MEASUREMENT OF PRESSURES 



CoVo 



1S9 



VM = 



C h C2 cos RoCoi 



It is evident that the denominator has zeros whenever (tan RoCo^)/RoCco 

 = —C2/C, corresponding to voltage resonances which are not in prac- 

 tice infinite because of cable losses. The response for C2 = 2C is 

 plotted in Fig. 5.19 (curve (a)) as a ratio of the value for a given RoCco 

 to the value for RoCco = 0. The transient response to an applied step 



1.5 



10 



ixl 05 



12 3 4 



REDUCED TIME t/RC 



Fig. 5.20 Step transient response of piezoelectric gauge circuit for various 



cable terminations. 



voltage Vo at time t = can be computed by series expansion of Eq. 

 (5.13) in powers of e~^^^'i' and term-by-term transformation. The result 

 for the first signal and the first reflected signal is 



v,{t) = CoVo I 



( t - sRoC y 



The response for C-i = 2C, relative to the response as ^ — > o© , is plotted 

 in Fig. 5.20 (curve (a)). The time interval t = RoC before any re- 

 sponse develops is of course the transit time, and the second interval of 

 2RoC represents the time for the first reflection at the receiving end to 

 travel the length of the cable and back. It is evident that, while the 

 infinite response for C2 = has disappeared, the approximation to a 

 step response over these intervals is very poor. 



