Quantifying nonlinear electric–acoustic mixing in lead zirconium titanate with a vector network analyzer

Designing devices such as acoustic transducers, filters, and duplexers requires accurate electrical permittivity, piezoelectric coefficients, and acoustic sound speed of the material. While there are methods for measuring some of these properties at a range of frequencies, there are few metrologies for measuring the relationships between nonlinear electric and acoustic properties, as given by the mixing products. Here, we test a method for extracting the properties of lead zirconium titanate by measuring the nonlinear mixing of electric and acoustic waves. Our experiment used a block of lead zirconium titanate mounted on top of a coplanar waveguide that was connected to a vector network analyzer. A piezoelectric transducer acoustically actuated the sample from above, which modulated the electrical signal in the coplanar waveguide. A vector network analyzer in frequency offset mode measured the modulation as second-order mixing products. Vector network analyzer-based measurements are particularly well suited for these nonlinear measurements due to their wide dynamic range and ability to capture frequency dependence of mixing products. The proof-of-concept results show many coupled electric–acoustic modes that are significant relative to the noise floor of the vector network analyzer. Broader impacts of the research could be the development of new metrologies for measuring nonlinear susceptibilities.