594 
24 
it is subjected to additional explosions. The peak voltage in the cable sig- 
nal decreased from 22 millivolts in the first explosion to 6 millivolts in 
the tenth, while that in the TMB cable fluctuated between 1 and 2 millivolts. 
This effect of "aging" on the rubber cable, due to repeated explosions, had 
been observed previously at the Underwater Explosives Research Laboratory. 
The investigators at that laboratory report that the change is reversible; if 
an "aged" cable is put aside for a week or two it reverts to its former state 
and again gives rise to large signals. Other rubber-sheathed cables showed 
the same features in even greater degree. 
When large numbers of gages with copper cables were used simultane- 
ously on a ship, the noise level became objectionably high, probably as a re- 
sult of eddy currents through the copper tube which serves as a return lead. 
One way to overcome this difficulty may be to replace the present combination 
of single conductor and grounded copper tube with a double conductor enclosed 
in a copper tube, the latter acting only as a shield. 
DISTORTION DUE TO INSUFFICIENT TIME CONSTANT 
Another type of distortion of the gage signal occurs when the time 
constant of the circuit is too small compared to the duration of the signal. 
The following analysis provides practical criteria for the magnitude of the 
time constants needed to reduce this kind of distortion to a given percentage. 
A piezoelectric gage circuit may be represented as in Figure 14. 
To minimize distortion caused by leakage of the signal charge 
through the input resistance of the amplifier, the time constant of the cir- 
cuit expressed by the product RC must be large compared to the duration of 
the signal. : 
The piezoelectric gage generates a charge which is proportional to 
the applied force. Since the peak pressure due to an underwater explosion 
occurs almost instantaneously, the peak charge is generated at the very start. 
As the pressure decreases, the crystal reabsorbs as much charge as it pre- 
viously generated; this reverses the original current. 
Q(t) is the charge produced by the crystal; i.e., the 
true gage response which it is desired to measure, 
q(t) is the observed charge on the capacitor, 
C is the combined distributed capacitance of the 
cable plus the terminating lumped capacitance, 
Ris the input resistance of the amplifier, 
Piezoelectric 
Gage RC is the time constant of the circuit, and 
tg, ty, and i, are the instantaneous currents in the 
indicated branches of the circuit. 
Figure 14 - Simplified Equivalent Circuit of a Piezoelectric Gage 
