2 justification for this statement will be proved in Section 2.2.13. Zo = = (2.2.25) 2.2.11.2 Voltage reflection coefficient (Tv) in transmission lines Zo = = (2.2.26) The same principles described above can also be The minus sign in Equation 2.2.27 occurs because we use applied to electrical energy. This is best explained by the mathematical convention that current flows to the right Figure 2.2.12 where we have a signal generator with are positive; therefore, current flows to the left are negative. a source impedance, Zs, sending electrical waves through a transmission line whose impedance is Zo, into a load impedance, ZL. If the load impedance (ZL) is exactly equal to Zo, the incident wave is totally absorbed in the load and there is no reflected wave. If ZL differs from Zo, some of the incident wave is not absorbed in the load and is reflected (2.2.27) 14 Some authors use different symbols for voltage reflection coefficient. Some use , while others use Pv. In this book, where possible, we will use for components and Pv for systems. CHAPTER 2.2 Transmission lines Required: for (a), (b), (c), (d). Sorting out terms in respect of Solution Use Equation 2.2.28. (a) with ZL = 50 $ (2.2.28) Returning to Equation 2.2.24 and recalling Equation with ZL = open circuit = 8 O 2.2.23 (2.2.29) As the match between the characteristic impedance of the transmission line Z and the terminating impedance ZL (c) with ZL = short circuit = 00 improves, the reflected wave becomes smaller. Therefore, using Equation 2.2.28, the reflection coefficient de- creases. When a perfect match exists, there is no reflected wave and the reflection coefficient is zero. If the load Z on the other hand is an open or short circuit, none of the incident power can be absorbed in the load and all of it will (d) with ZL = 75 S be reflected back toward the source. In this case, the re- flection coefficient is equal to 1, or a perfect mismatch. Thus the normal range of values for the magnitude of the reflection coefficient is between zero and unity. Example