82 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



which would be difficult or impossible to cut from crystals, and the 

 direction of the mechanical or electrical axis can be selected by 

 jDolarization in the desired plane. Furthermore, the relatively large 

 capacitance of the barium titanate piezoelectric elements can be 

 considered an advantage. Mullins 1 has subjected barium titanate 

 cylinders to large compressive forces and reports output voltages 

 up to 60,000 volts just prior to crushing. 



frequency response (electric) . The equivalent circuit of a piezo- 

 electric input transducer is shown in Fig. (1-2)64. C c is the capaci- 

 tance of the piezoelectric element. R c is the leakage resistance of the 



piezoelectric element; it is usually 



II 



c c 



Rr 



± AC S 



&n nT "T" 



:R, 



Fig. (1-2)64. Equivalent circuit of a 

 piezoelectric transducer and electric 

 load. 



high, of the order of 10 8 to 10 10 

 ohms. The resistance between 

 the terminals is, in general, deter- 

 mined by the load resistance R L 

 (order of 10 6 to 10 7 ohms). C L is 

 the capacitance of the subsequent 

 stage (load) plus that of the 

 connecting cables. 



At medium andhighfrequencies, 

 the voltage E across the load is determined primarily by the capac- 

 itances C c and C L . These capacitors form a voltage divider, the voltage 

 E is EC e /(C c + C L ), independent of the frequency. If the output 

 voltage is large, it can be reduced by an increase of C L , i.e., by the 

 parallel connection of a shunt capacitor C s . At low frequencies, the 

 voltage E across the load is determined primarily by the reactance of 

 C c and the impedance of the parallel combination C L and R L . The 

 voltage E is then dependent upon the frequency and decreases with 

 decreasing frequency. The low-frequency response can be improved 

 bjr increasing C c (using a transducer with high capacitance) or by 

 increasing the load resistance R L . For a steady-state mechanical 

 force the transducer furnishes no output voltage. 



A means to overcome this difficulty and to measure steady-state 

 loads with piezoelectric elements has been devised by Perls and 

 Kissinger. 2 A crystal is driven by an electric oscillator at its reso- 

 nance frequency, and the applied voltage (or the current) is measured. 

 If mechanical stress is applied to the crystal, its resonance frequency 

 or its power absorption will change. In the linear part of the opera- 

 tion characteristic of this device, the output varies by 4 volts for a 



1 Mullins, loc. cit. 



2 T. A. Perls and C. W. Kissinger, Natl. Bur. Standards Rept. 2390a, p. 12, 

 June, 1955. 



