Peaks and Nulls of Two Antenna

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Dan86

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Hi, relatively new to the forum so wondering if there is somebody who may be able to help.

I am doing a project where I am looking at setting up a measurement of the peaks and nulls of two antennas operating at 868 MHz, with one of the antennas being fed with the same signal amplitude but being approx. 90 degrees out of phase with the other.

Before I do this though I have been asked to determine this with calculations to see if the peaks and nulls that are calculated will then correlate to what I will then measure in a lab. The only thing here is I am not sure where to start as I jumped straight in looking at spherical co-ordinates with integrals etc. but was told to just look at the problem as two point sources and use basic trigonometry to work out the peaks and nulls and then to do some vector addition. Can somebody point me in the right direction of how to do this and if it can be done as simply as that without having to jump into high level mathematics?
 

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What pattern of ripples form on a pond when you toss in one stone, then toss in a second stone at a spot exactly 1/4 wavelength away?

This is similar to the pattern resulting when you overlap a:

a) sine curve (emanating from a point source)
and
b) cosine curve (emanating from a nearby point source).
 
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Hi and thank you for your reply.

I can see what you are asking me to picture and I understand then that you would end up with constructive or destructive interference between the two points. In that way then would I be correct in saying that you would always get the same antenna pattern of peaks and nulls regardless of frequency (assuming the separation is always quarter wavelength)? I understand that if both antennas being fed in phase would produce a different antenna pattern to one where one of the antennas is out of phase.

If the antenna patterns would always be the same then I am not sure why I would need to determine the peaks and nulls as most textbooks give a number of different antenna patterns for different phase inputs so I could just refer to them.
 

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Your initial exercise seems to be a special instance where a sinewave is duplicated at an integer fraction 1/4 of its wavelength. Peaks and troughs just happen to combine in the classic interference pattern.

However the scenario could be altered to resemble what you probably picture:

Certain radio stations direct their broadcasts toward one direction during the day, and in a different direction at night.
These stations use two or three transmitting antennae, planted so many feet apart, and feed them an identical broadcast differing by certain phases. Thus the station changes its area of coverage, one phase for daytime, another phase at night. The area of coverage creates lobes and nulls big as a continent.

I'm sure the math requires extensive calculations, to determine what distance (fraction of a wavelength) to separate the antennas (point sources), and what the phase change must be in order to create desired lobes and nulls.
 

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