OPEN-WIRE TELEPHONE LINES 753 



Like the attenuation, the impedance of an open-wire circuit in a 

 narrow band of frequencies may be radically changed by interaction 

 with adjacent circuits. These large irregularities in the impedance 

 commonly accompany absorption peaks in the attenuation, and are, of 

 course, due to the inadequacy of the line transpositions. 



Phase Change and Velocity of Propagation 



The imaginary component of /3 of the propagation constant is known 

 as the phase constant because it indicates the change in the phase of the 

 voltage and current in circular radians per unit length of line. 



The value of the phase constant is given by 



/32 = 1/2 [V(i?' + LW)(G2 + CV) + (LCco^ - RG)]. (10) 

 If E} and G^ are small compared to LW and CW it is clear that 



/3 = w VLC radians per mile. (11) 



For an open-wire pair the value of ^ is approximately 0.035 radian 

 per mile, or 2 deg. per kilocycle per mile. The latter figure is a con- 

 venient one to remember. 



The constant ^ also enters into the familiar expression for the velocity 

 of propagation 



F = - miles per second. (12) 



The velocity of propagation on open-wire lines approaches the veloc- 

 ity of light, which is 186,000 miles per second. The velocity is reduced 

 below this value by the increase of capacity due to the presence of the 

 other wires and the insulators, by the internal inductance, and by the 

 presence of resistance and leakage conductance. Values of the velocity 

 of transmission for open-wire pairs are presented in Fig. 17. At fre- 

 quencies above a few hundred cycles the velocity of transmission is, 

 apart from the effect of line irregularities, practically constant through- 

 out the frequency range. 



In the last few years increasing attention has been focused upon the 

 phase characteristic of the open-wire circuit. One of the reasons for 

 this is that different velocities of transmission for different frequency 

 components in a signaling band (which are obtained when the phase 

 shift of the circuit is not a linear function of the frequency) may give 



