This paper presents an approach to study and simulate the signal transmission characteristics over the access low voltage distribution networks in Tunisia within narrowband frequency (up to 500kHz). A theoretical model of a two-port network is built to derive the transfer function of a typical low voltage power line communication network. This model is designed based on two wires widely used, the transfer function uses chain parameter matrices describing the relation between input and output voltage and current of the two-port network. Furthermore, the effects of variations in the direct length, branch length and branch load on the channel frequency response are examined. The results of simulation presented in this paper shows that the transfer function is largely affected by the network configuration.