Advanced types of the sensitivity analysis in frequency and time domains

The majority of standard tools for computer-aided design can perform only limited types of the sensitivity analysis: Spice determines operating-point sensitivities, and SpectreRF contains a parametric sensitivity analysis that can be used for determining the phase noise, for example. In the paper, some new types of the sensitivity analysis in frequency and time domains are described. These types of the analysis are not implemented in the standard circuit simulators.In the frequency domain, a procedure for determining the sensitivities of the noise figure is suggested. First, an improvement of the method for computing the noise figure is presented, which incorporates necessary circuit matching and eliminates the subtraction of output noise from the load at each frequency. Second, a simple formula is derived for computing the sensitivities of the noise figure. The sensitivity analysis in the frequency domain is generally demonstrated by means of a distributed microwave amplifier. The application of the sensitivity analysis of the noise figure for improving the noise properties of a monolithic microwave amplifier is described.In the time domain, a new recurrent formula is derived for the sensitivity analysis that efficiently uses high-order expressions of the algorithm for implicit numerical integration. Since the chosen integration algorithm is more flexible than the more frequently used Gear's one, the suggested formula leads to more efficient procedure. The sensitivity analysis in the time domain is important for analyzing symmetrical microwave circuits, because their operating-point sensitivities are zero in principle. For this reason, the significance of the proposed method is demonstrated by an analysis of a symmetrical radio-frequency CMOS multiplier. As an unusual example of exploiting the method, a temperature sensitivity analysis of a power operational amplifier is described.