Analysis of Multiconductor Transmission Lines (Wiley Series in Microwave Transmission Lines and Lumped Circuits (Electromagnetism) (Electromagnetism) . Analysis of multiconductor transmission lines / by Clayton R. Paul. – 2nd ed. p. cm. ISBN (cloth). 1. Multiconductor transmission lines. 2. ANALYSIS OF MULTICONDUCTOR. TRANSMISSION LINES. Second Edition. CLAYTON R. PAUL. Professor of Electrical and Computer Engineering.
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Analysis of Multiconductor Transmission Lines, 2nd Edition () cover This enables instructors to emphasize two-conductor lines or MTLs or both. on multiconductor transmission lines, utilizing Branin's method, which is In this paper, an equivalent circuit model for the analyses of the radiated susceptibility. conductor transmission line analysis accurately captures. transmission lines, with per-unit length inductance and capacitance given by L and C, re-.
The newly derived circuit theory of multiconductor transmission lines is universal, and establishes the validity of the practice of noise reduction. Keywords: electromagnetic noise, new circuit theory, symmetric three-line circuit, normal mode, common mode, coefficients of potential I.
Introduction Electricity is the most convenient form of energy in modern life. Our circumstances environment are necessarily filled with electromagnetic noise emitted from all types of electric devices. As a consequence, all electric devices should be used under the electromagnetic compatibility EMC rule. The problem that causes this situation is that there is no theoretical framework to clearly define electromagnetic noise in circuit theory.
At the frontier of particle accelerators, particularly synchrotrons using time-dependent magnetic fields, we cannot tolerate the usual amount of electromagnetic noise. In an effort to reduce the noise level in the cooler synchrotron TARN2, which was built and commissioned at the Institute for Nuclear Study of the University of Tokyo, one of the authors K.
Hence, for the construction of the Heavy Ion Medical Accelerator in Chiba HIMAC , a careful theoretical study of a three-line circuit system was made based on lumped-parameter circuit theory. Consequently, a symmetric three-line S3L circuit system was constructed for the power supply, noise filter and a chain of magnets for the synchrotron with a third hard-wired central ground line. The S3L circuit is a new concept of noise reduction, which is not at all known within the community.
Recently, we have introduced the fundamental concept for the boundary conditions of lumped parameter circuits and the MTL system 16 , There were, however, several ingredients, whose details were not described explicitly.
One is the coupling devices such as dependent power sources in the lumped parameter circuit and another is the explicit algorithm for the treatment of the radiation terms. Figure 1 A coupled system of lumped parameter circuits and multi-conductor transmission lines. Model of discretization at the boundary of lumped parameter circuit with any number of MTLs, where lumped parameter circuits are connected at both ends.
Lumped circuits consist of passive elements and independent and dependent sources and coupled elements. Here, U and I are the potential and current vectors and the subscript d represents the MTL, and m and n denote discretized time and space, respectively.
In the PEEC method, in order to perform a SPICE-like simulation, the distributed conductive materials are divided into small cells, and each cell is regarded as a set of connected lumped elements of inductance and capacitor 18 , 20 , This method is, however, not straightforward to express the common and normal modes that need to be considered when evaluating electromagnetic noise.
Hence, in the PEEC method, it is difficult to find the ideal configurations for the reduction of electromagnetic noise. On the other hand, in our method, the use of the characteristic impedance and the incidence matrix with the standard circuit theory enables us to connect to the telegraphic equation and to evaluate the coupling of the normal and common modes explicitly The aim of this paper is to use a circuit theory to obtain discretized equations for the boundary conditions between a lumped parameter circuit and MTL system in order to perform a time-domain analysis of electromagnetic noise.
In the first part of Section 2, we introduce the incidence-potential equation IPE for the lumped parameter circuit for node potentials and element currents. The IPE includes an incidence and an impedance matrices, which are sufficient to describe a lumped parameter circuit.
We then add controlled sources and coupling devices to the IPE. In Section 3, we discretize the matrix equation so that it can be used for a time-domain analysis of the lumped parameter circuit, which includes capacitors and inductors.
In Section 4, the matrix equations are combined with the discretized equations for the MTL system. This provides a boundary condition for the connection of the lumped parameter circuit to the MTL system.
Matrix Equation for Lumped Circuit Including Controlled Sources And Coupling Devices We shall begin with construction of coupled equations for the lumped parameter circuit in order to connect smoothly with the MTL equations at the boundary. The potential and current are the independent variables in the MTL equations 9 , 15 , and it is better to use node potentials rather than element voltages in the lumped parameter circuit.
We consider first a lumped parameter circuit with independent power sources without the coupled elements as dependent power sources. We introduce the incidence matrix AT, where the column numbers describe element currents associated with each node point numbered as a row number in the circuit.
We formulate next the dependent power supplies as shown in Fig. The treatment of the dependent power sources can be applied to other coupling devices such as mutual inductances and the transistors as the non-linear devices.
The element numbers and the node potentials are indicated.
Full size image Since the third and fourth terms of Eq. As shown in Fig. The rewritten E expresses independent voltage sources. We can now use all the above expressions containing U and I to rewrite the IPE 3 to include the controlled sources.
We note here that this Eq. In this case, by calculating the inverse of the matrix on the right-hand side of Eq.
For the time-domain analysis, the time-domain impedances can be defined as elements of the impedance matrix Z From Eq. Using the above expressions 11 , we obtain a discretize IPE from Eq. The sign changes in Eq. Since this Eq. In our approach, we prefer to treat these quantities explicitly as the consequence of the discretization of the time dependent equations as shown in the time domain IPE This is because MTL equations of distributed circuit are given in the coupled differential equations for potentials and currents in the standard FDTD method 9 , and the expression in time dependent IPE 12 can naturally express the boundary condition between the lumped parameter circuit and the MTL system as discussed in the next section.