This paper proposes a dimensionless approach to analyze the multi-parametric stability behavior of switching converters, which can be characterized by a nonlinear time-periodic (NTP) system. The main objective is to analyze how multiple circuit parameters affect the stability patterns of the derived NTP system and to simplify the parametric complexity of such NTP system. In contrast to previous work, the proposed method focuses on the parametric resultant relationships of the NTP system in the sense of topological equivalence, and investigates its stability in terms of the homeomorphic NTP system. Firstly, an equivalent stability theory of NTP systems is proposed. Then, based on the equivalent theory, a normalized map is introduced and various interesting properties are derived so as to formulate the dimensionless approach. Moreover, the approximate solution of the NTP system in dimensionless parameter space is calculated by using the Galerkin method, and its stability pattern is identified with the help of eigenvalue analysis approach. Finally, a case study of one-cycle controlled Zeta PFC converter is discussed in detail to exemplify the application of the proposed method. These analytical results agree well with those ones obtained from experimental measurements.