Electric Circuit Theory and the Operational Calculus¹

So far in our discussions of wave propagation in lines and wave-filters, 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 Z1 and the distant end closed by a second terminal impedance Z2. We now take up the problem presented by such a system.