Multiconductors

Calculation of long-term interference voltages is involved with a multiconductor problem which, in contrast to the short-term interference that derives from a one-pole grounding short circuit, in this case is related to the superposition of alternating magnetic fields of all the conductors of one or several three-phase systems as well as the ground wire. 

Includes all installation, materials, conduits, wiring, multiconductor cables, junction boxes, termination panel, miscellaneous supports, etc. 

The accuracy and efficiency of HO FDTD schemes in relation to the improved PMLs and the generalized integration schemes of Section 5.5 are verified by means of several 2- and 3-D realistic waveguide problems. These include inclined-slot coupled T-junctions, thin apertures, power-bus printed board circuits (PCBs), and multiconductor microstrip transmission lines. The majority of the discretized models involve consistent grids that are compared to the respective second-order FDTD realizations. 

Of equal importance for modern EMC structures are the circularly shielded multiconductor transmission lines and the cylindrical cavity-backed apertures of Figure 7.18. Due to their wideband function range, the former are found to be very useful in the construction of ultra-bandwidth microwave elements, junctions, and couplers, while the latter are commonly involved in the solution of penetration or shielding problems. 

C.R. Paul, Analysis of Multiconductor Transmission Lines. John Wiley Sons, 2008. 

I I) General requirements for temporary wiring—(A) Feeders shall originate in a distribution center. The conductors shall be run as multiconductor cord or cable assemblies or within raceways or, where not subject to physical damage, they may be run as open conductors on insulators not more than 10 feet (3.05 m) apart. 

Conductors shall also be so located or guarded as to protect them from physical damage. Multiconductor portable cable may supply mobile equipment. An equipment grounding conductor shall be run with circuit conductors inside the metal raceway or inside the multiconductor cable jacket. The equipment grounding conductor may be insulated or bare. 

In a multiconductor system separated by nonconductive mediums, capacitance (C) is the proportionality constant between the charge (q) on each conductor and the voltage (V) between each conductor. The total equilibrium system charge is zero. Capacitance is dependent on conductor geometry, conductor spatial relationships, and the material properties surrounding the conductors. 

Donaldson PEK (1983) The cooper cable an implantable multiconductor cable for neurological prostheses. J of medical and biological engineering and computing 21 371-374... 

To analyze a transient in a distributed-parameter line, a traveling-wave theory is explained for both single- and multiconductor systems. A method to introduce velocity difference and attenuation in the multiconductor system is described together with field test results. Impedance and admittance formulas of unusual conductors, such as finite-length and vertical conductors, are also explained. 

It should be noted that the impedance and admittance in this equation become a matrix when a conductor system is composed of multiconductors. Remember that a single-phase cable is, in general, a multiconductor system because the cable consists of a core and a metallic sheath or a screen. In an overhead conductor, no conductor internal admittance y exists, except a... 

For the multiconductor illustrated in Figure 1.3, the outer-media impedance is obtained in the same manner as Equation 1.15 [6] ... 

Pollaczek derived a general formula that can deal with earth-return impedances of overhead conductors, underground cables, and multiconductor systems composed of overhead and underground conductors in the following form [7,13] ... 

Equations 1.40 through 1.42 hold true for the multiconductor system shown in Figure 1.17, provided that the coefficients Z, Y, R, L, G, and C are now matrices and the variables V and I are vectors of the order n in an n-conductor system. 

Let us define matrix P as a product of series impedance matrix Z and shunt admittance matrix 7 for a multiconductor system ... 

As discussed in Section 1.4.1, analysis of a multiconductor system requires a number of computations of functions. The application of eigenvalue theory makes it easy to calculate matrix functions. This is a major advantage of eigenvalue theory. 

This equation shows that each mode is independent of the other modes therefore, a multiconductor system can be treated as a single-conductor system in a modal domain. The solutions in a modal domain can be found by n operations, whereas solving Equation 1.138 in an actual domain requires time complexity of o(n ) since the coefficient matrix is an n x n matrix. Matrix A is called the voltage transformation matrix as it transforms the voltage in a modal domain to that in an actual domain. 

By applying modal transformation, differential equations in a multiconductor are given as ... 

The unknown coefficients Vf and in the general solution expressed as Equation 1.110 are determined from boundary conditions. There are many approaches to obtain voltage and current solutions in a multiconductor system. The most well-known method is the four-terminal parameter (F-parameter) method of two-port circuit theory. The impedance parameter (Z-parameter) and the admittance parameter (Y-parameter) methods are also well known. It should be noted that the F-parameter method is not suitable for application in high-frequency regions, while the Z- and F-parameter methods are not suitable in low-frequency regions because of the nature of h5q)erbolic functions. 

Vj and Vj. are the voltage vectors at the sending and receiving ends in a multiconductor system... 

The coefficients F -F in a multiconductor system are obtained in the same manner as in Equation 1.87, considering a matrix form from Equations 1.110 and 1.111 ... 

Note that F and F4 are not the same in a multiconductor system, but they are the same in the case of a single-conductor system. 

In a multiconductor system, the transformation matrix A is also frequency dependent. Frequency dependence is significant in the cases of an untransposed vertical overhead line and an underground cable. In the former, more than 50% difference is observed between Afj (i, /th element of matrix A) at 50 Hz and 1 MHz. In an untransposed horizontal overhead line, the frequency dependence is less noticeable. 

For a multiconductor system, this equation is applied to each modal wave. 

Let us consider the vertical multiconductor system illustrated in Figure 1.61. In the same manner as the finite-length horizontal conductor, the following impedance formula is obtained ... 

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