There are provided an ultrasonic transducer and methods for designing and manufacturing the same. The ultrasonic transducer includes a piezoelectric composite layer configured to be in acoustic communication with a sample and having at least partially decoupled acoustic impedance and electrical impedance properties. The piezoelectric composite layer includes an array of spaced-apart piezoelectric regions, each being made from a piezoelectric material, a filler material positioned between adjacent spaced-apart piezoelectric regions, the filler material comprising a polymer matrix and a non-piezoelectric material in contact with the polymer matrix. In some embodiments, the ultrasonic transducer includes an electrically insulating non-piezoelectric composite layer extending over the piezoelectric composite layer for electrically insulating the piezoelectric composite layer from the sample, the electrically insulating non-piezoelectric composite layer being acoustically matched to the piezoelectric composite layer and the sample.