| Abstract | U pravokutnom utoru okruženom beskonačno permeabilnim sredstvom nalazi se skup serijski povezanih pravokutnih dionih vodiča kojima teče harmonijska struja. Pošavši od pretpostavki koje vrijede za ravni val, izvedeni su analitički izrazi za porast radnog otpora i smanjenje induktiviteta po jedinici duljine dionih vodiča. Prvo poglavlje je uvodno. U drugom poglavlju dane su Maxwellovih jednadžbe u diferencijalnom obliku za pokretno i mirujuće sredstvo u vremenskom području. U slučaju linearnog, izotropnog i homogenog sredstva bez nezavisnih izvora, iz Maxwellovih jednadžbi, dobiju se prigušene valne jednadžbe za jakost električnog polja i jakost magnetskog polja. U slučaju dobrih vodiča mogu se zanemariti pomačne struje, pa tada prigušene valne jednadžbe postaju tzv. difuzijske jednadžbe. Difuzijske jednadžbe nisu prigušene valne jednadžbe, ali one odlični numerički aproksimiraju prigušene valne jednadžbe u dobrim vodičima. U trećem se poglavlju polazi od Maxwellovih jednadžbi u diferencijalnom obliku za harmonijsko elektromagnetsko polje bez nezavisnih izvora. Za harmonijsko polje, prigušene valne jednadžbe polja kao i difuzijske jednadžbe polja u linearnom, izotropnom i homogenom sredstvu bez nezavisnih izvora postaju Helmholtzove homogene diferencijalne jednadžbe. U četvrtom poglavlju dane su jednadžbe ravnog harmonijskog elektromagnetskog vala kao i rješenja Helmholtzovih homogenih diferencijalnih jednadžbi za harmonijsko polje u linearnom, izotropnom i homogenom sredstvu. U petom su poglavlju dobiveni analitički izrazi za radni otpor i unutarnji induktivitet po jedinici duljine dionog vodiča protjecanog istosmjernom i harmonijskom strujom. U šestom su poglavlju dobiveni analitički izrazi za faktor porasta radnog otpora dionog vodiča, a u sedmom su poglavlju dobiveni analitički izrazi za faktor smanjenja unutarnjeg induktiviteta razmatranog dionog vodiča. U osmom poglavlju je dan numerički primjer koji sadrži MATLAB programe za izračun faktor porasta radnog otpora dionih vodiča i faktora smanjenja unutarnjeg induktiviteta i to za ukupno pet dionih vodiča u pravokutnom utoru. Iz analitičkih izraza i grafova u numeričkom primjeru slijedi da s porastom frekvencije dolazi do sve većeg potiskivanja struje prema vrhu dionog vodiča pa stoga s porastom frekvencije raste radni otpor po jedinici duljine razmatranog dionog vodiča, dok induktivitet po jedinici duljine pada. Najmanje je potiskivanje struje u dionom vodiču na dnu utora, a najveće u dionom vodiču na vrhu utora. |
| Abstract (english) | In a rectangular slot, which is surrounded by an infinitely permeable medium, there is a set of series connected rectangular conductors through which a harmonic current flows. Starting from the assumptions valid for a plane wave, analytical expressions for the increase of the active resistance and the decrease of the inductance per unit length of partial conductors are derived. The first chapter is introductory. In the second chapter, Maxwell's equations are given in differential form for moving and stationary medium in the time domain. In the case of a linear, isotropic and homogeneous medium without independent sources, from the Maxwell's equations, attanuated wave equations for electric field strength and magnetic field strength are obtained. In the case of good conductors, the displacement currents can be neglected, and then the attanuated wave equations become the so-called diffusion equations. Diffusion equations are not attanuated wave equations, but the excellent ones numerically approximate attanuated wave equations in good conductors. In the third chapter, we start from Maxwell's equations in differential form for a harmonic electromagnetic field without independent sources. For a harmonic field, the attanuated field wave equations as well as the diffusion field equations in a linear, isotropic and homogeneous medium without independent sources become Helmholtz homogeneous differential equations. In the fourth chapter, the equations of a plane harmonic electromagnetic wave are given, as well as the solutions of Helmholtz homogeneous differential equations for the harmonic field in a linear, isotropic and homogeneous medium. In the fifth chapter, analytical expressions for the active resistance and internal inductance per unit length of a partial conductor, through which a harmonic and direct current flow, are obtained. In the sixth chapter, analytical expressions for the factor of increase of the active resistance of the partial conductor are obtained, and in the seventh chapter, analytical expressions for the factor of reduction of the internal inductance of the considered partial conductor are obtained. In the eighth chapter, a numerical example is given that contains MATLAB programs for computing the factor of increase of active resistance of partial conductors and factor of decrease of internal inductance for a total of five partial conductors in a rectangular slot. From the analytical expressions and graphs in the numerical example it follows that with increasing frequency there is an increasing push of current towards the top of the partial conductor and therefore with increasing frequency the active resistance per unit length of the considered partial conductor increases, while the inductance per unit length decreases. The least current is suppressed in the partial conductor at the bottom of the slot, and the largest in the partial conductor at the top of the slot. |
