Contribution to the measurement of the electromechanical coupling factor k(33) of piezoelectric ceramics

The piezoelectric properties influence the resonant frequency of the longit udinal modes of vibrations of piezoelectric bars. The influence on the fund amental mode of vibration is high and rapidly decreases with the harmonic o rder. We describe a resonance method for measurement of the electromechanic al longitudinal coupling factor k(33) that is based on the difference in th is influence on the fundamental mode frequency and on third overtone one. T he resonance frequency is derived from the phase characteristic. The method is convenient if modern impedance analyser who can realise accurate phase measurements is used. This method is very useful for measurement of couplin g factors k(33) of resonators, which work in the frequency range near the m easured one, and if their static capacity is small.