m MEASUREMENT OF PRESSURES 



through the shunting circuit, and reduction of terminal voltage by the 

 crystal sharing charge with any shunt capacit3^ From this point of 

 view, it is logical to think of using the crystal with a preamplifier or 

 other impedance matching device close to it, which would minimize 

 shunting effects and permit connection to the recording circuits with 

 greater freedom of choice as to the electrical properties of the connect- 

 ing elements. This solution, however, is a matter of considerable prac- 

 tical difficulty, as the impedance circuit must be sufficiently stable and 

 rugged not only to survive the explosion and withstand rough usage, but 

 also to operate properly while subjected to explosion pressures. 



Although these difficulties can probably be overcome, the more 

 profitable line of development has been found to be use of direct cable 

 connection from the gauge to the recording equipment situated at a 

 safe distance from the explosion. The necessary distance for service 

 weapons is several hundred feet or more and use of cables this long 

 presents a number of problems, both in handling and maintenance of 

 the rigging and in achieving suitable electrical properties. 



A. Cable termination. Although for slowly changing signals an 

 electrical cable can be regarded as simply a lumped capacity, it is evi- 

 dent that for sufficiently rapid changes the time required for the signal 

 to traverse the cable will no longer be negligible. The speed of propa- 

 gation of a signal along an electrical cable is somewhat less than that of 

 light or other electromagnetic radiation in free space, the value depend- 

 ing on the dielectric constant of the insulating material in the cable. 

 For a cable of total distributed inductance L and total distributed ca- 

 pacitance C (these "total" values refer to values per unit length multi- 

 plied by the length), the transit time can be shown to be \^LC or, in 

 terms of the surge impedance Ro of the cable defined as Ro = ^L/C, 

 transit time = RoC. 



If the surge impedance is expressed in ohms and the capacitance in 

 microfarads the transit time is in microseconds. For a 1,000 foot cable 

 with a capacitance of 30 mm/* per foot and 50 ohms impedance the time 

 required for a signal to travel the length of the cable is 1.5 ^sec. In 

 this case, the cable can legitimately be regarded as a simple lumped 

 capacity only for signals which change insignificantly over such time 

 intervals. Even for such signals it is often necessary to examine the 

 question of how this capacity is properly measured, as discussed in 

 part (B). 



If the cable cannot be treated as a lumped capacity, a more detailed 

 investigation is necessary. It is a familiar fact that the propagation of 

 signals along a cable generally results in electrical reflections at the ends 

 of the cable unless the cable is properly terminated. The voltage at 

 the receiving end of a cable is then an initial signal related to the origi- 



