antenna array problem

i have a question:
three point source antenna with equal amplitude and phase are placed at the corner of triangle as figure shown.
find array factor and plot it.

I am facing similar problem to obtain end fire pattern of similar config. For this type array, there is a problem of unequal phase and so my calculated array factor is not distance independent even in far field when we are looking in the end-fire pattern.

i searching for solution of this problem not a new problem
thanks

Use circular array factor, for eaxmple, on page 467 of Stutzman's book., with N =3 and Phi = 120 degrees.

this is a delta phase problem

so look for delta rhythms in rf antenna

this is a 'stub' matched system

so is a 1/2 delta gain array

any one can solve this problem and upload it
thanks

no one have a solution?
this is kraus problem (1th edition - 1959)

Sorry,

what is the problem ?
the array factor formula (assuming true the following 3 conditions: all elements are a) equal, b) oriented in the same way and c) operating at the same frequency) is general ! it can handle any kind of geometry (linear, planar and 3D). The array factor is function of only a) geometry (scaled in wavelength) and b) excitation law (amplitude and phase). The formual is weel known and is reported in any antenna book.
Please clarify your problem or provide an exampe.

bye.

i want to know that where i can use the array factor formula? what is origin in this problem and ....

if your antennas are equal e "oriented" in same way, you can apply the array factor formula. Anyway I see that you array is made of only three elements (on triangular grid), that I suppose stay on a common plane, so to maximise the peak directivy in the boresight direction you have just to fed them in phase with the same amplitude !

the array factor in you case is (with t and f angular coordinates):

F(t,f) = Sum(i=1..3)[A(i)*Exp(B(i))*exp(x(i)*sin(t)*cos(f)+y(i)*Sin(t)* Sin(f)]

as shown in the formula only gemetrical positions and excitations are involved.

The directivity is proportional to F(t,f)^2. If you want take into account the common radiating element factor (Ec(t,f)) you have

E(t,f) = Ec(t,f)*F(t,f)

attached the contour plot of your configuration !