I have a confusion regarding the notation of radiation pattern of an antenna array. Some literatures use, say, $$F(r,\theta,\phi)$$ to denote the same while others use $$F(\theta,\phi)$$I would appreciate if anyone tells me the proper notation for the same. I am writing a report and I am not sure which notation to follow to represent the radiation pattern(field/power).
Correct Notation of Radiation Pattern of an Antenna
antennaradiation
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For a compound box antenna the formula is similar and this might be useful: -
Obviously they are not using A and B to denote the aperture dimensions but, I suspect that "r" is going to be exactly the same i.e. distance between centre of aperture and measurement point.
Simply put: both are different ways of harnessing the properties of using multiple antennas.
In a Phase array the antennas are usually placed in a repetitive pattern like a matrix or circles or hexagons. Often the distance between the antennas is always the same. Phased arrays are used to make these many antennas behave as one antenna with certain properties like a more narrow beam pattern (where the antenna is sensitive and/or emits more power).
I find smart antennas a misnomer as the antennas are not smart at all, the "smart" bit is in the signals which are used with the antennas. This can be used for improving reception by beam-forming or the reverse: enhanced sensitivity in a certain direction.
This "smart antenna" signal processing is also used with Phased Arrays.
You could say that some smart Antenna systems are a simple form of Phased Array. Where a simple Phased array might use 9 antennas, a smart antenna system might use 3 antennas.
You could call any Phased array with signal processing a Smart Antenna system but I would not call any smart Antenna system a phase array. for example some laptops have 2 or 3 Wifi antennas for beamforming and Mimo. You would not call that a phase array but I think it would be OK to call that a smart antenna system.
Best Answer
The inclusion of r makes it a near-field measurement. The far-field measurement is an approximation based on the assumption that r is approaching infinity, which in practise means that r is many times larger than the antenna.
If you care about near-field effects, then you must use the near-field form. If you don't care about near-field, i.e. if your antennas are spaced apart by at least a few tens of their size, then you should simplify your report by using only the far-field radiation patterns.
The near-field expression probably gives you a direct expression for field-strength or power at each (r, theta, phi) point in space, whereas the far-field expression usually just tells you the antenna gain with respect to isotropic (dBi) in each (phi, theta) direction. The way you use each expression therefore differs because one includes propagation loss and the other does not; you must account for 1/r^2 (= -20log(r) dB) propagation losses if you're using the far-field patterns to compute total power transfer between antennae.