Electrical Communication is a free textbook on the basics of communication technology. See the editorial for more information....

Mid-Series and Mid-Shunt Iterative Impedance

Suppose that another identical T section is connected ahead of terminals 1-2 of Fig. 19(a). The input impedance to this new T section also will be ZKT, because, in accordance with the definition for iterative impedance, this new T section also will be terminated with ZKT. The same reasoning applies, of course, to the π section of Fig. 19(b).

Now suppose that an infinite number of T sections (or an infinite number of π sections) are in tandem forming an iterative or recurrent structure. The input impedance of the infinite number of T sections, or the input impedance of the infinite number of π sections, also will be the iterative impedance, whether or not the distant end at infinity is terminated in the iterative impedance. The line is so long that an electric signal never reaches the distant end, and hence it makes no difference how the end at infinity is terminated. Thus, the input impedance of an infinite number of identical recurrent sections equals the iterative impedance of a network.

As was shown in Figs. 4, 5, and 6, a group of T sections or π sections, when connected one after the other, "blend into" the same basic structure (Fig. 4). The only difference between the two will be at the sending and receiving ends. Here the end sections will be "one half" of a T section or "one half" of a π section, giving a mid series termination or a midshunt termination (page 141). Thus, except from the standpoint of the performance at the input or the output terminals, it makes no difference whether a recurrent group of identical networks is T sections, π sections, or "blended together" as in Fig, 4. The matter of importance is how the structure is terminated. If it is terminated in midseries, then the input (and ouput) impedance is the midseries iterative impedance given by equation 45; if it is terminated in mid-shunt, then the input (and output) impedance is the midshunt iterative impedance given by equation 46.

Last Update: 2011-06-05