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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?

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1 Answer 1

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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.

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  • \$\begingroup\$ 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? \$\endgroup\$
    – MRB
    Commented Mar 8, 2022 at 16:05
  • \$\begingroup\$ My bad, you are correct. Distance is R. D is the antenna dimension. Updated post. \$\endgroup\$
    – Aaron
    Commented Mar 8, 2022 at 16:15
  • \$\begingroup\$ 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? \$\endgroup\$
    – MRB
    Commented Mar 8, 2022 at 16:17
  • \$\begingroup\$ 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) \$\endgroup\$
    – Aaron
    Commented Mar 8, 2022 at 16:26
  • \$\begingroup\$ 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? \$\endgroup\$
    – MRB
    Commented Mar 8, 2022 at 18:04

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