The piezoelectric crystal unit—Definitions and methods of measurement

The properties of a piezoelectric crystal unit as a circuit element are characterized and defined, in terms of a general equivalent circuit that is valid at any frequency up to and including the lower UHF ranges but reduces to the conventional equivalent circuit if the parameters are properly redefined. The characteristic values such as resonance frequency and resistance, parallel resonance frequency and resistance, etc., for a crystal unit with or without other reactive elements in series and/or parallel are tabulated and their significance is illustrated with the aid of the crystal impedance and admittance diagrams. These diagrams are also used in deriving and describing the methods to be followed when determining the crystal equivalent circuit parameters by impedance bridge measurements. Techniques are developed for use with various types of impedance and admittance bridges and the relations required to determine the resonance resistance R
1
, resonance frequency f
s
, and quality factor Q
0
of the motional arm, and the reactance X
^-
0
of the parallel capacitance from the measured quantitites are listed. The effects of transmission lines of various lengths between the plane of measurement in the bridge and the crystal unit are fully considered. The nature and magnitude of the sources of measurement errors, exclusive of errors in bridge calibration, are examined.