The quantitative investigation of parameters in the renegerator is essential for the optimization of thermoacoustic devices, while the majority of the previous research only considered parameters of the working field, working gas and the hydraulic radius. Based on the linear thermoacoustic theory, this paper extracts a normalized parameter for low-amplitude conditions, which is called the regenerator operation factor. By extracting the regenerator operation factor and relative hydraulic radius, the influence of frequency on the efficiency can be controlled and offset. It can be found that thermoacoustic devices with different frequencies can perform the same efficiency by adjusting the radius in proportion to the axial length. Finally, this paper synthetically optimizes the dimension of the thermoacoustic regenerator by taking the regenerator operation factor, relative hydraulic radius and acoustic field parameter as variables. Conclusions in this paper are of great significance for explaining the best working conditions of engines and directing the miniaturization and optimal design of thermoacoustic devices.