CABLE DESIGN AND MANUFACTURE 



207 



The characteristic impedance of a transmission line is determined by: 



Zo = b -y/e log -J ohms 



where e is the dielectric constant of the insulating material, D is the 

 inside diameter of the outer conductor, d is the diameter of the inner 

 conductor, and 6 is a numerical coefficient. If the dielectric constant of 

 the insulating material (polyethylene) does not vary, control of charac- 

 teristic impedance reduces to control of capacitance. This follows from 

 the fact that the capacitance, C, is related to the D/d ratio as follows: 



D ... ke 



- = antilog ^ 



where fc is a numerical coefficient. 



Precision control of capacitance during the insulating process is 

 achieved by a double-loop linear servo system, as shown in a simplified 

 block diagram, Fig. 7. The two loops consist, respectively, of one capable 

 of introducing relatively fast capacitance corrections of only modest 

 accuracy and of one capable of highly precise capacitance control on a 

 relatively long time basis. The servo system controls the capstan payout 



SUPPLY 

 REEL 



><] extruder 



TJ- 



_n 



COOLING TROUGH 



PAYOUT 

 CAPSTAN 



DRIVE 

 MOTOR 



^ 



DIAMETER 

 "SENSING 

 UNIT 



DIAMETER 

 CONSOLE 



MOTOR 



SPEED 



CONTROL 



HIGH -PASS 

 FILTER 



RECORDER 



^ 



SUMMING 

 NETWORK 



CAPACITANCE 



MONITOR TAKE- 

 ELECTRODE UP 

 —7 REEL 



OSCILLATOR 



'/////////, 



BRIDGE 



REFERENCE 

 STANDARD 

 CAPACITOR 



DETECTOR 



RECORDER 



LOW -PASS 

 FILTER 



Fig. 7 — Simplified block diagram of capacitance monitor servocontrol system. 



