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I understand the formula for calculating the far field distance from an antenna is:

Distance = (2D2)/λ

Is the D in the above equation the length of the antenna under test (antenna under test is a small PCB antenna)? In which direction (1 or 2 in the image below)?

Far field test set up

Whilst trying to research this, I came across an image [Source]

Image showing formula found online

But I was sure the formula for converting between wavelength and frequency was:

Frequency = 1/λ

Are there two formulas?

ocrdu
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MRB
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1 Answers1

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Are there two formulas?

No.

\$\large\frac{1}{f}=time\$ (of one period)

\$\large\frac{c}{f}=\lambda\$ (wave length in meters)

\$D\$ is the largest length on the antenna: So, on a typical monopole, \$\frac{1}{4}\lambda\$
src. wikipedia

Based on your DUT image, (1), is the largest length.

Aaron
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  • how could I forget 1/f was period and not wavelength! As for the Wikipedia page you linked regarding D in the equation, I read this before posting my question and it states: 'where D is the largest dimension of the radiator'. Am I misunderstanding? – MRB Mar 08 '22 at 16:05
  • My bad, you are correct. Distance is R. D is the antenna dimension. Updated post. – Aaron Mar 08 '22 at 16:15
  • in which direction should this dimension be in? For example if it is a small PCB antenna, is D the length in the direction of the measurement antenna (1) I'm my image above or is D always the largest dimension, no matter how the PCB antenna is orientated? – MRB Mar 08 '22 at 16:17
  • If the antenna is electromagnetically short, \$D\$ doesn't matter, use the centroid. If the antenna is electromagnetically long, then "\$D\$ is the largest physical linear dimension of the antenna" (or diameter if a dish) – Aaron Mar 08 '22 at 16:26
  • sorry I am not understanding, if I have a PCB mount antenna, 'use the centroid', where am I measuring from, the centroid (centre of then antenna I am assuming) to where? – MRB Mar 08 '22 at 18:04
  • @MRB Is your antenna shorter than half of the wavelength? If so the near field is the region within a radius r ≪ λ ... it's all in the wiki – Aaron Mar 08 '22 at 18:59
  • @MRB There is no actual dividing line between the near field and the far field. Using the largest antenna distance for D means the line you are drawing errs on the side of being too far away from the antenna, instead of too close. – user253751 Oct 29 '22 at 00:37
  • When making far field measurements, you really can't be "too far" away from the antenna. This assumes, of course, that you can adequately all or most of the radiating energy. The 2D^2/lambda formula is generally taken to mean the minimum distance from the antenna that is considered the far field. – SteveSh Oct 29 '22 at 01:34