Recently I've build a trap dipole for 20/40/80m bands. I followed an article by John DeGood, NU3E and got following measurements:
- From balun to 20m trap: 485 cm
- From 20m trap to 40m trap: 362 cm
- From 40m trap to the end of the arm: 530 cm
You can find a complete description of the antenna (including descriptions of the balun, used wire, etc) here and here (in Russian, but Google Translate should manage; please email me if you got any questions).
Since 20m trap acts as a loading coil on 40 and 80 meters and 40m trap acts as a loading coil on 80m the antenna turned out to be much shorter than a full-size 80m dipole, and thus probably less efficient on both 40m and 80m bands. I would like to estimate what is the efficiency of the antenna on these bands relative to corresponding full-size dipoles (not an absolute efficiency). The problem is I'm not a mathematician and don't know much about antenna theory.
I was thinking about the following method:
It is based on the fact that the current distribution in the antenna is sinusoidal; it radiates more in the proximity to the balun and almost doesn't radiate at the end of the arm. The radiation and size of the coil are considered neglectable.
I used SciPy to calculate an efficiency of the dipole on 40m band:
>>> from scipy.integrate import quad as integrate >>> from math import cos, pi >>> wl = 40 # 40 m band >>> bc = 4.85 # 485 cm before the coil >>> ac = 3.62 # 362 cm after the coil >>> integrate(cos, 0, ((bc)/(wl/4))*(pi/2)) + \ ... integrate(cos, ((wl/4 - ac)/(wl/4))*(pi/2), pi/2) 0.847610828074005
... and got 84.76% efficiency comparing to a full-size 40m dipole. Naturally this is only a rough estimate, and I'm not interested in calculating a very-very accurate value.
Now I have two questions. 1) Is this method more or less OK or is it completely wrong? If it's wrong could you please suggest a better method? 2) Can this method be generalized for 2 and more coils? The problem is that I don't know in which phase the current is between two coils. Thus currently I can only estimate an upper (70%) and lower (41.1%) bounds for 80m, by ignoring one of the coils, and tell that the actual efficiency is somewhere in between (55.5%).