Scanning acoustic microscopy (SAM) using impulsive signals is useful for characterization of biological tissues and cells. The operating center frequency of an ultrasonic device strongly depends on the performance characteristics of the device if the measurement is conducted by using impulsive signals. In this paper, a method for the design of ultrasonic devices for SAM using impulsive signals was developed. A new plane-wave model was introduced to calculate frequency characteristics of loss of ultrasonic devices by taking into account the conversion loss at the ultrasonic transducer, the transmission loss at the acoustic anti-reflection coating, and the propagation loss in the couplant. Ultrasonic devices were fabricated with a ZnO ultrasonic transducer using two acoustic lenses with aperture radii of 1.0 mm and 0.5 mm, respectively. The frequencies at which measured losses became minima corresponded to the calculation results by the plane-wave model. This numerical calculation method is useful for designing ultrasonic devices for acoustic microscopy using impulsive signals.