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Antenna theory detection of angle of incidence

  1. Mar 1, 2015 #1
    Assume a 2D problem. Given a linear antenna array, lets say 3 antennas distributed around the z axis, how could we extract the incidence angle of the received wave?
    Having 3 antennas equally spaced by λ/2 in the z axis and connected to each other, the result gain would be a function of ϑ (angle of incidence). The problem is that there are 2 values of ϑ between 0 and 90 degrees where I would get the same gain.
    I want to have a bijective function so that given a gain we can extract the incidence angle.
    Can I achieve that by changing the space between the antennas?
  2. jcsd
  3. Mar 4, 2015 #2
    I think you are looking for an antenna with two overlapping beams. You need to use two antennas to do this, each fed to a separate receiver, and the angle is found from the ratio of the two outputs. If the beams are roughly sine shaped, and cross at 70% EMF, then the ratio will approximate the tan of the angle measured from one beam maximum..
  4. Mar 4, 2015 #3
    Thanks for taking the time to answer.
    Sorry I'm new in this. what is the ratio and how can i find it? 70% EMF? could you give me a more visual explanation?
    I also thought about another approach and I want to know if it is possible: how about a sawtooth frequency modulated signal, if I mix the output of the antennas, I get frequency which is proportional to the angle, right?
  5. Mar 4, 2015 #4

    jim hardy

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    I think you're knocking at the door of a subject "Radio Direction Finding"

    which has got tremedously clever last few decades..... i've only peeked into it out of curiosity....

    Try searching on that term, and 'phased array"
  6. Mar 4, 2015 #5


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    What are the directional characteristics of your antennas? You will need to assume the polarisation of the incoming signal. The product of the signal and pattern will give you the received signal power. If you only have three elements in the array, given power only there will be a great many solutions to the orientation of the Poynting vector. There will be significantly less solutions if you use phase and power, but there will still be too many solutions to resolve an accurate direction.
    What are you really trying to do?
  7. Mar 5, 2015 #6
    Well, the thing is that I have a FM transmitter and I want to locate it in space. I thought of incrementing the frequency of the transmitter linearly with a sawtooth modulation, and then put a product detector between to spaced antennas, will it work? Each antenna is going to receive a slightly different frequency at some given time and the difference between this two frequencies is apparently related to the angle. and between 0 and 90 degrees there is apparently one solution. It is like if we have a gradient of frequency in the direction on k. Is it a good idea? It's a little bit the principle of an FMCW radar but applied to find the angle
  8. Mar 5, 2015 #7


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    A few thoughts:
    The "modern" way folks do direction finding is digital and would require an ADC for each element. I am guessing this is not practical for you. If that is practical, then you can do any number of fancy techniques, although they will require a calibration of the array (to account for the fact that the cables, receivers, etc. for each channel are not identical).

    The option mentioned by tech99 sounds like what radar people call "monopulse" - a google search will likely help you find stuff on that topic. It is a clever way to do this with minimal hardware. The FAA uses this technique in the ground receivers that communicate with the transponders on aircraft; it allows them to estimate the azimuth angle toward the aircraft.

    I think the frequency ramp idea is clever. You will have to work out how accurately you can measure the frequency difference and what that implies for how fast you need to ramp the frequency in your transmitter. Ramping slow gives you smaller frequency shifts but gives more time to measure them; ramping fast has higher frequency shifts and less time to measure them. You will be limited by the fact that your frequency resolution will be essentially 1/(measuring time). It isn't obvious to me that all the numbers will work out in your favor, but if they do you may be in business.

  9. Mar 5, 2015 #8
    Thank you for you answer @jasonRF .

    For the frequency ramp, time and resolution: that's a big problem if I don't want to separate antennas more than 1 meter. I can't find any formulas but I guess i wont be able to do .

    I was thinking of a sinusoidal frequency drift (instead of a ramp) which has no discontinuity so I can take the time I want to measure, or am I wrong? I suppose it requires a little bit more signal processing..

    I just saw monopulse radar and it seems complicated..
  10. Mar 5, 2015 #9

    jim hardy

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    would comparing phase of signals arriving at the different antennas carry any information?
  11. Mar 5, 2015 #10
    Thank you for answering @jim hardy
    Yes, basically that's the idea if I chose a continuous wave, but how can i perform that? is there any analog phase comparator for this? Like in PLL? could you recommend me anyone?
  12. Mar 5, 2015 #11
    There is a technique called Doppler DIrection Finding, where antennas placed in a ring are switched to the receiver sequentially. This produces phase modulation of the incoming signal. The phase of the modulation depends on the direction of the transmitter. An FM receiver demodulates the phase modulation, and compares the resulting tone with the phase of the switching signal to ascertain the direction.
  13. Mar 5, 2015 #12
    thank you @tech99
    Do you think It is hard to build? PIN diode for switching, controller... How many antennas could I use?
  14. Mar 5, 2015 #13

    jim hardy

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    Thanks tech99 for the terminololgy. As i said i've only peeked into the world of RDF because the techniques are so interesting.
    OMNI VOR system for air navigation is delightfully clever.

    Here's a hobbyist kit, i think it uses 4 antennas
    http://www.ramseyelectronics.com/Ramsey-Doppler-Direction-Finder-Kit/dp/B0002T5SU6 [Broken]

    and here's an amateur built doppler finder

    a search on 'fox hunting' turns up lots of amateur articles.

    ARRL is where i'd start..

    i dont know enough to say whether this device might be handy for your task
    but it appears quite powerful. I learn a lot by reading application notes.
    about 25 bucks at Digikey

    old jim
    Last edited by a moderator: May 7, 2017
  15. Mar 5, 2015 #14
    That was really usefull @jim hardy .

    the phase detector seems to me a good idea and it is not expensive.

    I think that I will take that way if I don't find inconvenients.

    What do you think are the advantages of doppler based ones over phase detector direction finders?
  16. Mar 5, 2015 #15

    jim hardy

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    I'm abjectly unqualified to offer an opinion.

    But very interested ! keep us posted .

    old jim
  17. Mar 5, 2015 #16


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    I am qualified to offer an opinion. I have done my time in real world DF.
    Doppler is the way to go. 4 elements is the minimum.
  18. Mar 5, 2015 #17
    Thank you for answering.

    Why? Could you give me the reason why a phase detector wouldn't work ? Or what ar doppler advantages over other types of DF?
  19. Mar 5, 2015 #18


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    The field of DF antennas is complex. There is no simple reason or answer in the real world, only experience can guide you. If for some reason one was always better than another, then the other would no longer be used. Many systems are still used because their fields of application overlap.

    For tracking VHF FM carriers you need a system that does not have multiple nulls. Doppler does not need to be rotated to identify which side of which null the transmitter is on. Doppler covers a wide frequency range. Doppler can be mounted on a vehicle, it resolves 360° and so will unambiguously point to the transmitter as you drive around. The question comes as to how accurately you need to know the bearing, and will near field or multi-path signals limit the resolution of your system.

    Phase measurements are really “time of arrival systems”. They are more applicable to physically rotated pairs of elements or fixed antenna arrays of 16 or more dipoles.

    Crossed loops are usually employed in amplitude measuring system. Without added complexity they only resolve 180°.
  20. Mar 6, 2015 #19
    Well if I use 3 spaced by λ/2 antennas and a phase detector i would have a null every 90° right?

    What i really want is a simple system to detect the angle between 0 and 90° or 0 and 180° (would be better but not necessary) both azimuth and altitude.

    I have a few questions about Doppler:
    - Can I find both azimuth and altitude using this method? with how many antennas?
    - If the transmitter is moving fast, will his Doppler affect the results?
    - Do you know any simple implementation or example of Doppler based DF for a DIY?
    Last edited: Mar 6, 2015
  21. Mar 6, 2015 #20


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    Your question is too general to answer with any certainty. It depends on how you intend to connect it.

    Are you prepared to aim the array to null the phase or do you want an automated system that gives you a bearing in degrees?

    No. Simple Doppler DF gives azimuth only. A minimum of 4 elements but 8 or 16 is better.

    You can calculate it based on relative speed. If things move at a few % of the speed of light then the received signal will shift out of the RX bandwidth.

    Google ' doppler df kit '
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