On the Relation Between Optimal Wideband Matching and Scattering of Spherical Waves

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

“…The limitations for scattering of dipoles were derived previously in [3], whereas [29] derives matching limitations by relating the matching problem to scattering of spherical waves by a high-contrast sphere (with innite static relative permeability and permittivity). Both these references contain more mathematical background, and the interested reader is referred there.…”

“…A general approach to derive sum rules and physical limitations for passive systems presented in [4] is used, cf. also [3,29]. In order to use it, expressions for the low-frequency asymptotic expansions of the scattering and transition matrix elements are required, and this is the topic of Section 2.2.…”

“…The sum rules, in turn, are used to obtain the limitations, or inequalities. Similarly as in the case of optimal broadband matching [29,38], the limitations presented in this paper make up an optimization problem. Its solution is discussed briey.…”

“…In form, the sum rules and limitations derived here are similar to those from optimal broadband matching of the spherical waves. Matching of ideal dipoles, the lowest order spherical waves, was considered by Hujanen et al [21], while higher order waves was treated by Villalobos et al [38], Nordebo et al [29], as well as Kogan (see [24] and references therein). One advantage that follows from the approach adopted in the present paper is that the shape and static material properties of the antenna are highlighted.…”

“…also [3,29]. It relies on the well-known connection between passive systems and Herglotz (or positive real)…”