Estimation of Analog Parametric Test Metrics Using Copulas

Abstract

A new technique for the estimation of analog parametric test metrics at the design stage is presented in this paper. This technique employs the copulas theory to estimate the distribution between random variables that represent the performances and the test measurements of the circuit under test (CUT). A copulas-based model separates the dependencies between these random variables from their marginal distributions, providing a complete and scale-free description of dependence that is more suitable to be modeled using well-known multivariate parametric laws. The model can be readily used for the generation of an arbitrarily large sample of CUT instances. This sample is thereafter used for estimating parametric test metrics such as defect level (or test escapes) and yield loss. We demonstrate the usefulness of the proposed technique to evaluate a Built-In-Test (BIT) technique for an RF Low Noise Amplifier (LNA) and to set test limits that result in a desired trade-off between test metrics. In addition, we compare the proposed technique with previous ones that rely on direct density estimation.

Statistical modelling of analog circuits for test metrics computation

“…As a case study, in Section V we evaluate a BIT technique for a 1.9 GHz cascode LNA designed in a 0.25 p.,m BiCMOS ST Microelectronics technology. The obtained results are compared with the ones presented in [5]. Finally, Section VI concludes the paper.…”

“…As we can see, the Gaussian copula given by Equation (9) has not an analytical form because of the presence of multiple integrals in the formula. In [4] [5] it is proposed to estimate it using Monte Carlo techniques by generating a large sample of this copula from which it will be estimated. In this paper, we use an efficient algorithm presented in [10][11] to calculate accurately this copula function.…”

“…Different multivariate probability density estimation tech niques have been considered to generate a statistical model of the CUT, including a multivariate Gaussian approach [4], the use of Copulas Theory [5] or the use of a non-parametric method [6]. Once this model has been obtained, all these previous techniques generate a large sample of several mil lion instances.…”

Efficient Production Binning Using Octree Tessellation in the Alternate Measurements Space

“…This can be done entirely relying on simulations, circuit models or by using available data on the production run with already binned ICs. Of course, accelerating techniques for obtaining representative bin border circuits can also be used, such us statistical blockade [20], stratified sampling [21], copula theory [22] or estimating the probability density function using kernels [23]. The defined bins in the specification space will map to arbitrary regions in the measurements space which will be used for binning the forthcoming circuits.…”

Quality metrics for mixed-signal indirect testing

“…In this work, the use of Kendall's Tau rank correlation coefficient [7], [8] is proposed for rating the suitability of a set of candidate measures to be used in alternate testing. Let (x 1 , y 1 ), (x 2 , y 2 ), .…”