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## corner reflector theory

Dec 11th 2012, 19:20

#### K1ZON

Joined: Jun 26th 2012, 09:17
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I have recently retaken and passed my general class after a lapse of almost 40 years.
I am trying to relearn antenna theory and have run into some concepts that I cannot quite figure out. I want to understand just how a corner or parabolic reflector works for use on the 2 meter band. On the description of several corner reflectors, some in the ARRL Antenna Handbook, they seem to work as true reflectors where angle of incidence is equal to the angle of reflection but some of the solid corner reflectors do not seem to fit with any optical theory of reflection. Also some have individual elements comprising the reflector and could behave like the reflector element on a Yagi beam where the wave is retransmitted off that reflector but again the angles and phase shifts seem to be all off. (My understanding and probably not true.)
I also would like to learn exactly how the director in a Yagi antenna works and how to calculate the phase shift as I make elements longer than resonant and it becomes inductive or shorter and the element goes capacitive.
I’m not looking for anyone to explain it to me, although that would be helpful, but a pointer to some good texts that get to this level of detail for a non-engineering background would be very useful.
Dec 12th 2012, 01:22

#### W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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Here are two references that may be useful
http://fermi.la.asu.edu/w9cf/yagipub/index.html

http://www.eham.net/ehamforum/smf/index.php?topic=45961.5;wap2

The hard part is calculating the current on the wires--it is a challenge due to the mutual coupling between the elements--which is precisely what makes a Yagi different from previous phased arrays. But, once you have the current distribution, you can divide up the wires into small segments and calculate the effect of each small segment in the far field.

Zack :Lau W1VT
ARRL Senior Lab Engineer
Dec 12th 2012, 16:08

#### aa6e

Joined: Apr 4th 1998, 00:00
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Antennas are hard, if you want to understand them from first principles (Maxwell's Equations). But -- anything will radiate. Hams work closer to the latter style. Modern antenna modeling software (like EZ-NEC) is very quick and useful, but it may not give you "fundamental" understanding. This software divides up the elements into small segments and tries to find a self-consistent set of currents that result when you drive one or more elements.

When you're thinking about optical analogs, they are easiest in the range of "geometrical optics", i.e. when reflectors (or lenses) are very large in terms of wavelengths. This is not true of most 2 M antennas, but it works for large parabolic dishes, for example.

The theory of "images" can be useful to visualize what's happening, even for smaller antennas. For example, a quarter wave vertical above a ground plane has a reflection "image" under the ground plane. I.e., The radiation pattern (and impedance) are easy to relate to a half wave vertical in free space. That's what an observer "sees" from a far distance. (Actually, the impedance is half. An exercise for the reader.)

A dipole + (large enough) 90 degree corner reflector "looks like" 4 dipoles in free space with appropriate phasing, just as if you were looking at the dipole visually and the reflectors were optical mirrors.

I can't say much more without math or pictures!

73 Martin AA6E
Dec 12th 2012, 19:26

#### K1ZON

Joined: Jun 26th 2012, 09:17
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Thanks for the quick responses.
One quick question - should a parabolic or corner reflector be configured using a true reflection theory? Or do I need to also consider a wave being retransmited from the reflector such as in the reflector element of a Yagi? And is this decision frequency related ie. the higher the frequency the more the waves act as light waves do?
Dec 12th 2012, 23:23

#### W1VT

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Joined: Apr 4th 1998, 00:00
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Depends what you are trying to calculate--in many applications, the side and rear lobes are jsut as important that the gain--your satellite dish won't work if it picks up too much noise from nearby trees. In this case, you may need to consider diffraction theory.

Radio waves and light waves are the same, just different sizes. Thus, they reflect and scatter the same as long as you scale the reflecting and scattering media appropriately.

Zack Lau W1VT
ARRL Senior Lab Engineer
Dec 13th 2012, 16:27

#### aa6e

Joined: Apr 4th 1998, 00:00
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An optical approach might get you in the right ballpark, but amateur radio antennas are almost always "small" in terms of wavelengths. Your corner reflector will not be more than a wavelength in size, most likely, so it won't act quite like a perfect reflector. You can model this in EZ-NEC as a collection of wires to give you a pretty realistic approximation. Of course, it's also possible to build a reflector and a dipole and play around with spacings, etc. That's the time honored empirical approach!

73 Martin AA6E