The indoor access network is characterized by several branches that cause many reflections. In this paper, we present an approach to model the transfer function of electrical power lines for broadband power line communication. The assuming channel consists of three wires, which is widely used in many countries. As an application of the proposed method, the effect of line length from transmitter to receiver, branched line length and number of branched are also studied. From the frequency response of the transfer function (magnitude and phase), it is seen that the position of notches and peaks in the magnitude responses are largely affected in terms of attenuation by the electrical network which consists of 15 branches.

The power-line communications (PLC) has been applied as a data transfer method in both public electricity distribution networks and indoor distribution networks. The profile of these applications has been different. The devices developed for domestic use are mainly designed for the purpose of controlling electric devices at home. For example, the current and most common functions (

The design of an appropriate communication system, the choice of modulation and coding schemes, and the evaluation of performance, require the knowledge of the end-to-end PLC channel responses in a wide range of frequencies up to 75 MHz [

Several approaches for modelling the transfer characteristics of power lines can be found in literature. The most widely used model for the power line channel transfer function H(f) is the multipath model proposed by Philipps [

Actually, the proposed model is the result of a topdown approach: the various parameters need to be determined through measurements. As such, it is not suitable for the computation at first of the actual transfer function of a given link. Alternative models, based on the multiconductor transmission line theory (MTL), have been proposed in the case of indoor channels [2-5].

The objective of this paper is to calculate the transfer function for a power line communications channel which consists on fifty branches. As an application of the proposed method, the effect of line length from transmitter to receiver, branched line length and number of branched are also studied.

In this part, we are going to see the influence of line length on response of the PLC channel.

We consider a typical medium voltage line of a power line communications which consists of fifteen branches. The PLC network and all branches are formed by three conductors. All the lines have the following per unit length parameters [

where, r is the radius of the conductors (r = 0.8 mm), D is the distance between the conductors (D = 3.2 mm), s is the electric conductivity of the conductors (s = 5.5758 × 10^{7}), µ is the magnetic permeability (, µ_{0} = 4p·10^{–7} H/m, µ_{r} = 1), e is the dielectric constant (e = e_{0}e_{r}, e_{0} = 8.8542 × 10^{–12 F/m).}

The configuration under study is given in

Figures 3(a)-(d) shows the magnitude of the transfer function versus frequency H(f) [

Figures 3(a)-(d) shows the corresponding phase responses. It is observed that as the line length increases there are rapid changes in the phase response. The effects of branch length are studied next.

We now consider the configuration as given in _{i} = 2 m, 3 m, 4 m and 5 m for i = 1:15 branches) with the distance between every branch is constant and equal to 3 m. The fifteen branches are terminated by open circuits.

We calculate the transfer characteristics with respect to the receiver [

As the length of branched line increases the number of notches increase. The phase response (

We consider the power line channel with distributed branches as shown in

Note that for each case the distances between the transmitter and the receiver were equal but not equally distributed [(case 1 ec_{1} = ec_{2} = 24 m), (case 2 ec_{1} = ec_{2} = ec_{3} = ec_{4} = ec_{5} = 3 m ec_{6} = 33 m), (case 3 ec_{1} = ec_{2} = ec_{3} = ec_{4} = ec_{5} = ec_{6} = ec_{7} = ec_{8} = ec_{9} = ec_{10} = 3 m ec_{11} = 18 m) and (case 4 ec_{i} = 3 m i = 1:16)]. The terminations of all the branches are connected on open circuit.

The parametric study conducted in this paper showed that the number of branches, the length of the line and length of connections leads an attenuation of the transfer function.

In this paper, we were interested in modeling transfer function of electrical power lines for broadband power line communication.

A detailed study of factors influencing wave propagations in the medium voltage lines was done.

The magnitude of the transfer function is reduced and selective versus the frequency.

We showed that the notches in PLC channel do not depend on the line length from the position of the transmitter and receiver. The pulse distortion does not depend on the line length between transmitter and receiver. The position of notches in frequency response depends on the branched line length. The increase in branched line length tends to limit the available bandwidth in the medium voltage channel.

We also showed that the position of deep notches does not change with a number of distributed branches. As the number of distributed branches increases the amplitude of notched points tends to increase.

The peak points in the frequency responses tend to fluctuate as number of distributed branches increases.

The study of these phenomena is crucial for improving the performance of the PLC channel.