# Horn antenna Radiation pattern

Ok This might sound dumb but I am trying to get an equation for the radiation intensity of a pyramidal horn antenna in spherical coordinates. I got a whole bunch of books and they all have the same equation: $$\mathbf{E}_\theta = \frac{j\, e^{-j k r}\, E_0\, A\, B\, (1 + \cos(\theta))\, \sin(\phi) ...}{8\, \lambda\, r}$$ $$\mathbf{E}_\phi = \frac{j e^{-j k r} E_0\, A\, B\, (1 + \cos(\theta)) \cos(\phi) ...}{8\, \lambda\, r}$$

Ive got like 4 different text books about the subject and the all of them have those exact same equations. But not a single one says what $r$ is anywhere. Anybody know what this is?

Sorry to ask but I've been searching for hours. Can't find a single source that explicitly says what $r$ is.

• Each point in a polar coordinate system is specified as the angle φ and radius r from a center point. – George White Feb 14 '14 at 7:07

## 2 Answers

For a compound box antenna the formula is similar and this might be useful: - Obviously they are not using A and B to denote the aperture dimensions but, I suspect that "r" is going to be exactly the same i.e. distance between centre of aperture and measurement point.

• Thanks! Thats what my intuition was just didn't make any sense to me to depend on radius because the units for radiated power are in Watt/steradian not W/m^2 – RBF06 Feb 14 '14 at 18:17

Spherical coordinates are normally denoted by r, Θ, and φ. Your equation is in terms of those coordinates. r is the distance from the source origin (horn antenna) to the point given by the values of r, Θ, and φ. Thus you already have the answer to your question.