"David Harper" wrote
I had a simple question in regards to phased array antenna patterns.
If a phased array is trying to send a narrow beam in a specific
direction, how do the other side lobes get reduced and/or eliminated?
Are the individual antenna transmitters/elements not omnidirectional
themselves? If not, what are the characteristics of their patterns?

I ask this because I'm trying to understand how tracking radars can
send narrow beams in the desired direction without significant
secondary lobes to interfere with returns from the desired lobe.

Thanks in advance for any insight!

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To understand how things work it is necessary to be familiar with elementary
trigonometry. Its quite simple really.

Without trigonometry you just have to accept that's the way things are.