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A method for Soft Fault Diagnosis of Linear Analog Circuits Using the Laplace Transform Technique

Tadeusiewicz Michał, Ossowski Marek, Korzybski Marek

International Journal of Electronics and Telecommunications

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2021

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Vol. 67, No. 3

531--536

EN

This paper is focused on multiple soft fault diagnosis of linear time-invariant analog circuits and brings a method that achieves all objectives of the fault diagnosis: detection, location, and identification. The method is based on a diagnostic test arranged in the transient state, which requires one node accessible for excitation and two nodes accessible for measurement. The circuit is specified by two transmittances which express the Laplace transform of the output voltages in terms of the Laplace transform of the input voltage. Each of these relationships is used to create an overdetermined system of nonlinear algebraic equations with the circuit parameters as the unknown variables. An iterative method is developed to solve these equations. Some virtual solutions can be eliminated comparing the results obtained using both transmittances. Three examples are provided where laboratory or numerical experiments reveal effectiveness of the proposed method.

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A Verification Technique for Multiple Soft Fault Diagnosis of Linear Analog Circuits

Tadeusiewicz M., Ossowski M.

International Journal of Electronics and Telecommunications

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2018

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Vol. 64, No. 1

83--89

EN

The paper deals with multiple soft fault diagnosis of linear analog circuits. A fault verification method is developed that allows estimating the values of a set of the parameters considered as potentially faulty. The method exploits the transmittance of the circuit and is based on a diagnostic test leading to output signal in discrete form. Applying Z-transform a diagnostic equation is written which is next reproduced. The obtained system of equations consisting of larger number of equations than the number of the parameters is solved using appropriate numerical approach. The method is adapted to real circumstances taking into account scattering of the fault-free parameters within their tolerance ranges and some errors produced by the method. In consequence, the results provided by the method have the form of ranges including the values of the tested parameters. To illustrate the method two examples of real electronic circuits are given.

3

New Aspects of Fault Diagnosis of Nonlinear Analog Circuits

Tadeusiewicz M., Hałgas S., Kuczyński A.

International Journal of Electronics and Telecommunications

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2015

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Vol. 61, No. 1

83-93

EN

The paper is focused on nonlinear analog circuits, with the special attention paid to circuits comprising bipolar and MOS transistors manufactured in micrometer and submicrometer technology. The problem of fault diagnosis of this class of circuits is discussed, including locating faulty elements and evaluating their parameters. The paper deals with multiple parametric fault diagnosis using the simulation after test approach as well as detection and location of single catastrophic faults, using the simulation before test approach. The discussed methods are based on diagnostic test, leading to a system of nonlinear algebraic type equations, which are not given in explicit analytical form. An important and new aspect of the fault diagnosis is finding multiple solutions of the test equation, i.e. several sets of the parameters values that meet the test. Another new problems in this area are global fault diagnosis of technological parameters in CMOS circuits fabricated in submicrometer technology and testing the circuits having multiple DC operating points. To solve these problems several methods have been recently developed, which employ different concepts and mathematical tools of nonlinear analysis. In this paper they are sketched and illustrated. All the discussed methods are based on the homotopy (continuation) idea. It is shown that various versions of homotopy and combinations of the homotopy with some other mathematical algorithms lead to very powerful tools for fault diagnosis of nonlinear analog circuits. To trace the homotopy path which allows finding multiple solutions, the simplicial method, the restart method, the theory of linear complementarity problem and Lemke’s algorithm are employed. For illustration four numerical examples are given.

4

Multiple soft fault diagnosis of analog circuits using restart homotopy method

Tadeusiewicz M., Hałgas S.

Elektronika : konstrukcje, technologie, zastosowania

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2013

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Vol. 54, nr 12

87-91

EN

This paper offers a method for multiple soft fault diagnosis of nonlinear circuits containing bipolar and MOS transistors. The method enables us to locate faulty elements and evaluate their parameters, using a nonlinear algebraic type test equation which may possess several solutions. To find the solutions the homotopy concept is applied and a homotopy differential equation written. Next the terminal value problem is formulated and solved using the restart approach. As a result different sets of parameters which satisfy the diagnostic test can be found rather than one specific set. Two numerical examples show that the proposed approach is simple and improves the diagnosis of analog circuits.

PL

Praca dotyczy diagnostyki wielokrotnych uszkodzeń parametrycznych w układach nieliniowych zawierających tranzystory bipolarne i tranzystory MOS. Zaproponowano metodę umożliwiającą lokalizowanie uszkodzonych elementów i określanie ich wartości na podstawie analizy testowego, nieliniowego równania algebraicznego, które może posiadać wielokrotne rozwiązania. W celu wyznaczenia tych rozwiązań zastosowano koncepcję homotopii i utworzono homotopijne równanie różniczkowe. Sformułowano zagadnienie końcowe i rozwiązano je numerycznie używając procedurę restartu. Takie podejście umożliwia znalezienie różnych zbiorów wartości elementów potencjalnie uszkodzonych, które spełniają test diagnostyczny. Zamieszczone w pracy dwa przykłady obliczeniowe pokazują, że zaproponowana metoda jest prosta, nie wymaga dużych mocy obliczeniowych oraz usprawnia diagnostykę analogowych układów nieliniowych.