Method for determining the permittivity spectrum of a cable, from a time or frequency-domain reflectometry representation

Abstract

Method for determining a permittivity spectrum of a transmission line, the method comprising the steps of: Obtaining (301) a frequency reflectogram for a transmission line, Determining (303), from the frequency reflectogram, an estimate of the transfer function of the transmission line, Calculating (304, 305), from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum. Figure 3

Description

Title of the invention: Method for determining a permittivity spectrum of a cable, from a temporal or frequency representation of reflectometry

[0001] The invention relates to the field of systems and methods for non-destructive diagnosis or characterization of cables and in particular the field of reflectometry methods for characterizing the physical properties of a cable with a view to analyzing its state of health and monitoring, for example, its aging.

[0002] The invention relates more specifically to a method for determining a permittivity spectrum of the insulation of a cable, i.e. complex permittivity values ​​as a function of frequency.

[0003] The invention applies to any type of electrical cable, in particular power transmission cables or communication cables, in fixed or mobile installations. The cables concerned may be coaxial, two-wire, parallel lines, twisted pairs, cable strands or other. The invention may also apply to mechanical cables, for example infrastructure support cables such as an elevator or a bridge.

[0004] More specifically, the cables must be insulated because the invention makes it possible to characterize the insulation of the cable.

[0005] A general problem that the invention aims to solve concerns the characterization of cables, more generally transmission lines, from the physical parameters of their insulation.

[0006] The characterization of a cable aims in particular to enable monitoring, via the evolution of this characterization, of the state of a cable, in particular its aging. It can also enable the appearance of defects to be detected when the estimated parameters differ from the initial characterization.

[0007] Among the parameters used to characterize the insulation of a cable, the permittivity of the material from which the insulation is made represents one of these characterization parameters. In general, the variation of the permittivity of a material as a function of frequency is not data provided in the cable manufacturing instructions.

[0008] There is therefore a need to determine non-destructively an estimate of the complex permittivity of the insulation of a cable as a function of frequency.

[0009] The state of the art includes different methods for characterizing a cable.

[0010] The Applicant's patent application FR3025320 describes a method for determining the linear parameters of a transmission line. It makes it possible to find the linear RLCG parameters of a cable from a measurement of reflec- tometry. If the geometry of the cable is known, it is possible to deduce the complex permittivity of the insulation from the values ​​of C and G. However, this technique does not allow the spectrum of permittivity to be found, this being assumed to be constant (or affine) over the frequency band studied for the algorithm to work.

[0011] Reference [1] describes a dielectric spectroscopy technique which makes it possible to determine the linear parameters C and G of a cable as a function of frequency, by a non-destructive in situ measurement. If the geometry of the cable is known, it is possible to calculate the spectrum of the complex permittivity of the insulator. This technique can however only be used up to frequencies of the order of magnitude of MHz, because it takes the approximation that there is no propagation effect along the cable (wavelength small compared to the length of the cable).

[0012] There are then different techniques which make it possible to measure the permittivity of a sample of insulation, possibly cut from a cable, specially prepared for this measurement. These are destructive techniques for the cable. This makes it possible to overcome the propagation effects in the cable, and to carry out a characterization at higher frequencies. Given that the geometry of the sample is controlled, it is possible to determine the value of the complex permittivity from the measurements carried out. For example, we can cite publication [2] which uses the reentrant cavity and dielectric resonator techniques, to make measurements on a sample between 100 MHz and 20 GHz.

[0013] The aforementioned methods do not allow the permittivity of a cable to be determined over a wide range of frequency values, in a non-destructive manner and without prior knowledge of the geometry of the cable. The invention thus aims to overcome these drawbacks.

[0014] The invention relates to a method for determining the complex permittivity of the insulation of a cable from a frequency reflectometry measurement.

[0015] The proposed method is non-destructive and makes it possible to characterize the complex permittivity over the entire operating frequency band of a cable without prior knowledge of the geometry of the cable.

[0016] The subject of the invention is a method for determining a permittivity spectrum of a transmission line, the method comprising the steps of: - Obtain a frequency reflectogram for a transmission line, - Determine, from the frequency reflectogram, an estimate of the transfer function of the transmission line, - Calculate, from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum.

[0017] According to an alternative embodiment, the method according to the invention further comprises a step of: - Estimate, from the measurement, a first reflection coefficient at the input of the noisy transmission line and / or a second reflection coefficient at the input of the non-noisy transmission line, - The estimate of the transfer function of the transmission line being further determined from the first noisy reflection coefficient and / or the second non-noisy reflection coefficient.

[0018] According to a particular aspect of the invention, the step of estimating a first reflection coefficient at the input of the noisy transmission line comprises the sub-steps of: - Applying an inverse Fourier transform to the frequency reflectometry measurement, - Remove from the measurement the peak corresponding to the end of the transmission line, - Apply a direct Fourier transform to the result obtained.

[0019] According to a particular aspect of the invention, the step of estimating a second reflection coefficient at the input of the non-noisy transmission line is carried out by calculating an average of the frequency reflectometry measurement over a predefined low frequency interval.

[0020] According to an alternative embodiment, the method according to the invention further comprises a step of: - Calculate, from the real part of the permittivity spectrum and an estimate of the attenuation of the transmission line or a function of said attenuation or the modulus of the transfer function, the imaginary part of the permittivity spectrum.

[0021] According to an alternative embodiment, the method according to the invention further comprises a step of: - Determine a first estimate of the attenuation of the transmission line over a first low frequency interval from the frequency reflectometry measurement or the transfer function and the length of the transmission line, - Estimate, from the first attenuation estimate and the real part of the permittivity spectrum, a vector k as a function of the frequency, - Determine a second estimate of the transmission line attenuation over the entire frequency band from the transmission line transfer function and the transmission line length, - Calculate the imaginary part of the permittivity spectrum from the second estimate of the attenuation, from said estimated k vector and from the real part of the permittivity spectrum.

[0022] According to a particular aspect of the invention, the step of estimating a vector k as a function of the frequency comprises the steps of: - Calculate a first estimate of the vector k from the first estimate of the attenuation and the real part of the permittivity spectrum, - Apply a regression function to the first estimate of the vector k, the regression function depending at least on the square root of the frequency.

[0023] According to a particular aspect of the invention, the real part of the permittivity spectrum is taken equal to a predefined constant value.

[0024] According to an alternative embodiment, the method according to the invention further comprises a step of determining a likelihood coefficient of the calculated permittivity spectrum consisting of: - Determine a new estimate of a frequency reflectogram from the calculated permittivity spectrum, - Calculate a likelihood coefficient reflecting the difference between the frequency reflectometry measurement and the new estimate of the frequency reflectogram.

[0025] According to a particular aspect of the invention, the step of determining a new estimate of a frequency reflectogram comprises the sub-steps of: - Determine an estimate of the characteristic impedance of the transmission line, - Determine an estimate of a geometric factor from the characteristic impedance and the real part of the permittivity spectrum, - Determine an estimate of the RLCG parameters of the transmission line from the geometric factor and the permittivity spectrum, - Determine the estimate of the frequency reflectogram from the estimated RLCG parameters.

[0026] In an alternative embodiment of the invention, the transmission line is composed of two sections of lines of different permittivities, the calculated permittivity spectrum corresponds to an average complex permittivity for the transmission line, the method further comprises the steps of: - Receive a first value of complex permittivity C] corresponding to a first section of the line, - Determine a second complex permittivity value ^2 corresponding to a second section of the line using the following relation: C2 = ( / 2e, A ( / + r ( / - 2 / ; ) ) , with e the spectrum of per- complex mittivity, / the length of the transmission line, l] the length of the first section and F a measure of the reflection coefficient at the interface between the two sections, determined from the frequency reflectogram.

[0027] The invention also relates to a system for determining a permittivity spectrum comprising measuring equipment configured to carry out a frequency reflectometry measurement on a transmission line and a processing unit configured to execute the steps of the method according to the invention.

[0028] The invention also relates to a computer program comprising instructions for executing the steps of the method according to the invention and a recording medium readable by a processor on which is recorded a program comprising instructions for executing a method according to the invention, when the program is executed by a processor.

[0029] Other characteristics and advantages of the present invention will appear better on reading the description which follows in relation to the following appended drawings.

[0030] [Fig.1a] represents a diagram of a first example of a time domain reflectometry system,

[0031] [Fig.lb] represents a diagram of a second example of a time domain reflectometry system,

[0032] [Fig.2] represents an example of a reflectogram obtained with the reflectometry system of figures 1a or 1b for a simple cable,

[0033] [Fig.3] represents a flowchart detailing the steps of implementing a method for determining a complex permittivity spectrum according to an embodiment of the invention,

[0034] [Fig.4a] represents an example of frequency reflectometry measurement (real part),

[0035] [Fig.4b] represents an example of frequency reflectometry measurement (imaginary part),

[0036] [Fig.5a] represents an example of a Fourier transform module of the frequency measurement of figures 4a and 4b,

[0037] [Fig.5b] represents a zoom on the end of cable peak of [Fig.5a],

[0038] [Fig.6] represents a flowchart detailing the steps necessary for determining an estimate of the imaginary part of the permittivity, according to one embodiment of the invention,

[0039] [Fig.7] represents an example of regression applied to determine a vector k,

[0040] [Fig.8] represents a flowchart detailing a likelihood coefficient calculation according to an embodiment of the invention,

[0041] We will first recall some general points relating to the methods of analysis and monitoring of the condition of a cable, by reflectometry.

[0042] [Fig. 1a] describes a diagram of an example of a reflectometry system capable of carrying out a reflectometry measurement on a cable, for example a fre- The invention is positioned in the context of reflectometry methods for characterizing a cable, in particular its insulation.

[0043] In [Fig.1a], a cable 104 is shown whose insulation is to be characterized. This cable has, for example, a defect 105 at any distance from one end of the cable. The single cable 104 of [Fig.1a] is shown for purely illustrative purposes in order to explain the general principle of a reflectometry method.

[0044] A reflectometry system 101 according to the invention comprises an electronic component 111 of the integrated circuit type, such as a programmable logic circuit, for example of the FPGA type, or microcontroller, adapted to perform two functions. On the one hand, the component 111 makes it possible to generate a reflectometry signal s(t) to be injected into the cable 104 under test. This digitally generated signal is then converted via a digital-to-analog converter 112 and then injected 102 at one end of the cable. Alternatively, the signal can be generated directly in an analog manner by means of a network analyzer. The signal s(t) propagates in the cable and is reflected on the singularity generated by the defect 105. The reflected signal is backpropagated to the injection point and then captured 103, digitally converted via an analog-to-digital converter 113, and transmitted to the component 111.The electronic component 111 can further be adapted to execute the steps of the method according to the invention which will be described below in order, from the signal s(t) received, to determine a reflectogram or several reflectograms.

[0045] The reflectometry system 101 can be implemented using a network analyzer.

[0046] The reflectogram(s) may be transmitted to a processing unit 114, of the computer, personal digital assistant or other type, to display the results of the measurements on a human-machine interface and / or to execute the steps of a cable characterization method which will be described below.

[0047] The system 101 described in [Fig. 1a] is an exemplary embodiment which is in no way limiting. In particular, the two functions performed by the component 111 can be separated into two distinct components or devices as illustrated in the example of [Fig. 1b]. The injection point and the signal measurement point can also be taken at any location on the cable and not at its end.

[0048] In [Fig. 1b], a first device 101 is shown, dedicated to generating the reflectometry signal and injecting it into the cable, and a second device 116 is shown, dedicated to measuring the signal at any point on the cable and then calculating the reflectogram via a component 115.

[0049] The component 115 may be an electronic component of the integrated circuit type, such as a programmable logic circuit, for example of the FPGA type or a microcontroller, for example a digital signal processor, which receives the signal measurements and is configured to execute the method according to the invention. The component 115 comprises at least one memory for saving the last signal samples generated and injected into the cable and the last measured signal samples.

[0050] As is known in the field of diagnostic methods by time-domain reflectometry, the position dDF of a fault 105 on the cable 104, in other words its distance from the signal injection point, can be directly obtained from the measurement, on the calculated time-domain reflectogram R(t), of the duration tDF between the first amplitude peak recorded on the reflectogram and the amplitude peak corresponding to the signature of the fault.

[0051] [Fig. 2] represents an example of a reflectogram R(n) obtained using the system of [Fig. 1a] or 1b, on which a first amplitude peak is observed at an abscissa N and a second amplitude peak at an abscissa N+M. The first amplitude peak corresponds to the reflection of the signal at the injection point in the cable, while the second peak corresponds to the reflection of the signal on an impedance discontinuity caused by a fault.

[0052] Various known methods are possible to determine the position dDF (distance from the peak of the end of the cable or from the clear fault). A first method consists of applying the relationship linking distance and time: dDF=Vg -tDF / 2 where Vg is the speed of propagation of the signal in the cable. Another possible method consists of applying a proportionality relationship of the type dDF / tDF = Lc / t0 where Lc is the length of the cable and t0 is the duration, measured on the reflectogram, between the amplitude peak corresponding to the impedance discontinuity at the injection point and the amplitude peak corresponding to the reflection of the signal on the end of the cable.

[0053] The reflectometry measurement can be carried out in the time or frequency domain. In the case of a frequency measurement, the measurement can be carried out by successively injecting into the cable 104 several sinusoids at different frequencies sweeping a predefined frequency range in which it is desired to characterize the cable.

[0054] A frequency reflectometry measurement corresponds to a transform in the frequency domain of a time reflectogram when the injected signal is a pulse signal. More generally, a time reflectogram corresponds to a convolution of the inverse Fourier transform of a frequency reflectogram by the injected time signal, when the latter is different from a Dirac pulse. In other words, the time reflectogram is equal to the inverse Fourier transform of the product of the frequency reflectogram by the Fourier transform of the injected signal. Thus, it is possible to move from a measurement in the time domain to a measurement in the frequency domain and vice versa via known techniques.

[0055] [Fig.3] details the steps of implementing a method for determining the permittivity of the insulation of a cable 104 as a function of the frequency, according to one embodiment of the invention.

[0056] The method begins at step 301 with a frequency reflectometry measurement carried out on a cable to be analyzed.

[0057] The measurement 301 can be carried out by means of the device described in [Fig.1a]. It can consist of injecting into the cable 104 several successive sinusoidal signals by varying the frequency of the sinusoid in a frequency range in which it is desired to analyze the response of the cable.

[0058] For each frequency, the measuring device performs a measurement of the phase shift between the injected signal and the reflected signal and a measurement of the ratio of the amplitudes between the injected and reflected signals. From these two quantities, a complex reflectometry measurement is obtained as a function of the frequency which is represented in an example given in Figures 4a and 4b which respectively give the real part and the imaginary part of the frequency reflectometry measurement.

[0059] Without departing from the scope of the invention, any other method of measurement by reflectometry may be envisaged provided that it makes it possible to generate a frequency reflectogram. In particular, it is possible to carry out a temporal measurement using a broadband temporal signal and then to calculate a frequency reflectogram from the Fourier transform of the temporal reflectogram. In particular, broadband reflectometry methods such as the OMTDR (“Orthogonal Multi-tone Time Domain Reflectometry”) or MCTDR (Multi Carrier Time Domain Reflectometry”) methods may be used to carry out step 301.

[0060] The following steps 302-305 of the method aim to calculate an estimate of the permittivity from the frequency reflectometry measurement. These steps can be implemented by a processing unit embedded in the measuring device or remote from it, in which case the measurement(s) are transmitted to this processing unit via data transmission means.

[0061] Subsequently, it is assumed that the real and imaginary permittivities are almost uniform along the cable.

[0062] In step 302, an estimate of the reflection coefficient at the input of the cable is determined, i.e. at the injection point corresponding to the interface between the measuring equipment 101 and the cable 104.

[0063] In practice, two estimates are made. The first estimate, denoted rE, corresponds to the said reflection coefficient to which the measurement noise is added. The second estimate, denoted rE0, corresponds to the denoised reflection coefficient.

[0064] Thus, we have TE = rE0 + b, where b denotes the measurement noise over the entire reflectogram.

[0065] Step 302 consists of applying an inverse Fourier transform to the frequency reflectometry measurement. A temporal representation of the modulus of the inverse Fourier transform is then obtained, illustrated, in an example, in [Fig.5a]. This representation is similar to a temporal reflectogram.

[0066] In [Fig.5a], a high amplitude peak 501 can be identified at the end of the reflectogram. This peak corresponds to the reflection of the signal on the end of the cable opposite the injection point.

[0067] [Fig.5b] represents a zoom on the end peak of cable 501.

[0068] To estimate the reflection coefficient at the cable input, it is necessary to remove the end-of-cable peak 501 from the time reflectogram.

[0069] To do this, the half-width of this peak 501 is estimated using an empirical formula and then the samples of the time reflectogram located in a time interval centered on the maximum of peak 501 and with a half-width equal to that estimated are set to zero. For example, the half-width of the end-of-cable peak is taken equal to j, where 1 is the total length of the cable expressed in meters and fmax is the maximum frequency of the reflectometry measurement expressed in GHz.

[0070] According to an alternative embodiment, the width of the peak 501 corresponding to the time interval to be filtered (set to 0) can be estimated via other formulas. For example, if an estimate of the attenuation a along the cable is available, it is possible to estimate the half-width of the peak 501 as being equal to:

[0071] d = y *l*finax' by taking an average over the whole or part of the frequency band (by varying f).

[0072] After removing peak 501 from the time reflectogram, a direct Fourier transform is applied to the result to return to the frequency domain and a first estimate rE of the reflection coefficient at the cable input plus noise is obtained.

[0073] Alternatively, it is possible to reverse the processing by first applying a direct Fourier transform at step 302 and then an inverse Fourier transform at this step.

[0074] Then, the second estimate rE0 of the reflection coefficient at the input of the noise-free cable is determined by an average of the frequency reflectometry measurement obtained in step 301 over a range of low frequency values, for example equal to [0 200 MHz],

[0075] Without departing from the scope of the invention, other methods are possible for filtering the noise, for example applying a filter to the first estimate rE so as to remove the noise.

[0076] In step 303, an estimate of the denoised transfer function of the

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[0094] cable alone (excluding interface with measuring equipment at the cable input) as a function of frequency, for example using the following relationship: H-____(1) 0 i-ri(rrH(FDÆrE) where FDR denotes the initial frequency reflectometry measurement. Relation (1) can be approximated as H (2) 0 1-¾ Alternatively, relation (2) can be replaced by other approximations such as = FDR -VE , H = , Ho = FDR. 0 1-¾ In the case where the approximation used depends only on the FDR measurement or only on one of the two coefficients r£ or r£0, step 302 is deleted or adapted accordingly (calculation of one of the two coefficients only). In an alternative embodiment of step 303, an additional filtering step may be applied to the transfer function by means of the following steps. A Fourier transform (direct or inverse) is applied to the transfer function and then all the signal except the peak corresponding to the end of the cable is removed from the result, and then a Fourier transform (inverse or direct, respectively) is applied. At step 304 we can then calculate the real part of the permittivity as a function of the frequency using the following relationships: v = - 4jrlf / arg(H0) (3) é = c&v2 (4) v is the signal propagation speed in the cable, as a function of the frequency, arg() denotes the argument function which allows the phase to be extracted from the transfer function Ho, £ is the real part of the permittivity co is the speed of light in vacuum According to a particular embodiment of the invention, the proposed method further comprises a step 305 of determining the imaginary part of the permittivity as a function of the frequency. An example algorithm for implementing step 305 is described in [Fig.6]. It starts at step 601 with a first estimate of the attenuation of the signal along the cable carried out only over a low frequency interval, for example equal to [0 200 MHz], using the following relationship: _ ln(J|FW2 (5) a~ 21 IIFDRII designates the standard for frequency reflectometry measurement calculated over the low frequency interval,

[0095] In denotes the natural logarithm operator.

[0096] 1 is the length of the cable.

[0097] Alternatively relation (5) can be replaced by _ M ll^oll ) a~ 2 /

[0098] A usual analytical model of low-loss cables can be given by the relation a = %(RC+LG)-

[0099] At low frequencies, we can make the approximation that the LG term is negligible compared to the RC term, we can therefore use equation (5) to estimate the left-hand side of this relationship which corresponds to the attenuation.

[0100] Then, in step 602, a vector k is calculated, from the attenuation calculated in step 601, the propagation speed of the signal and the real part of the permittivity calculated in step 304, by means of the following relation:

[0101] k = -^ (6)

[0102] In an alternative embodiment, a regression step is applied to the vector k obtained in order to filter the fluctuations in the value of k around an average value.

[0103] For example, we apply a regression function proportional to Vf or a regression function in a+bVf, or aVf +bf or even a+bVf+cf, where a, b and c are regression coefficients.

[0104] [Fig.7] illustrates an example of the result obtained for the vector k after a re regression in Vf represented by curve 701.

[0105] At the end of this regression step we obtain a number k0 such that k= k0. Vf.

[0106] Then, in step 603, a second estimate of the attenuation of the signal is calculated. along the cable, this time over the entire frequency band used to obtain the transfer function Ho, using the following relationship:

[0107] n _ bi(||zz0|| ) (7) (Zq — " 2 /

[0108] At step 604, the imaginary part of the permittivity spectrum can then be determined by following the development below.

[0109] We know the following relationship which links the RLCG parameters of the cable, the speed of the signal and the attenuation of the cable which is equivalent to the real part of the propagation factor h

[0110] So we have: [YES] = + LG) (8)

[0112] R is the linear resistance, L is the linear inductance, C is the linear capacitance and G is the linear conductance.

[0113] Furthermore, it is estimated, by extrapolation, that, over the entire frequency band considered, the following relationship is satisfied:

[0114] RC^Jf.e'W

[0115] By combining equations (8) and (9) we obtain an expression for the linear conductance G:

[0116] G = {(2^-k^ 6') (10)

[0117] We also know, from Maxwell's equations, that: [0H8] G^fC^ (H)

[0119] e" is the imaginary part of the permittivity

[0120] We also know that £ — -X_ (12)

[0121] Using equations (10), (11) and (12) we obtain:

[0122] É=vïe{2^-k^ e') (13)

[0123] Furthermore, we know that g = C^lv2 (equation (4)), we therefore deduce an expression for the imaginary part of the permittivity:

[0124] ek^x / f 6')

[0125] Step 604 thus consists of determining e” as a function of the frequency using relation (14).

[0126] The expressions developed above to establish relation (14) are preferably adapted for high frequencies, i.e. short cables. By high frequencies is meant, for example, frequency values ​​greater than or equal to 1 MHz which corresponds to a cable length of at most 100 m. By low frequencies is meant frequency values ​​less than 10 kHz.

[0127] In the case where the cable to be analyzed is long and requires the use of analytical expressions compatible with low frequencies, certain expressions used above, in particular to define the parameters R and L, must be modified. At low frequencies, the linear resistance is independent of the frequency, it is then necessary to carry out a constant regression on the vector k to obtain the number ko.

[0128] In an alternative embodiment corresponding to a low frequency operating mode (suitable for long cables), the expression used to define the inductance (relation (12)) is replaced by the following value which is also constant as a function of the frequency:

[0129] At = ^+^(12') 4^ Zzr 5

[0130] q0 is the permeability of the vacuum

[0131] It is a geometric factor which is a parameter of a cable.

[0132] This parameter can be estimated for example using the following relation:

[0133] Ç — , where Zc is the characteristic impedance of the cable

[0134] ) denotes an average

[0135] is the permittivity of vacuum

[0136] The geometric factor is given by the relation _ m / ÉÛ for a coaxial cable, di is the inner diameter of the insulation and d2 is the outer diameter of the insulation.

[0137] Expression (14) for the imaginary part of the complex permittivity is modified to:

[0138] 4 , pA(14')

[0139] Expression (14') is valid when the entire analyzed frequency band corresponds to a low frequency interval compatible with the expression of L above.

[0140] In this case, this expression is used to perform step 604.

[0141] In the case where the analyzed frequency band is wide and includes both a low frequency part and a high frequency part in such a way that the expressions of the values ​​of L and R evolve in the frequency band, the expressions of L and R can be obtained by simulation as a function of the geometry of the cable.

[0142] In a particular embodiment of the invention, the method further comprises an optional step 306 aimed at calculating a likelihood coefficient of the results obtained. This step aims to verify whether the approximation hypotheses taken to carry out the calculations are consistent with the operational situation. For example, certain parameters such as the frequency, or the noise level or other environmental parameters can influence the reliability of the hypotheses taken for the calculations. The determination of a likelihood coefficient makes it possible to validate that the results obtained are consistent.

[0143] For this, step 306 aims to simulate the frequency reflectogram obtained from the permittivity estimates obtained in steps 304 and 305, then to compare the result with the frequency measurement initially received in step 301.

[0144] [Fig.8] shows a diagram of an example of an algorithm used to carry out step 306.

[0145] In step 801, an estimate of the characteristic impedance of the cable is determined using the following relationship: 101461 z ^ / z 1^)(15) X ° 1-1 EQ /

[0147] r£0 is the reflection coefficient calculated in step 302

[0148] Zs is the impedance of the measuring equipment

[0149] Re() denotes the real part of the expression in parentheses,

[0150] Then in step 802, the geometric factor is estimated using the following relationship and from the real part of the permittivity calculated in step 304.

[0151] pl6)

[0152] In step 803, the parameters R,L,C,G of the cable are estimated using the expressions following from the real and imaginary parts of the permittivity calculated at

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[0166] steps 304 and 305 and the number kO. <17' if 2zr€c ■ L = “— c G = ^ëf ^0 is the permeability of vacuum. Then in step 804 an estimate of the frequency reflectogram FDR' is calculated at means of the following relationships y = ^R + 2mfL ) *(G + 2m fC) Zc = ^R + 2mfL) l(G + 2mfC) Zç-Z^ \ FDR' = rE + (18) i+r£0 expi^Z) y is the cable propagation factor In step 805, a likelihood coefficient is calculated which reflects the proximity or the difference between the FDR' estimate of the frequency reflectogram obtained in step 804 and the initial measurement obtained in step 301. To compare these two measurements, we convert them, for example, into the time domain by multiplying each by the Fourier transform of a Gaussian pulse and then applying an inverse Fourier transform to the result. The likelihood coefficient is obtained, for example, by calculating a distance between the two time domain reflectograms, for example, a root mean square error or any other suitable metric to estimate the similarity between two curves. The root mean square error can be calculated on all or part of the signal, for example to give different weights to different parts of the signal associated with particular areas of a cable. Alternatively, a likelihood coefficient can be calculated directly by comparing two reflectograms in the frequency domain. The calculation of a likelihood coefficient makes it possible to associate a level of likelihood with the permittivity estimates made in order, for example, to correct these estimates if other estimation methods are available or to relaunch the estimation method on other measurements made on the same cable. In an alternative embodiment of the invention, an improvement can be made for the case where we wish to characterize a succession of two sections of cables which are different from each other.

[0167] In such a scenario, it is possible to model a cable that is divided into two parts by considering each part as being substantially homogeneous.

[0168] In this case, by applying the invention to the entire cable, a single permittivity spectrum is obtained which corresponds to a function of the permittivity spectra associated with the two sections.

[0169] However, if the permittivity spectrum of the first part of the cable is known, and the position of the junction between the two cables can be determined, either visually or by a location method based on reflectometry, it is then possible to determine the permittivity spectrum of the second part of the cable. This method remains valid in the more general case where the cable is divided into several zones but where only one permittivity spectrum is unknown.

[0170] For example, if a cable is composed of two sections, and the permittivity C] and the length I) of the first section are known, as well as the reflection coefficient r at the interface between the two sections, then the method according to the invention is applied to the entire cable to determine the equivalent permittivity e of the entire cable of length / and then the permittivity ^2 of the second cable section is deduced using the following relationship: [01711 e2= ,'l}(^(l+r(l-2l,))e,) m

[0172] The invention makes it possible to characterize a cable by estimating its complex permittivity. This data then makes it possible to evaluate the condition of the cable, for example its aging by comparing, over time, the evolution of the permittivity values ​​in the frequency band.

[0173] In particular, the invention makes it possible to characterize the cable throughout its operating frequency band and thus makes it possible to detect changes in the permittivity values ​​in certain frequency bands in particular.

[0174] Furthermore, precise knowledge of the permittivity of a cable makes it possible to improve simulations of the cable's behavior, in particular reflectometry simulations which require fine modeling of the cable's response to the injection of a signal.

[0175] The invention allows non-destructive, in situ and on-board monitoring for the surveillance and characterization of a cable.

[0176] In an alternative embodiment, the method according to the invention can be applied to frequency or time reflectograms obtained by simulation and not by measurement.

[0177] The invention can be implemented by means of the device described in figures 1a and 1a. lb, in particular component 111.

[0178] Alternatively, the invention can be embedded directly in a connector connecting a measuring device to a cable to be characterized so as to be able to produce an embedded system. In this variant, the component 111 is directly embedded in a connector which connects a signal generator to a cable to be characterized. References

[0179] [1] SV Suraci, D. Fabiani, S. Roland, and X. Colin, “Multi scale aging assessment of low-voltage cables subjected to radio-chemical aging: Towards an electrical diagnostic technique », Polymer Testing, vol. 103, p. 107352, nov. 2021, doi: 10.1016 / j .poly merte sting .2021.107352.

[0180] [2] B. Givot, J. Krupka, K. Lees, R. Clarke, et G. Hill, « Accurate Measurements of Permittivity and Dielectric Loss Tangent of Low Loss Dielectrics at Frequency Range 100 MHz - 20 GHz », in 2006 International Conférence on Micro waves, Radar & Wireless Communications, mai 2006, p. 232-235. doi: 10.1109 / MIKON.2006.4345157.

Claims

1.

2.

3.

4. Claims A method for determining a permittivity spectrum of a transmission line, the method comprising the steps of: - Obtain (301) a frequency reflectogram for a transmission line, - Determine (303), from the frequency reflectogram, an estimate of the transfer function of the transmission line, - Calculate (304,305), from the phase of the transfer function, the real and / or imaginary part of a permittivity spectrum. A method of determining a permittivity spectrum according to claim 1 further comprising a step of: - Estimate (302), from the measurement, a first reflection coefficient at the input of the noisy transmission line and / or a second reflection coefficient at the input of the non-noisy transmission line, - The estimate (303) of the transfer function of the transmission line being further determined from the first noisy reflection coefficient and / or the second non-noisy reflection coefficient. Method for determining a permittivity spectrum according to claim 2 in which the step of estimating (302) a first reflection coefficient at the input of the noisy transmission line comprises the sub-steps of: - Apply an inverse Fourier transform to the frequency reflectometry measurement, - Remove from the measurement the peak corresponding to the end of the transmission line, - Apply a direct Fourier transform to the result obtained. A method of determining a permittivity spectrum according to any one of claims 2 or 3 wherein the step of estimating (302) a second reflection coefficient at the input of the non-noisy transmission line is achieved by calculating an average of the frequency reflectometry measurement over a predefined low frequency interval.

5. Method for determining a permittivity spectrum according to any one of the preceding claims further comprising a step of: - Calculating (305), from the real part of the permittivity spectrum and an estimate of the attenuation of the transmission line or a function of said attenuation or of the modulus of the transfer function, the imaginary part of the permittivity spectrum.

6. Method for determining a permittivity spectrum according to claim 5 comprising the steps of: - Determining (601) a first estimate of the attenuation of the transmission line over a first low frequency interval from the frequency reflectometry measurement or the transfer function and the length of the transmission line, - Estimating (602), from the first attenuation estimate and the real part of the permittivity spectrum, a vector k which is a function of the frequency, - Determining (603) a second estimate of the attenuation of the transmission line over the entire frequency band from the transfer function of the transmission line and the length of the transmission line, - Calculating (604) the imaginary part of the permittivity spectrum from the second estimate of the attenuation, from said estimated vector k and from the real part of the permittivity spectrum.

7. A method for determining a permittivity spectrum according to claim 6 wherein the step of estimating (602) a vector k as a function of frequency comprises the steps of: Calculate a first estimate of the vector k from the first estimate of the attenuation and the real part of the permittivity spectrum, - Apply a regression function to the first estimate of the vector k, the regression function depending at least on the square root of the frequency.

8. A method for determining a permittivity spectrum according to any one of claims 5 to 7 wherein the real part of the permittivity spectrum is taken equal to a predefined constant value.

9. Method for determining a permittivity spectrum according to any one of the preceding claims further comprising a step of determining a likelihood coefficient (306) of the calculated permittivity spectrum consisting of: - Determining (801,802,803,804) a new estimate of a frequency reflectogram from the calculated permittivity spectrum, - Calculating (805) a likelihood coefficient reflecting the difference between the frequency reflectometry measurement and the new estimate of the frequency reflectogram.

10. Method for determining a permittivity spectrum according to claim 9 wherein the step of determining a new estimate of a frequency reflectogram comprises the sub-steps of: - Determining (801) an estimate of the characteristic impedance of the transmission line, - Determining (802) an estimate of a geometric factor from the characteristic impedance and the real part of the permittivity spectrum, - Determining (803) an estimate of the RLCG parameters of the transmission line from the geometric factor and the permittivity spectrum, - Determining (804) the estimate of the frequency reflectogram from the estimated RLCG parameters.

11. A method of determining a permittivity spectrum according to any preceding claim wherein the line of transmission is composed of two sections of lines of different permittivities, the calculated permittivity spectrum corresponds to an average complex permittivity for the transmission line, the method further comprises the steps of: - Receiving a first complex permittivity value corresponding to a first section of the line, - Determining a second complex permittivity value ^2 corresponding to a second section of the line by means of the following relation: = + )e,) < with e the complex permittivity spectrum, l the length of the transmission line, 1} the length of the first section and F a measurement of the reflection coefficient at the interface between the two sections, determined from the frequency reflectogram.

12. System for determining a permittivity spectrum comprising measuring equipment configured to carry out a frequency reflectometry measurement on a transmission line and a processing unit configured to execute the steps of the method according to any one of the preceding claims.

13. Computer program comprising instructions for carrying out the steps of the method according to any one of claims 1 to 11

14. A processor-readable recording medium having recorded thereon a program comprising instructions for executing a method according to any one of claims 1 to 11, when the program is executed by a processor.

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