The current transformer (CT) is the data source of relay protection. With the development of grid, a new topic is presented due to various class CT connected to relay protection. To solve this problem, the transfer characteristics of P and TPY class CT are analyzed firstly and the main affecting factors are pointed out in this paper. Then the reason of low remanence is explained theoretically based on equivalent circuit model of TPY class CT and the numerical simulation for which is carried out using Jiles-Atherton theory of ferromagnetic hysteresis. The characteristics and laws during a saturated condition are described. Formulas are developed for estimating the transient response of Rogowski coil CT, which show the consistency with P and TPY class CT. Finally, the transient response of three types CT is compared and its effect on relay performance is discussed.