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Two theoretical optimal antenna questions

Discussion in 'Antennas, Feedlines, Towers & Rotors' started by M0AGP, Jul 28, 2020.

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  1. N3OX

    N3OX Ham Member QRZ Page

    My contribution there is a GUI frontend for using Tim Molteno's PyNEC library in a Jupyter notebook, so it does collect data on wire segments and radii and all that.

    My computations so far ignore most of the input data and just pull out the x,y coordinates, but it was a convenient interface I had available.

    My wire widget GUI project is described here:

    PyNEC is here, and is very interesting, especially for optimizations:

    I think PyNEC allows a huge number of segments and exposes some NEC features that I don't know are available outside of writing and executing raw NEC decks (which I am not really familiar with).

    I intended to add a PyNEC simulation to that notebook after I compute the currents, but unfortunately I had trouble last night installing and importing the PyNEC library in Google Colab. This issue doesn't seem to be PyNEC specific, many pre-installed Python libraries seem to be affected, so I don't know when or if that might be resolved :/

    PyNEC is an extremely cool tool. I've found it challenging to install on Windows but I think it's usually very straightforward to install and use in a Python installation on Linux. The Colab issue is new. I had it working in Colab last year without issue.
    M0AGP likes this.
  2. N3OX

    N3OX Ham Member QRZ Page

    M0AGP likes this.
  3. M0AGP

    M0AGP Ham Member QRZ Page

  4. N3OX

    N3OX Ham Member QRZ Page

    Yes, this PDF under "ARRL LOG COORDINATE SYSTEM" is what I find right now as a reference. I think I worked it out from there, but not sure. It's been a while.
    M0AGP likes this.
  5. M0AGP

    M0AGP Ham Member QRZ Page

    OK - result! Although I don't know how much gain this has - Dan, can you run it through PyNEC/EZNEC pls?

    Here is the antenna layout diagram for the 16 quarter wave 20m idealized verticals in the 20m by 20m back yard:
    an here is the optimal pattern on a linear plot, an ARRL-style plot (but wrong tick marks - sorry - haven't figured that out in Excel yet) and also a full logarithmic plot (in dB) - note not from EZNEC - this is based on isotropic radiators, so the real pattern should be slightly more directional:
    and here is the vertical slice along the beam heading (linear scale):
    And for completeness here are the currents and phases (pasted in rather than photographed in case someone wants to play with this (sorry a bit ugly):

    Verticals currents phases
    Src #1 0.5015 109.176
    Src #2 1.0000 -85.016
    Src #3 1.0000 85.016
    Src #4 0.5015 -109.176
    Src #5 0.0938 -82.532
    Src #6 0.2770 96.857
    Src #7 0.2770 -96.857
    Src #8 0.0938 82.532
    Src #9 0.0938 -82.532
    Src #10 0.2770 96.857
    Src #11 0.2770 -96.857
    Src #12 0.0938 82.532
    Src #13 0.5015 109.176
    Src #14 1.0000 -85.016
    Src #15 1.0000 85.016
    Src #16 0.5015 -109.176

    And to use this you need to know the numbering scheme of the verticals. Here is the info photographed from Dan's notebook:

    It seems like a lot of info but in fact there are only a few different numbers, which correspond approximately to 1/8 and 3/8 wavelengths for the x and y coordinates for vertical placement and also an approximate 1/4 wave vertical length. The wires are defined EZNEC style.

    Health warning - impractical to implement
    In my first attempt at calculating this, I had rounded off the spacings to three significant figures, and got a lopsided and weird looking beam pattern. As Dan had noted previously, these optimal solutions can be unstable with respect to imperfections in current and phase. I think they may also be unstable with respect to spacing accuracy. So the above solution should be considered a theoretical answer.

    I think the practical answer will probably be to use a 4 square array or 8 circle array, as they seem relatively robust to inaccuracies.

    It's been a slightly long road, but I think we have given an approximate answer to the first theoretical question, at least when it comes to the phased array solution (we still need the gain and ideally f/b ratio and half power beam width).

    For the case in which we allow for one driven element and multiple parasitic elements, I have an idea to throw out there to the crowd, but will put that in another posting in this thread.
  6. N3OX

    N3OX Ham Member QRZ Page

    Free space azimuth pattern implemented as half-wave vertical dipoles:

    Freespace elevation pattern:

    Elevation comparisions at azimuth max against a 5 element yagi @ 10m height over conductivity = 0.005S/m, dielectric constant = 13 Real/High Accuracy ground


    The two traces of the vertical array have vertical dipole centers at 6m up (tips at 65cm above ground) and 12m up

    All files:

  7. M0AGP

    M0AGP Ham Member QRZ Page

    Thanks for that Dan!
    With 14dBi theoretical gain, that is a great "in theory" antenna. Even though it is effectively unbuildable it is nice to see what the best you could do would be given height restrictions and an other half who would let you build it. I'm not sure what's less realistic: building that 4 by 4 phased array or my wife letting me stuff the entire back yard with verticals...
  8. M0AGP

    M0AGP Ham Member QRZ Page

    Ok so part 2 of this question is “what is the best you could do with parasitic elements?”

    To make the problem more concrete, let’s not get into mixtures of phased arrays and parasitic elements. Unless someone out there has a great idea?

    I have a question.

    Say you had one fed element in the middle of a circle containing say 8 parasitic elements. Leaving it like that would be pointless, but I wonder if you could effectively “switch off” all of the parasitic element apart from one by connecting a capacitor or loading coil between the base of the vertical and the ground plane? If the capacitance is large enough would the now non-resonant verticals mainly not affect the resulting 2 element beam?

    In other words, every parasitic vertical has a capacitor to the ground plane, but we use relays to short out the capacitor on the parasitic we want to actually use.

    And by extension, we try to build a switchable vertical beam that can point to any of 8 compass headings, putting a few more directors in each direction - whatever fits.

    I have the feeling the answer might be “yeah they tried that in the 1930s and it didn’t work.”
  9. N3OX

    N3OX Ham Member QRZ Page

    I updated the calculator notebook so it computes and reports the optimized directivity in the target az/el direction:

    Az 0.000 deg, El 0.000 deg
    Optimized Dmax = 14.40dB
    Src # : mag (A) | phase (deg)
    Src #1: 0.501483 | 109.176305
    Src #15: 1.000000 | 85.015509
    Src #16: 0.501483 | -109.176305

    The directivity is the free-space gain for a lossless antenna.

    I think if you had theoretical current sources, you can steer the pattern all over too, although some of the circular-symmetry arrays are great for that as well.

    I think the space of geometries needs to be explored more, in addition to practical feeding. Here's a comparison with a pair of horizontally stacked (~15m separation) 12m-boom vertical yagis, though obviously you give up steerability :)


    This is positioned so the reflector tips are about the same height off the ground as the lower vertical dipole array.


    And smacked right up against the edges of the yard at 20m spacing


    Interestingly the free-space gain at zero degrees elevation is better for the square than the yagis:


    Attached Files:

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  10. N3OX

    N3OX Ham Member QRZ Page

    There was a beam design in the ARRL antenna book that was a bunch of dipoles around a tower using their coax stubs as the loading elements for parasitics, but that was basically two element antennas I think.

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