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I know that the directivity of the monopole is twice the directivity of the dipole because the transmitted power in case of the monopole is distributed only across a half of the space.

But why the input impedance of the monopole is half of the impedance of the dipole? Is there some proof to that?

gop664
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  • "I know that monopole has twice of the directivity than the monopole " I'm going to guess that is a typo. – Math Keeps Me Busy Jan 07 '22 at 20:32
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    Does this answer your question? [Why does 1/4 wavelength have a ground plane and 1/2 wavelength needs none?](https://electronics.stackexchange.com/questions/480508/why-does-1-4-wavelength-have-a-ground-plane-and-1-2-wavelength-needs-none) – Andy aka Jan 07 '22 at 21:55

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It's a simple symmetry argument:

enter image description here

from https://en.wikipedia.org/wiki/Monopole_antenna

The fields from the two arrangements in the figure are the same above the ground. The monopole has the same current but half the voltage, hence has half the impedance. For the same current it also radiates half the power as it is radiating into half the space.

Tesla23
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  • Hello Tesla,If we apply V voltage on dipole then it will be Z=V/I if we apply V on monople then by mirroring it will be Z=2V/I so its twice the impdeance of the dipole. Where did i go wrong in the logic? THanks. – rocko445 Jan 07 '22 at 22:40
  • Z=V/I, same I in both, half V for the monopole – Tesla23 Jan 07 '22 at 22:55
  • Hello,Why in monopole we have half the voltage? we have the same voltage source as the dipole and mirroring cause this voltage to double instad of being half – gop664 Jan 08 '22 at 12:53
  • In the diagram I showed, you are driving the monopole against the groundplane with a voltage V, generating the current I (ignote the image shown - it is not real). Hence it's impedance is V/I. For the dipole you need to apply 2V across the terminals to generate I, hence the impedance is 2V/I, or twice that of the monopole. – Tesla23 Jan 10 '22 at 01:58