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Antenna building seems to be more of an art form rather than a science.
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I can understand that it could seem that way. I assure you, it's most certainly a science. That a Youtube video fails to offer instruction in the science is not proof that antenna design is haphazard.
Here's a bit of bed-time reading on the science of antennas:
http://www.cromwell-intl.com/radio/r...-antennas.html A link to Edmund Laport's textbook
Radio Antenna Engineering, published in 1952 is included.
The laws of physics apply, and therefor an understanding of math and physics are crucial to being able to design antennas as well as any other electronic circuit.
My experience in circuit design is fairly basic. But I have been able to design and build a few simple antennas over the years, thanks to the work of much smarter minds than mine.