Electric Circuit Theory and the Operational Calculus Chapter IX, The Finite Line with Terminal Impedances

The Finite Line with Terminal Impedances So far in our discussions of wave propagation in lines and wavefilters, we have confined attention to the case where the impressed voltage is applied directly to the infinitely long line. We have found that, by virtue of this restriction, the indicial admittance functions of the important types of transmission systems are rather easily derived and expressible in terms of well known functions, and the essential phenomena of wave propagation clearly exhibited. In practice, however, we are concerned with lines of finite length with the voltage impressed on the line through a terminal impedance Zj and the distant end closed by a second terminal impedance Z 2 . We now take up the problem presented by such a system. Let K = K(p) denote the characteristic operational impedance of the line, and 7 = y(p) the operational propagation constant of the line. We have then V=Ae-yx+Be^x, 1 = K jfAe-vx-^-Bey*, (240)