A two-dimensional ultrasonic transducer array includes a plurality of transducer elements, with each element having a plurality of piezoelectric layers. The transducer elements vary in transverse areas of radiating regions. The effect of the variations in transverse areas on the electrical impedances of the elements is at least partially offset by varying the specific impedance, i.e., impedance per unit area, of the transducer elements in the array. In a preferred embodiment, the specific impedance is varied by selecting the electrical arrangements of piezoelectric layers in each element according to the transverse area of the element. Series, parallel and series-parallel arrangements are employed. This impedance normalization improves the electrical connection of the transducer elements to driving circuitry. In alternative embodiments, impedance normalization is achieved by varying element thicknesses, element materials and/or degrees of poling across the two-dimensional array.