In this paper, we study the transmission through a mesoscopic ring with a quantum dot embedded in one of its arms with the one-dimensional wave guide theory. We discuss the detailed process of the phase change when a resonant tunneling through the dot occurs. We find that when the state of the dot is far from a resonance, the transmission coefficient is periodic with a period equal to the flux quantum Φ0. However, when a resonant tunneling through the dot occurs, the transmission coefficient is a periodic function of Φ with a period [Formula: see text]. This phenomenon is consistent with the experimental results.