Effective Coupling Factor of Single-Degree-of-Freedom Transducers

The effective electromechanical coupling factor is widely used by practical transducer designers as an index of performance potential in evaluating new or proposed transducers. However, the properties of the effective coupling factor and its associated formulas do not appear to be well documented even for simple transducers. In an attempt to correct this situation, tables of formulas are presented here for the effective coupling factor in terms of equivalent-circuit parameters and in terms of measured immittance data. The treatment is restricted to lumped-parameter transducers with negligible electric or magnetic dissipation. The significance of the effective coupling factor as an indicator of the limits of physical realizability is illustrated by the instability occurring in electrostatic, variable-reluctance, and moving-coil transducers. Many influences conspire to degrade the effective coupling factor to a lower value than the intrinsic coupling factor of the active material incorporated in the transducer structure. Examples are leakage inductance and eddy-current shielding in magnetostrictive transducers, and stiffness augmentation of a simple resonator by its auxiliary structure. The stiffness of a liquid-filled cavity has a degrading effect even when the cavity is self-resonant. Whenever an extended transducer circuit can be reduced to single-degree-of freedom form, the effective coupling factor will serve as a powerful tool for quickly revealing possible deterioration in performance resulting from the circuit additions.