DDD-based symbolic sensitivity analysis of active filters

Abstract

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.

Fully graph solution of the sensitivity of switched circuits

“…The problem of sensitivity determination has been investigated in a great number of publications during the last decades [15], [16], [17], [18], [19], [20], [21] and many others. A typical problem here is the determination of the derivates in the sensitivity expressions and its decision had been searched in different ways.…”

Symbolic nodal analysis of analog integrated circuits using pathological elements

“…In addition, models based on nullors and/or pathological elements also allows us to include parasitic circuit elements [4], such as input and output impedances and gain [5]. Additionally, symbolic nodal analysis of nullor and/or pathological circuits can also be applied to perform noise [9] and sensitivity analysis [10].…”

“…In the same way, the ideal filter characteristics for the bandpass and high-pass responses are given by (7) and (8). Noise and sensitivity analysis can be performed by applying [9], [10]. v h = Iing1g2gBP gHP g 3 in + IinsC1g1g2gBP gHP g 2 in /∆ ideal (5)…”

“…When applying symbolic nodal analysis techniques, the use of active device models based on nullors and/or pathological elements has demonstrated advantages in the formulation of small and sparse matrices [2], [7], [9], [10]. In addition, models based on nullors and/or pathological elements also allows us to include parasitic circuit elements [4], such as input and output impedances and gain [5].…”

“…Fortunately, symbolic nodal analysis has demonstrated to be a useful tool to derive behavioral expressions of analog ICs [1], [2], [4], [5], [6], [7]. The formulated equations are easily solved by applying determinant decision diagrams (DDDs) [2], [7], [8], [9], [10], and parallel simulations accelerate time computation when deriving exact symbolic expressions [11]. However, compact models for the active devices are required to generate small matrices and to derive simplified analytical expressions.…”