Air-coupled ultrasonic non-destructive testing (NDT) provides an ideal solution for rapid scanning of large specimens. Unfortunately, despite decades of research, many challenges remain to render air-coupled ultrasonic methods a broadly effective sensing modality for high impedance materials due to low energy transmission between air and the solids being inspected. In this paper, we present experimental results and theoretical analysis of an electrical spark source focused by an ellipsoidal reflector. This acoustic source, which generates a short duration, high amplitude signal in air, is of high interest for air-coupled NDT for high impedance materials and has been shown to excite wave motion in concrete without contact. Theoretical modeling using weak shock theory and the KZK equation is used to predict the temporal and spatial features of the pressure field in the region of the geometric focus. We also present a series of experimental studies that characterize the spark generated acoustic wave in both free-field and the focused conditions. The bandwidth and directivity of the focused spark source are shown to be adjustable by changing the spark gap size and the reflector geometry. Finally, experimental results from three reflectors made of different material and geometries are presented.