Application ofArtificial Neural Network forEfficient Hardware Characterization ofHigh-Speed Interconnect Systems

Theimpact ofprocess variations, operating conditions andenvironmental changes onhigh-speed system performances isbecoming moresignificant duetotheshrinking bit time andsupply voltage. Consequently, accurate and exhaustive characterization isessential toimprove therobustness andyield ofcurrent systems. However, thestatistics ofthesystem performance obtained fromlimited measurement canbeunrepresentative ofthefmal product. Thispaper describes theapplication ofanartificial neural network (ANN)togenerate theperformance distribution andstatistics ofchip-to-chip communication system frommeasurements. Asetofexperiments isperformed onahardware system tocapture therelationships between system parameters andperformance. Themeasured data is then used totrain theneural network that isused toefficiently generate realistic distributions andstatistics ofthesystem performance. Theaccuracy oftheproposed approach isverified using aprototype system. Thesensitivity ofsetup and hold times ofthesystem isstudied asfunctions ofsupply voltages andtemperature. Theresults oftheproposed method arealso compared tothose frommeasurements andregression models. I.Introduction Insuring thedesign ofarobust multi-gigabit system forhigh-volume production isverychallenging. Asboth data rates increase andthesupply voltages reduce with therapid advance ofsilicon process technology, system timing andvoltage margins haveshrunk correspondingly. Theimpact ofprocess variations andenvironmental changes hasa morepronounced impact than everbefore. Accurate evaluation ofthese effects using simulation isunreliable. Random jitter andsupply noise arechallenging tomodel. Asaresult, system verification hasshifted moreandmoreto laboratory measurements using system prototypes. However, hardware characterization ofcomplete multi-gigabit systems that cover process variation andoperating andenvironmental conditions ischallenging andexpensive. It requires time-consuming andcomplex repetitive laboratory measurements. Somemeasurements areimpossible or extremely expensive tosetup. Forexample, inorder toreliably evaluate process variations onthesystem performance, a large number ofprototypes hastobebuilt withpre-specified parameter values. Various operating conditions arenot easy toreplicate inthelaboratory. Anevengreater challenge isthat thepowersupplies, temperature, andhumidity of thesubcomponents cannoteasily becontrollered with pre-defmed relationships during measurement. Therelationships between system parameters andperformance aregenerally nonlinear. Mapping these relationships frommeasurements using traditional techniques isdifficult, ifnotimpossible. Forarbitrary (not monotonic) mappings, thetraditional approximation methods donotwork.Thecomplexity ofthemodels and computational cost ofgenerating themgrows exponentially with thenumber ofvariables. Multi-variate polynomials or Volterra series expansions islimited tomildly nonlinear mappings. Thedetermination ofthecoefficients forahighorder arbitrary nonlinear system isnumerically unstable. Evenfor amildly nonlinear high-dimensional system, itisvery difficult togenerate andmanage thelarge number ofparameters. Other approximation methods also suffer fromthis curse ofdimensionality. Newerapproaches forsupporting thechallenging repeated measurements needed togenerate accurate distributions andstatistics arehighly desirable forimproving therobustness andyield ofhigh-speed systems. Recently, neural networks havebeenusedforelectromagnetic-based