# Far-field power-pattern of the antenna array Beam-Steering

1. Jan 11, 2015

### banigeo

Hi all,
I have a problem to firstly understand and secondly solve this problem :
here is the Problem :
Consider three (coherent) antennas variously arranged on the x-y-plane where each individual antenna radiates an isotropic electric field E(x).
1 - Write down an expression for the far-field power-pattern of the antenna array in the x-y-plane.
2 - Configure the phase of each individual antenna in such a way, that the resulting power-pattern of the antenna-array will have a maximum at a chosen angle α .
3 - plot the normalised power-pattern as polar-plot both in natural- and logarithmic scale for at least two different look-angles.

2. Relevant equations
Ei(r,t) = E0(xi)ei(k.r - ωt + kxi sin(θ))

3. The attempt at a solution

Z = 0

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Last edited: Jan 11, 2015
2. Jan 15, 2015

### Staff: Mentor

Welcome to the PF.

Can you please show an attempt at a solution? We require that before we can be of much tutorial help.

You should certainly be able to write the phase differences for the sources to maximize the power at the RX antenna.

3. Jan 17, 2015

### banigeo

Hi Berkeman,

here is some solution, which I tried and also there is some more tips about question :

Epw=E0 ei(k.x - wt)
E0=1 , pw=Plane Wave
all of them have the maximum amplitude = 1

E1=ei(k.x - wt)=1
E3=ei(k.r3-wt)=ei(kr1-wt)e-ikr13

what is k ? >>> k=k.e^α

Thank You,