Abstract.
When calculating the basic parameters of even very simple strip
elements, quite serious mathematical difficulties arise. Therefore, the
construction of simplified and approximate mathematical models that allow obtaining
results for strip elements of complex and bulky configuration, or with the
irregularities of the dielectric filling in a clear and convenient form is an
important and urgent problem. The resonator of electromagnetic oscillations
with a two-connected cross-section perpendicular to the axis of wave
propagation is considered. A special case of such a resonator is a strip
resonator, which is a half-wave segment of a metal strip line placed in a
cylindrical cavity filled with a homogeneous isotropic dielectric and
surrounded by a metal screen. After the three-dimensional problem is reduced to
the one-dimensional, the finding of current nodes at the ends of the resonance
strip is reduced to the problem of finding a solution of zeros of the ordinary
differential equation of the second order under special initial conditions. This
is quite naturally used to find the relationship between the geometric
dimensions and resonant frequencies of resonant devices of a fairly wide class.
The authors of this paper propose to solve the problem of finding zeros of the
differential equation of the first order with one initial condition, that more
strictly, more simply and more precisely instead of finding solutions of the
simplified differential equation of the second order with certain initial
conditions.
Key words:
strip resonator, complex and bulky configuration, heterogeneity of
dielectric filling, electromagnetic oscillations, differential equation, zeros,
special boundary conditions, special initial condition.
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