Electromechanical Modeling of Ultrasonic Transducers
A general model of an ultrasonic flaw measurement system can be developed using the fundamental reciprocity formulation of Auld . This general model can be reduced to a more explicit form by assuming that the waves incident on the flaw are quasi-plane waves, resulting in the Thompson-Gray measurement model . In the Thompson-Gray model, the frequency components of received voltage, V0(ω), in a pitch-catch immersion setup can be written in a product fashion as V0(ω)=β(ω)P(ω)M(ω)T1(ω)C1(ω)A(ω)T2(ω)C2(ω) where P(ω) accounts for the time delay in going from the transmitting transducer to the receiving transducer, M(ω) is due to the material attenuation, T 1(ω) and T 2((ω) are transmission terms that characterize the amplitude changes when going through the fluid- solid interfaces on transmission and reception, respectively, C 1(ω) and C 2(ω) are diffraction correction terms that account for the finite beam characteristics of the transducers on transmission and reception, and A(ω) is the far field scattering amplitude of the flaw. The term β(ω) is an “efficiency factor” that is a function of the electrical properties of the pulser/receiver, the associated cabling, and the ultrasonic transducers. Thus, β(ω) accounts for all the electrical to mechanical and mechanical to electrical conversion processes that contribute to the entire measurement process.