TRANSMISSION LINKS FOR RADIO SYSTEMS 421 



proportional to the square root of resistivity. Numerically, the loss 

 for copper lines of optimum ratio, neglecting leakage, is: 



db 0.128 VXI^ 



1000 ft. bin. 



A plot of (5) for one particular frecjuency (/ = 20 mc.) is shown in 

 Fig. 5. 



It is important to emphasize one precaution in the use of concentric 

 lines. The high degree of isolation afforded by concentric-tube lines 

 may be easily destroyed. Owing to pick-up from near-by antennas 

 or from other sources, currents of appreciable magnitude may be flow- 

 ing upon the exterior of the sheath. Spurious couplings between the 

 antenna and the line or between the equipment and the line may intro- 

 duce these currents into the shielded circuit. In this manner the dis- 

 crimination of a receiving circuit against undesired signals may be 

 destroyed. Also, the currents flowing upon the exterior of the sheath 

 may destroy the directional characteristic of the antenna to which the 

 line is connected. Grounds placed at frequent intervals are useful in 

 reducing these currents. Sometimes it Is both desirable and convenient 

 to bury the line in the earth. Additional improvement is obtained by 

 constructing the circuits which transform the antenna impedance to 

 the line impedance so as to obtain rigorous symmetry to ground. 



III. Open- Wire Lines 



The losses in open-wire lines may not be determined in as simple a 

 manner or with the degree of certainty that Is possible with concentric- 

 tube lines owing to the complex nature of the electromagnetic field 

 about open-wire lines. The high-frequency resistance of one conductor 

 may be obtained from the foregoing equation (3) by assuming that the 

 radius of the outer pipe is infinite. The characteristic impedance of 

 balanced open-wire lines Is obtained with sufificient accuracy from: 



2D 

 Zo = 276 logio-T-ohms, (2e) 



in which D is the axial spacing and d is the wire diameter. Some 

 typical results for the resistance of a single conductor appear in Fig. 6. 

 At first thought it would appear that, owing to the high resistance 

 of a single conductor, the losses in open-wire lines are higher than in 

 concentric-tube lines. In practical constructions, however, open- 

 wire characteristic impedances 5 to 10 times greater than those 

 for concentric-tube lines are easily obtained. For example, the loss of 



