Multiconductor Transmission Line Theory Research Articles

Immunity to Conducted Noise of Data Transmission Along DC Power Lines Involving Twisted-Wire Pairs Above Ground

In this paper, immunity of differential dc power lines, recently considered as the physical layer for power line communications (PLC) onboard spacecraft, is assessed from the theoretical viewpoint. The analysis focuses on conducted immunity of the PLC channel to noise generated by the terminal units of the power line (PL). Particularly, multiconductor transmission line theory and modal decomposition are used to characterize the susceptibility of the PLC link to common mode and differential mode (DM) components of the conducted noise. Closed-form expressions for signal and noise contributions at the receiving modem are derived and used to develop design rules for the involved coupling/decoupling networks. By combining the spectral properties of the PL noise with the propagation properties of the link, it is shown that DM signaling, besides assuring a nearly flat channel frequency response, results to be more immune to the PL noise. Finally, the role that possible unbalance of the power units may play on the system conducted immunity and radiation properties is discussed by deriving analytical expressions of the longitudinal and transversal conversion loss associated with the PL terminal networks.

Multiconductor Transmission Line Models for Modal Transmission Schemes

We investigate modal transmission schemes used to reduce echo and internal crosstalk in a multichannel link using an untransposed multiconductor interconnection. The core of such a modal transmission scheme is an appropriate multiconductor transmission line (MTL) model of the interconnection. The standard theory of modal signaling, which emphasizes modal voltages, modal currents, and associated eigenvectors is summarized. Then, we present new results of MTL theory: three theorems on generalized associated eigenvectors and two high-frequency approximations. These results are needed to explain an assumption used in some modal transmission schemes.

FORMULATION OF MULTIWIRE MAGNETIC TRANSMISSION-LINE THEORY

Time- and frequency-domain theory of multiwire magnetic transmission lines is presented for the flrst time. The familiar theory of electric multiconductor transmission lines (MTL) is based on the manipulation of two matrices, the longitudinal impedance and the transverse admittance. However, for magnetic MTLs, the key matrices are the transverse impedance and the longitudinal admittance. It is shown how the latter matrices are deflned and how they should be used to determine the modal propagation constants and modal characteristic wave admittances that characterize the various travelling wave modes of magnetic MTLs. The theory is illustrated considering a three-wire system with three-fold symmetry. Simulation results, in the range 0.1GHz to 10GHz, are presented, showing that the magnetic MTL can exhibit superluminal phase velocity and zero attenuation dispersion.

Multi-Frequency and Dual-Mode Patch Antenna Based on Electromagnetic Band-gap (EBG) Structure

Microstrip patch antenna with multi-frequency and dual-mode is presented in this communication. The introduction of metamaterial substrate made of modified mushroom-type electromagnetic band-gap (EBG) structure enables the multi- functions. The composite right/left-handed transmission line (CRLH TL) theory and multi-conductor transmission line (MTL) theory are introduced to analyze and design this kind of antenna. Three modes including one monopolar radiation pattern in the n=0 mode and two patch-like radiation patterns in the n=-1, 1 modes respectively are analyzed and can be tuned by the parameters of the EBG structure. Since geometry of the radiating patch does not affect the infinite wavelength mode, circular polarization (CP) is obtained for the n=+1 mode by truncating the square radiating patch with linear polarization (LP) for the n=0 mode staying unchanged. Thus dual polarized antenna is obtained. Two prototypes of probe-fed patch antennas are fabricated to verify the theory analysis.

Exploiting the Phantom-Mode Signal in DSL Applications

In order to meet the ever-increasing bandwidth demand of the users, new “digital subscriber line” (DSL) technologies are being developed. In addition to the traditional differential mode of the telephone line, telecom operators are now looking in to the exploitation of the phantom-mode signal. New transmission line models, using the multiconductor transmission lines theory, were developed to support this extended use. In this paper, it is shown that the phantom mode is an eigenmode of the quad cable system, and hence, according to the theory, there is no crosstalk between this mode and the differential mode.

Optimal cable assembly for reducing conducted electromagnetic interference in the traction system

The present work deals with a method of modelling a traction system in PSpice with the consideration for optimal cable arrangements for reducing conducted electromagnetic interference. Multiconductor transmission line (MTL) theory is adopted to model the cable which connects the pulse-width modulation (PWM) source inverter and the motor. A simple decoupling transformation method is proposed and used to transform the MTL into several single transmission line, which can be easily modelled in PSpice. The PWM controlled voltage source and induction motor are also included in this model. Thus, the full model for a traction system is realised in PSpice. From system simulation, the voltage oscillation in the cable is observed and the conducted electromagnetic noise in the system is studied. The relationship between the frequency of the noise and the length of feeding cables are also demonstrated in this work. In order to mitigate the high-frequency noise, a cable system with a fourth parallel earth conductor is proposed and the noise level is indeed reduced by this technique. This modelling procedure for traction system can be used for any specific application like the electrified railway traction system.

Detection of power transformer winding deformation and variation of measurement connections using a hybrid winding model

This paper employs a hybrid model of a disc-type transformer winding for frequency response analysis (FRA) of winding deformation and measurement parameter influence. The model is based on multi-conductor transmission line (MTL) theories and treats every disc of a transformer winding as a transmission line. Three types of winding deformation and two types of measurement connection variation have been simulated by changing the values of the corresponding electrical parameters. Meanwhile, the frequency range of FRA is extended to 10MHz. Various scenarios have been included in the simulation studies and two statistical indicators have been adopted in result analysis. Simulation studies have shown that winding deformation and measurement connection variation can be reflected in frequency response by changing certain parameters of the hybrid model. Simulation results also suggest the frequency ranges in which the failure modes are most distinguishable and their characteristics.

Multiconductor Transmission-Line Theory with Electromagnetic Radiation

We have constructed a new multiconductor transmission-line (MTL) theory with electromagnetic radiation starting from the Maxwell equations. We express scalar and vector potentials in terms of retardation charges and currents and complete a set of MTL integro-differential equations by using the continuity equation and the ohmic-conductor equation with resistance. We naturally obtain coefficients of potential P and inductance L in the transverse electromagnetic (TEM) mode as singular terms of the retardation scalar and vector potentials. We first analyze a linear one-line antenna system and show that the remaining scalar and vector potentials after the removal of the TEM mode terms are responsible for electromagnetic radiation. We then discuss the MTL equation for a two-conductor transmission-line system. As a realistic case, we discuss a three-conductor transmission-line system to enable the inclusion of the effect of circumstances. We demonstrate that a three-conductor transmission-line system with a symm...

TOWARDS BROADBAND OVER POWER LINES SYSTEMS INTEGRATION: TRANSMISSION CHARACTERISTICS OF UNDERGROUND LOW-VOLTAGE DISTRIBUTION POWER LINES

A complete methodology is employed to determine the transmission characteristics of low-voltage/broadband over power lines (LV/BPL) channels associated with underground power distribution networks, in the light of the multiconductor transmission line (MTL) theory. The established bottom-up approach, already used to treat overhead and underground MV/BPL transmission, is extended to analyze BPL transmission in three-phase N-conductor underground lines with common shield and armor. This analysis shows that these cables may support N + 2 modes, giving rise to N + 2 separate transmission channels which reduce to N+1 if the armor either does not exist or is grounded and to N if the shield is also grounded. In addition to the generalized analysis, a simplifled approximation concerning three-phase N-conductor underground cables is also presented. Taking the generalized analysis and the simplifled approximation into account, their numerical results concerning attenuation in various underground LV/BPL channels in the frequency range 1{100MHz are validated against relevant sets of simulations and measurements with satisfactory accuracy and compared to corresponding results of overhead and underground MV/BPL channels. It has been verifled that the attenuation in overhead and underground BPL channels depends drastically on power distribution grid type, MTL conflguration, and cables used. Moreover, the attenuation in underground LV/BPL channels exhibits a lowpass behavior, is signiflcantly higher than that of overhead MV/BPL ones, and is comparable to that of underground MV/BPL ones. A consequence of the proposed methodology is that it

Carbon Nanotubes Bundled Interconnects: Design Hints Based on Frequency- and Time-Domain Crosstalk Analyses

In this paper, the crosstalk problem for carbon nanotubes (CNTs) bundled interconnects is modeled in the framework of the multiconductor transmission line (MTL) theory by using a fluid description of the conduction phenomena in CNTs. Two two-port models for a two-line interconnect (one aggressor and one victim) are proposed. The first is based on the full-MTL equations coupling each CNT in the bundles. The second, which is a reduced order TL model coupling the CNT bundles, is derived from the first one and used for fast computations. The crosstalk models are used to study the impact on relevant electromagnetic performances of some actual technological and design aspects, such as the variability of the number of conducting CNTs in each bundle, their position in the cross section, the proximity of the signaling lines, the cross-sectional aspect ratio, and some advances in CNT manufacturing techniques. Both frequency- and time-domain characteristics are evaluated and compared with those of ideally scaled traditional copper interconnects. The results are compared with those obtained by simplified approaches, showing, in particular, that simple RC models may underestimate the crosstalk.

Transfer Characteristics Modeling of Four-Conductor Cables in Power-Line Communications

This paper presents an approach to model the transfer function of a four-conductor power-line cable for power-line communications. The model is derived from multiconductor transmission-line theory by taking into account all couplings between the conductors. The model allows one not only to determine the transfer function, but also the interference characteristics of that transmission medium. The transfer function for a straight line without branches is obtained first, and then crosstalk is derived. Finally, an N-branch network is simplified based on a generalization of the transmission matrix method. The transfer characteristics of the equivalent network are derived in a similar way as for a straight line.

Transmission Characteristics of Low-Voltage Distribution Networks in China Under the Smart Grids Environment

With the decision to construct the smart grids around China, the power line communications (PLC) on the low-voltage (LV) distribution networks have become one of the potential technologies to commute the information between the end users and the power provider. In order to provide communications services with different priorities under the smart grids environment, it is a must to design a completely new PLC system with variable information rate, which means understanding of the LV PLC channel characteristics become vital. This paper presents the measurement results of channel properties of LV PLC systems after giving a general overview of the topologies for the typical LV distribution networks in China. The testing results show that the main reason influencing the reliable communication of high-speed data of power line is the attenuation of the high-frequency signal, which exhibits more obviously in the branch of power line. It is almost impossible to use the frequency range from 10 to 20 MHz for the reliable communications from distribution transformer to end user, so it must be solved with the aid of such means as the repeater and the modulation schemes. Considering the signal's attenuation, the lower frequency range from 2 to 10 MHz is more suitable for the high-speed data access system. Based on the general topologies of the LV distribution networks, a new method with the help of the reflection matrix based on the multiconductor transmission line theory is proposed to model the channel transfer functions, taking into account of the source inner impedance matrix. The simulation results fit the measured data quite well and verify the feasibility of the proposed modeling scheme.

Broadband Transmission via Underground Medium-Voltage Power Lines—Part I: Transmission Characteristics

The transmission characteristics of underground medium-voltage/broadband over power line (MV/BPL) channels are examined analytically. By appropriately modifying multiconductor transmission-line theory, the bottom-up approach, already used to treat overhead MV/BPL transmission, is extended to analyze BPL transmission in three-phase underground MV lines with common shield and armor. ThIS analysis shows that these cables may support five modes, giving rise to five separate transmission channels which reduce to three if the shield and armor are grounded. The numerical results concerning attenuation in underground MV/BPL channels have been validated against relevant sets of measurements and compared to the relevant results of overhead MV/BPL channels. It has been verified that the attenuation in underground MV/BPL channels exhibits a lowpass behavior and is significantly higher than that of overhead ones.

Group-Delay Engineered Noncommensurate Transmission Line All-Pass Network for Analog Signal Processing

A group-delay engineered noncommensurate transmission line two-port all-pass network for analog signal-processing applications is presented, analytically modeled, and experimentally demonstrated. This network consists of transversally cascaded C-sections, which are distributed implementations of the bridged-T equalizer lumped circuit. It is obtained by interconnecting the alternate ports of adjacent lines of a 2N -port coupled transmission line network with transmission line sections, and it is modeled using multiconductor transmission line theory with per-unit-length capacitance matrix C and inductance matrix L. By allowing the different C-sections of the network to exhibit different lengths, a generalized group-delay engineering procedure is proposed, where quasi-arbitrary group-delay responses are achieved by combining the group-delay responses of C-sections with different lengths. A computer design approach based on genetic algorithms is applied for synthesis, which consists of determining the structural parameters of the different C-section groups. Using this approach, noncommensurate networks are group-delay engineered in edge-coupled stripline technology, and Gaussian, linear and quadratic group-delay responses are realized. The theoretical results are validated by experiment. Finally, two application examples of analog signal processing-a tunable impulse delay line and a real-time frequency discriminator-using the proposed dispersive noncommensurate all-pass networks are presented.

Analysis of Shielded Electromagnetic Bandgap Structures Using Multiconductor Transmission-Line Theory

In this paper, multiconductor transmission-line (MTL) theory is utilized in network analysis of shielded electromagnetic bandgap (EBG) structures. Such structures are emerging in the power distribution network of modern electronic systems to provide noise suppression. Many of them can be conveniently modeled using transmission-line circuits. By applying Floquet's theorem to the MTL model of their unit cell, dispersion diagrams and therefore insight to their modal behavior are obtained in a matter of a few seconds. Two sample shielded EBG structures are examined using the MTL approach. Their one-dimensional dispersion diagrams and insertion loss profiles are generated and compared with full-wave simulations.

Loss Angle and Permittivity Determination of a Dielectric Rod Using a Three-Wire Cage-Shape System

A simple innovative measurement system is proposed for the simultaneous determination of the loss angle and permittivity of a cylindrical dielectric rod at high-frequency regimes (megahertz band). The measurement method, based on multiconductor transmission-line (MTL) theory, explores the frequency-domain resonant features of the new proposed structure, which consists of three equally spaced wires where the cylindrical rod is tightly caged inside. The wires are bonded together at the far end of the MTL structure, while at the sending end, only two are bonded. The input impedance of the transmission line is measured against the frequency, with sharp peaks being observed when the length of the structure comes close to an odd multiple of a quarter wavelength. A theory is developed showing how the propagation parameters of the MTL device depend on the dielectric rod properties, and based on that, a measuring technique is devised for retrieving the loss angle and permittivity of the rod from the critical resonance frequencies and input impedance maximum values. Experimental results are presented to show the effectiveness of the method.

Three Conductor Transmission Line Theory and Origin of Electromagnetic Radiation and Noise

We construct a new multiconductor transmission-line theory with coefficients of potential and inductance. We provide coupled differential equations for potential and electric current with coefficients that are given by geometrical configurations of a transmission-line system. We provide a general solution to coupled differential equations explicitly for three-conductor transmission-lines. We derive coupled differential equations for the normal and common modes of lines 1 and 2, where common-mode current goes through line 3. The common mode acts as an antenna for radiating electromagnetic waves and any electromagnetic devices and conductors placed around the major conductor transmission-lines (lines 1 and 2) act as receivers of electromagnetic waves. This is the source of electromagnetic noise in the circumstance around the transmission-line system. The transmission-line system receives noise from the circumstance through the common mode.

Hybridization of the Scattering Matrix Method and Modal Decomposition for Analysis of Signal Traces in a Power Distribution Network

A hybrid scattering matrix method (SMM) and a modal decomposition technique for analysis of signal traces in the power distribution network of an electronic package are presented in this paper. Applying the modal decomposition of the waves propagating inside the power-ground (P-G) planes and the signal traces, the electromagnetic fields can be decomposed into the parallel-plate mode and the transmission-line mode. The former is analyzed by using the SMM for the finite P-G planes with multiple vias. The multiconductor transmission-line theory is applied to model the micro-stripline and stripline in the package. Numerical simulations are illustrated for coupling analysis of P-G vias to the signal traces in the package and examined through experimental and numerical validations.

A New Circuit Model for Carbon Nanotube Interconnects With Diameter-Dependent Parameters

In this paper, a new circuit model for the propagation of electric signals along carbon nanotube interconnects is derived from a fluid model description of the nanotube electrodynamics. The conduction electrons are regarded as a 2-D charged fluid, interacting with the electromagnetic field produced by the ion lattice, the conduction electron themselves, and the external sources. This interaction may be assumed to be governed by a linearized Euler's equation, which provides the nanotube constitutive equation to be coupled to Maxwell equations. A derivation of a circuit model is then possible within the frame of the classical multiconductor transmission-line (TL) theory. The elementary cell of this TL model differs from those proposed in literature, due to the definition of the circuit variable corresponding to the voltage. When considering small nanotube radius, we obtain values for the kinetic inductance and quantum capacitance that are consistent with literature. These values are corrected here to take into account the influence of larger values of radius properly. Conversely, the value of the per unit length resistance is roughly half of the value usually adopted in literature. The multiconductor TL model is used to study the scaling law of the parameters with the number of carbon nanotubes in a bundle.

A Hybrid Winding Model of Disc-Type Power Transformers for Frequency Response Analysis

The paper presents a hybrid model of disc-type power transformer winding for frequency response analysis (FRA) based on traveling wave and multiconductor transmission line (MTL) theories. Each disc of a winding is described by traveling wave equations, which are connected to each other in a form of MTL matrix model. This significantly reduces the order of the model with respect to previously established MTL models of transformer winding. The model is applied to frequency response simulation of two single-phase transformers. The simulations are compared with the experimental data and calculated results using lumped parameter and MTL models reported in other publications. It is shown that the model can be used for FRA result interpretation in an extended range of frequencies up to several mega Hertz and resonance analysis under very fast transient overvoltages (VFTOs).