Physical Bounds and Sum Rules for High-Impedance Surfaces

Abstract

High-impedance surfaces are articial surfaces synthesized from periodic structures. The high impedance is useful as it does not short circuit electric currents and reects electric elds without phase shift. Here, a sum rule is presented that relates frequency intervals having high impedance with the thickness of the structure. The sum rule is used to derive physical bounds on the bandwidth for high-impedance surfaces composed by periodic structures above a perfectly conducting ground plane. Numerical examples are used to illustrate the result, and show that the physical bounds are tight.

Physical Bounds of Antennas

“…Considerations about directivity limitations of antennas are presented in [78]. Bandwidth limitations for infinite array antennas are analyzed in [21,22,75] using the results in [49,94], see Sec. 7.…”

“…Here, the low-frequency expansion from [49] is used to extend the results to periodic structures. The sum rule is transformed to the bandwidth bound [22,75,94] [43,44,45] is labeled "100 %".…”

Physical Bounds of Antennas

“…Sum rules have been used to derive physical bounds on electromagnetic systems such as matching [23], radar absorbers and array antennas [22,75,94], antennas [33,43,44], scattering [34,103], high-impedance surfaces [49], and metamaterials [41,52,104]. The sum rules are integral identities that often relate the parameter of interest integrated over all frequencies with some low-frequency quantity.…”

Bandwidth Limitations for Scattering of Higher Order Electromagnetic Spherical Waves With Implications for the Antenna Scattering Matrix

“…Specic issues addressed are e.g. radar absorbers [32], high-impedance surfaces [8,18] and metamaterials [13]. Various antenna limitations have received considerable attention recently (a review can be found in the book by Volakis et al [39]).…”