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Input Resistance of Horizontal Loops Above a Conducting Ground Plane
Author(s) -
Galejs Janis
Publication year - 1971
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs006i011p01011
Subject(s) - loop (graph theory) , lossy compression , current (fluid) , plane (geometry) , physics , square (algebra) , mathematics , limit (mathematics) , geometry , ground plane , mathematical analysis , optics , mechanics , telecommunications , statistics , combinatorics , computer science , antenna (radio) , thermodynamics
Analytical expressions are derived for the resistance of a finite loop with a uniform current distribution located above a lossy half‐space. For loops of radii p 0 large relative to the skin depth δ of the lossy medium, the resistance remains the same as for a long, straight, horizontal wire. For p 0 much less than δ, the loop resistance is proportional to the square of ( p 0 /δ). Numerical solutions show that the above formulas are not valid under conditions of nonuniform loop current at loop elevations h that are a small fraction of δ. The resistance expressions of a magnetic dipole are obtained only in the limit of h ≫ δ.