Abstract: The mass analyzer based on quadrupole field theory, including quadrupole and ion trap, control and screen ions by a non-magnetic, alternating electric field, which was the first proposed by Professor Paul in 1953. Since the birth of quadrupole, ion trap and other related mass spectrometry technologies have been developed relatively maturely, which have made a significant impact and contribution to mass spectrometry. This paper deduced and interpretd the complete physical and mathematical formulae of the design and generation process of the quadrupole field. The process of obtaining the potential distribution of the quadrupole field, the obtaining process of boundary conditions such as electrode shape and voltage on the electrode, and the process of deducing the quadrupole structure and ion trap structure according to the potential distribution of the quadrupole field were discussed. In the above processes, for the purpose of binding ions, a general potential (Prof. Paul called it “allgemeinste potential” in German) distribution equation was obtained by introducing a simple harmonic motion model. And then, according to the basic laws of electromagnetic field and Maxwell’s equation, the condition of zero electric field divergence was introduced. Based on this, through the discussion of the two simplest solutions and boundary conditions, the structure and field distribution equations of the quadrupole and the ion trap were obtained, respectively. This content was an important supplement to the elaboration on the theory of quadrupole field mass spectrometry, which was helpful for a deeper understanding of basic principles of quadrupole field. At the same time, this paper provided a potential mass analyzer design method. Firstly, the design began with the conception of the state of ion motion, and then a force that could control the movement of ions according to the idea was found. Secondly, combined with the basic laws of electromagnetic fields, the general equation and its limiting conditions for the potential distribution that could form this force were obtained. Thirdly, according to the easy-to-operate settings in practice, the boundary conditions of the field (such as electrode shape, electrode voltage, etc.) were obtained, and the intermediate variables in the general equation were replaced with these operable physical parameters. At last, according to the potential distribution equation, the ion motion equation was calculated, and the mathematical relationship between the masstocharge ratio and the controllable physical parameters was found. And finally, a mass analysis method for controlling and separating ions was obtained. This kind of design method has important reference significance for theoretical research and original innovation research related to mass spectrometry.