The increasing penetration of renewable energy resources, such as wind and solar, is changing AC grid dynamics. Potential dynamic stability issues such as small signal instability may occur when these resources are connected to a grid with low strength, i.e., a weak grid. In this paper, the relationships between small signal stability and grid strength measured with short circuit ratio (SCR), along with the relationships between the stability boundary and critical SCR (CSCR) are analytically studied in a single-infeed power electronic system (SIPES). On this basis, these relationships are extended to a multi-infeed power electronic system (MIPES) through eigenvalue decomposition techniques to define the so-called generalized short circuit ratio (gSCR) and critical gSCR (CgSCR) for small signal stability analysis. The defined gSCR and CgSCR are the generalized representation of SCR and CSCR for SIPESs in MIPESs. The gSCR can assess the grid strength of a MIPES in terms of its small signal stability while the CgSCR can characterize the stability boundary of a MIPES. In addition, the condition of CgSCR = CSCR is satisfied for a MIPES with homogeneous power electronic devices. This enables the proposed method based on the gSCR to simplify the complex stability analysis of MIPESs into the stability study of SIPESs. The efficacy of the proposed gSCR and CgSCR is validated with eigenvalue analysis and time-domain simulations.