MEASUREMENT OF PRESSURES 191 



The transient responses for this network are readily obtained by the 

 same methods as before. For Ri = R^ = Ro, the result is 



VM = ^ 



\ 2RoC I ^ 6 V 2i?,C / 



e 2R,C -\- 



t> RoC t> SRoC 



and for Ri = R2 = kRo one obtains 



IYC\ RoC J 



VM = J^^^ ( ^^T^^ 1 e-iJ^^m:c + 



f> RoC 



This expression is plotted in Fig. 5.20 (curve (c)) for the value k = 1.12 

 (i.e., Ri = R2 = \.12 Ro). It is seen that the saw tooth characteristics 

 of single-ended terminations are replaced by a smooth rise similar to 

 critical damping characteristics in simple R-L-C circuits. The time to 

 rise to the final value is of the order 1.5 RoC, which for a 600 foot cable 

 with Ro = 50 ohms, C = .015 fif is about 1 microsecond. This time is 

 short enough to permit faithful transmission of exponential pulses with 

 a time constant of 100 microseconds or more, and so is adequate for 

 shock wave measurements of charges larger than about 10 pounds. 

 The necessary or obtainable performance under other conditions is easily 

 predicted by obvious proportions. 



The double-ended compensation described has been used for many 

 shock wave measurements on service weapons (22), and has proved 

 very satisfactory. A practical problem in its use is the necessity of in- 

 corporating an electrical network at the gauge end of the cable. Tests 

 have shown, however, that the network can be placed fifty to seventy- 

 five feet from the gauge if necessary without significant loss in perform- 

 ance, and the network can be spliced into the cable as a waterproof 

 assembly. 



From the point of view of explosion pressure measurement, it is evi- 

 dent that compensation for cable transmission characteristics is im- 

 portant chiefly for short duration shock waves, and is so much less 

 critical in measurement of the more sustained "bubble pulses" as ordi- 

 narily not to be necessary. The compensations discussed by no means 

 represent the ultimate in performance readily attainable; they have, 

 however, proved adequate without further elaboration. 



B. Dielectric properties of cables. The discussion of cable charac- 

 teristics so far given has been based on the assumption that, except for 

 the distributed nature of the parameters, the cable capacitance could be 

 regarded as a constant independent of the nature of signal applied to 



