This paper is an extension of a previous work by the authors on developing a thermodynamic model that capture effectiveness of the Atkinson/Humphry cycle for power production. The analysis first starts with the simplest cycle, the ideal cycle, and gradually expands to include variable specific heat effects and including component losses during compression and expansion processes. The results are explicit formula of work output and efficiency in terms of pressure and temperature ratios. The results stress and confirm the performance potential of a pressure-gain combustion cycle employing constant-volume combustion. Finally, a state-of-the-art engine concept utilizing Humphrey cycle for power production is introduced and a more generalized thermodynamic mode to evaluate performance of this engine is developed.