I wonder how many engineers fully understand the term “isotropic radiator”. We recently had an interesting discussion about this. What is really interesting is the fact that although an isotropic radiator cannot exist in practice, it is used in so many antenna synthesis and theoretical applications that one commonly finds the term used as if such a device does in fact exist in reality!

In order to clear up any confusion around isotropic radiators, we need to first make sure about the definition of the term “isotropic radiator” (some people – even university lecturers and highly regarded academia – confuse this term with “omnidirectional radiator”). The IEEE standard defines these two terms quite clearly as:

**Isotropic radiator**, *A hypothetical, lossless antenna having equal radiation intensity in all directions.*

Note: An isotropic radiator represents a convenient reference for expressing the directive properties of actual antennas.

**Omnidirectional antenna**, *An antenna having an essentially non-directional pattern in a given plane of the antenna and a directional pattern in any orthogonal plane.*

Few if not none, antenna textbooks explain why an isotropic antenna is theoretically impossible. However Silver gave a simple proof more than six decades ago (S. Silver (Ed), Microwave antenna theory and design, MIT Rad Lab Series, McGraw-Hill, 1949, pp 78-79). Subsequently, in 1954, Mathis offers a more complicated proof after invoking an obscure mathematical theorem of Brouwer, 1909.

Isotropic radiators are commonly used in array synthesis to determine the antenna factor which is then multiplied by the vector field of the single element in an array to synthesise the array pattern.

I remember how I once spent quite a lot of time struggling to analyze an array of radiators in a full-3D EM simulation tool to determine the array factor of a base station antenna. The array patterns in my simulations all showed a ?glitch? (extremely high field value) in a specific direction and only after lots of investigation and ?debugging? I realized that the field vector orientation in the isotropic element patterns that I was trying to use as array elements was undefined (or rather ambiguous) at the poles (theta = 0 and theta = 180).

The analogy used by an antenna engineer I know describes the problem quite well: ?The direction of field vectors at the poles of an isotropic radiator are undefined, just like the direction of the hairs at the crown of your head ? it?s just something one has to make a peace with!?.

Author: Robert Kellerman