TABLE OF CONTENTS Up to now we have only considered an infinitely long uniform transmission in the z-direction. We found that such a structure supports voltages and currents which we have labeled as forward waves and backward waves (Eqs. 9.27 and 9.28)
We would now like to focus on a terminated transmission line as shown in Fig. 9.9. In the figure we show a coaxial line terminated in a load impedance Z L at z = 0. Therefore, at the load, the following relation must hold
or substituting z = 0 into the above equations
Henceforth we shall denote normalized impedances such as z L = Z L/ Z 0 with lowercase letters. Since there are two free variables V + and V ? and the constraint imposed by the load (Eq. 9.33), these parameters are now related. The variable ? L = V ?/ V + parameterizes this relationship. For obvious reasons, we call ? L the load reflection coefficient since it represents the fraction of the wave reflected from the load relative to the forward wave. Thus rewriting the previous equation in our new notation, we have
The above equation is easily inverted
We see that when a transmission line is terminated, the voltage and current on the line take on more specific forms due to the constraint of Eq. 9.33, which results...
