Second-Order Generalized Integrator based Quadrature Signal Generator (SOGI-QSG) has been widely used in single-or three-phase power converter systems due to its simplicity and flexibility. However, its dynamic response is not only decided by its damping gain but also influenced by the input-signal parameters, especially when a fast response is required for usages such as grid synchronization. As a result, the parameter design of the SOGI-QSG becomes complicated. Theoretical analysis shows that it is caused by the inaccurate magnitude-integration characteristic of the SOGI-QSG. To solve this problem, an Accurate-Magnitude-Integrator based QSG (AMI-QSG) is proposed. The AMI has an accurate magnitude-integration characteristic for the sinusoidal signal, which makes the AMI-QSG possess an accurate First-Order-System (FOS) characteristic in terms of magnitude than the SOGI-QSG. The parameter design process of the AMI-QSG can thus be as simple as the typical FOS. Besides, the structure of the AMI-QSG is further configured to be able to extract the dc component and harmonic components. The effectiveness of the proposed structures and the correctness of the theoretical analysis are evaluated by experimental results.