Abstract: A compliance tube is introduced into a single-stage looped traveling wave thermoacoustic engine for phase adjustment. The engine's onset characteristics with various locations, inner diameters and lengths of the compliance tube are analyzed. The oscillation frequency and onset temperature difference are calculated by the grid transfer matrix method, based on the linear thermoacoustic theory. The calculated results are then compared with the experimental results to verify the rationality of the calculation method. The calculated results show that the compliance tube can improve the engine onset characteristics, which dramatically lowers the onset temperature difference. The location has significant influence on the onset characteristics, and there exists optimal inner diameter and corresponding length of the compliance tube to achieve the lowest onset temperature difference, while the influence of the compliance tube size on the oscillation frequency is not apparent.