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Sensitivity analysis helps circuit designers to determine boundaries to predict the variations that a particular design variable will generate in a target specification, if it differs from what is previously assumed. It is quite important in designing active filters, but the major drawback is the need of generating the symbolic transfer function, from which the normalized sensitivity formula is usually applied. In this paper we show the usefulness of applying determinant decision diagrams (DDDs), to compute sensitivities without generating the symbolic transfer function, previously. Basically, we propose replacing all symbols in the DDD graph by their numerical values, except one, i.e. the variable of interest. Therefore, all sensitivities are computed by applying Cramer's rule and by constructing one DDD for each symbol. We demonstrate the computing time gain compared to generating the fully symbolic transfer function and then applying the normalized sensitivity formula.

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A new graph-based symbolic technique (GBST) for deriving exact analytical expressions like the transfer function H(s) of an analog integrated circuit (IC), is introduced herein. The derived H(s) of a given analog IC is used to compute the frequency response bounds (maximum and minimum) associated to the magnitude and phase of H(s), subject to some ranges of process variational parameters, and by performing nonlinear constrained optimization. Our simulations demonstrate the usefulness of the new GBST for deriving the exact symbolic expression for H(s), and the last section highlights the good agreement between the frequency response bounds computed by our variational analysis approach versus traditional Monte Carlo simulations. As a conclusion, performing variational analysis using our proposed GBST for computing the frequency response bounds of analog ICs, shows a gain in computing time of 100x for a differential circuit topology and 50x for a 3-stage amplifier, compared to traditional Monte Carlo simulations.