ISCAS 2000 -IEEE
International Symposium on Circuits and Systems,
May 28-31.2000,
Geneva,
Switzerland
c'
Integer-Code DC Fault Dictionary Jerzy RUTKOWSKI
Jan MACHNIEWSKI
Institute ofElectronics, Silesian University ofTechnology, Akademicka 16 44 lOOGliwice, POLAND email:
[email protected] 1.2 Definition offaults. Abstract This paper addresses itself to computer-aided diagnosis 1.3 Selection of excitation(s). Simulation of F+ 1 conditions of nominal circuit. For of analog circuits by means of simulation-before-test approach, ~ condition, computation of measurements the so called dictionary approach. New method of dictionary each constrUction is presented. The method combines three V=[VI ,..,Vm'''' VMI]and matrix of sensitivities 5, where previously presented methods, namely: sensitivity based method Smp=aV,jaXpand X=[XI''''Xp,'''Xp] are circuit parameters. of finding arnbiguity sets in measurement space and Step 3: M=M+ 1. For each measurement trom the set corresponding binary signatures, information channel based {V}-{Vop,}: method of finding minimum set of measurements and a method 3.1 For all F+l conditions, mapping ofthe tolerance region trom of the integer-code dictionary formulation, based on the the parameter space !RPinto the measurement space RM, 3.2 Formulation ofambiguity sets. introduced quasi Hamming distance between signatures. Step 4: Selection ofthe optimum measurement and adding it to the set {Vo~}' l. Introduction Check whether degree offault isolation is adequate: Histoncally, electronic circuits were almost analog and lfYES, then GO TO Step 5. were designed with discrete components. The advent of Check whether M=M,: integrated circuit (IC) technology have allowed the development IfYES/NO, then GO TO Step 1.3/3. of much larger electronic systems. However, such systems can Step 5: Determination ofthe integer-code dictionary be constructed almost entirely with digital techniques, many --------------------systems still have analog components. Therefore analog testing is a vital part onc overall design. The field of analog testing is The dictionary construction will be illustrated by a simple still immature in contrary to digital testing, which utilizes example, common-source amplifier originaUy considered by completely different techniques. A large number of algorithms L.Milor [2] and shown in Fig. l. and theoretical findings for analog fault diagnosis have been developed throughout the 1980's and 1990's [7],[8],[9]. For given limited accesability to internal nodes in analog ICs, fawt vcc dictionary methods are the most commonIy used in practice [3]. Among them the de integer-code dictionary seems to be most promising and we confine ourselves to such approach. Onginal W/L=IO solutions at every step ofthe dictionary construction have been Xi proposed by the author [4],[5],[6]. The consruction is presented below, Step by Step, where: . F+ listhe number of simulated circuit conditions at the beforetest stage, good circuit plus F faults, "s . M, is the total number of aUpossible measurements, voltages 1.9V in accesible nodes and eventually excitation(s) current(s), M is the optimum number of measurements providing 100% isolation of circuit conditions. {V} is a set of aU measurements . {VoPt}is a set ofthe selected measurements
.
.
--------------------
Fig.1 Common-source amplifier
~:M=O; {Vo~}={-} I. I Circuit description (model).
0-7803-5482-6/99/$10.00 mooo IEEE
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Dimension ofparameter spaceP=2: X=(R"Rz); R,n=7.5k, Rz"=lk Number ofal! possible measurements M,=2: {V}= {Vd,V,} Number ofsimulated faults F=3: f=1: Rz=0.5Rzn, f=2: W=0.3wn, f=3: source-drain short.
basis for finding ambiguity sets. Solution ofthis task is trivia!. Now, each region is described by the foIlowing inequalities: a/lVI +... a/IV, +...
+ a/(M-IJVM-I+VM ,:;c/ + a/(M-I)VM.l+VM"?c/ (4)
2. Finding of ambiguity sets in measurement space In previous works [1],[3] the heuristic range of -:t;0.7V (diode voltagedrop) around nominal measurement has been accepted as reasonabJe for fau]t detection.. The more sophisticated approach, taking into account the design tolerances, has been proposed in [2] for Go!No Go test. In this approach the tolerance box is mapped trom the pararneter space ]RPinto the measurement space ]RMby means of sensitivity analysis. New, simple method for finding such mapping in multidimensional case, al!owing to distinguish al! simulated circuit conditions (not only "good" circuit tToma]] others, as in Go!No Go test) has been presented. in [5]. For given al!owable deviations of parameters (design tolerances) and sensitivity matrix (calculated in Step 2), tolerance region can be mapped
intothe measurementspace]RM:
a/lVI
+.
. . + a/(Mol)VM.1 +VM ':;CZ1'/
a/lVI
+. ..
+ a/(M-l,VM.1 +VM "?cz/
Next, each pair of regions is checked whether they intersect (form arnbiguity set). Step by Step description of such checks is presented below.
------------------------------------------------------------
Step 1: Find vertices of al! F+ 1 regions. At each boundary (line for M=lor pIane for M>I) ofthe region, values ofP-M+1 parameters are fixed at tolerance margins Xp' or Xp+whiJe a]] other parameters have arbitrary values. Based on this observation, a simple algorithm of finding the region vertices trom equations ofits boundaries has been elaborated [5]. Step 2: For each individual condition f=O,I,..,F find the corresponding signature: Wf=[W/'" Wbf... w/]
(5)
Each bit ofthe signature represents one constraint designated by one inequality of (4).
AV=SAX
(1)
.
Ifthe b-th constraint
is fulfilled for al! vertices ofTf, t h e n
w/=I. . If the b-th constraint is not fulfil!ed for any vertex of Tf,
where: AV = [A VI' . . AVM)' ; AX = [AX,' . . AXp)'.
then Wbf=O. Su
S
"0
= [SI . . . . SP] =;
SIP
:. .
[SMI ...
. lf the b-th constraint is fulfilled for some but not al!
S =av mfax p' at X=Xn
ofTf,
'mp
SMP]
Essential!y, the problem is one of computing the centrosymmetric polytope which in mathematical terms is the image of a paral!elpiped under a linear transformation (I). Planes, boundaries ofthe region in ]RMare designated by equations (2). allAVI
+.
..
+ al(M'l)AVM-I + AVM
= -:t;b, (2)
aIlAVI +...
+ aI(MoIJAVM.1+ AVM =-:t;bI
Thus, to describe the region total ofI.M coefficients have to be calculated, where:
vertices
then Wbf=Q>.
The totallength ofthe signature, is equal the total number of al! constraints: B=2T(F+I). Step 3: For each pair ofregions Tkand Tl, k,1=O,l,..,F,designate the quasi-Hamming distance: B d(wk,wl)=dkl=L
boi
wbke Wb'
(6)
where: leO=I, lel=O, le=O. Check the distances dkl' If dkl>O,then regions Tk and T1 do not intersect. If dld=O,then regions Tk and T' intersect, Le. the k-th and the I-th circuit conditions can not be distinguished by the given M measurements.
~
------------------------------------------------------------I=
(:J
(3)
To find al! coefficients, we will consider, one by one, total ofI combinations ofM-1 pararneters. For the i:th combination, first coefficients
