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?
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?
The question is about representative real-world antennas, not the conical model you used. Since there is some power radiated in side and back lobes, real world beam widths are slightly narrower than your conical model. I would guess that the test answers are based on NEC-4 model using yagis as the antenna type. In any case, the three incorrect answers for each of questions is far enough removed from reality that the exact model in use is immaterial. Memorization is the correct approach, since the point behind the questions is that a candiate for Extra should have enough RF engineering knowledge to know the approximate relationship between beam width and gain without resorting to a model.
ReplyDeleteI considered the possibility that they're based on Yagis; I've found Yagi gain tables that are at least very similar, although not identical. However, a Yagi with a gain of 30 dB would have a bloody large number of elements (a 31-element Yagi has a gain of 19.64 dB, in one article I read earlier today), so I'm of the opinion that these questions actually do reflect a theoretical antenna model of some sort.
ReplyDeleteThe language of the question strongly implies that they are considering a theoretical ideal antennas, spherical cows if you will.
ReplyDeleteCertainly a number of other questions on the test are dealing with mathematical objects which only loosely match their less perfectly constructed physical counterparts.
My initial reaction to seeing the question was "whatever the manufacturer provided polar diagram says it is" or "roughly whatever the method of moments simulation says". ... :) Which would be the correct answer for a real antenna.
The solid angle approach is accurate enough to give a reasonable rough answer to the question.. certainly good enough to have a first guess at the behavior of a real device.
If the test intended something other than simplistic idealized antennas then they should be more specific. What if I build a many wavelength wide highly sparse phased array? I'd could have directionality far in excess of what you'd expect from a projection from gain.
"that a candiate for Extra should have enough RF engineering knowledge to know the approximate relationship between beam width and gain without resorting to a model."
I'd be more willing to buy that argument if the answers weren't fairly close together in this case (E9D21) 12dBi gain, whats the beamwidth?, a) 34 deg, b) 45 degrees, c) 58 degrees, d) 51 degrees.
Call the 1.05 dB value Martin's Constant. :P
ReplyDeleteI found a page that gives a formula, but no explanation for it.
ReplyDelete