Generalized impedance method for calculation reflection and passage of waves through multi-layer structure. Part 4. Criterion of applicability of stepped approximation of nonuniform medium

The correctness of applicability of stepped approximation for calculation the reflection, propagation and dissipation coefficients by falling the wave to multi-layer structure is investigated. The starting distribution is the linear increasing of wave number from initial to final points of structure. As an approach it is employed the presentation of structure as a combination from layers in each if it’s the wave number is constant but from one layer to other increases by stepped manner. It is formed 12 distributions with increasing fractional of distribution of structure to steps. It is shown that the dependence of reflection coefficient from the fractional distribution of structure with constant of its length has powerfully indented resonance character. It is shown that for expulsion the possibility of resonances excitation the half of minimum wave length must be more then whole length of structure. From this demand it is found the critical as so maximum value of wave number which is equal to ratio of number “pi” to the whole length of structure. It is found that the correct approximation of linear increasing by stepped is the so as which maximum of wave number is less than critical. It is found that in practice near the critical value for the achieve the correction (near 5%) it is enough the distribution of structure on seven steps which have equal high and length. When the maximum of wave number is more than critical number the anyone increasing of distribution (so as increasing of steps quantity) for increasing of approximation precision of linear structure by stepped does not achieved.