SaM - Coarse Approximation of the Lumped Parameter Model of an Ultrasonic Transducer

Remeber:

In the “ultrasonic transducer” lecture we have summed it up well: “The lumped parameter approximation of this device is an extreamely coarse approximation, since the the wavelenght ${\lambda }_w$ is NOT larger than the dimension of the crystal ($h$)“. So ${\lambda }_w\ngtr h$ ⇒ coarse approximation.

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==What I want to outline here is that for sure in this kind of device we don’t have the condition needed for a good approximation with lamped parameter. So lamped parameter models require a wavelength which is much larger than the dimensions of the piezoelectric crystal==:

• $\lambda$ : wavelength
• $t$ : thickness of the piezoelectric slice.
• $D$ : ???TODO maybe area of the piezoelectric crystal.

==We need to take into account also space variation.
So differential equation with partial derivatives, because we have time and space, so both variations need to be taken into account==.