The QPI (quasiparticle injection) devices have the most transistor-like characteristics in many superconducting three-terminal devices. In particular, Quiteron which operates with the principle of suppression of the energy gap only to modulate the conductance of the output junction has a promising feature, such as a large gain, non-latching operation, and binary inversion. In this paper, we have investigated the behavior of the energy gaps to analyze the characteristics of the QPI devices. Current-voltage characteristics of QPI device is calculated by using these values of the energy gaps. First we have introduced the nonequilibrium GL equation. Then we have derived a set of equations for QPI devices by using this equation. It is found that the energy gap of middle layer has the singularity under quasiparticle injection and the QPI device may have a large gain for suitable junction resistances.
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