326 BELL SYSTEM TECHNICAL JOURNAL 



7 = -tanh ^ 



5 



"^ (Zi + G'2)(5i - G'O - (Z2 + G<,){S, - Gi) J ' ^ ^ 



where the symbols in equations (10) and (11) have the following 

 meanings: 



Zi = the first termination applied to the available terminals at 



the far end ot the line (ohms) 



Z2 = the second termination applied to the available terminals 



at the far end of the line (ohms) 



^i = the impedance measured at the available near-end terminals 



corresponding to the termination Zi (ohms) 



52 = the impedance measured at the available near-end terminals 



corresponding to the termination Z2 (ohms) 



Gi = the ground-connection impedance at the near end of the 



line (ohms) 



G2 = the ground-connection impedance at the far end of the 



line (ohms) 



5 = length of the line (kilometers) 



K = characteristic impedance (ohms) 



7 = propagation constant (hyps per kilometer) 



3. Effective Height. The effective height of a wave-antenna is 

 defined as the ratio of the voltage produced at any specified point in 

 the antenna to the potential gradient of the electromagnetic field 

 producing that voltage. If the constants of the antenna system 

 are known, the effective height at any point in the antenna system 

 may be calculated from the value at any other point in the system. 



A convenient way to measure an effective height of a wave-antenna 

 and obtain a value which may be easily correlated with wave-antenna 

 theory is to introduce in series with the initial-end terminating im- 

 pedance a voltage which produces the same output current from the 

 antenna as is produced by an electromagnetic wave. The ratio of this 

 induced voltage to the potential gradient of the electromagnetic field 

 has been called "the effective height referred to the characteristic 

 impedance." For small values of the quasi-tilt angle, the total 

 potential gradient of the electric field is very closely equal to the 

 vertical component of the electric field, so that within the precision 

 of measurement we may write: 



//«- ^ . (12) 



