a simple question about the receiving antenna
Since the antenna receiving power is proportion to its antenna aperture and hence the antenna gain by:
Ae=lambda^2*Gain/(4*pi)
And the short dipole (infinite-small) gain is 1.5 and the half wavelength dipole gain is 1.64 from classical antenna textbook.
So does it means that the short dipole can receive similar level of power as that of the half-wavelength dipole? So what's the advantage of using the half wavelength dipole in typically?
And the other question is that whether the receiving power by multipling the antenna aperture with the incoming wave power density is the maximum available power? And we can only get this value by complex-conjugate the antenna input impedance?
Thanks in advance.
There is no real advantage for receiving as long as you have a lossless matching network to transform the antenna impedance (very low resistance, very high reactance) to the optimum source impedance for the first receive amplifier minimum noise figure.
At HF and lower even this is not done since the atmospheric noise is so large that even a short antenna produces more noise than the first receive amplifier.
Dear ABC:
I think you confuse things: A RF power transmitted by an antenna is not specified by its aperture or structure.
We use antennas as components in communication systems: then their gain is determined by your formula if aperture antennas are used. Dipole antennas are often preferred for their simplicity. A half-wave dipole is preferred due to that it is matched to a transmission line with a characteristic impedance of 50-70 Ohms.
Other antennas have other impedances, often complex; this requires matching circuits, adjustment, etc.
A "short dipole" is usually an approximation in calculations, replacing a "point source". The shorter the radiating element related to wavelength, the poorer is its radiating capabilities. Nowadays many inventors introduce their "ceramic" antennas, shortened so they fit into small packages. Such antennas are quite poor radiators, so they are suitable for very short range communication only. A good antenna is always comparable in size with the wavelength.
You should study more antenna basics to better understand how antennas work.