3-16The impedance presented to the input terminals of the transmission line is not merely the resistanceof the wire in series with the impedance of the load. The effects of series inductance and shuntcapacitance of the line itself may overshadow the resistance, and even the load, as far as the inputterminals are concerned.To find the input impedance of a transmission line, determine the impedance of a single section ofline. The impedance between points K and L, in view B of figure 3-16, can be calculated by the use ofseries-parallel impedance formulas, provided the impedance across points M and N is known. But sincethis section is merely one small part of a longer line, another similar section is connected to points M andN. Again, the impedance across points K and L of the two sections can be calculated, provided theimpedance of the third section is known. This process of adding one section to another can be repeatedendlessly. The addition of each section produces an impedance across points K and L of a new and lowervalue. However, after many sections have been added, each successive added section has less and lesseffect on the impedance across points K and L. If sections are added to the line endlessly, the line isinfinitely long, and a certain finite value of impedance across points K and L is finally reached.In this discussion of transmission lines, the effect of conductance (G) is minor compared to that ofinductance (L) and capacitance (C), and is frequently neglected. In figure 3-16, view C, G is omitted andthe inductance and resistance of each line can be considered as one line.Let us assume that the sections of view C continue to the right with an infinite number of sections.When an infinite number of sections extends to the right, the impedance appearing across K and L is Z_{0}.If the line is cut at R and S, an infinite number of sections still extends to the right since the line is endlessin that direction. Therefore, the impedance now appearing across points R and S is also Z_{0}, as illustratedin view D. You can see that if only the first three sections are taken and a load impedance of Z_{0} isconnected across points R and S, the impedance across the input terminals K and L is still Z_{0}. The linecontinues to act as an infinite line. This is illustrated in view E.Figure 3-17, view A, illustrates how the characteristic impedance of an infinite line can becalculated. Resistors are added in series parallel across terminals K and L in eight steps, and the resultantimpedances are noted. In step 1 the impedance is infinite; in step 2 the impedance is 110 ohms. In step 3the impedance becomes 62.1 ohms, a change of 47.9 ohms. In step 4 the impedance is 48.5 ohms, achange of only 13.6 ohms. The resultant changes in impedance from each additional increment becomeprogressively smaller. Eventually, practically no change in impedance results from further additions to theline. The total impedance of the line at this point is said to be at its characteristic impedance; which, inthis case, is 37 ohms. This means that an infinite line constructed as indicated in step 8 could beeffectively replaced by a 37-ohm resistor. View B shows a 37-ohm resistor placed in the line at variouspoints to replace the infinite line of step 8 in view A. There is no change in total impedance.

Integrated Publishing, Inc. - A (SDVOSB) Service Disabled Veteran Owned Small Business