By Mikhail V. Nesterenko, Victor A. Katrich, Yuriy M. Penkin, Sergey L. Berdnik (auth.)

ISBN-10: 0387763600

ISBN-13: 9780387763606

ISBN-10: 0387763627

ISBN-13: 9780387763620

*Analytical and Hybrid tools within the conception of Slot-hole Coupling of Electrodynamic Volumes* arose from the unique learn effects, by no means prior to released, first got by means of the authors at Karazin Kharkov nationwide college, Ukraine.

Impetuous improvement of technical possibilities of laptop for the final two decades, and a strong set of numerical tools to be had within the arsenals of investigators have pressured the working-outs attached with the quest of analytical suggestions of radiophysical difficulties backward. even if, at this time, in fact obtrusive that optimum use of laptop calculations will be in response to program of analytical equipment of boundary difficulties resolution. those equipment let to extend workstation use potency and likewise extend their calculation talents to resolve complicated electrodynamic problems.

The authors’ event within the improvement of analytical the right way to clear up the issues of diffraction of waveguide electromagnetic waves on slot coupling holes serves as a great tool to readers drawn to either the sector of theoretical electrodynamics and the sphere of sensible workings-out of multi-functional waveguide units and platforms utilizing slot-coupling elements.

Topics lined during this publication are:

- problem formula and preliminary imperative equations
- the averaging method
- analytical resolution of the imperative equations for a current
- induced magnetomotive forces approach for research of coupling slots in waveguides
- resonant iris with the slot arbitrary orientated in an oblong waveguide
- stepped junction of the 2 oblong waveguides with the impedance slotted iris

This ebook is meant for tutorial and business researchers excited by Microwave concepts, in addition to complicated scholars learning Radiophysics and utilized Electrodynamics.

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**Additional resources for Analytical and hybrid methods in the theory of slot-hole coupling of electrodynamic volumes**

**Example text**

16) is the slot own field in the infinite screen. 8) are analogically alike, but the slot own field functions differ from each other sufficiently in these equations because these equations are obtained by different methods. Let us represent J (s) in the form of the power series at the α small parameter: J (s) = J0 (s) + α J1 (s) + α 2 J2 (s) + ... 18) where f [s, J (s)] = f [s, J (s)] + f 0 [s, J (s)] is the total slot own field. 15) and having equated the multipliers at the α similar degrees in both the right and left equation parts between each other, we obtain the following differential equations system: d2 J0 (s) + k 2 J0 (s) = 0 , ds 2 d2 J1 (s) + k 2 J1 (s) = i ωH0s (s) + f [s, J0 (s)] , ds 2 d2 J2 (s) + k 2 J2 (s) = f [s, J1 (s)] , ds 2 ...............................................................

Asymptotic Methods in the Theory Nonlinear Fluctuations. 17. : Asymptotic Methods in the Theory of Differential and Integral-differential Equations. PHAN, Tashkent (1974) (in Russian) Chapter 3 Analytical Solution of the Integral Equations for the Current by the Averaging Method In this chapter the asymptotic averaging method has been used to obtain the general approximate analytical expression for the magnetic current in the slot applied both for the adjusted slots (k L = nπ/2, n = 1, 2, 3, .

Jn (±L) = 0. 21) where m and n are the integers. 21), J0 ≡ 0 , f [s, J0 (s)] ≡ 0 in the first approximation: ⎧ iω k ⎨ J (s) = α J1 (s) = − α sin k (L − s) sin 2k L ⎩ s H0s s sin k L + s ds −L L H0s s sin k L − s ds + sin k (L + s) s ⎫ ⎬ ⎭ . 22) As it is seen, the slot own field functions f [s, J (s)] are not involved in the current expression, which, mainly defines the slot resonant and energetic characteristics. Evidently, it is necessary to obtain the following approximations to take into account f [s, J (s)], which, however, meets sufficient mathematical difficulties.

### Analytical and hybrid methods in the theory of slot-hole coupling of electrodynamic volumes by Mikhail V. Nesterenko, Victor A. Katrich, Yuriy M. Penkin, Sergey L. Berdnik (auth.)

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