MEASUREMENT OF PRESSURES 183 



where C is the capacitance of the cable. To caUbrate the system, a 

 known voltage Vs is applied to Cs in series with the gauge circuit and 

 the resultant voltage Vc is given by 



C + Co-^C. 



The ratio of voltages Vp and Vc, and hence ratio of deflections of a linear 

 indicating instrument, is then 



Vp ^ KAP 



Vc CsVs 



This ratio is, however, independent of both the circuit capacitances C 

 and Co and of the deflection sensitivity of the instrument. The gauge 

 constant KA is thus determined in terms of known pressure P, voltage 

 Vs, and capacitance Cs. In effect, the result is equivalent to impressing 

 a charge Qs = CsVs on the circuit, hence the name "Q-step." 



In actual use, the circuit also determines the transient response 

 characteristics of the system for an equivalent charge Qs, provided only 

 that the condenser Cs has negligible shunt leakage currents and dielec- 

 tric absorption current. The necessary step voltage Vs to determine a 

 step response characteristic can be suppHed by a calibrated source, 

 either by a simple switch for static methods or by a more elaborate step 

 generator for more rapid transient measurements (see section 5.9). A 

 null method of gauge calibration has been described by Savic (97), in 

 which the piezoelectric charge from pressure change is balanced against 

 charge of opposite sign simultaneously applied from a known variable 

 voltage source and capacitance, the circuit arrangement being quite 

 sunilar to the Q-step technique. The piezoelectric constants originally 

 obtained for tourmaline by this method are several per cent lower than 

 accepted values, but later refinements in the method are reported to 

 have given results in good agreement.'^ 



5.8. Transmission of Piezoelectric Gauge Signals 



As suggested in section 5.4, the internal impedance characteristics 

 of piezoelectric gauges present several electrical problems in their use 

 for measurement of underwater pressures. For greatest efficiency a 

 piezoelectric gauge should be operated under essentially open circuit 

 conditions, that is, with the minimum possible shunting effect by the 

 input impedance of the electrical circuit connected to it. 



Two effects of a low value of shunt impedance were discussed in 

 section 5.7: neutralization of charge on the crystal faces by current flow 



i« Private communication from J. H. Powell of the Admiralty Undex Works. 



