Study of a signal propagation over a transmission line having a non-uniform topology

After the deployment of broadband transmission in order to meet the requirements of the different applications of the Internet and multimedia data transmissions, ADSL systems (Asymmetric Digital Subscriber Line) are widely used. The PLC (Power Line Communication) is booming. To optimize the transmission of these systems, we should describe or diagnose the transmission medium. This support is typically a twisted copper pair or possibly a neutral phase transmission PLC. The defects on the lines do not alter the traditional telephony transmission, but starts presenting deviations with increasing frequency flow. The merge of high frequency power line transmission is generally accompanied with many propagation problems and attenuations due to the characteristics of the deployed systems and used cables. In fact any transmission line system presents variations in its geometry, causing modifications to the transmitted signal. This article presents a theoretical study that helps understand the transfer function of a cable with non-uniform geometry or defaults. Formalism is proposed in order to calculate the lumped parameters that vary as a function of the line´s geometry. Then an approach of calculating these transfer functions is proposed.