Differences in output between pattern and directivity functions?

I found some discrepancies between the outputs [D1,az,el] = pattern(...) and D2 = directivity(...) in the phasedarray toolbox.

I want to check the directivity of a phased array of gaussian antennas which is pointing a beam in the intended direction (AZ1,EL1), but towards other directions (AZ2,EL2,...,AZN,ELN), to see how directive the pattern is towards other antennas and its potential interference power. The fact is that the angles are very precise and can get up to 15 decimal digit degrees. I can give as input this specific angle pair in 'directivity', and also in 'pattern' if a sort them from smallest to largest, and I also tried different angular resolutions, from 1 degree to 0.01 degree. The fact is that if the angle is integer (eg. [88 79]), it gives me basically the same directivity in both functions (-74.781749272249385 dBi for pattern and -74.781684184414985 for directivity), but if the input direction of arrival gets finer and finer towards the real direction, [88.089410546696229 79.020281159979618], 'directivity' gives me -83.046719336574199 dBi, while pattern, with an approximation to the second decimal digit, so [88.09 79.02], gives me -54.871540844506427 dBi. It's almost 30 dB difference. It seems that with more decimal digits, directivity approximates down, and pattern approximates up.

It's not that important but I was curious if there are different methods to calculate the directivity in these two functions.

Answer 1

[Gagan Agarwal]

Hi Paolo Fiore

The variation in the results obtained from the two functions can be attributed to the implementation of a minimum sampling grid of 0.1 degrees in the integration process for computing array directivity within the "directivity(...)" function.

The accuracy of the directivity value is impacted by this constraint on the sampling grid, particularly when the beamwidth of the array pattern is narrower than the specified grid.

Although both the pattern and directivity functions utilize the same calculation methodology, the directivity function is specifically influenced by the limitations imposed by the minimum sampling grid.