Variation-Aware Design of Custom Integrated Circuits: A Hands-on Field Guide by Trent McConaghy Kristopher Breen Jeffrey Dyck & Amit Gupta

Author:Trent McConaghy, Kristopher Breen, Jeffrey Dyck & Amit Gupta
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

# samples to hit average of 1 % error

Circuit

# process variables

# MC samples

# LHS samples

# OSS samples

OSS speedup = #MC/#OSS

GMC filter

1,468

285

215

65

4.38x

Comparator

639

325

255

180

1.81x

Folded opamp

558

295

250

245

1.20x

Current mirror

22

550

440

55

10.0x

Low noise amp

234

95

50

80

1.19x

4.5.8 OSS Experiments: Convergence of Statistical Estimates

This section compares Optimal Spread Sampling (OSS) to pseudo-random sampling by analyzing error convergence versus sample number for a variety of representative circuits.

The experimental setup for each circuit was as follows. We did 30 runs of OSS, where each run had 1,000 samples. We did 30 runs of pseudo-random sampling, where each run had 1,000 samples as well. Each run had a different random seed. We pooled together all samples from the 30 OSS runs and 30 pseudo-random runs, and from the pooled data, we measured mean, standard deviation, and yield.9 We treated these measures as our “golden” reference values of mean, standard deviation, and yield.

On each run of either OSS or pseudo-random (MC), at a given number of samples, we estimated mean, standard deviation, and yield. The relative error was the estimated value, divided by its “golden” reference value. Then, the average error is taken across 30 runs. We computed average error for both OSS and pseudo-random, from 50 samples to 1,000 samples.

We plotted average error for OSS versus number of samples, as shown, for example, in Fig. 4.24’s bottom solid line curve. On the same plot, we also plotted average error for pseudo-random versus number of samples as the top solid line curve. The plot is log–log so that the trends can be observed in linear form. To further facilitate comparison, we also performed a least-squares linear fit on the OSS curve, and the pseudo-random (MC) curve. These are shown as the dotted lines in the plot.

Fig. 4.24Convergence of pseudo-random sampling versus OSS in estimating mean of bandwidth (bw) on a variable gain amplifier. OSS is the lower curve

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