We study the spectro-temporal characteristics of two repeating fast radio bursts (FRBs), namely, FRB 20180916B and FRB 20180814A, and combine the results with those from our earlier analysis on FRB 20121102A. The relationship between the frequency drift rate, or slope, of individual sub-bursts and their temporal duration is investigated. We consider a broad sample of possible dispersion measure (DM) values for each source to understand the range of valid sub-burst slope and duration measurements for all bursts and to constrain our results. We find good agreement with an inverse scaling law between the two parameters previously predicted using a simple dynamical relativistic model. The remarkably similar behaviour observed in all sources provides strong evidence that a single and common underlying physical phenomenon is responsible for the emission of signals from these three FRBs, despite their associations with different types of host galaxies at various redshifts. It also opens up the possibility that this sub-burst slope law may be a universal property among repeating FRBs, or indicates a distinct subclass among them.
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