Efficient calculation of surface impedance for rectangular conductors

Abstract

We have developed a new expression for the frequency-dependent surface impedance of a rectangular bar that is easily used, and is numerically efficient. By dividing the metal bar into rectangular and square sections, skin depth-induced current crowding to the surfaces and corners can be accurately modeled. Comparison to measured data shows excellent agreement over a wide frequency range, covering the transition from dc-like behavior to skin-depth limited behavior.

Skin effect in a thin cylindrical metallic wire

“…Switching to cylindrical coordinates in the latter equa tion [14] and choosing the symmetry axis of the wire for the polar axis Z, we find (5) The solution of Eq. (5) will be performed with the use of the method of moments [14], according to which the function g in the two moment approximation reads as…”

“…Investigation of the manifestations of the skin effect under different conditions still remains an important problem, which has been confirmed by a wide spectrum of scientific publications [5][6][7].…”

Interconnect series impedance determination using a surface ribbon method

“…Another method uses geometrical segmentation to mimic electromagnetic wave distribution inside the conductor with non-uniform transmission lines (Technique B) [5]. A modified version of this method is obtained by making the conductor a hollow tube, with wall thickness of 36 (where 6 is the skin-depth) as the frequency increases (Technique C).…”

“…A modified version of this method is obtained by making the conductor a hollow tube, with wall thickness of 36 (where 6 is the skin-depth) as the frequency increases (Technique C). For the comer regions the same technique is used as in [5], while for the rectangular regions the simple hyperbolic tangent expression is used. However, since the thickness of the wall is always 36, the argument to the special functions (hyperbolic tangents and the Bessel functions in [5]) is always the same at each frequency once the frequency is high enough such that 36 is smaller than thickness of the conductor.…”

“…For the comer regions the same technique is used as in [5], while for the rectangular regions the simple hyperbolic tangent expression is used. However, since the thickness of the wall is always 36, the argument to the special functions (hyperbolic tangents and the Bessel functions in [5]) is always the same at each frequency once the frequency is high enough such that 36 is smaller than thickness of the conductor. For lower frequencies the dc resistance is used for that section.…”