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13 
Transmission Line 
Transmission Line 
Figure 8 - Schematic Diagram of a Transmission Line Circuit 
In Figure 8 ie ne is the voltage produced by a generator, 
Z, is the impedance of the generator, 
x is a distance along the transmission line, varying from 
Oto 1; 
E(z)e4"* is the voltage at x between the pair of conductors which 
constitute the transmission line, 
Z is the combined impedance of the resistances, inductances, 
and capacitances as used in particular cases, 
e, =E,e?”* is E(l)e?**, the output voltage, 
Z,1is the terminating impedance, and 
© is the frequency of the impressed voltage, in radians 
per second. 
These quantities are related by the equation 
[z, +z J[e! —ryr,¢ 77 ae 
where Z, = ae is the surge impedance of the cable, defined as that 
impedance which must terminate both ends of a dissipationless line 
to make it a distortionless line, 
R is the resistance per unit length of the line, with both conductors 
in series, 
G is the leakage conductance from one conductor to the other, per 
unit length, 
L is the distributed inductance per unit length, 
C is the distributed capacitance per unit length, 
a = VR + jLw\(G + 7Cw) is the propagation function of the line, 
