Abstract
In the determination of electromechanical parameters of a piezoelectric vibrator having low figure of merit or low Q by the resonance-antiresonance method, some corrections are necessary to obtain reliable values. In the present paper, some approximate formulas are proposed to make corrections in terms of γ' and β (defined by eqs. (7) and (8)) or of Y_m and β. The vibrator is described by the admittance (1) or (2). The dielectric loss angle φis assumed to be independent of frequency. In the half-width method and the equivalent-resistance method, the formulas [I], [II] and [III] are usually used to determine the parameters. For a given set of K, γ and φ, eqs. (5) and (6) give x_m, x_n and x_1, x_2. Errors of [I], [II] and [III] are obtained from the calculation of the ratios to true values (eqs. (9), (11) and (13)), and the results are shown in Figs. 1 and 2, where the exact solutions are also shown. The coordinates are chosen so as to be represented by observables. In ξ3, approximate correction formulas are derived on the basis of the through-the-center approximation. The geometrical configurations are shown in Fig. 3. The deviations of w_m^2 etc. from w_0^2 can be determined by tan φ_m etc. , as shown by (18) and (21). In the half-width method, a series of equations from (23) to (39) produce a set of approximate formulas of correction [IV・1]〜[IV・3], where X and Z are given by (40). In the equivalent-resistance method, a parameter p of (41) is introduced instead of Y_m. Calculations from (42) to (56) give correction formulas as shown in [V・1]〜[V・6]. The errors of [IV] and [V] are found not to be ignorable, therefore some trials are made in 3. 3 to improve these formulas. Examination of error distributions against w leads to the formulas [VI] and [VII]. The fractional errors of [VI] and [VII] are shown in Fig. 4. They are nearly within a few percent over the practical ranges of w-1 and 1/X or 1/ξ. Accordingly, the approximate formulas [VI] and [VII] are found to be of practical use.
