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Soft Fault Diagnosis in Embedded Switched-Capacitor Filters

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Abstract

This paper presents a scheme to diagnose soft faults in switched-capacitor (SC) filters embedded in the PSoC1 processor from Infineon. The work addresses faults that cause reductions in the values of the filter capacitors due to degradations produced by electrical stress. The diagnosis scheme employs the step response of the pass band output of the filter under test. After simple signal processing steps, the test signal is delivered to a nearest neighbor (1NN) classifier that uses a similarity measure (dynamic time warping) to compare the incoming waveform with patterns stored in a dictionary. The signals in the dictionary are obtained from the filter's step response (using its transfer function) under fault-free and faulty conditions. The diagnosis characterization procedure consists of evaluations at different abstraction levels, including transfer function level simulations in MatLab (over a wide range of faulty conditions), SPICE level simulations, experimental fault injection, and on-chip signal measurements using the internal resources of the processor. All the simulations consider non-ideal effects like noise, jitter, thermal drift, capacitors mismatch, and inter-chip variation in offset voltages at a reasonable computational cost. The evaluations, performed at different abstraction levels, show an excellent performance of the method for diagnosing the addressed faults.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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Funding

This work was supported by Universidad Tecnológica Nacional and Universidad Nacional de Córdoba.

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Authors and Affiliations

  1. Mechatronics Quality Research Group, Facultad Regional Villa María, Universidad Tecnológica Nacional, Villa María, Argentina

    Emanuel A. Dri, Eduardo A. Romero & Gabriela M. Peretti

  2. Electronics and Instrumental Development Group, Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Córdoba, Argentina

    Eduardo A. Romero & Gabriela M. Peretti

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  1. Emanuel A. Dri
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Correspondence to Gabriela M. Peretti.

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Appendices

Appendix A: Selection of the Parameters for Characterizing the Non-ideal Effects

We adopt noise, offset voltage (and its thermal drift), and jitter values for simulation-based characterizations. In the following, we explain the criteria for their characterization.

The election of noise characteristics is based on experimental observations performed in this research and previous work [7, 9]. In these experiences, it was possible to observe that the noise is considerably higher when external measurement equipment (oscilloscope) is used for implementing the scheme. Therefore, we inject noise in the ideal signals for emulating the observed one in this situation, the worst-case scenario. Specifically, we simulate noise using two Gaussian sources. One has a signal-to-noise ratio (SNR) of 53 dB and is applied to the entire signal. The other replicates the impulsive noise caused by other equipment in the surroundings of PSoC1. It has an SNR of 33 dB and is applied only to 7% of the points of the waveform.

Regarding the offset voltage of the filters, the manufacturer reports a maximum of 140 mV that drifts with the temperature. On the other hand, the range considered for the jitter is ± 3 μs, corresponding to the duration of the clock phases in the filter under test [10].

Capacitor mismatches are also obtained from the manufacturers, assuming a normal distribution because the vendor does not disclose information about it. It is incorporated into each filter by randomly modifying the ratios between capacitors in the filter's TF. The random number generator used for this purpose is Gaussian, with a mean of 0 and a standard deviation of 3σ = 0.2%. This configuration ensures that 99.73% of the values lie within the range ± 0.2%.

The DTW algorithm employed in our proposal uses a single configuration parameter, the DTW window. After evaluating multiple values for this parameter, we determined that 20 samples-window produced the best performance. We found that 20 samples were the minimum that offers 100% of fault diagnosis in all the capacitors, ranging from ~ 12 to ~ 42%. A lower number of samples worsen the diagnostic results, while a larger number of samples do not improve the results but increase the diagnosis time.

Additionally, the algorithm has two requirements for processing the signals:

• The t=0 timestamp of the input signals must be aligned to the step input instant.

• The sample rate of the signals must match the one used to generate the faults dictionary. For the studies presented here, the sample rate adopted was 1MHz.

The value adopted for FM is based on the data obtained by simulations at the TF level, previously reported in the paper. We performed trials with different values and selected the more conservative one. Our results show that the method delivers 100% correct diagnostics when the faults are outside the uncertainty region. It also labels a given result as unreliable when the fault is in the uncertainty region. Furthermore, SPICE simulation and experimental data confirm that the selected value for FM reaches a robust performance.

Finally, there are parameters adopted for the characterization campaigns. The fault granularity used in the simulations at TF levels is small, allowing a detailed performance evaluation in a wide range of deviation faults. To study the method's behavior in many runs, we repeat the diagnosis procedure 100 times for each level of injected fault, changing the injected non-ideal effects for each run. To evaluate the impact of capacitor mismatches on the diagnosis results, we generate a population of 960 filters with a different mismatch.

When SPICE simulations are used, we adopt a single filter. This obeys the high computational cost of such detailed simulations. Experimental evaluations also consider only one filter because they aim to determine the feasibility of the implementation in a real environment aimed at in-field diagnosis applications.

Appendix B: Characterization of the Diagnosis Performance in Two Additional Cases of Study

This appendix extends the characterization of the diagnosis scheme by addressing two different case studies named Filter 2 and Filter 3.

Tables 12 and 13 report the specifications of these filters and their capacitor configurations. These filters are evaluated under the conditions established in Sect. 4.2. In addition, we maintain the number of individuals in the population (960), the capacitors' mismatches, and the previously described NJTd effects for comparative purposes.

Table 12 Functional parameters of Filter 2 and Filter 3
Full size table
Table 13 Design parameters of Filter 2 and Filter 3
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Tables 14 and 15 summarize the diagnosis results of these new cases, grouping them in four deviation regions (R1 to R4):

  1. 1.

    R1 the results are always fault-free and reliable (FM > 54%).

  2. 2.

    R2 uncertainty region (FM < 54%) for small deviation faults. The diagnosis outcomes transition from the fault-free to the correct faulty capacitor.

  3. 3.

    R3 The diagnosis results are correct (FM > 54%).

  4. 4.

    R4 zones of large deviations in C3 and CA for which the diagnosis results are declared unreliable (FM < 54%).

Table 14 Diagnosis results for Filter 2
Full size table
Table 15 Diagnosis results for Filter 3
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The diagnosis results for these filters are very similar to those observed for Filter 1, showing the robustness of our procedure. The main differences are observed for the ones of large deviations in C3 and CA for R2 regions (with FM < 54%). For Filter 1, this region is the narrowest, with a maximum span of 3.8%. For Filters 2 and 3, the extensions of these regions are 5% and 4%, respectively.

Regarding the uncertainty regions for large deviations, Filter 1 presents three for capacitors C1, C2, and C3. Similarly, Filters 2 and 3 showed this behavior for capacitors C3 and CA only.

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Dri, E.A., Romero, E.A. & Peretti, G.M. Soft Fault Diagnosis in Embedded Switched-Capacitor Filters. Circuits Syst Signal Process 42, 3153–3180 (2023). https://doi.org/10.1007/s00034-022-02262-6

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