As an EE with sense of physics I ran into the same confusion. Your instincts regarding reciprocity, effective area and all that were in the right direction and with a few more steps you would have had your satisfying 'Eureka' moment.
Most of these comes from the Pathloss Equation which it turns out is a stitch up to make things simpler and easy (but wrong).
It's best explained with respect to parabolic antennas but applies to all antennas. The key point to picking this apart is to consider reciprocity which states that the that an antenna is "the same" as either a transmitter or a receiver. In particular the gain is is the same.
So gain is the increased power with respect to an isotropic radiator. With a parabolic antenna the focus (ie beam width) of the transmitting beam does depend on frequency due to geometric concerns and as such, in the path loss equation the the antenna gain appears as frequency dependant as it ought to.
However, reciprocity requires that the receiver also have an identical, frequency dependant gain. The gain of the receiver though depends only on its physical (or effective) area and not on its frequency.
In the pathloss equation you can see that the loss goes as the reciprocal of the square of the distance, which it should, but also goes the reciprocal of the square of the frequency. This frequency term (which causes the equation to violate conservation of energy, normally a bad thing) is there to cancel out the bogus frequency term incorporated into the gain of the receiving antenna due to the also bogus reciprocity law.
So to simplify, in an electromagnetic link between two antennas, the gain of the transmitting antenna depends upon the frequency of the transmitting carrier, because the focus of the beam varies with frequency. The signal then drops off as 1/r^2 in the normal way (with no frequency component) and the gain of the receiver depends only on its size. A bigger receiver antenna captures more energy from the receiver. That's it, simple and sensible.
Effective area is a separate topic for long wavelength transmissions but also sensible in the end.
Most of these comes from the Pathloss Equation which it turns out is a stitch up to make things simpler and easy (but wrong).
It's best explained with respect to parabolic antennas but applies to all antennas. The key point to picking this apart is to consider reciprocity which states that the that an antenna is "the same" as either a transmitter or a receiver. In particular the gain is is the same.
So gain is the increased power with respect to an isotropic radiator. With a parabolic antenna the focus (ie beam width) of the transmitting beam does depend on frequency due to geometric concerns and as such, in the path loss equation the the antenna gain appears as frequency dependant as it ought to.
However, reciprocity requires that the receiver also have an identical, frequency dependant gain. The gain of the receiver though depends only on its physical (or effective) area and not on its frequency.
In the pathloss equation you can see that the loss goes as the reciprocal of the square of the distance, which it should, but also goes the reciprocal of the square of the frequency. This frequency term (which causes the equation to violate conservation of energy, normally a bad thing) is there to cancel out the bogus frequency term incorporated into the gain of the receiving antenna due to the also bogus reciprocity law.
So to simplify, in an electromagnetic link between two antennas, the gain of the transmitting antenna depends upon the frequency of the transmitting carrier, because the focus of the beam varies with frequency. The signal then drops off as 1/r^2 in the normal way (with no frequency component) and the gain of the receiver depends only on its size. A bigger receiver antenna captures more energy from the receiver. That's it, simple and sensible.
Effective area is a separate topic for long wavelength transmissions but also sensible in the end.