Spectral approach to the synthesis of metal grating angular and frequency filters

Abstract

A number of works are devoted to the examination of angular bandpass filters and frequency selective surfaces capable of carrying out a suppression of side lobes of directional pattern. As a rule, these filters consist of a number of dielectric layers, separated by air interlayers. Excessive weight, cost and high sensitivity to changing the polarization characteristics, low level of suppression out of pass band, etc, should be related to disadvantages of them. Changing dielectric layers to metal gratings is one of possible ways to clear the troubles.

This work describes the spectral synthesis, rigorous analysis and theoretical investigation of metal strip periodic grating angular (BPAF) and frequency (BPFF) band-pass filters. Two types of filters, the resonators of which are formed by two infinite strip gratings in H- or E-plane of incident wave, are considered. All synthesis and analysis algorithms are based on rigorous mathematical models.

Traditional methods of the filter synthesis are based on a preliminary design of low-frequency filters taken as prototypes. It is possible if we define the propagation constant for the zero-order Floquet harmonic as τ = κcosφ, with κ = l/λ (l is period of the all strip grids, A. is the wavelength in free space) But, in the high frequency part of the single-wave range (κcosφ ≥ 0.85) this approach leads to mistakes. Direct synthesis method is based on a spectral representation of the zero-order Floquet-wave coefficients for all resonators in the vicinity of their complex eigenfrequencies τ_j. It allows to obtain the reflection coefficient for any number of resonators. Comparing this expression with approximating polynomial we obtain simple set of equations for quality factors Q_j of all resonators. Procedure of resonator synthesis based on the given frequency Reτ₀ and quality factor Q_j reduces, as a matter of fact, to the search of geometry of the resonator having the eigen frequency τ = Reτ₀ – iReτ₀/(2Q_j).

Two types of filters in H- or E-plane are considered. It has been shown that filters of the first type have spurious passbands, and they are more difficult to be manufactured. A good agreement between theoretical and simulated results was observed. In high-frequency part of the singlewave range the suggested approach has no mistakes and can be used for the synthesis of bandpass and band-stop filters in any transmission lines with discrete spatial spectrum.