beamwidth equation
two equation for parabolic (dish) antenna are:
1- teta=70(lambda/d) , d:diameter , lambda:wavelength.
2- teta=sqrt(31000/D) , D:Directivity(G/eta), sqrt:root2(radical).
but the result of calculations for the equations are not the same?
what is exact and right equation for beamwidth?
thank you for attention.
hello,
I am afraid that there is no "exact and right equation" for that, and the expresions you have are approximations which must be used knowing the limitations.
The first one comes from the pattern of a circular dish, which is mathematically described by a bessel function. The value is orientative but it is quite close to real. However the equation is different for a square aperture.
The second one comes from the direcivity-solid angle relation, which is D=4pi/Omega. By aproximating Omega=TetaxPhi, and assuming Teta=Phi you get teta=sqrt(41250/D). Somebody made a further approximation of 41250->31000, but you cannot use it as an exact number, and depends of your antenna configuration, I mean it is not the same a circular aperture, where you can assume Teta=Phi, and a linear array, where the orthogonal beamwidth is much wider than the along-array beamwidth.
However the results fit quite well one with the other, for example d=2xlambda => teta = 35deg. That surface gives a direcivity of 39.5 (15.9dBi), and using the second equation with 41250 (not 31000) the beamwidth is 32.3deg. You cannot obtain much more precission with these equations. The only way you have to have an exact value is to simulate your antenna/array/dish
rgds
Kraus or Silver have helpful books on the subject. You might want to look into those. There is no one exact formula. The radiation characteristics of a antenna depend on many factors including those mentioned above.
Expressions you cite are useful but also approximations.