CONTROLLABILITY AND OBSERVABILITYDEFINITIONS:Why we need them?Gate-level Testability Measures: SCOAP L. H. Goldstein, "Controllability / Observability Analysis of Digital Circuits"NAND Gate:High level Testability MeasuresDetection probability using testability measures:Future needs:4/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725011CONTROLLABILITY AND CONTROLLABILITY AND OBSERVABILITYOBSERVABILITYKALYANA R KANTIPUDIKALYANA R KANTIPUDIVLSI TESTING ’05VLSI TESTING ’05 TERM PAPERTERM PAPER4/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725022DEFINITIONS:DEFINITIONS:Controllability: The difficulty of setting a particular logic Controllability: The difficulty of setting a particular logic signal signal to 0 or 1 to 0 or 1Observability: The difficulty of observing the state of a Observability: The difficulty of observing the state of a logic logic signal signal Applicable for both combinational and sequential testability Applicable for both combinational and sequential testability measuresmeasures. . Combinational Testability measures: Spatial domainCombinational Testability measures: Spatial domainSequential Testability measures: Temporal domainSequential Testability measures: Temporal domain4/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725033Why we need them?Why we need them?We need testability information of a circuit We need testability information of a circuit Why?Why?DFT (DFT (Design-For-TestabilityDesign-For-Testability))We need module-level or Register-Transfer-level measures for thisWe need module-level or Register-Transfer-level measures for thisWhy?Why?There will be no independent gates in VLSI circuitsThere will be no independent gates in VLSI circuitsATPG (ATPG (Automatic Test Pattern GenerationAutomatic Test Pattern Generation))We need gate-level measures for thisWe need gate-level measures for thisWhy?Why?We need to know the easily controllable and observable We need to know the easily controllable and observable nodes in a cktnodes in a cktWhy?Why? 4/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725044Gate-level Testability Measures: Gate-level Testability Measures: SCOAP SCOAP L. H. Goldstein, "Controllability / Observability Analysis of Digital L. H. Goldstein, "Controllability / Observability Analysis of Digital Circuits"Circuits" combinational zero controllability (CC0)combinational zero controllability (CC0)combinational one controllability (CC1)combinational one controllability (CC1)combinational observability (CO)combinational observability (CO)sequential zero controllability (SC0)sequential zero controllability (SC0)sequential one controllability (SC1)sequential one controllability (SC1)sequential observability (SO)sequential observability (SO)Primary Inputs:Primary Inputs:The combinational controllabilities(CC0 & CC1) are set to The combinational controllabilities(CC0 & CC1) are set to ‘1’‘1’ and all sequential controllabilities(SC0 & SC1) are set to and all sequential controllabilities(SC0 & SC1) are set to ‘0’‘0’Primary Outputs:Primary Outputs:Both combinational and sequential observabilities are set to Both combinational and sequential observabilities are set to ‘0’‘0’4/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725055NAND Gate:NAND Gate:But every ATMG has a restriction: It has to be linear. It cannot be NP-CompleteSCOAP: All inputs to all logic elements are independentWhat about reconvergent fan-outs? CC1(I)CC0(Z)CC0(Z) = CC1(A) + CC1(B) + 1= 2 CC1(I) + 1ABCC0(Z)CC1(I)CC0(Z) = CC1(I) + 14/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725066High level Testability High level Testability MeasuresMeasuresModule-level measures:Module-level measures:Every module has its own characteristic FunctionEvery module has its own characteristic FunctionA probability spectrum from the truth-tables of prim. o/ps of modulesA probability spectrum from the truth-tables of prim. o/ps of modulesC & O values are calculated from the probability spectrumC & O values are calculated from the probability spectrumRegister-Transfer-level measures:Register-Transfer-level measures: (J. E. Stephenson and J. Grason ’76)(J. E. Stephenson and J. Grason ’76)As network of components interconnected by unidirectional linksAs network of components interconnected by unidirectional linksTwo tasks:Two tasks:Control Task:Control Task: Propagating controllability from the circuit primary inputs, Propagating controllability from the circuit primary inputs, through other components, to the inputs of the componentthrough other components, to the inputs of the componentObservation Task:Observation Task: Propagating observability from the outputs of the Propagating observability from the outputs of the component component through other components to the primary outputs of the through other components to the primary outputs of the circuitcircuit Controllability(CY) and Observability(OY) of each node is calculated using Controllability(CY) and Observability(OY) of each node is calculated using complex formulae. complex formulae. TMEASTMEAS4/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725077Detection probability Detection probability using testability using testability measures:measures:V. D. Agrawal and M. R. Mercer, “Testability Measures-What Do They Tell Us?” Represented detection probability as an exponential function:So, the fault coverage is given by:  vNitieNvf0111)(Gives only a rough estimation of fault coverage.Found that 70% of the hard-to-test faults are actually detectable.Inference:“Testability measures cannot be the only criteria for DFT.”itietP)(4/26/054/26/05Kantipudi: ELEC7250Kantipudi: ELEC725088Future needs:Future needs:Need for accurate testability measuresNeed for accurate testability measuresNeed more ATMG tools like TMEAS and Need more ATMG tools like TMEAS and ITTAP ITTAP Conclusion:Conclusion:The present accuracy of testability measures is not enough; For them to be the only criteria in DFTDynamic testability measures will be of much more help for an