solution

What I am confused on is how aperature comes into play because if I have X antennas spaced Y wavelengths apart for the array, total aperature (A_t in eqn #2) is what will change. I just don't know how to get A_t from A_e if I know what the antenna spacing is.

As an example, let's say I know the directivity of one antenna is 10 (which 10 dBi). But if I have 3 of them and let's say they're spaced 0.25 wavelengths apart, what is the directivity of the array?

From eqn #1, A_e would be (10 * (.25L)^2) / (4 * 3.14) = 0.0497L^2 = 0.05L^2
(I'm using L for lambda)

So what is the aperature of the array if I know the aperature of one antenna is 0.05L^2 ? Once I have that I would be able to use eqn #2 to figure out the array's total directivity. But the relationship between A_e and A_t is unknown to me.

Thanks.

Last edited: Nov 15, 2008
2. Nov 15, 2008