(2.2.46) Transmission lines can be made to behave like elec- trical components, such as resistors, inductors, capac- and using the definition for voltage reflection coefficient itors, tuned circuits and transformers. These components are usually made by careful choice of transmission line characteristic impedance (Zo), line length (l) and termination (ZL). The properties of (2.2.47) these components can be calculated by using well known expressions for calculating the input impedance where of a transmission line. l = line length equal to distance l = voltage reflection coefficient at load 2.2.13.1 Impedance relations in Tvl = voltage reflection coefficient at distance l from transmission lines r = propagation constant = (a + jB) nepers/m We shall now recall some transmission line properties At any point on a transmission line of distance l from the which you learnt in Sections 2.2.11.2 and 2.2.12.2 to show you how the input impedance varies along the line and how transmission lines can be manipulated to pro- vive = (2.2.48) duce capacitors, inductors, resistors and tuned circuits. These are Equations 2.2.28 and 2.2.29 which are re- peated below for convenience: (2.2.49) (2.2.28) Dividing Equation 2.2.48 by Equation 2.2.49 and using Equations 2.2.28 and 2.2.29 (2.2.50) (2.2.29) In previous derivations, voltage and current references Defining Z as impedance at point l, and Z as the line have been taken from the input end of the line. Some- characteristic impedance, Equation 2.2.50 becomes times, it is more convenient to take voltage and current references from the terminating or load end of the line. (2.2.51) This is shown in Figure 2.2-14. Transmission lines CHAPTER 2.2 Substituting Equation 2.2.28 in Equation 2.2.51 results Equation 2.2.53, we will get Equation 2.2.54. The input impedance of a low loss transmission line is given by the expression (2.2.54) Multiplying out and simplifying where Zin = input impedance (ohms) Zo = characteristic impedance of line (ohms) Sorting out Z and ZL gives ZL = termination load