By F. Rachidi, S. Tkachenko

The overview of electromagnetic box coupling to transmission traces is animportant challenge in electromagnetic compatibility. using the transmission line (TL) approximation idea has authorized the answer of a giant diversity of difficulties (e. g. lightning and EMP interplay with energy lines). although, the continuous bring up in working frequency of goods and higher-frequency assets of disturbances (such as UWB platforms) makes TL simple assumptions now not applicable for a undeniable variety of functions. within the final decade or so, the generalization of classical TL conception take into consideration excessive frequency results has emerged as a tremendous subject of analysis in electromagnetic compatibility. This attempt led to the elaboration ofthe so-called "generalized" or "full-wave" TL conception, which contains excessive frequency radiation results, whereas maintaining the relative simplicity of TL equations.This publication is equipped in major elements. half I offers consolidatedknowledge of classical transmission line concept and differentfield-to-transmission line coupling versions. half II offers differentapproaches built to generalize TL idea.

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Additional info for Electromagnetic Field Interaction with Transmission Lines : From Classical Theory to HF Radiation Effects (Advances in Electrical Engineering and Electromagnetics)

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It can be shown that eqns (19b) and (17b) are similar, excepting that the low-frequency approximation of ground propagation constant was used in eqn (17b).    g (h + h )   2  g d  2   1 +  g k l   +  g kl   2    2   jwm0    Sunde-log Z gkl ( jw ) = ln   2 2 2π  gg dkl    gg (hk + hl )    +  2     2   (19b) As mentioned earlier, we next discuss the asymptotic nature of the ground impedance as the frequency tends to infinity based on the field penetration depth.

7 Frequency-domain solutions Different approaches can be employed to find solutions to the presented coupling equations. Sections 7 and 8 present some commonly used solution methods in the frequency domain and in the time domain, respectively. To solve the coupling equations in the frequency domain, it is convenient to use Green’s functions that relate, as a function of frequency, the individual coupling sources to the scattered or the total voltages and currents at any point along the line. Green’s functions solutions require integration over the length of the line, where the distributed sources are located.

Let us make reference to the same geometry of Fig. 1, and let us now take into account losses both in the wire and in the ground plane. The wire conductivity and relative permittivity are sw and erw, respectively, and the ground, assumed to be homogeneous, is characterized by its conductivity sg and its relative permittivity erg. The Agrawal et al. coupling equations extended to the present case of a wire above an imperfectly conducting ground can be written as (for a step by step derivation see [1]) dV s ( x ) + Z ′ I ( x ) = E xe ( x, h) dx (31) dI ( x ) + Y ′ V s ( x) = 0 dx (32) where Z' and Y' are the longitudinal and transverse per-unit-length impedance and admittance respectively, given by [1, 9] (in [1], the per-unit-length transverse conductance has been disregarded) Z ′ = jw L ′ + Z w′ + Z g′ Y′ = (33) (G ′ + jwC ′ )Yg′ (34) G ′ + jwC ′ + Yg′ in which • L', C' and G' are the per-unit-length longitudinal inductance, transverse capacitance and transverse conductance, respectively, calculated for a lossless wire above a perfectly conducting ground: L′ = m0  h m  2h  cosh −1   ≅ 0 ln     2π a 2π  a  for h >> a (35) 14 Electromagnetic Field Interaction with Transmission Lines C′ = 2 πe0 −1 cosh (h / a ) ≅ G′ = 2 πe0 ln(2h / a ) for h >> a sair C′ e0 (36) (37) • Z'w is the per-unit-length internal impedance of the wire; assuming a round wire and an axial symmetry for the current, the following expression can be derived for the wire internal impedance [10]: Z w′ = gw I 0 (gw a ) 2πasw I1 (gw a ) (38) ________________ where gw = √ jwm0(sw + jwe0erw) is the propagation constant in the wire and I0 and I1 are the modified Bessel functions of zero and first order, respectively; • Z'g is the per-unit-length ground impedance, which is defined as [11, 12] h Z g′ = jw ∫ Bys ( x, z ) dx −∞ I − jw L ′ (39) where Bys is the y-component of the scattered magnetic induction field.

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