Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
Distinct design regimes appear when the PT and RPT results are compared to the requirement. The horizontal black line in Fig. 3-11 represents a performance requirement of 280µm, and the design regimes are indicated by dashed vertical lines. In regime A (∆ = 0.01% to ∆ ≈ 2%), the uncertainty is very low and can be ignored since the worst-case prediction from the PT design is below the requirement. As the uncertainty increases, the worst-case PT performance moves beyond the requirement and the design moves into regime B. In this regime, (∆ ≈ 2% to ∆ ≈ 7%), it is necessary to use RPT optimizations to find a design that meets the requirement at the worst-case uncertainty vertices. However, RPT also has its limits, and once the uncertainty becomes larger than ∆ ≈ 7% even the robust designs fail to meet the requirement in the worst-case realizations. In this regime, labelled C, neither the PT nor the RPT designs are adequate. At these high uncertainty levels, RPT is unable to produce a design that is both insensitive to uncertainty and meets the aggressive performance requirement. Performance Requirement [µm] 400 350 300 250 200 150 100 50 1 2 1: PT, RPT 2: RPT 0 0 5 10 15 20 25 Uncertainty (%) Figure 3-12: Performance requirement vs uncertainty: PT and RPT designs. 104
The requirement chosen here is somewhat arbitrary, but it is important to note that as the requirement changes so does the level of uncertainty that can be tolerated by each design. To illustrate this point consider the contours shown in Figure 3-12. The performance requirement is shown on the y-axis, and the maximum level of uncer- tainty that can be tolerated is plotted along the x-axis. The dark patch in the upper left sector of the plot, Region 1, represents the design regime that can be accommo- dated with PT design methods. As the value of the performance variance increases, indicating more relaxed requirements, a higher level of parametric uncertainty can be tolerated. For example, if σreq = 250µm, then just over 2.3% uncertainty variation can be tolerated with PT design techniques. However, if the performance requirement is tightened to 200µm then only ≈ 1% variation in the uncertainty parameters can be tolerated. The RPT design, Region 2 (light patch), covers a greater uncertainty range than the PT design, significantly opening the design space. At a performance requirement of 350µm the RPT design can accommodate over 16% variation in the uncertainty parameters. This value is a significant improvement over the PT design. However, as the performance requirement becomes more aggressive, the RPT design, like the PT design, can tolerate much less uncertainty. At a requirement of 200µm, theRPT design can tolerate ≈ 2.5% variation in the uncertainty parameters, only slightly better than the PT design at the same level. Although the RPT design methods do result in designs that are significantly more robust than simple PT, they are not adequate for high-performance and high-uncertainty designs, as evidenced by the large unfilled area in the lower right corner of the plot. 3.5 Summary Robust performance tailoring is a design methodology that is used to produce designs that are robust to parametric uncertainty. In this chapter the effects of uncertainty on the PT design are explored motivating the need for robust design techniques. Three different robust cost functions are reviewed and applied to the SCI development 105
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Distinct design regimes appear when the PT and RPT results are compared to<br />
the requirement. The horizontal black line in Fig. 3-11 represents a performance<br />
requirement of 280µm, and the design regimes are indicated by dashed vertical lines.<br />
In regime A (∆ = 0.01% to ∆ ≈ 2%), the uncertainty is very low and can be ignored<br />
since the worst-case prediction from the PT design is below the requirement. As the<br />
uncertainty increases, the worst-case PT performance moves beyond the requirement<br />
and the design moves into regime B. In this regime, (∆ ≈ 2% to ∆ ≈ 7%), it is<br />
necessary to use RPT optimizations to find a design that meets the requirement at<br />
the worst-case uncertainty vertices. However, RPT also has its limits, and once the<br />
uncertainty becomes larger than ∆ ≈ 7% even the robust designs fail to meet the<br />
requirement in the worst-case realizations. In this regime, labelled C, neither the PT<br />
nor the RPT designs are adequate. At these high uncertainty levels, RPT is unable<br />
to produce a design that is both insensitive to uncertainty and meets the aggressive<br />
performance requirement.<br />
<strong>Performance</strong> Requirement [µm]<br />
400<br />
350<br />
300<br />
250<br />
200<br />
150<br />
100<br />
50<br />
1<br />
2<br />
1: PT, RPT<br />
2: RPT<br />
0<br />
0 5 10 15 20 25<br />
Uncertainty (%)<br />
Figure 3-12: <strong>Performance</strong> requirement vs uncertainty: PT and RPT designs.<br />
104
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