The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields

Abstract

A form of circuit which is of considerable interest for the transmission of high frequency currents is one consisting of a cylindrical conducting tube within which a smaller conductor is coaxially placed. Such tubes have found application in radio stations to connect transmitting and receiving apparatus to antennre. As a part of the development work on such coaxial systems, it has been necessary to formulate the theory of transmission over a coaxial circuit and of the shielding against inductive effects which is afforded by the outer conductor. This paper deals generally with the transmission theory of coaxial circuits and extends the theory beyond the range of present application both as regards structure and frequency.

Towards Broadband Over Power Lines Systems Integration: Transmission Characteristics of Underground Low-Voltage Distribution Power Lines

“…Equation (8) has been analyzed in [19,38,39,44,45,55,56,59,77]. Z inn is the N ×N per-unitlength impedance matrix of the N + 1-conductor TL [22,24,27,40]; Z S−M is the N × 1 per-unit-length shield-mutual matrix impedance; Z (N +1)(N +1) is the sum of: the per-unit-length shield-out impedance, the insulation between per-unit-length shield-armor impedance, and the per-unit-length armor-in impedance; Z A−M is the per-unit-length armor-mutual impedance; and Z (N +2)(N +2) is the sum of: the per-unit-length armor-out impedance, the insulation between perunit-length armor-earth impedance, and the per-unit-length ground impedance [38,39,47,[78][79][80]. Z is a symmetric matrix [19,[22][23][24][25][26][27][28]81].…”

“…is the per-unit-length shield-armor insulation admittance; and Y (N +2)(N +2) is the per-unit-length armor earth insulation admittance and the per-unit-length ground admittance in series [38,39,47,[78][79][80]82]. Y is a symmetric matrix [19, 22-24, 26-28, 81].…”

A Full Frequency-Dependent Cable Model for the Calculation of Fast Transients

“…The reference conductor (or common return conductor) of all loops is the radius of the fictive hull cylinder R H . The complete impedance matrix of a system appears as represented in Equation (5) and contains the subconductor matrices of each individual phase. The rank of the impedance matrix Z is equal to the number of all subconductors in the enclosed area n all .…”

“…Ametani [35] determined the impact of semiconducting layers by modifying Schelkunoff's method [5]. Semiconducting layers can also be considered with the subconductor method.…”

“…The frequency-dependent earth return impedance is considered with an fictive earth conductor given by Carson [3] and Pollaczek [4]. The skin effect within the cable core is implemented using Schelkunoff's equations [5]. The proximity effect between the conductors and the skin effect in the shield are neglected.…”