WAVEGUIDE rRANS.\riSSION 319 



transmission line also leads to a reflection coefftcient having a magnitude of 

 unity. In this case, the resulting standing wave will be characterized as 

 follows: (a) If the capacitance is zero, (reactance equal to minus infinity), 

 the reflection will correspond to that from the open end of a transmission 

 line, and a voltage minimum will be found at a distance of a quarter wave 

 from the end. [See Fig. 3.6-3 (g).] (b) If the capacitance is increased from 

 zero to a small finite value, the distance to the nearest voltage minimum 

 will be somewhat less than a quarter wave. [See Fig. 3.6-3(f).] (c) If the ca- 

 pacitance is increased progressively toward infinity (reactance zero), the 

 distance to the nearest voltage minimum will approach zero. [See Figs. 

 3.6-3(e) and 3.6-3(d).] The limiting condition, in which the terminating 

 capacitance is zero, is comparable with that in which the termination is an 

 infinitely large inductance. 



3. If a pure resistance is connected at the end of a transmission line, the 

 magnitude of the reflection coefftcient varies with the resistance chosen. 

 The relations are such that: (a) If the terminating resistance is infinite, the 

 magnitude of the reflection coef^cient will be unity and its sign will be posi- 

 tive. [See Fig. 3.6-3(h).] (b) If the terminating resistance approaches the 

 characteristic impedance of the line, the distance to the nearest voltage 

 minimum will remain constant, but the magnitude of the reflection coefficient 

 will approach zero. [See Figs. 3.6-3(i) and 3.6-3(j).] (c) If the terminating re- 

 sistance is made less than characteristic impedance, the sign of the reflection 

 coefficient will be reversed, and, as the terminating resistance approaches 

 zero, its magnitude will approach unity. [See Figs. 3.6-3(k) and 3.6-3(1).] 



When the terminating resistance is infinite, the reflection is comparable 

 with that in an ideal open-end line, and the nearest voltage minimum will 

 be found at a distance of a quarter wave. When the terminating resistance 

 is zero, the reflection is comparable with that in a closed-end line, and the 

 voltage minimum will appear at the end of the line and also at a point one- 

 half wave closer to the generator. If the line is terminated in a pure resistance 

 of intermediate value, the voltage minima of such standing waves as may 

 be present will be found at the end of the line for all values of the resistance 

 that are less than characteristic impedance and a quarter wave removed from 

 the end of the line for all values greater than characteristic impedance. When 

 the terminating resistance equals characteristic impedance, there is no 

 standing wave. 



If, instead of terminating the line considered above in an inductance coil 

 or in a capacitance or a resistance, we assume that it continues indefinitely 

 into a mass of material having either a conductivity or a dielectric constant 

 different from that of air, similar reflections may take place at the surface. 

 A particular e.xample is shown in Fig. 6.2-8. In general, a part of the wave- 

 power arriving at the surface will be reflected and a part will be transmitted. 



