An Approximation for the Characteristic Impedance of Shielded-Slab Line

• Published in: IEEE transactions on microwave theory and techniques Vol. 27; no. 6; pp. 557 - 559
• Main Author: Riblet, H.J.
• Format: Journal Article
• Language: English
• Published: IEEE 01.06.1979
• Subjects: Capacitance; Geometry; Impedance; Jacobian matrices; Slabs; Tin
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.1979.1129670

It is shown how the parametric expressions for t/b and w/b of shielded-slab line, given by means of elliptic integrals in terms of two independent real parameters a and k, can be inverted. First q' = exp (-pi K/K') is expressed as an odd power series in exp (-pi v/(b - t)) whose coefficients are irrational functions of t/b. Here, w is the width of the slab, t is its thickness, and b is the spacing between the infinite parallel plates. Then k is expressed in terms of q' by a well-known formula, and an expression is derived which gives a in terms of q' and w/(b - t). When the series expressions for a and k are substituted in the formulas which yield the total capacitance C/sub 0/, of the shielded-slab line, it is found that the fringing capacitance C/sub f0/=C/sub 0//4 - w/(b - t), is given by an even power series in exp (-pi w/(b - t)), at least to the eighth power. These coefficients, which are irrational functions of t/b, are given explicitly. Finally, comparisons are made with exact values of Z/sub 0/.