 # Theory of Operation - Ground Effects

{The document was scanned from the original using Optical Character Recognition in January 1998. Some errors or variations from the original may exist. Comments added to clarify points that may not be obvious or to indicate changes to the original document are inclosed in curly braces "{ }" such as this introduction. Some corrections (e.g. spelling) and format editing were made without indication. Due to the poor quality of the original, equations were recreated rather than scanned. Comments, editing, equation creation, and scanning by R.L. Cross, from January 1998 to ??? 1998 }

## Ground Effects

GROUND EFFECTS:

{In the original J.H.Richmond computer program there was no provision for a groundplane.} In the modified antenna analysis computer program, finite and infinite {conductivity} ground effects were added by using the reflection coefficient technique. The method in which this technique was used required the generation of an image structure. In this section the reflection technique will be discussed in detail. In order to apply ground effects to the electric field, the field for the image structure was first calculated as if a ground were not present, Then, the field was decomposed into parallel and perpendicular components. (A parallel component is the component which is parallel to the plane of incidence. A perpendicular component is one which is perpendicular to this plane. The plane of incidence is the plane containing the normal to the reflecting surface and the incident ray.) Consider an image monopole with the electric field in the L direction. The ray, is a vector which is perpendicular to L and passes through the point of interest. To apply reflection technique, the plane of incident must be found. It is advantageous to define a new coordinate system ( , , z) where and {are} parallel to the xy plane with in the plane of incident and perpendicular. If the direction cosines (cosx, cosy, and cosy) are known, it can be shown that the components of the field in the  plane {i.e. the xy plane} have the following relationship: where = arctan(cosy/cosx). Now the reflection coefficients for the interface can be applied as: where and will be defined later in this section. Appling the matrix equation above yields: (the square matrix is unique, in that, the inverse is equal to the original matrix). Since the image direction is opposite to the original monopole, that is, the z component of the field, which is in the plane of incidence, is given by: From electro-magnetic theory the reflection coefficients for the fields in medium (1) at the interface with another medium (2) are defined as: for the perpendicular component for the parallel component

where is the angle of incidence as measured from the normal to the interface and where the subscripts correspond to the mediums above.

To determine the relationship between , and , a perfect ground (infinite conductivity with relative dielectric constant of zero) was investigated.

limit = -1

limit = +1

But, for a perfect ground the contributions to the field from the image monopole would be equal to the field of the original monopole but opposite in sign due to the chosen reference direction, therefore In summary, the contribution to the electric field of a monopole over a ground plane at a given point is given by: where where E is the field without the ground plane present and 