A general equation is derived that describes the behavior of a piezoelectric transducer with a nonuniform distribution of piezoelectric coefficient within its bulk, when submitted to an arbitrary distribution of acoustic pressure. Based on this equation, an expression for the receiving transfer function of the transducer is calculated. The results demonstrate the dependence of the transfer function on the distribution of piezoelectric coefficient, and that it is possible to benefit from a nonuniform distribution to optimize the transfer function. The general equation also describes the influence of the external electric circuit loading the transducer, which leads to another independent means of optimizing the transfer function. The proposed model combines effects of piezoelectric material characteristics, acoustic backing, and electric loading, without resorting to Mason or other equivalent circuits for the transducer.