IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
655
Abstract— Multiconductor Transmission Line (MTL) theory is utilized here for modeling the transfer function of power cables in the indoor environment. This approach allows us to determine a circuit model that well characterizes the underlying physics of signal propagation over power-line (PL) cables and that also allows us to account for particular wiring practices common in residential and business environments. In Part II of this work, we will show how the proposed approach allows one to compute a priori and in a deterministic fashion the transfer function of any PL link by using two-port transmission matrices, as commonly done for telephone channel modeling. In this two-part work we will cross several layers of abstraction following a bottom-up approach: starting from the definition of circuit models in this paper, we will arrive at a method for the computation of the transfer function of an indoor PL link in
Part II of this work. Moreover, as discussed in Part II, the approach followed here allows us to unveil some special properties of the PL channel that were never reported earlier, such as the symmetry of the transfer function.
Index Terms— Communication channel, modeling, multiconductor transmission line, power cables, power-line communications, transfer function, transmission line discontinuities, wire communication cable.
I. I NTRODUCTION
T HERE is today a renewed interest in PL communication, and several field trials are presently being carried
out throughout the world [2]. The rationale behind providing
high bit-rate data services exploiting the power grid resides in the vast infrastructure in place for power distribution, and the penetration of the service could be much higher than any other wireline alternative. Moreover, access to the Internet is becoming as indispensable as access to electrical power.
Since devices that access the Internet are normally plugged into an electrical outlet the unification of these two networks seems a compelling option. There is also growing interest in the prospects of re-using in-building PL cables to provide a
broadband Local Area Network within the home or office [3].
The major advantage offered by PL-based home-networks is the availability of an existing infrastructure of wires and wall outlets so that frequent revision or new cable installation is averted.
Manuscript received April 23, 2004. Paper no. TPWRD-00198-2004.
T. Banwell is with Telcordia Technologies, Red Bank, NJ 07701 USA (e-mail: bct@research.telcordia.com).
S. Galli is with Telcordia Technologies, Piscataway, NJ 08854 USA (e-mail: sgalli@research.telcordia.com).
Digital Object Identifier 10.1109/TPWRD.2005.844326
Besides the traditional access and home-LAN applications,
PLCs also have other interesting applications. Today in the construction of vehicles, ranging from automobiles to ships, from
aircraft to space vehicles [4], separate cabling is used to estab-
lish the underlying physical layer of a local command and control network. As LAN technology and associated networking protocols continue to advance, local command and control networks will evolve toward broadband local networks, supporting a proliferation of sophisticated devices and software-based applications.
In spite of the renewed interest in PL communications, this technology still faces several technical challenges and regulatory issues: the PL channel is extremely difficult to model; it is a very noisy transmission medium; PL cables in the 120–240V secondary distribution systems are often unshielded, thus becoming both sources and targets of electromagnetic interference
(EMI); transformers can introduce severe distortion in the absence of bypass couplers.
Considerable effort has been devoted recently to determining accurate channel models for the PL network environment, both for the indoor and outdoor cases. However, ascertaining the transfer function is a nontrivial task since PL characteristics may change due to the particular topology of a given link and adjoining circuits. Several approaches have been followed
for characterizing the PL channel [5]–[11]. In particular, an
interesting approach is to describe the PL channel as if it were affected by multipath effects. The multipath nature of the PL channel arises from the presence of several branches and impedance mismatches that cause multiple reflections.
Although this approach has been proven to describe to some
extent signal propagation along PL cables, [5]–[7], the multi-
path model is an intrinsically incomplete description of the PL channel and presents at least four major disadvantages. First, this modeling is based on parameters that can be estimated only after the actual channel transfer function has been measured.
Second, resonant effects due to parasitic capacitances and inductances are not explicitly taken into account. Third, for the indoor case, there is a high computational cost in estimating the delay, amplitude and phase associated with each of the many present paths. Fourth, particular wiring and grounding practices are not included in the model.
There have also been attempts in the past to model the
PL channel as a two-conductor transmission line (TL) (see
[10]–[13], and references therein). In those contributions,
however, the proposed models led to an incomplete circuit representation that was not capable of fully explaining the
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656 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 physics of signal propagation over PL cables. In particular, these approaches neglected two major points: 1) the presence of a third conductor, which makes the problem one of MTL theory; and 2) the effects of particular wiring and grounding practices.
The above mentioned approaches share a common deficiency in that they are only able to partially describe the underlying physics of PL signal propagation and, therefore, do not allow the unveiling of general properties or any embedded determinism of the PL channel. The unavailability of a model that fully describes signal propagation along PL cables led the PL community to often reach overly pessimistic conclusions: the PL channel is impossible to model a priori , does not allow for the superposition of effects, and has very little or no determinism
embedded in it [14].
Since PL technology appears to be more mature for the indoor home-networking scenario than for the outside broadband access one, we will focus here on the modeling of the indoor PL channel and, in particular, on the transfer function between outlets. A new approach to the characterization of the indoor PL channel has been investigated and is described here. Building on a successful model for signal propagation in multi-pair cate-
gory 5 UTP links [16] utilizing MTL modal decomposition [17],
[18], the new approach for the first time takes into account im-
portant grounding practices imposed by the United States National Electric Code (NEC) (see Section II). There is an extensive literature on MTL theory and mode decomposition (see
[16]–[18] and references therein); however, these results have
been seldom applied to the determination of an analytical model of the transfer function of an MTL that may be effectively used
in the modeling of communications channels [16]. To the best
of the Authors’ knowledge, there are only two recent examples of the application of MTL to the modeling of communications
media. After the proposed approach was first presented in [8] for
the indoor PL channel case, a similar approach based on MTL theory was recently presented for the outdoor PL channel case
in [9]. The second example is given by the work of Cioffi and
Fang on the modeling of crosstalk in the twisted-pair environment, where an MTL approach is followed for the determination of an analytical model for the individual pair-to-pair coupling
functions within a binder [15].
The proposed MTL approach will lead us to a model consisting of two coupled circuits representing the propagation and interaction of the two dominant modes that propagate along the
PL cable. In particular, the first circuit will account for differential-mode propagation while the second circuit will account for the excitation and propagation of the pair-mode, which is the second dominant mode and arises prominently with certain grounding practices. This second circuit represents what we refer to as the “ companion model.
” As shown in Part II of
this work [1], this approach will allow us to find very important
and useful results not previously reported in the literature, and to claim that the PL channel, when properly modeled, exhibits greater determinism than commonly believed.
This paper is organized as follows. An overview of common wiring practices for the residential and business environment is given in Section II. The MTL approach to the modeling of a PL link and its validation via experimental results is described in
Fig. 1.
Layout of a typical residential or commercial premises power line network. A service panel feeds multiple branching paths that include receptacle or outlet circuits, fixed or embedded appliances and lighting circuits. Ground bonding at the service panel is also indicated.
Section III. In Section IV, we derive the complete circuit model for a given PL link by introducing the companion model for pairmode propagation. Concluding remarks are offered in Section V.
II. R ESIDENTIAL AND B USINESS I NDOOR W IRING T OPOLOGIES
Power cables used for single-phase indoor wiring are comprised of three or four conductors in addition to the ubiquitous earth ground. These include “hot” (black), “return” (white), safety ground (green or bare) and the occasional “runner” (red) wires, all confined by an outer jacket that maintains close conductor spacing. Common nonmetallic (NM type) power cables differ from traditional twisted pair cables in that the mutual capacitance of the black and white signal conductors pF/m is significantly smaller than the mutual capacitance between the signal wires and the central ground conductor or – pF/m.
Residential and commercial premises PL networks usually comprise a service panel feeding multiple branching paths that include receptacle or outlet circuits, fixed or embedded appliances and lighting circuits. Fig. 1 illustrates some important differences between these three types of circuits. Receptacle circuits are typically dedicated 15 or 20 amp branching circuits that exhibit symmetry in the connections of black and white wires, which preserves differential balance with respect to the safety ground. Embedded appliances are typically dedicated nonbranching receptacle circuits with 20–50 amp rating. In contrast to receptacle circuits, lighting circuits have significant asymmetry between hot and return wires created by the insertion of dedicated switches in the “hot” side that produces considerable differential and pair-mode coupling. While the
“white” return wires and safety grounds are isolated throughout all distal network branches, the United States National Electric
Code (NEC) mandates that the return (white) and ground wires should be connected together or “bonded” at the main service panel.
The circuit in Fig. 2 illustrates one phase in a service panel with four circuit breakers. The black wires are each fed via separate circuit breakers while the white wires connect to the

BANWELL AND GALLI: NOVEL APPROACH TO THE MODELING OF THE INDOOR POWER LINE CHANNEL PART I 657
Fig. 3.
Equivalent circuit of a long cable, illustrating the relationships between modal and wire currents. Two transformers extract the pair-mode signal.
Fig. 2.
Diagram of a typical service panel with four circuit breakers. Two branch cables are explicitly shown along with two additional loads L2 and L3.
mains transformer return (RTN) via a common terminal block.
The safety grounds are connected to earth ground via a second terminal block. Element represents a low resistance shunt connecting the ground and return paths, a practice referred to as
“bonding”. There is substantial mode coupling created by the electrical path through , which has been largely ignored in previous models of indoor PL links.
The present discussions will chiefly address signal propagation over receptacle circuits implemented with two-conductor
10 to 14 gauge ( – ) nonmetallic cables with ground.
It will be assumed that the more complex lighting circuits are fed from separate breakers. Although complex network topologies can exist, the prevailing regulations, when followed, greatly simplify the analysis of signal transmission over receptacle circuits.
ground conductor makes the problem of characterizing signal propagation on indoor power cables a natural problem of MTL theory. MTL theory provides a method for finding eigenstates of the matrix telegrapher’s equation which break down a system of conductors and earth ground into simple TL’s, each of
which corresponds to a single mode of propagation [18]. On the
basis of this analysis, signals at the inputs of an MTL are first decomposed into modal components, which propagate along the respective modal TL’s and, finally, are properly recombined at the output ports. The voltage and current transformation matrices contain the weighting factors that determine the amounts of signal that couple between each of the ports and each modal
TL [17].
In the case of indoor PL networks, the modes propagating along the cable are not independent and mode coupling often occurs. In particular, strong coupling between modes occurs at a few points in the house, most notably at the point of ground bonding at the breaker box, the mains feed, and lighting circuits interrupted by switches. Since lighting and outlet circuits are usually fed from separate breakers, the effects of bonding often mask the effects of lighting circuits. An equivalent circuit will be derived in the next section for all propagating modes and mode coupling effects will be characterized.
III. M ULTICONDUCTOR A NALYSIS OF P OWER L INE C ABLES
Consider first a transmission line (TL) consisting of two isolated conductors. Such a configuration supports four modes of propagation along the TL in the TEM approximation, two spatial modes, each with two directions of propagation. The spatial modes are often referred to as differential mode (or balanced or odd-mode) and common mode (or longitudinal or even-mode).
The differential mode current is almost always the functional current responsible for carrying the desired data signal along the line. It is possible to excite only a differential propagating mode along a two-conductor TL, e.g., a twisted-pair cable, by differential signaling, i.e., by driving the two conductors with antipodal signals. However, if there are imbalances or asymmetries between the two conductors, common mode components may arise even when the two conductors are differentially driven. The presence of common mode currents on a cable does not inherently degrade the integrity of differential mode data signals. However, if mechanisms exist where energy can be transferred from common mode to differential mode, then the common mode current can become a dominant interference signal. This phenomenon is called mode conversion or mode coupling.
Cables typically used for single-phase indoor power distribution are comprised of three conductors. The presence of a third
A. Analysis of Three-Conductor Transmission Lines
A three-conductor cable supports six propagating modes
(TEM approximation), three spatial modes (differential, pair and common modes) each for two directions of propagation.
The differential mode current represents an “odd-mode” signal with current confined to the white and black wires and is generally the desired signal. The pair-mode current represents an “even-mode” signal with current flowing between the safety ground wire and the white/black wires “tied together.”
The fields associated with the two modes and are well confined to the cables and consequently these modes exhibit low attenuation. The third common mode current represents overall cable current imbalance, which creates a current loop with earth ground. Common mode current is highly dependent on cable installation and the characteristic impedance for this lossy mode is variable and not readily characterized:
– .
Fig. 3 is an equivalent circuit for a semi-infinite cable that illustrates the relationship between the two modal currents and and the three wire currents , and de-
scribed by MTL theory [17]. Similar circuits are often used

658 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
Fig. 4.
Equivalent circuit for the deconvolution of the three propagating modes for a three-conductor cable as described by (3)–(4).
in SPICE numerical simulation of MTL’s [19], [20]. The dif-
ferential-mode is represented by the characteristic impedance
, whose value ranges from 70–140 for typical power cables. Pair mode excitation depends on the two parameters and
, which together describe cable asymmetry. The parameters shown in Fig. 3 are not independent. While the ratio is determined by cable geometry, it is possible to select , in which case the pair-mode current the pair-mode impedance equals . In this case, ranges from 50 to 60 .
Let vector represent the differential, pair-mode and common-mode currents, respectively, for waves propagating in a forward direction 1 . The corresponding propagating voltages are related to these currents by a diagonal matrix of characteristic impedances
the following modal transformations (see [16] and references
therein):
(3)
(4)
(1)
Likewise, the voltages and currents of the three modes that propagate in the reverse direction satisfy the corresponding relationship
(2)
For modeling purposes, it is important to describe how the voltages and currents seen on the individual wires map into the respective spatial modal components that propagate independently. Let and be the currents and voltages on the three wires, respectively. These are directly measurable quantities. The amplitudes of the three propagating spatial modes at any point are related to the wire voltages on the cables by
1
Subscripts c
(or 1) and c
(or 2) denote the sections of the cable before and after a discontinuity, respectively. Superscripts and denote forward and backward travelling waves. Finally, bold letters denote vectors and matrices.
The modal matrices describe lossless transformations for which ; consequently, the transformation matrices satisfy the following relationships:
(5)
The parameter – describes asymmetry between the black and white wires relative to the ground conductor. The value of for NM cable is sensitive to small variations in conductor spacing due to the relatively small value of . The factor describes the shielding produced by the ground conductor: for NM type cable, complete shielding gives
, and cables with tightly twisted signal pairs, such as category 5 UTP, have
[16].
Fig. 4 shows an entire end-to-end equivalent circuit for a finite section of power cable. The transformers implement the transformations specified in (3)–(4). The three propagating modes are represented by Thevénin equivalent circuits for the respective modal transmission lines. An incident differential signal on the left characterized by and , for example, appears at the far right end of the cable as a dependent voltage
, where is the complex propagation constant for the differential spatial mode and is the position along the TL.

BANWELL AND GALLI: NOVEL APPROACH TO THE MODELING OF THE INDOOR POWER LINE CHANNEL PART I 659
B. Cable Modeling: Terminations and Discontinuities
Let us first calculate the impedance of a semi-infinite cable.
The application of a voltage at the input of a semi-infinite cable can only excite forward propagating modal voltages, so that and . From (4), we have
The reflected waves in MTL circuits are often described by
matrix reflection coefficients defined as (see (106) in [17]):
(11)
The current and voltage matrix reflection coefficients are related through (1) and (2), which yields the transformation
Now, recalling (3) and (5), we can write:
(12)
From the previous results, one can deduce the following closed form expressions for the voltage and reflection coefficients where
(6)
(13)
(14)
This is the terminal impedance one would observe looking into the semi-infinite long cable. The corresponding matrix for the conductance seen looking into a semi-infinite cable is
(7)
Any discontinuity in a cable arising from interconnections and termination mismatches induces coupling between modes.
Consider next the far end of a cable that is excited by a purely differential incident wave and terminated in an arbitrary linear network described by impedance matrix
Depending on , the reflected wave may contain one or
.
more modal components. It is possible to find the relationship between and by expressing cable voltages and currents in terms of propagating modes
Reflections are suppressed when , which occurs with when
, i.e., reflections are suppressed is equal to the input impedance of a semi-infinite long cable.
We next consider two special cases that are particularly relevant to indoors PL applications: a cable interrupted by a shunt conductance situated between the active wires and ground return, and multiple cables joined at a common location. Let conductance matrix describe the currents flowing as a result of shunt conductances placed between the three conductors and earth return. When situated between cable sections, the effective termination seen by the excited cable is
. Substitution of this conductance into
(10) yields and, then, by solving for the reflected currents where we have exploited the relationships in (1), (2), and (5).
Equation (8) can be rewritten in terms of instead of
(8)
(9)
Equation (9) may be recognized as a generalization of the familiar scalar reflection coefficient for a two wire TL. One can also derive a corresponding expression for the voltage reflection created by
(15)
In the present work, we have examined mode coupling produced by a differential shunt placed between hot and return wire, bonding through a shunt resistance fault condition created by a shunt resistance and the between hot and safety ground. The conductance matrix for this example is shown in (16), at the bottom of the page. The differential shunt and bonding provide two distinct cases of interest. Let us consider again the case where the excitation consists of a purely differential incident wave load is represented by a differential shunt
(16) with into (15) gives
. A typical
. Substitution of
(17)
(10)
There is no spatial mode coupling with a differential shunt.
Several other useful reflection coefficients can be derived from
(16)

660 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 substitution of (16) into (15). Normal bonding is modeled by
, whereas the fault condition with black wire connected to ground is modeled by differential mode reflection coefficients for each case are
. The
(18.a)
(18.b)
(18.c)
The last two expressions involve mode coupling through the shunt. It is worth noting that the reciprocal of each scalar reflection coefficient above exhibits a simple linear dependence on the independent parameters or .
PLC networks often have more than two cables feed from a common point. The termination represented by n cables and a general shunt can be described by
. The reflections created in this case are given by (10) as
Fig. 5.
Measured differential reflection coefficient as a function of shunt resistance for bonding and fault conditions with
14=2 cable. Experimental validation of the linear variation of
01= with
R and
01= with
R
, as predicted by (18.b) and (18.c). Open circles represent normal bonding
(white to ground), while the solid points represent black to ground connections.
This expression reduces to Equation (15) with terms in
. The two represent mismatch created by multiple cables.
With , the voltage reflection does not involve mode coupling and is simply , which vanishes for . The given expression for example, for the two-conductor case and is general; for
(e.g., a bridged tap in twisted-pairs) becomes a scalar equal to
Section II.C in [21]). The second term involving
coupling between differential and pair modes. The differential mode reflection for identical cables created with just predicted by (19) is
(see produces
(19) or . According to (18.b) and (18.c), the ratio of intercept to slope is . The nominal slopes are 0.085 and 0.051 respectively, while the corresponding intercepts are 3.2 and 2.7. From the results in Fig. 5, we deduce and with expected values.
, which are consistent
Equation (19) is a good model for ground bonding in PLC networks, in which case describes lossy transformer coupling between differential and pair modes through . The next section will elaborate on this observation. Although MTL theory facilitates accurate description of complex cable configurations, it does not readily permit direct calculation of end-end transmission behavior. The next section shows that the effect of pair mode coupling can be isolated in a companion model which is amenable to ABCD matrix analysis.
(20) where denotes the differential mode reflection with
. Equation (20) clearly reduces to (18.b) for with . Experiments were performed which validate the proposed MTL approach. Differential mode reflections and were measured by placing bond shunts or fault shunts in the middle of four 15.2 m sections of cable
( case). Parameter was computed from the incident wave amplitude to be 146.2
. Both and are plotted in Fig. 5 as a function of shunt resistance. A linear relationship is evident and the regression coefficients range from 0.998 to 0.9997. The different slopes are caused by cable asymmetry with – . Reflection measurements can be affected by unintentional mode coupling; however, the ratio of intercept to slope in Fig. 5 is insensitive to measurement conditions since it represents the Thevénin impedance seen by
IV. N ETWORK M ODELING : T HE “C OMPANION ” M ODEL
Fig. 6(a) shows an equivalent circuit for three or more cables terminating on the service panel. The two dominant cable modes are represented; hot, return and ground busses are also indicated. Thermo-magnetic circuit breakers have a series inductance of about 50 nH, which is comparable to other “parasitic” lead inductances present within the service panel. In the absence of substantial variability in cable asymmetry or parasitic lead inductance, transformer coupling forces the center-tap nodes , and to a common potential. The distribution of center-tap currents within the mode transformers is not apparent to the propagating modes on the branch circuits. For these circuits, the center-taps appear to be joined by a phantom wire.
Neglecting parasitic lead inductance, the individual mode coupling transformers can be lumped into a single auto-transformer as shown in the circuit of Fig. 6(b). The auto-transformer can be replaced by a 2:1 transformer as indicated in the bottom circuit in Fig. 6(b). It is now apparent that the differential and pair modes can be treated as two independent networks that share a common topology as shown in Fig. 6(c). It is a simple exercise

BANWELL AND GALLI: NOVEL APPROACH TO THE MODELING OF THE INDOOR POWER LINE CHANNEL PART I 661
Fig. 6.
(a) Equivalent circuit for three or more cables terminating on the service panel. The points
X ; X
, and
X are equipotential. (b) The effect of the individual mode transformers represented by a single auto-transformer. (c) Separation of differential and companion pair mode circuits. The two modal circuits share a common topology.
Fig. 7.
Wiring model used in our experiment: two rooms, one breaker box, one mains feed and five outlets.
to derive (20) from the bottom circuit in Fig. 6(c) since the 2:1 transformer produces a 4:1 impedance transformation.
The pair mode circuit can then be considered a companion to the differential circuit. Therefore, we can now state that the differential and pair modes can be modeled as two independent networks of simple two-conductor TL’s strongly coupled at one location through a modal transformer .
Without any loss of generality, we will consider an indoor wiring model having two branches with five outlets and a breaker box as shown in Fig. 7. This particular layout will also be used for the experiments described in Part II of this work
(see Section V in [1]). The equivalent circuit of this indoor
PL link is given in Fig. 8, where the characteristic impedances and propagation delays (ns/ft) of each cable are also given.
Resistor models the (low) impedance seen looking into the low voltage transformer, and is the differential termination of the network. The two networks representing the two modes have identical transmission line topologies but different termination impedances. The distal ends of pair-mode transmission lines are terminated in capacitors with similar values. Since the network representing the pair-mode excitation is determined by the differential mode network topology, we refer to the uncoupled pair-mode model as the “companion model”. To facilitate explicit reference to mode amplitudes, the effective mode transformer in Fig. 6(c) has been replaced by its Thevénin equivalent circuit as shown in Fig. 8. This figure illustrates how the test network in Fig. 7 can be partitioned into nearly independent differential-mode and companion pair-mode networks.
The upper portion of Fig. 8 describes differential-mode signal propagation while the lower section describes pair-mode signal excitation and propagation over the companion network; the gray area shows the principal point of mode coupling through
. Each cable section in Fig. 7 has an element in both mode circuits in Fig. 8. The feed line entering the low voltage transformer sees an impedance and does not have a pair-mode element since the return provides grounding as indicated in Fig. 2.
Starting from the circuit model in Fig. 8, an equivalent model expressed in terms of cascaded 2PN’s will be derived in Part II
of this work [1]. Once the equivalent 2PN representation is ob-
tained, it is possible to represent the PL link by means of transmission, or ABCD, matrices, only. This modeling, reminiscent

662 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
Fig. 8.
The final circuit model of the power line link in Fig. 7, where the mode transformer has been replaced by its Thevénin equivalent: differential circuit model (upper section) and its “companion model” (lower section).
of the classical modeling of twisted pairs, is more useful than the circuit model in Fig. 8 from a communications point of view, since it provides us with a more convenient way to compute the transfer function of any PL link. Moreover, on the basis of the proposed approach, we will be able to unveil special properties
of the PL channel not reported earlier [1].
V. C ONCLUSION
The common denominator and limitation of previously reported channel models for the PL environment lie in the fact that the PL channel has been treated from a mere phenomenological or statistical point of view. These approaches allow us to describe the channel only partially, and prevent us from unveiling particular properties of it.
In this work, we proposed a novel approach to the problem of indoor PL channel modeling, based on MTL theory and modal decomposition. The necessity of an MTL approach is due to the fact that indoor power cables consist of three conductors, and not just two as for the classical twisted-pair and coaxial cable cases. Additionally, common grounding practices (as mandated by the US National Electric Code for commercial and residential premises) induce nonnegligible mode coupling effects that cannot be described without resorting to MTL theory and mode decoupling techniques.
The MTL approach followed here leads us to a model consisting of two coupled circuits representing the propagation and interaction of the two dominant modes, the differential and the pair-mode. The first circuit accounts for differential-mode propagation while the second circuit, the companion model , accounts for the excitation and propagation of the pair-mode. We have shown that neglecting mode coupling and, therefore, the companion circuit shown in the lower portion of Fig. 8, leads to an incomplete circuit model that is not capable of fully representing the physics of signal propagation on PL cables (as also experi-
mentally verified in Section V of [1]).
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Thomas Banwell (M’90) received the B.S. degree in chemical physics from Harvey Mudd College, Claremont, CA, in 1978, and the M.S. degree in electrical engineering and Ph.D. degree in applied physics from the California Institute of Technology, Pasadena, in
1980 and 1986, respectively. He received the Ph.D.
degree from UNDNJ-New Jersey Medical School.
He has been with Telcordia Technologies, Red
Bank, NJ, since 1986. He pursues problems related to performance limitations in low-power/high-speed electronic circuits that arise in public telecommunications network access and data processing applications and variable bit-rate optical transmission systems. His interests in circuit theory have expanded to include modeling physiological processes such as uterine contraction. He has authored or coauthored many technical papers and has seven patents.
Stefano Galli (S’95–M’98–SM’05) received the
M.S. and Ph.D. degrees in electrical engineering from the University of Rome "La Sapienza," Rome,
Italy, in 1994 and 1998, respectively.
After receiving the Ph.D. degree, he continued as a
Teaching Assistant in Signal Theory at the Info-Com
Department. In 1998, he joined Bellcore (now Telcordia Technologies), Piscataway, NJ, in the Broadband Networking Research Department where he is now a Senior Scientist. His main research efforts are devoted to various aspects of xDSL systems, wireless/wired home networks, personal wireless communications, power-line communications, and optical code-division multiple access (CDMA). His research interests include detection and estimation, communications theory, and signal processing. He is a reviewer for several IEEE journals and conferences and has published many papers. He holds three patents and several pending ones. He also served as a Co-Guest Editor for the Feature Topic "Broadband is Power: Internet
Access through the Power Line Network" ( IEEE Communications Magazine ,
May 2003), as Co-Guest Editor for the special Issue on Power Line Communications of the IEEE Journal on Selected Areas in Communications.
Dr. Galli is serving as Chair of the IEEE Communications Society Technical Sub-Committee on power line communications. He also served as Technical Program Committee member of several IEEE conferences, such as the
IEEE International Symposium on Power Line Communications (ISPLC’04,
ISPLC’05), and is serving as the general Co-Chair of the IEEE Workshop on
Signal Processing Advances in Wireless Communications (SPAWC’05).