LETTER

Modeling of broadband power line communication channel basedon transmission line theory and radiation loss

Donglin He1,2, Yizhen Wei1, Shuang Cui3, Wei Hua1, Xueyu Duan1, and Liang Liu1,4a)

Abstract One challenge with broadband power line communication is theusage of the unshielded transport channels, which still had many interfer-ence factors when used to transmit high-speed data, such as noise,attenuation, reflection, radiation and time-varying impedance. In thispaper, a two-wire power line is regarded as a long-line antenna. Basedon the transmission line theory, reflection theory and radiation loss oflong-line antenna, a theoretical model of two-wire power line communi-cation transfer function has been established. The channel transmissioncharacteristics of a power line network can be obtained with its basicelements, the geometric size, the characteristics of the conductor materialand the surrounding medium, the structure of power line network, includ-ing the power line length, the number of branches and branch terminalload. In the frequency band of 1–200MHz, the simulated transfer func-tions of the proposed model are in accordance with the measured results,which proved that the model could accurately predict the power linechannel characteristics, and provides theoretical pre-selection guidanceof frequency band, power setting and dynamic range for high-speedbroadband power line communication.Keywords: broadband power line communication (BPLC), radiation loss,transmission line theory, transfer functionClassification: Electromagnetic theory

1. Introduction

Broadband Power Line Communication (BPLC) is a spe-cial communication technology that uses widely coveredpower lines to transmit high-speed data and media signalsparticularly suitable for some old buildings, enterprises,mines, public venues and some other places with difficul-ties to renew the wiring network [1, 2, 3]. However, thepower line is designed to transmit 50/60Hz power. Whenit is used as a high-speed transmission channel, somespecial characteristics, such as noise interference, electro-magnetic radiation, time-varying impedance and attenua-tion [4, 5, 6, 7], are the bottleneck problem that restrict thedata transfer rate and distance of BPLC. The transferfunction of a power line channel reflects the affection ofthese channel characteristics of electromagnetic radiation,

time-varying impedance and attenuation. Therefore, it isnecessary to work on the channel characteristics of powerline networks as the key factors to improve the quality ofBPLC include an appropriate selections of a spectrumband-with, a suitable output signal level of a transmittingterminal, and a properly designed input signal dynamiterange in a receiving terminal according to its power linetransfer function. Modeling and analyzing the transferfunction of a power line network channel becomes animportant research in the BPLC field.

These last decease, many researches have studied onthe accurate channel transmission characteristics of variouspower line networks [8, 9, 10, 11, 12, 13, 14, 15, 16, 17,18, 19, 20, 21, 22, 23]. The top-down or bottom-upmodeling methods are widely used to build the Power LineCommunication (PLC) channel models [9, 10]. A PLCchannel model with lattice structure operating in the fre-quency band of 1–30MHz is presented in [20], and wherethe measured impedance and attenuation factors werepublished in [15]. A simulation of a certain indoor powerline network has been achieved without compare withmeasured results [21]. Another ADS and CST modelswithin an extended the frequency up to 1.3GHz have beensimulated, which different from the measured results [22].In [23], the power line radiation is described as a dipoleantenna. The ABCD method is used to calculate thechannel transfer function of the relay assisted PLC channelin [24]. Based on the top-down approach, an analyticalPLC channel transfer function formula with a limited set ofparameters is established within the frequency band below500 kHz [25]. Based on the transmission line theory, in [26]presents a frequency dependent causal RLGC (f) model at1–50MHz by testing the S-parameters of a three-phasefour-wire busbar distribution system.

Despite these achievements on the PLC, the channelmodel still needs to be further studied in order to accuratelyestimate the channel attenuation and Spectrum character-istics of a complex power line networks, and provide aguidance of PLC band pre-selection, power setting anddynamic range selection. A radiation PLC transfer functionmodel based on the transmission and radiation theory isproposed in this paper.

This paper is organized as follows: Section 2 willillustrate some foundation concepts to build the power lineBPLC model, including the transmission line theory andthe long wire antenna radiation theory. Section 3 willanalyze the reflection factors alone the main line at differ-ent branches, calculate the transmission efficiency of a

DOI: 10.1587/elex.16.20190370Received June 6, 2019Accepted June 21, 2019Publicized July 12, 2019Copyedited August 25, 2019

1College of Electronics and Information Engineering atSichuan University, Chengdu 610065, China2Second Research Institute of Civil Aviation Administration ofChina, Chengdu 610041, China3Nanjing Changfeng Aerospace Electronics TechnologyCompany, Nanjing 210000, China4College of Cybersecurity at Sichuan University, Chengdu610207, Chinaa) liangzhai118@163.com

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Copyright © 2019 The Institute of Electronics, Information and Communication Engineers

PLC channel and present the transfer function model. InSection 4, the accuracy of the proposed irradiate model iselucidated by comparing the simulations with the measuredresults. Finally, the contribution of the research is given inSection 5.

2. Parameters of parallel two-wire power line

2.1 Equivalent distribution parametersA two-wire power line is regarded as a parallel two-wiretransmission line with evenly distributed parameters in thispaper. The distributed parameters per unit length can bestated as Inductance L, Capacitance C, Resistance R, andConductivity G

L ¼ �

�ln

D þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 � d2

p

dð1Þ

C ¼ �"

lnD þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 � d2

p

d

ð2Þ

R ¼ 2

�d

ffiffiffiffiffiffiffiffi!�

2�2

rð3Þ

G ¼ ��1

lnD þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 � d2

p

d

ð4Þ

Where, μ is the permeability of the medium between thetwo-wires, D is the distance between the two-wires, d is thediameter of the wire, ε is the permittivity of mediumbetween the two-wires, ! ¼ 2�f is the angular frequency,f is the operating frequency, �2 is the conductivity of thewire, and �1 is the equivalent conductivity of the mediumbetween the two-wires.

The characteristic impedance Z0 and propagation con-stant γ [27] of a parallel two-wire power line are definedas

Z0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR þ j!L

G þ j!C

sð5Þ

� ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðR þ j!LÞðG þ j!CÞ

p¼ � þ j� ð6Þ

Where, α is the attenuation constant, and β is the phaseconstant.

2.2 Modification of propagation constant for radiationloss

According to the electromagnetic theory, any signal trans-mitted in the power line network causes an electromagneticradiation to the environment, and a power line can beregarded as an antenna [28]. The electromagnetic energywill attenuate during the transmission via the power linedue to the radiation. The irradiate attenuation could beequivalent to an ohmic loss on the line. In order to simplifyanalyze, it is premised that each segment of the power linecould be approximately equivalent to a different antenna,although the structure of the power line network are com-plex. Suppose that the parallel two-wire transmission linecould be equivalent as a long wire antenna and its mirrorimage under the ground [29], as shown in Fig. 1, the

radiation loss can be imported into the transfer functionmodel of power line channel.

If the transmission current I0, on a long wire antennawith a length of l, is constant, which means a constantamplitude with a continuous phase lag. The attenuation ofthe current on the line is ignored in this paper. The antennais placed along the z axis, with the feeding point placedat the origin of the coordinate, as shown in Fig. 1. Thefar-zone radiation field E� of the antenna is

E� ¼ jI02r

e�j�r sin �Z l

0

e�j�z0e j�z

0 cos �dz

¼ I0l

2rsin � sinc

�l

2ð1 � cos �Þ

� �e�j�re�j

�l2ð1�cos �Þ

ð7Þ

Where, ¼ ffiffiffiffiffiffiffi�="

pis the wave impedance, r is the distance

from the origin to the field point, θ is the angle between thehalf-line r and the z axis, λ is the wavelength.

According to the “Poynting vector method” [30], if thetransmission line has a mismatch impedance load with thetraveling wave coefficient K, the antenna radiation powerPr of the traveling wave portion can be obtained

Pr ¼ K

�

S

jE�j22

� ds

¼ KI20

4�lnð2�lÞ � 0:4229 � Cið2�lÞ þ sinð2�lÞ

2�l

� � ð8Þ

Where, Cið2�lÞ is

Cið2�lÞ ¼Z 2�l

1

cos �

�d� ð9Þ

The radiated power could be considered as an ohmic lossevenly distributed over the antenna. Therefore, the lossresistance Rr per unit length is

Rr ¼ K

2�llnð2�lÞ � 0:4229 � Cið2�lÞ þ sinð2�lÞ

2�l

� �ð10Þ

The radiation loss factor could be introduced into thepropagation constant �0

�0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðR þ Rr þ j!LÞðG þ j!CÞ

pð11Þ

3. PLC channel model

As an example, a PLC network with N branches(N 2 ð0;1Þ), as shown in Fig. 2, is chosen to analyzethe impacts of the load impedance and reflection at thenodes on the transfer function. Notice that each power linesegment is regarded as a segment of a transmission line.

The shortest path between the signal source terminaland the load terminal is chosen to be the main line, which isdivided into N þ 1 segments by N nodes. Set the single

Fig. 1. Long wire antenna.

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source voltage Vg, the internal resistance Zg. And Um

represents the voltage at the mth node, the mth main linesegment length is lm, the mth branch length is lbm, the mainline terminal load is ZL, and the mth branch load is Zm. It isassumed that the characteristic impedance of each segmentis Z0 to simplify the analysis in this paper.

Therefore, the ratio of Um to Umþ1 can be obtained as

Um

Umþ1¼ ð1 þ �mÞe��0lmþ1

1 þ �me�2�0lmþ1

ð12Þ

Where, �m is the reflection coefficient at the z ¼ m0 plane,and then the equality could obtain the traveling wavecoefficient Km.

�m ¼ Zsm � Z0Zsm þ Z0

ð13Þ

Km ¼ 1 � j�mj1 þ j�mj ð14Þ

The reflection analysis starts from ZL to ZS alone the mainline. The input impedance Zsm at the z ¼ m0 plane equal tothe parallel connection of Zlm and Zem. Where, Zlm is theinput impedance of the segment lm with the load Zsm�1(Zsm�1 by recursive relations are obtain), and Zem is theinput impedance of the branch lbm with the load Zm, asshown in Fig. 3.

Zsm ¼ ZlmZemZlm þ Zem

ð15Þ

Zlm ¼ Z0Zsm�1 coshð�0lmÞ þ Z0 sinhð�0lmÞZ0 coshð�0lmÞ þ Zsm�1 sinhð�0lmÞ ð16Þ

Zem ¼ Z0Zm coshð�0lbmÞ þ Z0 sinhð�0lbmÞZ0 coshð�0lbmÞ þ Zm sinhð�0lbmÞ ð17Þ

Notice that, at the signal source plane, there are

UNþ1Vg

¼ ZsNþ1ZsNþ1 þ Zg

ð18Þ

Therefore, the ratio of the source voltage to the terminalvoltage is obtained

U0

Vg¼ UNþ1

Vg

UN

UNþ1� � � Um

Umþ1� � � U1

U2

U0

U1

ð19Þ

The transfer function HðfÞ of power line networks withwave source and terminal load is

HðfÞ ¼ 2U0

Vgð20Þ

4. Comparison of simulated and measured results

Different PLC test cases are selected to compare the simu-lated and measured results. Each case has different powerline lengths, number of branches and branch terminal loadimpedances of f5:3�; 50:8�; 1197�;1g to represent im-pedances of low, RF standard, high, and open circuitð1;OCÞ, respectively [31].

The parameters of the two-wire power line (2 � 1mm2)are listed in Table I. The parameters of the single-branch,double-branch and multi-branch networks cases are shownin Fig. 2, as shown in Table II, III and IV.

A Vector Network Analyzer is utilized to measure thetest cases, as shown in Fig. 4. The Tx port of the powerline network is connected to port A (port impedance is50Ω) and the Rx port is connected to port B (port impe-dance is 50Ω).

The scattering parameters S21 of different cases aretested. The calculated modeling results and the experimen-tal results are shown in Fig. 6, 8 and 10 to verify thevalidity of the model.

4.1 Single-branch networkFig. 5 is a diagrammatic sketch of a single-branch network,whose parameters are shown in Table II, Zg ¼ Zl ¼ 50Ω.

Fig. 6-(a), (b), (c), (d) show the comparison of thebasic model simulated results (no radiation loss), the radi-ation model simulated results and measured results on thesingle branch network in the frequency range of 1–200MHz with the load impedances Z1 ¼ OC; 1197�; 50:8�;5:3�, respectively.

The measured results with different Z1 are highlyconsistent with that of the radiation model. It proves that

Fig. 2. Multi-Branch PLC network.

Fig. 3. Input impedance Zsm parameterization.

Table I. Parameters of the selected two-wire power line.

Parameter D d �1 �2 μ ε

Value 2.6 1.13 10�8 5:88 � 107 4� � 10�7 ð1:25=36�Þ � 10�9

Unit mm mm S/m S/m H/m F/m

Fig. 4. Schematic diagram of measurement setup.

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the different load impedances have different groove depthsand indicates that the radiation model are correct andeffective.

4.2 Double-branch networkThe diagrammatic sketch of double-branch network isshown in Fig. 7, and the parameters of the network arelisted in Table III, Zg ¼ Zl ¼ 50Ω.

The measured results and radiation simulated results ofthe double-branch network are shown in Fig. 8. For thedouble-branch network, radiation simulated results wascompared with experimental ones, which also proves thevalidity of model verified.

4.3 Three-branch networkOne three-branch network example is shown in Fig. 9 withthe parameters listed in Table IV, Zg ¼ Zl ¼ 50Ω.

Fig. 10 shows the measured results and radiation modelsimulated results of the three-branch network. Similarly, thepositions of attenuation notches of the measured resultscoincided well with the radiation simulated results in multiplebranches networks. This consistency of the attenuationnotches shows that this radiationmodel could correctly reflecta channel transfer characteristics of power line networks.

5. Conclusion

A novel channel transfer function model of power linecommunication, which is based on the parallel two-line

Table II. Single-branch network parameters.

No. l2 (m) l1 (m) lb1 (m) Z1 (Ω)

(1) 4 6 3 OC; 1197; 50:8; 5:3

Table III. Double-branch network parameters.

No. l3 (m) l2 (m) l1 (m) lb2 (m) lb1 (m) Z2 (Ω) Z1 (Ω)

OC OC

(2) 4 3 3 3 1 1197 5.3

50.8 OC

Table IV. Three-branch network parameters.

No.l4(m)

l3(m)

l2(m)

l1(m)

lb3(m)

lb2(m)

lb1(m)

Z3 (Ω) Z2 (Ω) Z1 (Ω)

(3) 4 3 5 3 3 1 1OC OC OC

1197 50.8 5.3

(a) Frequency (MHz) (b) Frequency (MHz)

(c) Frequency (MHz) (d) Frequency (MHz)

Fig. 6. Single-branch network with different Z1-(1).

Fig. 10. Measured and simulated results of Three-branch network withdifferent Z1, Z2 and Z3-(3).

Fig. 5. Single-branch network.

Fig. 7. Double-branch network.

Fig. 8. Double-branch network with different Z1 and Z2-(2).

Fig. 9. Three-branch network.

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transmission line theory, is proposed. The transfer functionis obtained by calculating the voltage ratio between asource and a terminal in a power line network with aradiation loss of a long wire antenna and a reflection factorin a transmission line with a mismatch load. In the fre-quency band of 1–200MHz, the feasibility of the methodand the correctness of the proposed model are verified bytested the single-branch, double-branch and three-branchnetworks with different load impedances. By known thegeometry size, the conductor and the surrounding mediumcharacteristics of the power line, the proposed radiatemodel could obtain the transfer function without attenu-ation measurement. This radiation model provides a reli-able method to predict the attenuation and spectrumgrooves of a PLC channel, and also provides a solutionfor the high-efficiency spectrum usage and the channelattenuation analysis of high-speed BPLC.

Acknowledgments

This work was supported by National Key Researchand Development Program of China (GrantNo. 2017YFB0308600) and Civil Aviation Joint Fund ofthe National Natural Science Foundation of China (GrantNo. U1733109).

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