A method and apparatus for a modified noise-coupled modulator using zero optimization technique is disclosed. By realizing the resonator coefficient as a part of branches other than those of the main transfer function, the problem of improving SQNR without degrading other specifications is solved. Second order noise coupling is used to implement zeros without using feedback branches going into the first integrator. Embodiments use a first-order modulator, second-order noise coupling and a resonator. It allows lower power consumption and smaller size by removing small capacitor values and gain factors and reducing the number of amplifiers.