انواع پیشرفته از تجزیه و تحلیل حساسیت در دامنه های فرکانس و زمان

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.

The Affirma RF circuit simulator [1] (it is also known as SpectreRF) contains a special type of the sensitivity analysis in the frequency domain, which models the frequency translation, and it can determine the sensitivity of the output to either up-converted or down-converted noise from power supplies or a local oscillator. In this section, the sensitivity analysis in the frequency domain is generally described, and a procedure for computing the sensitivities of the noise figure is defined subsequently. The sensitivity analysis in the frequency domain should use computational by-products of a conventional AC analysis, especially LL and UU matrices resulting from complex LU factorizations. For this reason, the sensitivity analysis (including the sensitivity analysis of the noise figure) is performed as a part of the AC analysis. The formulae of the sensitivity analysis have been implemented into an original software tool Circuit Interactive Analyzer (C.I.A.) [2].

The standard sensitivity analysis in the frequency domain, the noise sensitivity analysis, and a novel sensitivity analysis of the noise figure have been presented. Generally usable algorithms have been improved, implemented to and checked by the C.I.A. program. A method for using the sensitivities of the noise figure for its further improvement is also outlined. A novel recurrent formula for the sensitivity analysis in the time domain has been derived. It efficiently uses the computational by-products of the implicit integration algorithm. The implementation of the formula has been successfully tested by the analysis of a low-voltage low-power CMOS microwave multiplier. The correctness of programming the procedure has been tested by means of the classical finite difference analysis when presuming that the novel analytical formula gives more accurate results in principle. Nonstandard temperature sensitivity analysis has also been demonstrated, which is important for the circuits with a symmetry, especially in the operating-point design.