Experimenting With 2-D Parabolic Reflectors

I learned so much from my last question, I thought I'd give this a spin here:

Is there a practical, minimally-technical way to come up with a physical template for the proper curvature of a two-dimensional parabolic reflector to amp-up and directionally focus a vertical omnidirectional antenna? I've seen raw formulae, but they've lost me (I was an Art major). I've spent a few days searching on the web and haven't come up with anything like this except for very small examples:

formatting link
I'm thinking something like .5M-.75M across the horns, formed from a sturdy but controlably flexible material, possibly sheetmetal, that one could arch and keep in proper, trued configuration in a support jig/frame.

I'd also be interested in the relative merits of centered and offset reflectors in this sort of application.

Again, this is more by way of education than anything else, but I do intend to make some experimental examples and see how they perform using signal-strength recording programs.

Many thanks for any assistance!

Reply to
Always Thinkin'
Loading thread data ...

Always Thinkin' wrote:

I like those, but they are smallish. You could scale up. I use the EZ-12 Windsurfer.

I've seen formulae that I didn't bother with, since the images at freeantennas.com were good enough for me.

There is some "string theory", where you could draw your own of any size desired.

Supplied by "Don Widders"

Draw a line opposite the focus (where you would have the open face of the reflector) running parallel to the directrix. According to one definition of a parabola, fP = fd where fP is the distance from the focus to a point on the parabola and fd is the distance from the focus to the directrix. The line you drew is parallel to the directrix, so it's like offsetting the directrix by some distance. Since the new line is in FRONT of our reflector instead of behind it, point P will get CLOSER to the line as it gets farther from the focus (the farther off axis that P is located on the parabola.) Since the new line is parallel to the directrix, the rate at which the distance from P to the new line DECREASES is the same as the rate at which the distance from the directrix increases and also the same rate at which the distance from the focus to P increases. So the parabola can be expressed in terms of the new line as fP + fNL = K where fNL is the distance to the new line from the focus and K is some constant (the length of the string.) The T-square rides along the new line that represents the opening of the reflector. When the T-square is brought as far as possible from the focus, the cursor will be pulled all the way to the 'crotch' of the T-square (point 'c') so in this case the marker will be at point c and the string will be a straight line from point c to the focus. In this extreme case, fNL = 0 and fP = the length of the string.

I didn't want to change the length of the string for every point on the parabola, so instead of putting the T-square on the directrix, I put it on a parallel line on the other side of the focus. The directrix is closest to the parabola at the point of the axis. The new line is FARTHEST from the parabola at the point of the axis. As the distance from the focus to P increases, the distance from P to the new line decreases, so now we can use a string whose length does not change.

Supplied by "Don Widders"

The "changing length" string shockwave

formatting link
Rather large parabola ;-)
formatting link

Supplied by "Clive" Initial focal point determination program

formatting link

Article from Wireless World, with a drawing of the fixed length string

formatting link
The "fixed length" string animation
formatting link
The mercury mirror telescope
formatting link

Reply to
dold

Always Thinkin' hath wroth:

I'm partical to "Learn by Destroying". If you have broken and fixed something, you don't understand it.

Sure. I do it all the time. It's borrowed from wood aircraft and wood boat construction. Make a template with the proper curve using a sheet of thin 1/4" plywood. Draw the parabolic shape on the plywood and cut it to shape with a jig saw. I was building some rather large (8ft dia) sheet metal parabolic reflectors for weather satellite dishes this way. However, instead of using the plywood for a template, I was using it as part of the dish structure. I attached aluminum flashing to the plywood with a staple gun or tack hammer. I'll see if I can find some photos.

However, permit me to offer a clue. There's not much difference in gain with small reflectors of the same size between a parabolic dish, flat plate, or corner reflector. For example:

Flat plate (8.3dBi):

formatting link
Dish (7.7dBi):
formatting link
The flat plate reflector has 0.5dB more gain than the equivalent size dish. However, don't assume that this works for all sizes of dish and flat plates. The difference is bigger for larger diameter antennas.

Also, I should do a similar corner reflector for comparison, but not tonite.

See: |

formatting link
some construction details.

You can draw a parabola with two thumb tacks, carpenters square, string, and a pencil. |

formatting link
|
formatting link

I can't guess if this size antenna is suitable for your unspecified purpose. The design and construction of the dish is usually not a problem. At best, just buy a commercial dish or adapt something from a DBS pizza dish. The problem is designing the feed. Too wide a pattern and you have overspray. Too narrow a feed pattern, and you don't illuminate the entire dish resulting in gain loss. It's not easy.

Here's your homework for the next few days:

formatting link
's a chapter of offset feeds. Basically the advantage of offset feeds is that the feed itself does not block the signal. Also, the mount is out of the pattern. It's not horribly important for large diameter antennas, but is critical for small dishes. One thing for sure... calculating and building your own offset dish is a mathematical mess. I wouldn't even try.

Suggestion: Build or buy a directional reference antenna with a known gain. Spend some time learning how well it works at different frequencies (channels), and at different heights above the ground. Then, do you gain measurements using this reference antenna as a standard. If something changes in the test setup, it will change for both the reference and test antennas, and will be obvious.

Reply to
Jeff Liebermann

fixed

[...]

Hey, guys!

Thanks for these tips, but as soon as I posted this, a rolling rash of unrelated but _really_ terrible stuff started happening to several of my close friends here, and I've been busy with funerals, lawyers, cops and hysterically bereaved and distraught people. I haven't have the presence of mind to attend to more pleasant stuff like antenna design.

I'll get back to you on this maybe next week and we can have some fun with it! I'll be ready for some diversion, believe me!

Thanks!

Reply to
Always Thinkin'

Cabling-Design.com Forums website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.