Band Analysis of Acoustic Delay Lines Based on Single-Phase Unidirectional Transducers

This work presents a comprehensive band analysis for calculating the S21 and bandwidth (BW) of acoustic delay lines (ADLs) based on single-phase unidirectional transducers (SPUDTs). Focusing on the electrode layout, the amplitude and phase relationships of the incident fundamental symmetric (S0) Lamb wave and reflected waves at electrode centers (ECs) of Double SPUDT and Bottom Floating (BF) SPUDT unit cells across different frequencies are first investigated. Subsequently, ADLs are conceptualized as a model consisting of unit cells with transduction centers (TCs) and reflection centers (RCs) on each port, with an intermediate gap that introduces propagation loss (PL). Utilizing 1-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>m-thick aluminum nitride (AlN) and scandium-doped aluminum nitride (Al0.7Sc0.3N) thin films, theoretical modeling and finite element method (FEM) assisted calculations are conducted to compute the reflection (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Gamma $ </tex-math></inline-formula>) and transmission (T) coefficients for both Double SPUDT and BF SPUDT unit cells. The S21 and 5-dB BW in the center frequency (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f} _{c}$ </tex-math></inline-formula>) vicinity of the ADLs, with cell count (N) ranging from 3 to 13 and gap length (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{g}$ </tex-math></inline-formula>) ranging from 50 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$300~\mu $ </tex-math></inline-formula>m, are theoretically computed. The comparison with time-gated measurements demonstrates that the calculation errors are consistently below 5 dB<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>MHz. This analysis provides theoretical insight into the relationships among the ADL’s spectrum, PL, N, SPUDT structure, and piezoelectric film, offering valuable guidance for ADL performance optimization. [2024-0197]