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diff --git a/4.-Antenna-Array-Setup.md b/4.-Antenna-Array-Setup.md index 03eb857..2bb00a9 100644 --- a/4.-Antenna-Array-Setup.md +++ b/4.-Antenna-Array-Setup.md @@ -45,24 +45,24 @@ For both templates print the center pentagon and five arms separately, then glue ## Uniform Circular Array (UCA) -If you wish to determine radio sources from 360 degrees around the array, then the antennas should be arranged in a uniform circular array (UCA). The interelement spacing (the distance between the tip of each neighbouring antenna element in the array) needs to be set specifically for a range of interested frequencies. +If you wish to determine radio sources from 360 degrees around the array, then the antennas should be arranged in a uniform circular array (UCA). The interelement spacing (the distance between the tip of each neighboring antenna element in the array) needs to be set specifically for a range of interested frequencies. -You must design your array such that the interelement spacing I_e is less than half a wavelength λ of your highest frequency of interest -I_e=sλ +You must design your array such that the interelement spacing `I_e` is less than half a wavelength `λ` of your highest frequency of interest +`I_e=sλ` -where s is the wavelength spacing multiplier that must be <= 0.5 and λ is the wavelength in meters. +where `s` is the wavelength spacing multiplier that must be <= 0.5 and `λ` is the wavelength in meters. An array with an interelement spacing larger than this will experience what’s called ‘ambiguity’. Put simply, this means that the system may see the signal source coming in from more than one direction, and we have no way to know which is the true direction. This is obviously not ideal, so always keep the multiplier below 0.5. -Using a spacing multiplier less than 0.5 can also allow you to design a smaller array size, at the expense of some accuracy. Generally, down to s=0.2 is acceptable, and we typically set our arrays to s=0.33. It’s important to note that the accuracy of the direction-finding result diminishes with smaller spacing multipliers, and for 5-elements the accuracy starts to become unacceptable below around s=0.2. +Using a spacing multiplier less than 0.5 can also allow you to design a smaller array size, at the expense of some accuracy. Generally, down to `s=0.2` is acceptable, and we typically set our arrays to `s=0.33`. It’s important to note that the accuracy of the direction-finding result diminishes with smaller spacing multipliers, and for 5-elements the accuracy starts to become unacceptable below around `s=0.2`. As the interelement calculation depends on wavelength, you can conclude that lower frequencies require larger antenna array sizes. This shows that this type of radio direction finding method can be impractical for frequencies with large wavelengths as the arrays will take up a lot of space. For HF and the smaller VHF frequencies with large wavelengths, other radio direction methods like TDoA, Watson-Watt and manual Yagi based methods may be more appropriate. It may be useful to set up a UCA array by measuring the radius, rather than by measuring interelement spacing. The formula for calculating radius for a given spacing multiplier and wavelength is given by: -r= sλ/√(2 (1-cos(360/n)) +`r = sλ / √(2 (1-cos(360/n))` -where s = spacing multiplier, λ = wavelength in meters and n = number of antenna elements +where `s = spacing multiplier`, `λ = wavelength in meters` and `n = number of antenna elements` ## Uniform Linear Array (ULA) @@ -72,7 +72,7 @@ The advantage of ULA is greater accuracy resolution due to a larger possible ape The interelement spacing calculation is the same formula as for UCA. -I_e=sλ +`I_e = sλ` # Antenna and Coax Precision @@ -123,10 +123,10 @@ Obviously if you are running the antennas on a vehicle, you do not want the ante If the resolving resolution is 10 degrees, we can say that the actual bearing is somewhere within a 10-degree arc. Here we briefly explain the background theory behind what sort of accuracy resolution we can expect from a 5-element array system. With a 5-element circular array spaced at 0.5 λ, we might roughly expect a resolution of about 8 degrees. With a 5-element linear array we could roughly expect about 3.4 degrees. This is the best-case resolution, not considering external distortions like multipath. (This may appear inaccurate, but in practice when multiple readings are taken from many locations the inaccuracies simply average out and become negligible.) -To estimate the error, we used the Rayleigh resolution calculation from wave physics. The Rayleigh formula states that resolving resolution is given by θ=1.22λ/D, where D is the aperture of the antenna array. For a circular array the aperture is equivalent to the diameter, and for a linear array it’s equal to the total length. For a linear array however, it must be taken into account that the effective aperture will appear to be much smaller when seen from the sides. +To estimate the error, we used the Rayleigh resolution calculation from wave physics. The Rayleigh formula states that resolving resolution is given by `θ=1.22λ/D`, where `D` is the aperture of the antenna array. For a circular array the aperture is equivalent to the diameter, and for a linear array it’s equal to the total length. For a linear array however, it must be taken into account that the effective aperture will appear to be much smaller when seen from the sides. -So, using the formula given further above for array radius, then multiplying by two to get diameter, for an n=5 element circular antenna array with s=0.5 spacing we get an aperture of D=0.85λ . Therefore, the Rayleigh equation reduces to θ=1.22/0.85 = 1.44 rad = 83 degrees. +So, using the formula given further above for array radius, then multiplying by two to get diameter, for an n=5 element circular antenna array with s=0.5 spacing we get an aperture of D=0.85λ . Therefore, the Rayleigh equation reduces to `θ=1.22/0.85 = 1.44 rad` and `1.44 rad = 83 degrees`. -For a 5-element linear array its aperture is given by the total array length which is given by D = (n-1) * s λ. If we have n=5 elements and s=0.5 spacing, then θ=1.22/2 = 0.61 rad = 34 degrees. +For a 5-element linear array its aperture is given by the total array length which is given by `D = (n-1) * s λ`. If we have `n=5` elements and `s=0.5` spacing, then `θ=1.22/2 = 0.61 rad` and `0.61 rad = 34 degrees`. -Because we use ‘super-resolution’ algorithms like MUSIC, we can improve on the Rayleigh resolution by a very approximate factor of 10. So, we end up with a resolution of 83/10 = 8.3 degrees for the circular array, and 34/10 = 3.4 degrees for the linear array.
\ No newline at end of file +Because we use ‘super-resolution’ algorithms like MUSIC, we can improve on the Rayleigh resolution by a very approximate factor of 10. So, we end up with a resolution of `83/10 = 8.3` degrees for the circular array, and `34/10 = 3.4` degrees for the linear array.
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