Synthesis of Electromagnetic Bandgap Structures using Polar Curves and Mapping Functions

An approach to the design of electromagnetic band gap structures using polar curves and mapping functions is proposed. This investigation begins by deriving a polar form of the standard mushroom element. Combining this with a mapping function, an extended slot is cut from the mushroom element. The surface impedance is determined by two important parameters: the curve order and the gap width. Detailed investigations on the effects of these two parameters on the reflection phase of the newly-designed EBG structure are presented. Simulation and measurement results of the structures reflection phase and surface wave properties show good agreement. The key advantage of this concept is that it allows increased capacitance without increasing element dimensions or thickness and by changing the curve number k, the surface impedance can be increased or decreased on a per unit cell basis. This paper demonstrates that polar curves and mapping functions have potential in the design of high impedance surfaces and it is suggested that there are applications in non-planar surfaces and those with nonuniform unit cell.