PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 215 



vibration varies. The PI of some clamped or pressure-mounted crystals 

 has been found to vary as much as 50% with change in drive. Noticeable 

 frequency change also occurs. A change in the nature of secondary modes 

 as the amplitude is varied has also been observed. Some secondary modes 

 which interfere with large amplitude of vibrations practically disappear 

 when the amplitude is reduced. This may be explained by the fact that 

 certain modes are damped out by the pressure of the mounting and with 

 large amplitude of vibration the effect of the pressure is reduced. 



The dielectric loss of the holder was considered negligible in the theory 

 but it is found that certain phenolic holders have equivalent high-fre- 

 quency leakage resistances less than 100,000 ohms. This resistance is in 

 parallel with the crystal and will therefore reduce the PI according to the 

 equation 



^^ - WTTR. (^"^« 



where 



PI = resulting PI 



Pic = calculated PI 



Rl — equivalent high-frequency leakage resistance 



Because of these secondary effects which are not negligible it is essential 

 in measuring crystal activity that the frequency and voltage across the 

 crystal be known. Standard test circuits should simulate operating condi- 

 tions in this respect. With these considerations, a crystal PI meter has 

 been developed in which the frequency and amplitude may be adjusted to 

 correlate with various oscillators. The principle of operation and perform- 

 ance of this meter is described by C. W. Harrison.* 



Bibliography 



1. A. McL. Nicolson, U. S. Patent Nos. 1495429 and 2212845, filed in 1918. 



2. W. G. Cad}', The Piezo-Electric Resonator. I.R.E., Vol. 10, p. 83, April, 1922. 



3. G. W. Pierce, Piezo-Electric Crystal Resonators and Crystal Oscillators Applied to the 



Precision CaHbration of Wavemeters. Proc. Amer. Acad. Arts & Sci., Vol. 59, p. 

 81, 1923. 



4. A. Crossley, Piezo-Electric Crystal Controlled Oscillators. I.R.E., Vol 15, p. 9, Jan., 



1927. 



5. K. S. Van Dyke, The Electrical Network Equivalent of a Piezo-Electric Resonator. 



Physical Rev., Vol. 25, p. 895, 1925. 

 The Piezo-Electric Resonator and Its Equivalent Network. I.R.E., Vol. 16, p. 742, 

 June, 1928. 



6. E. M. Terrv, The Dependence of the Frequency of Quartz Piezo-Electric Oscillators 



Upon Circuit Constants. I.R.E., Vol. 16, p. i486, Nov., 1928. 



7. J. W. Wright, The Piezo-Electric Crystal Oscillator. I.R.E., Vol. 17, p. 127, Jan. 



1929. 



* "The Measurement of the Performance Index of Quartz Plates," this issue of the 

 B.S.TJ. 



