In this thesis, we study two topics on superconducting circuits. \nThe first topic is the tunable coupler for resonators. \nThis coupler is implemented with a superconducting circuit coupling with resonators in the dispersive regime. \nIt possesses a high on/off ratio and the coupling between two degenerate resonators can be turned off by tuning the frequency of the coupler via the biasing flux. \nWe present the design, the simulation, \nand the fabrication of the chip implementing this coupler. \nWe derive the Hamiltonian of the chip via formal circuit quantization. \nWe also present numerical results of the eigenenergies and the eigenstates of the chip. \nFrom the numerical results, \nwe show that the tunable coupling and the turn-off point can be realized on the chip. \n \nThe second topic is impedance engineering for enhancing the bandwidth of a Josephson parametric amplifier. \nBy transforming the input impedance seen by the Josephson parametric amplifier, \nthe frequency dependence of the gain function can be decreased and the bandwidth of the Josephson parametric amplifier can be enhanced. \nWe study impedance engineering for two different types of flux pumping Josephson parametric amplifier. \nFor each type of amplifier, \nwe develop a corresponding method of impedance engineering, \nand study implementing the method with transmission lines.