Criteria of impedance inhomogeneities approaching by delta-inhomogeneities
Introduction. Impedance δ-inhomogeneities are used for modeling of micro- and nanostructures. In this paper the criteria of impedance inhomogeneities approaching by δ-inhomogeneities are established. Input impedance of δ-inhomogeneities. Expressions for the δ-inhomogeneities input impedance in quantum-mechanical, electromagnetic and acoustic media are given. Delta-inhomoge-neities peculiarly transformed medium impedance, introducing a reactive component. The level of values and character of dependencies of the reactive components of the δ-inhomogeneities input impedance are illustrated. Criteria of delta-approaching for finite inhomogeneities. As a result of approximation error analysis for the input impedance expressions of finite size inhomogeneities (finite inhomogeneities) by input impedance expressions of δ-inhomogeneities criteria of δ-inhomogeneities approaching (δ-approaching) for finite inhomogeneities are obtained. According to these criteria inhomogeneity width should not exceed one-twelfth of the wavelength and normalized wave impedance values of electromagnetic and acoustic inhomogeneities should not exceed 0.5 or should be at least 2. Errors of delta-approaching for finite inhomogeneities input impedance characteristics. The analysis of the approximation errors of the finite inhomogeneities input impedance components characteristics by corresponding input impedance components characteristics of δ-inhomogeneities is fulfilled. Within the δ-approaching criteria the maximum (in magnitude) approximation error of finite inhomogeneities input impedance components is within about 30%. Errors of delta-approaching for finite inhomogeneities reflection coefficient characteristics. The analysis of the approximation errors of the finite inhomogeneities reflection coefficient characteristics by reflection coefficient characteristics of δ-inhomogeneities is fulfilled. Within the δ-approaching criteria the maximum (in magnitude) approximation error of finite inhomogeneities reflection coefficient is within about 15%. Conclusions. Criteria of finite inhomogeneities approaching by δ-inhomogeneities limit the inhomogeneity width by one-twelfth of the wavelength and normalized wave impedance values of electromagnetic and acoustic inhomogeneities should not exceed 0.5 or should be at least 2. By this criteria the maximum (in magnitude) error of δ-approaching of finite inhomogeneities input impedance components is within about 30%, and the reflection coefficient - 15%.