Waveguide for air-coupled ultrasonic phased-arrays with propagation time compensation and plug-in assembly

Waveguides allow grating lobe free beamforming for air-coupled ultrasonic phased-arrays by reducing the effective inter-element spacing to half wavelength. Since the sound waves propagate through the waveguide ducts, additional time delays are introduced. In this work, we present analytical, numerical, and experimental methods to estimate these time delays. Afterwards, two different waveguides are compared. The first one consists of equal-length ducts, requiring a time-consuming assembly process of the ultrasonic phased-array. In contrast, the second waveguide consists of Bézier-shaped ducts of unequal lengths but a planar input port allowing fast assembly. The analytical model is based on the geometric lengths of the waveguide ducts. The numerical model relies on a transient finite element analysis. All simulations are validated in an anechoic chamber using a calibrated microphone. The analytical (7.6% deviation) and numerical (3.2% deviation) propagation time models are in good agreement with the measurements. By using the analyzed propagation times for the compensation of the unequal waveguide duct lengths, we restored the beamforming capability without significant sound pressure level (SPL) loss. This work shows the possibility of reduced transducer assembly time for waveguided air-coupled phased-arrays without a reduced SPL.