On a Useful Tool to Localize Jacks in Wiring Network

Transcription

1 856 PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27 30, 2012 On a Useful Tool to Localize Jacks in Wiring Network M. Franchet 1, N. Ravot 1, and O. Picon 2 1 CEA, LIST, Embedded Systems Reliability Laboratory Point Courrier 94, Gif-sur-Yvette, F France 2 Université Paris-Est; ESYCOM, Marne-La-Vallée, France Abstract With the omnipresence of electronics, the reliability of wiring networks becomes crucial. As they tend to be more and more complex, knowing their topology is of greatful help for monitoring and maintaining them. In order to localize jacks as well as incipient damage, efficient diagnostic tools need to be developed. This article proposes to combine Time Domain Reflectometry (TDR) with time-frequency tools to do so. 1. INTRODUCTION As automobile, aeronautic and robotic systems more and more rely on electronics, the reliability and a good knowledge of their wiring networks are crucial. To efficiently monitor and maintain these networks, their topology have to be known. Most of the time a wiring network is not made of a single line but of several cables linked to each others with jacks. So knowing where these jacks are, is an important information for going back to the topology. Then once this information is known, the damaged portions of the network can be localized relatively to the jacks, which will facilitate and accelerate the mending. Besides, in a wiring network it can be the jacks themselves that are damaged. So it is important to be able to monitor their condition. Knowing where they are is the first step to study their ageing. One way to localize jacks in a network is to use reflectometry methods. It consists in injecting a signal into the wiring network and analysing the reflected signals at the injection point. One method is called Time Domain Reflectometry (TDR) (cf. [1 3]). Here a step or a pulse is injected. This method works quite well for detecting hard faults such as open or short circuits. However such as for soft faults (e.g., chafes), the reflections on jacks are of low amplitude (they are not perfectly matched to the line) and TDR may be not efficient enough to detect them. For doing so, some further signal processing tools can be used. In [4, 5] and [6], a method, called Joint Time Frequency Domain Reflectometry (JTFDR), based on the Wigner Ville Transform (WVT) and a normalized Time Frequency Function (TFC) has been proposed. It has shown promising results concerning soft faults (cf. [7]). This article shows that thanks to the WVT and the TFC, it is possible to localize a jack in a line. The WVT and the TFC will be defined in the first part. Then it will applied on experimental data. The second part exposes the measurement setups. The first line under test is made of two identical coaxial wires linked with a jack. The results are presented in part 4. The second type of line to be tested is made of two identical aeronautic wires (embedded in a set of several other wires) linked with a jack. 2. DEFINITION OF THE TFC Detecting weak signals, such as pulses reflected on jacks or soft faults, needs a good time and frequency resolution. That s why time frequency tools can be of useful help in reflectometry. Here the chosen method combines the Wigner Ville transform and a normalized Time Frequency Correlation (TFC) between the time frequency distribution of the injected signal (s(t)) and the reflected one (r(t)). Both the Wigner Ville Transform and the TFC are defined in the next subsections The Wigner Ville Transform The Wigner Ville Transform (WVT) is a quadratic time frequency tool, often used in detection problems. Due to its quadratic nature, cross-terms arise when computing the WVT of a multicomponent signal. As these cross-terms can mask real components or lead to false positives in the detection process, they have to be reduced. For doing so the pseudo Wigner Ville Transform (PWVT) has been used here (cf. [9]). This is a windowed version of the WVT. The WVT and the PWVT of a signal r(t) are defined in Equations (1) and (2). W r (t, ω) = 1 2π + r ( t τ 2 ) ( r t + τ ) e jτω dτ (1) 2

2 Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27 30, Figure 1: Soft Fault on a coaxial line. where r (t) is the conjugate of r and ω the pulsation (rad s 1 ). 1 P W r (t, ω) = + ( τ ) ( w w τ ) ( r t τ ) ( r t + τ ) e jτω dτ (2) where w(t) is the chosen window. In the following a gaussian window has been used. According to [8] the best choice is to use a window of the same size as the ones to be detected Definition of the TFC The WVT has a good time resolution but it can be not sufficient enough for detecting soft faults or localizing jacks. For this reason, the PWVT is combined with a normalized Time Frequency Crosscorrelation function (TFC). The TFC between the time frequency distribution of the injected signal s(t) and the reflected one (r(t)) is defined in Equation (3). Here the time frequency distribution of s(t) and r(t) are computed with the PWVT. They are noted P W s (t, ω) and P W r (t, ω). with: C sr (t) = 2π E r (t) E s E r (t) = E s = t =t+t s + t =t T s t =t+t s + t =t T s + + P W r (t, ω) P W s (t t, ω)dωdt (3) P W r (t, ω)dωdt (4) P W s (t, ω)dωdt (5) 3. EXPERIMENTAL CONDITIONS 3.1. The First Studied Case The Cable under Test Here the wiring network under test is made of two identical coaxial cables (RG58), whose characteristic impedance is Z c = 50 Ω. The first wire of 1 m is linked to the other one (of m long) with a jack of 3.3 cm long (ref: R ). The characteristic impedance of the jack is 50 Ω. The plastic jacket and the metallic shield have been removed (such a defect can be classified as a soft fault) at m from the beginning of the line (cf. Figure 1) and the far-end of the cable is left open circuited The Measurement System A vector network analyzer (Agilent E5071c 9 khz 4.5 GHz) has been used to inject a signal into the line and to measure the signal reflected at the injection point. The internal impedance of the analyzer is Z in = 50 Ω. The measurement setup is displayed in Figure 2. Two kinds of signals have been used: a gaussian pulse of 250 ps width at half maximum and a gaussian pulse of 500 ps width at half maximum. In each case the power of the injected signal is 0 dbm. 1 Actually the analytic signal of s(t) is used to compute the WVT. However in order to simplify, both will be written in the same manner.

3 858 PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27 30, Ω s(t) Z c Z f 1 Z c Z f 2 Z c Z L x =0 x 1 x 2 x 3 x 4 x = L Figure 2: Measurement setup. The red part of the cable corresponds to the jack and the blue one to the defect. Z L = +. Figure 3: TDR result with a gaussian pulse of 500 ps width at half maximum. Figures 4 and 3 present the TDR results in each case. Consider first the result for a pulse of 500 ps width. Four interesting areas can be observed. The first one (t [0; 1.4] ns) corresponds to the reflections at the beginning of the line because of a slight mismatch between the measurement setup and the line. For t [10; 12] ns the reflections at both ends of the jack, which is not perfectly matched with the line, can be seen. The pulses reflected at the beginning and at the end of the defect are visible for t [30.7; 32.6] ns. The pulse localized at t = ns corresponds to the reflection at the far end of the line. Let s now have a look at the result for a injected pulse of 250 ps width. Four areas can be observed too but results are better in term of localization. Indeed in this case we can see for t [9.76; 11] ns not only the pulses reflected one time at both end of the jack but also the ones reflected two times at both end of the jack. Comparing now the amplitudes of the reflections on the jack, the defect and the far end of the line, we can see that although pulses reflected on the jack and the defect can be seen on TDR results their amplitudes are much more smaller than the one reflected on the open circuit. Then the amplitudes of the waves reflected on the soft fault are about 2.7 higher than the one reflected at both end of the jack. So applying some signal processing tools on such data can be useful in order to make the detection of the connector and the soft fault easier The Second Studied Case Here a line composed of two identical aeronautic wires. It is gathered with several other wires. The first wire of 1.5 m long is linked to the second one (of 5.5 m long) with a jack of 4 cm long. The measurement setup is displayed in Figure 5. As can be seen, the line is not straight and has two bends. It is left open-circuited at its far-end. Measurements and injection have been done with the vector network analyzer (VNA) previously used. The signal injected into the line is a gaussian pulse of 7 ns width at half maximum, in order to reach a compromise between time resolution and attenuation. Figure 6 presents the TDR result. Five reflected pulses can be noticed. The first one at t 0 = 9.5 ns is due to the mismatch between the line and the measurement setup. The reflected pulse located at t 1 = ns corresponds to the reflection on the jack, whereas those at t 2 = 39.1 ns and

4 Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27 30, Figure 4: TDR result with a gaussian pulse of 250 ps width at half maximum. VNA 1.5m 3m Jack FirstBend Second Bend End of the line Figure 5: Measurement setup used in the second case. Figure 6: TDR result for the second case. t 3 = 62 ns correspond to the reflections on the first and second bends. The pulse reflected at the end of the line is visible at t = ns. One can notice that the pulses reflected on the jack and the bends (especially the one reflected on the second bend) are of lower amplitude than the one reflected at the end of the line.

5 860 PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27 30, RESULTS AFTER COMPUTING THE TFC PROCESS 4.1. Results Obtained in the First Case Figures 7 and 8 show the results obtained for each kind of injected signal after applying the TFC on the TDR results. For both cases T s and the width of the gaussian window are equal to the width of the injected signal. This is supposed to be the optimum parameters for computing the TFC. The positions of the peaks, which correspond to the reflections on the jack, the defect and the end of the line are presented in Table 1. Their positions in time have been converted to their positions in meter, considering that the propagating velocity in the line is: v p = m s 1. The corresponding relative errors are displayed in Table 2. The beginning of the jack and the defect (respectively 1 m and m) have been taken as reference to compute these errors. Considering first the results obtained with a pulse of 500 ps width, the first remark is that four peaks can be clearly observed. The first one at t = 0 ns corresponds to the reflections at the beginning of the line. The other ones correspond to the reflections on the jack, the defect and the far end of the line. One can notice that whereas the reflections on the jack and the defect result in two reflected pulses on the TDR data, only one peak is present on The TFC results. One interesting effect of the TFC is that the amplitudes of the peaks corresponding to the reflections on the defect and the jack are of same range than the one due to the reflection on the open circuit whereas they Figure 7: TFC result with a gaussian pulse of 250 ps width at half maximum. Figure 8: TFC result with a gaussian pulse of 500 ps width at half maximum.

6 Progress In Electromagnetics Research Symposium Proceedings, KL, MALAYSIA, March 27 30, Table 1: Peaks positions after computing the TFC. position (m) for position (m) for a pulse of 250 ps kind of position (m) for a a pulse of width and the same windowing as reflection pulse of 250 ps width 500 ps width the one for a pulse of 500 ps width on the jack ambiguous 1.03 on the defect Table 2: Relative errors after computing the TFC. relative error (%) relative error (%) relative error (%) for a pulse of kind of for a pulse of for a pulse of 250 ps width and the same windowing reflection 500 ps width 250 ps width as the one for a pulse of 500 ps width on the jack 0.3 ambiguous 3 on the defect Figure 9: TFC result with a gaussian pulse of 250 ps width at half maximum, computed as if it was for a pulse of 500 ps width. were far smaller on TDR results. This points out the usefulness of the TFC for the study and the detection of jacks and soft faults in wiring networks. Let s now have a look at the results obtained with a pulse of 250 ps. One obvious remark is that much more peaks are visible. This makes the interpretation of them more difficult especially for the first portion of the line. These peaks are not artefacts and results from the little variations of the reflectograms. They can be due to the noise and/or the small imperfections of the coaxial cable. So using a narrower pulse improves the time resolution but also leads to more complicated results when applying the TFC, if the cable under test is not of good quality. One can try to find a compromise in using a injected signal signal of 250 ps and computing the TFC as if it was of 500 ps (T s and the width of the gaussian window are chosen as if a pulse of 500 ps width had been used). The results are displayed in Figure 9. The number of peaks has significantly decreased and the peaks corresponding to the jack, the defect and the end of the line appear more clearly. However the relative error about the localization of the jack has increased. So the time resolution is decreased. In this case using this method makes the jack appear more clearly. But if some other small defects or jacks better matched to the line had been present the corresponding peaks of the TFC may have been reduced as the ones due to the intrinsic imperfections of the cable. So computing the TFC with the same parameters as the ones chosen for a pulse of 500 ps can t be systematically used.

7 862 PIERS Proceedings, Kuala Lumpur, MALAYSIA, March 27 30, 2012 Figure 10: TFC result obtained in the second case Results obtained in the second case Figure 10 displays the result obtained after applying the TFC on the TDR result. In this case T s and the gaussian window width are equal to the width of the injected signal. The TFC result is compared with the classical cross-correlation between the reflected signal and the injected one. Such a comparison makes more obvious the advantage of using the TFC. Indeed, whereas only the reflections at the beginning of the line, on the first bend and at the end of the line are visible on the classical cross-correlation result, the pulses reflected on the jack and the second bend become apparent after the application of the TFC. This confirms that the TFC can greatly enhance the capacity of detecting low amplitude signals, as the ones reflected on soft faults, jacks or even bends. 5. CONCLUSIONS This article has shown that localizing a jack in a wiring network is possible, thanks to TDR. Indeed as the jack is not perfectly matched with the line, if a signal is injected into the wire, a part of its energy is reflected back to the injection point. So this reflected signal is supposed to be visible on the reflectogram. However it has a low amplitude. In order to enhance the presence of the jack, some time frequency tools are of useful help. Here a method which combines the Wigner Ville Transform and the computation of a normalized Time-Frequency Cross-correlation function has been proposed and tested on 2 different kinds of lines. We have seen, in the first case (the coaxial line), that this makes the amplitude of the peaks corresponding to the reflected pulses on a jack and a soft fault be of the same range as the one due to a hard fault (open circuit). The second studied case confirms that the TFC can greatly enhance the presence of jacks and even bends. Besides whereas using a thiner injected signal improves the time resolution, the results of the TFC are more difficult to interpret. Indeed using a narrower signal makes the small intrinsic imperfections of the line more visible. So the number of peaks present in the TFC result will increase and the peak corresponding to the jack is buried into the others. One way to address this problem is to voluntarily decrease the time resolution when computing the TFC. This can be done in taking the same computation s parameters as for a wider injected signal. However if the amplitude of the reflected pulses on jacks or soft faults are of the same range as for the intrinsic imperfections they won t be detected. So this method has to be used with very good caution. Thanks to the TFC, jacks can be detected. This enables us to study the topology of the wiring network under test and to find the relative position to the jacks of defects. This will make their maintenance easier. Then knowing where jacks are is also a first step for monitoring their ageing. REFERENCES 1. Pan, T.-W, C.-W. Hsue, and J.-F. Huang, Time-domain reflectometry using arbitrary incident waveforms, IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 11, 2558

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