Circuit Theory of Coupled Transmission Systems

Abstract

A method of obtaining an exact circuit equivalence of a class of coupled transmission systems from Maxwell's equations is described. The solution for the propagating characteristics of the coupled transmission system can be readily obtained from the circuit analog. The process of reducing field equations to circuit equations is carried out for a particular coupled structure, a coupled helix system. The circuit theory yields frequencies of the coupled modes as functions of the propagation constant, rather than the propagation constant in terms of frequency. The circuit theory has the great advantage that it is as valid for strongly coupled systems as it is for weakly coupled systems. The usefulness of the approach is demonstrated by applying the theory to several slightly different propagating systems. Expressions for the energy and the power flow derived from the circuit theory are compared to the true power flow and the energy in the transmission system. It is shown that the energy of the system in the equivalent transmission line corresponds to the true energy, if the circuit is assumed to propagate slow waves. The power flow relation obtained from the circuit analog differs from the true power flow by the factor of (vp/vg) which is attributed to the dispersive nature of the circuit. Important relationships between impedances of the transmission system defined in various ways are obtained from the power flow relation.

Physics of chromatic focusing, post-acceleration and bunching of laser-driven proton beams in helical coil targets

“…Based on this good agreement between simulations and experimental data, a more detailed analysis of the current pulse propagation along the helical coil can be performed. This analysis is completed by an analytical model derived from the traveling wave tube theory 43,49 . In this section, we consider the case of a target with a long helical coil (L = 15 mm, p = 0.35 mm) described in Secs.…”

“…They demonstrate that a discharge current pulse propagates through the helical wire and generates an electromagnetic pulse (EMP), which affects on the protons dynamics. As the intrinsic inductance and capacitance of the helical structure depend on the frequency 49 , the discharge current pulse is subject to dispersion, which affects its propagation velocity along the helix axis and has a strong impact on the proton bunching. The current pulse dispersion is illustrated with an analytical model derived from the traveling wave tube theory 43,49 , which is in good agreement with the numerical simulations.…”

Impedance matching condition analysis of the multi-filar tape-helix Blumlein PFL with discontinuous dielectrics

“…Otherwise, the load voltage pulse consists of several discontinuous ladder sections that are caused by the repetitive reflections of electromagnetic wave at the side of the PFL Cheng, Liu, Qian, et al, 2009;. The helical BPFL is a kind of dispersive pulse delay line (Kompfner, 1947;Sichak, 1954;Kino et al, 1962). The common used "quasi-static" theory (Kompfner, 1947;Sichak, 1954;Kino et al, 1962;Lewis et al, 1959) and the "traveling wave method" based on telegraphers' equations can be employed to calculate the characteristic impedance of the helical PFL.…”

“…The helical BPFL is a kind of dispersive pulse delay line (Kompfner, 1947;Sichak, 1954;Kino et al, 1962). The common used "quasi-static" theory (Kompfner, 1947;Sichak, 1954;Kino et al, 1962;Lewis et al, 1959) and the "traveling wave method" based on telegraphers' equations can be employed to calculate the characteristic impedance of the helical PFL. However, these methods do not consider the effects of dispersion on the impedance matching condition of the BPFL, so that they have difficulty to accurately analyze the impedances of helical BPFL.…”

Hybrid Energy Storage and Applications Based on High Power Pulse Transformer Charging

“…Under some reasonable approximations, lumped capacitances can be used to substitute the corresponding distributed capacitances for simplification, and more useful and instructive results can be obtained [29]. Of course, the electromagnetic dispersion theory can be used to analyze the lumped inductance and lumped capacitance of the single-layer solenoid under different complicated boundary conditions [34][35]. In this section, an easier way is introduced to analyze and estimate the lumped capacitances of transformer windings.…”