By Fabrizio Frezza

This ebook is a concise advent to electromagnetics and electromagnetic fields that covers the facets of so much importance for engineering purposes through a rigorous, analytical remedy. After an creation to equations and simple theorems, themes of basic theoretical and applicative value, together with airplane waves, transmission traces, waveguides and Green's capabilities, are mentioned in a intentionally normal method. Care has been taken to make sure that the textual content is instantly available and self-consistent, with conservation of the intermediate steps within the analytical derivations. The ebook deals the reader a transparent, succinct path in easy electromagnetic conception. it's going to even be an invaluable look up device for college students and designers.

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**Example text**

Introducing the expression of P just found in the transformed constitutive relationship D = εo E + P we get: D = εo + 1 N q2 E. m (ωo2 − ω 2 ) + 2 j α ω So, in the model considered, the medium is a dielectric which is dispersive in time but stationary, whose dielectric constant is complex and dependent on ω: ε(ω) = εo + N q 2 (ωo + ω)(ωo − ω) − 2 j α ω = ε R (ω) + jε j (ω), m (ωo + ω)2 (ωo − ω)2 + 4 α2 ω 2 with ε R (ω) = εo + ε j (ω) = − (ωo + ω)(ωo − ω) N q2 , m (ωo + ω)2 (ωo − ω)2 + 4 α2 ω 2 2αω N q2 .

Therefore we can refer to scalar wave functions A(x, y, z) satisfying the ∇ 2 A + k 2 A = 0. The generic scalar complex wave function can always be written as follows: A(x, y, z) = M(x, y, z) e− j (x,y,z) , having highlighted magnitude and phase. We are usually interested in phase changes rather than in the phase value: in other words, the function is typically defined apart from an additive constant. © Springer International Publishing Switzerland 2015 F. 1007/978-3-319-16574-5_2 47 48 2 Properties of Plane Electromagnetic Waves In the particular case in which (x, y, z) = constant in a certain region of space, the wave is said to be stationary in that region.

E. in the presence of damping, the theorem is not valid for particular values of ω even for dissipative media. Damped free oscillations appear for these values of ω. The third observation is that the theorem is also valid for null conductivity medium, if in place of the dissipation due to the Joule effect other types of losses come into play, in particular when dielectric and magnetic losses, related to the dielectric constant and the permeability, appear. The medium is dispersive in such cases and either ε or μ are characterized by an imaginary part with negative sign.