Using perturbation theories and a distance in manifolds, this paper initiates a testability condition for k-faults diagnosis in analog circuits with tolerance. In this condition, this paper mathematically elaborates how testability of a circuit with tolerance depends on both nominal data and measurable signals of the circuit. In addition, it is shown that this condition provides a theoretical basis for reasonably application of extreme methods to locate faults.
Liu R W. A Circuit Theoretic Approach to Analog Fault Diagnosis. in Testing and Diagnosis of Analog Circuits and Systems. ed. by Liu R W. New York: Van Nostrand Reinhold, 1991, 1-35.[2]Togara Y, Matsumoto T, Arai H. IEEE Trans. on CAS, 1986, CAS-33(10): 992-1009.[3]张志涌,杨祖樱.电子科学学刊,1994,16(1): 18-25.[4]张志涌,杨祖樱.通信学报,1993,14(3):5-10.[5]Davis C, Kahan W M. SIAM J[J].Numer. Anal.1970, 7(1):1-46[6]Golub G, Van Loan C F. Matrix Computations. Baltimore: Johns Hopkins Uaiv. Press, 1983, 428-431.