On Statistics of the Reflection Coefficient of a Dissipative Multiwave Transmission Line with Random Section Lengths

The reflection coefficient is considered as a solution of a Cauchy boundary problem for a matrix Riccati differential equation. Variating of the Riccati equation leads to its linearization and permits to obtain the variation of the matrix reflection coefficient as a function of the variation of the real section length. A notion of dissipativity for the reflection coefficient is introduced. Under the dissipativity condition, statistical properties of the solution of the matrix Riccati differential equation are analyzed. The results obtained are compared with known theorems for non-dissipative transmission lines and with data of computer simulation for real transmission lines.