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A low-cost and comprehensive built-in self-test (BIST) methodology for analog and mixed-signal circuits is described. We implement a time-division multiplexing (TDM) comparator to analyze the response of a circuit under test with minimum hardware overhead. The TDM comparator scheme is an effective signature analyzer for on-chip analog response compaction and pass/fail decision. We apply this scheme to an oscillation-test environment and implement a low-cost and comprehensive vectorless BIST methodology for high fault and yield coverage. Our scheme allows a tolerance in the output response, a feature necessary for analog circuits. Both oscillation frequency and oscillation amplitude are measured indirectly to increase the fault coverage. We provide a theoretical analysis of the oscillation that explains why the amplitude measurement is essential. Simulation results demonstrate that the proposed scheme can significantly reduce test time of the oscillation-test while achieving higher fault coverage.