Typical half-wave dipole antenna parameters

From my bachelors degree, I have learnt the fundamental theory behind antennas. One of the main types is the half-wave dipole antenna. We've studied its radiation pattern (isotropic) and how it varies with the elevation angle. But we never used practical values (we didn't have labs on this).

The theoretical aspects behind its radiation pattern were the following equations:

$$\widetilde{E}_{\theta }=\frac{jI_{0}lk\eta_{0} }{4\pi }\left ( \frac{e^{-jkR}}{R} \right) \mathrm{sin} \theta$$ $$\widetilde{H}_{\phi }=\frac{\widetilde{E}_{\theta }}{\eta_{0}}$$ Where $$\I_{0}\$$ is the current within the antenna; $$\ l \$$ the length of the antenna, $$\k\$$ thewavenumber, $$\R\$$ the distance from the antenna; $$\\theta\$$ the elevation angle; $$\\eta_{0}\$$ the intrinsic ipedance of the medium (usually free space); $$\\widetilde{E}_{\theta }\$$ the electric field phasor; and $$\\widetilde{H}_{\phi }\$$ the magnetic field phasor.

$$\\widetilde{E}_{R }\$$ is assumed to be negligble. Also:

$$\widetilde{H}_{R }=\widetilde{H}_{\theta }=\widetilde{E}_{\phi }=0$$

The average power density at a given point is given by (using the Poynting vector): $$\overrightarrow{S}_{av}=\frac{1}{2} \mathrm{Re}\left [\widetilde{\overrightarrow{E}} \times \widetilde{\overrightarrow{H^{*}}} \right ]$$ My question is what are typical values for $$\I_{0}\$$, and other parameters, specifically for $$\2.45 \mathrm{GHz}\$$?.

I want to use this to approximate radiation density of these antennas:

• $I_0$ depends on how hard you drive the antenna. It isn't a direct antenna property. – Andy aka Aug 29 '20 at 10:11
• Assuming a 2.4GHz technology like Bluetooth, typical devices ("class 2") have a maximum output power of 2.5mW. Normally I'd say P=UI from there, except antenna theory is all black magic to me. I suspect that signal modulation will affect this somehow...? – Lundin Aug 31 '20 at 13:13