Reflection coefficient optimisation at feed of parabolic antenna fitted with vertex plate

An expression giving the reflection coefficient at the feed of a parabolic antenna fitted with a vertex plate is minimised. The parameters open to optimisation are the vertex plate radius and its distance from the centre of the antenna. Graphs of the reflection coefficient as a function of frequency for some optimisation frequencies are given and compared with the corresponding graphs obtained from another method and from the case where the vertex plate is missing.