Based on review and analysis of thermodynamic efficiency e of the Carnot cycle and the cycle with two isothermal and two polytropic processes, another thermodynamic cycle with two isentropic and two polytropic processes, which can achieve the Carnot value of thermodynamic efficiency, is testified theoretically. Thermodynamic efficiency expressions of a number of ideal regenerative refrigeration cycles are derived, including the ideal pulse tube refrigeration cycle. A classified branch chart and a plot of ideal thermodynamic efficiency of regenerative refrigeration cycles are given for the purpose of comparison.