We propose a unidirectional asymmetrical circular crack model, and we investigate the far-field body-wave radiation. The model is a quasi-dynamic one, as the slip is specified by employing Eshelby's static solution at every instant in time. However, unlike previously proposed symmetrical circular crack models that nucleate at the center of a circular fault and spread radially, symmetrically in all directions, the proposed model exhibits unidirectional propagation. We derive compact closed form expressions for the far-field pulse radiated by the source model. As expected, the radiation of the model exhibits strong azimuthal variation. We investigate the stopping phases of the model that are emitted when the rupture front stumbles on the circular barrier at the edge of the fault, and we examine their radiation pattern. We study the seismic energy and seismic efficiency of the model and compare them with those of the symmetrical circular crack model. We find that the seismic efficiency of the unidirectional asymmetrical circular fault model is smaller by a factor of approximately 2-3 as compared to the seismic efficiency of the symmetrical circular crack model. This is explained by the fact that the average rupture velocity of the asymmetrical model is smaller by a similar factor as compared to that of the symmetrical model. Finally, we employ various objective definitions of the corner frequency, and we investigate how their predictions compare with graphically picked corner frequencies.