Thursday, March 27, 2008

Symmetrical pattern antennas

There are four questions on Element 4 that are annoying me: E9D03, E9D19, E9D20, and E9D21. All four of these are of the form "What is the beamwidth of a symmetrical pattern antenna with a gain of x dB as compared to an isotropic radiator?". I've reasonably concluded that I am to assume I am asked to find the apex angle of a solid cone that cuts the unit sphere yielding a solid angle equal to the reciprocal of the gain represented by x dB.

I derived a formula for this: first, convert dB to gain: g = 10x/10; second, find solid angle: Ω = 4π/g; third, find apex angle corresponding to solid angle: θ = 2 cos-1 (1-2Ω). The problem is that this formula does not yield the "correct" answers.

I discovered that this formula is off by a constant factor of 1.05 dB. That is, if I add 1.05 dB to the gain before doing the calculations above, my approach above yields answers that are correct within significant figures. What I don't understand is where the 1.05 dB is coming from.

I'm just going to memorize the answers for the test; there are only four of these questions and it's not all that likely that I'll get even one of them, let alone two, so even if I do flub them it isn't terribly likely affect my chances of passing. But I'm annoyed that reason has gotten me this close, and no closer. Anyone who understands this stuff have an explanation?