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The standard tools for CAD have limited modes of the sensitivity analysis: PSPICE only contains a static mode and SCEPTER includes both frequency domain and static modes. However, many microwave systems use symmetric structures for enhancing the properties of the circuits. For such systems, the static sensitivities are zero on principle and therefore the time domain sensitivity analysis should be used. In the paper, a new recurrent formula for the time domain sensitivity analysis is derived, which uses the by-products of an implicit integration algorithm. As the selected integration algorithm is more flexible than the Gear's one used in the PSPICE family, the sensitivity analysis is more efficient in comparison with the standard CAD tools. An implementation of the method is demonstrated using the analysis of a low-voltage four-quadrant CMOS RF multiplier.