Key Design Parameters of Spherically Curved Piezo Elements: Radius, Aperture, and Thickness

Focused ultrasonic transducers often start with a deceptively simple sentence: "Use a spherically curved piezo to focus the beam." Then reality shows up. The beam does not focus exactly where CAD predicted. The resonance shifts when the element is bonded. Two parts from the same batch behave slightly differently. The "perfect" curvature is difficult or expensive to manufacture, and a small change in one geometric parameter quietly wrecks another.

This article is written for designers who already know the basics of piezo materials and thickness-mode resonance, and who want a practical mental model for spherically curved (custom spherical-cap piezo) ceramics. It is not a recipe. It is a map of the trade space.

We will focus on three parameters you specify early in a design.

• Radius of curvature (R). Sets the geometric tendency to converge.
• Aperture diameter (D). Sets the "lens size" and controls focal spot and intensity.
• Ceramic thickness (t). Dominantly sets thickness-mode resonance, but also couples into curvature stress, mode purity, and manufacturability.