Estimation method of equivalent relative permittivity for parallel-pair multi-core cables

Abstract

This invention relates to a method for estimating the equivalent relative permittivity of parallel-pair multi-core cables, solving the problem of non-invasive, rapid, and non-destructive testing of the equivalent permittivity of cables. It belongs to the field of cable parameter measurement technology. The invention includes: Step 1, fabricating a cable sample of length l; Step 2, measuring the crosstalk spectrum of the cable sample using a vector network analyzer; Step 3, identifying the maxima and minima in the crosstalk spectrum, calculating the average frequency difference Δf between the maxima and minima, and obtaining an estimated value of the equivalent relative permittivity of the cable sample based on the average frequency difference, where c represents the speed of light in a vacuum. This invention calculates the relative permittivity by measuring the crosstalk amplitude spectrum between the cores of shielded parallel-pair cables, without destroying the cable structure to fabricate samples of the cable insulation material, thus enabling non-invasive, rapid, and non-destructive testing of the equivalent permittivity of cables.

Description

Technical Field

[0001] This invention relates to a method for estimating the equivalent relative permittivity of parallel-pair multi-core cables, belonging to the field of cable parameter measurement technology. Background Technology

[0002] The equivalent relative permittivity (ERP) of high-speed data cables is a crucial parameter that directly determines the wave velocity and time delay within the cable. Furthermore, the ERP plays a vital role in estimating cable quality consistency and performance degradation. On one hand, the ERP of newly manufactured cables is primarily influenced by the quality of the cable materials and the processing steps during manufacturing; therefore, the ERP can serve as a basis for judging the quality consistency between different batches of cables. On the other hand, during use, cables are subjected to mechanical shocks, excessive temperature rise, and other factors, which can alter their mechanical structure and material properties, leading to degradation of performance parameters, including the ERP. Therefore, the ERP can also serve as an important parameter characterizing the performance degradation of cables during service. Traditional low-frequency dielectric constant calculation methods use the parallel plate capacitance method, which requires fabricating the test material into a cylindrical sample and inserting it into a clamp composed of parallel plates. The relative permittivity is calculated by measuring the capacitance of the resulting capacitor. High-frequency methods can employ the transmission line method, which also requires inserting a cylindrical sample into a coaxial clamp and calculating the relative permittivity by measuring the scattering parameters after sample insertion. When using these methods to test the dielectric constant of cable insulation materials, the material to be tested needs to be made into a sample of a specific shape. This not only causes irreversible damage to the cable under test, rendering it unable to function properly, but the sample processing may also affect the dielectric parameters of the material, causing the test value to deviate from the actual value. Therefore, the most ideal method for measuring the dielectric constant of cable insulation should utilize the structural characteristics of the cable and calculate its dielectric constant through appropriate transmission characteristics. Based on the structural characteristics of coaxial cables, the IEC 61196-1-125 standard describes a method for calculating its equivalent relative dielectric constant using the phase difference between the two ends of the cable; however, this method is not suitable for non-coaxial cables with poor uniformity. Summary of the Invention

[0003] To address the problem of how to achieve non-invasive, rapid, and non-destructive testing of the equivalent dielectric constant of cables, this invention provides a method for estimating the equivalent relative dielectric constant of parallel multi-core cables.

[0004] The present invention provides a method for estimating the equivalent relative permittivity of a parallel-pair multi-core cable, comprising:

[0005] Step 1: Make a cable sample with a length of l;

[0006] Step 2: Measure the crosstalk spectrum of the cable sample using a vector network analyzer;

[0007] Step 3: Identify the maxima and minima in the crosstalk spectrum, calculate the average frequency difference Δf between the maxima and minima, and obtain an estimate of the equivalent relative permittivity of the cable sample based on the average frequency difference.

[0008]

[0009] c represents the speed of light in a vacuum.

[0010] Preferably, in step 3, the average frequency difference is:

[0011]

[0012] Arrange the identified s maximum or minimum points in ascending order to form a frequency point sequence f. i , i = 1, 2, ..., s, where s represents the number of local maxima or minima;

[0013] Preferably, in step 3, the maximum point n in the crosstalk spectrum is identified. max or the minimum point n min satisfy:

[0014] A(n max )≥max{A(n max -t:n max +t)}

[0015] A(n min )≤min{A(n min -t:n min +t)}

[0016] Where A(n1:n2) represents the set of crosstalk amplitudes at the n1 to n2 frequency points, t represents the threshold of the extreme point search range, and A(n max ) represents the maximum point n max The crosstalk amplitude, A(n) min ) represents the local minimum point n min The crosstalk amplitude.

[0017] Preferably, in step 3, the threshold t for the extreme point search range satisfies:

[0018]

[0019] N represents the total number of frequency points sampled by the vector network analyzer, f M f represents the upper limit of the frequency range to be estimated. m ε represents the lower limit of the frequency range to be estimated. rM This represents the upper limit of the equivalent dielectric constant.

[0020] Preferably, in step 3, if the number s of the maximum or minimum points identified in the crosstalk spectrum according to the extreme point search range threshold t does not match the expectation, then the total number of frequency points N sampled by the vector network analyzer is increased.

[0021] Preferably, in step 1, the length l is:

[0022]

[0023] f m ε represents the lower limit of the frequency range to be estimated. rM ε represents the upper limit of the equivalent dielectric constant. rm This represents the lower limit of the equivalent dielectric constant.

[0024] The beneficial effects of this invention are that the method for measuring the average equivalent relative permittivity within a certain frequency range calculates the relative permittivity by measuring the crosstalk amplitude spectrum between shielded parallel cable cores. This method does not require damaging the cable structure to create samples of the cable insulation material, and can achieve non-invasive, rapid, and non-destructive testing of the cable's equivalent permittivity. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the measurement circuit of the present invention;

[0026] Figure 2 Example of a connector for connecting the vector network and the cable;

[0027] Figure 3 This is a schematic diagram of local disturbances in the crosstalk spectrum, with the horizontal axis representing frequency and the vertical axis representing crosstalk amplitude.

[0028] Figure 4 The graph shows the crosstalk spectrum measured at 25℃ and the distribution of the identified maximum points. The horizontal axis represents frequency and the vertical axis represents crosstalk amplitude.

[0029] Figure 5 The plot shows the equivalent relative permittivity calculated at different temperatures. The horizontal axis represents temperature, and the vertical axis represents the equivalent relative permittivity. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0033] This implementation calculates the equivalent relative permittivity of parallel-pair cables based on crosstalk spectrum: A shielded parallel-pair cable of a certain length can be considered a typical three-conductor transmission line system, and its crosstalk amplitude is affected by frequency. When the cable transmits high-frequency electromagnetic waves, the cable is an electrical long line, and the wave process on the cable cannot be ignored. The crosstalk signal near the crosstalk line is affected by the superposition of waves on the cable, exhibiting an approximately periodic relationship with frequency. This manifests as a periodic change in crosstalk amplitude with frequency, and the period of this change is directly related to the wavelength of the electromagnetic wave on the cable, i.e., the equivalent relative permittivity. Due to the influence of cable attenuation and arrangement, the crosstalk amplitude spectrum is not a perfectly periodic spectrum. The frequency period of the crosstalk spectrum can be estimated by the average interval between the maxima or minima of the crosstalk spectrum within a certain frequency range, and then the average equivalent relative permittivity of the cable within that frequency range can be estimated.

[0034] Proof of the periodic variation of the amplitude of the near-end crosstalk spectrum of three conductors with frequency under lossless conditions, ignoring dispersion effects:

[0035] Consider the problem of lossless uniform three-conductor transmission lines, and define:

[0036]

[0037]

[0038]

[0039]

[0040] L and C represent the transmission line current vector, transmission line voltage vector, transmission line inductance parameter matrix per unit length, and transmission line capacitance parameter matrix per unit length, respectively. These represent the current phasors at position z on the crosstalk transmitting line and the crosstalk receiving line, respectively. Let l represent the voltage phasors at position z on the crosstalk transmit line and the crosstalk receive line, respectively; G l m l R These represent the self-inductance of the crosstalk transmitting line, the self-inductance of the crosstalk receiving line, and the mutual inductance between the crosstalk transmitting line and the crosstalk receiving line, respectively; c G c m c RThese represent the self-capacitance of the crosstalk transmitting line, the self-capacitance of the crosstalk receiving line, and the mutual capacitance between the crosstalk transmitting line and the crosstalk receiving line, respectively.

[0041] Then the lossless three-conductor transmission line equation in the frequency domain is:

[0042]

[0043]

[0044] Furthermore, the terminal source and impedance matrix are defined:

[0045]

[0046]

[0047]

[0048] V S R S R L These represent the source voltage vector, the source resistance vector, and the load resistance vector, respectively. R S R NE R L R FE These represent the voltage at the source end of the crosstalk transmitter line, the output resistance at the source end of the crosstalk transmitter line, the output resistance at the source end of the crosstalk receiver line, the input resistance at the load end of the crosstalk transmitter line, and the input resistance at the load end of the crosstalk receiver line, respectively.

[0049] Then the solution for a transmission line of length L satisfies the termination condition:

[0050]

[0051]

[0052] The transmission line equations are now decoupled, and the chain parameter matrix can be obtained from (5) and (6):

[0053]

[0054] in:

[0055] Φ 11 =cos(βL)12 (13)

[0056]

[0057]

[0058] Φ 22 =cos(βL)12 (16)

[0059] β represents the propagation constant of the three-conductor transmission line system, and 12 represents the second-order identity matrix.

[0060] Combining the terminal conditions (10) and (11), we can obtain:

[0061]

[0062]

[0063] For (17), if the resistances between the two load wires and ground are equal, both being R, then (17) becomes:

[0064]

[0065] Dividing both sides by R, we get:

[0066]

[0067] Let R approach positive infinity, which is equivalent to the case where the load terminals of both lines are open-circuited. The above equation becomes:

[0068]

[0069] Expanded to:

[0070]

[0071] Considering wave speed Using Cramer's rule, the crosstalk receiver current can be easily calculated:

[0072]

[0073]

[0074] B = c m cos(βL) + jvsin(βL)(c G +c m )c m (R S -R NE (25)

[0075] remember Let the electrical angle of the cable be:

[0076]

[0077]

[0078]

[0079] Ignoring dispersion effects, V R(0) is a periodic function of θ with period π, that is, a function of L with period λ / 2, and with respect to frequency. with It is a periodic function.

[0080] The method for estimating the equivalent relative permittivity of parallel-pair multi-core cables in this embodiment includes:

[0081] Step 1: Determine the length l of the cable sample based on the required estimated frequency band, and make the cable sample;

[0082] Step 2: Measure the crosstalk spectrum of the cable sample using a vector network analyzer;

[0083] Step 3: Identify the maxima and minima in the crosstalk spectrum, calculate the average frequency difference Δf between the maxima and minima, and obtain an estimate of the equivalent relative permittivity of the cable sample based on the average frequency difference.

[0084] In this embodiment, based on the conclusion that the amplitude of the crosstalk spectrum changes periodically with frequency, and considering that the period of the frequency change is directly related to the wavelength of the electromagnetic wave on the cable, i.e., the equivalent relative permittivity, it can be determined that the average frequency difference between the extreme points of the crosstalk spectrum satisfies the following relationship:

[0085]

[0086] Easy to obtain:

[0087]

[0088] c represents the speed of light in a vacuum.

[0089] This embodiment calculates the relative permittivity by measuring the crosstalk amplitude spectrum between the shielded parallel cable cores. It does not require damaging the cable structure to make samples of the cable insulation material, and can achieve non-invasive, rapid and non-destructive testing of the equivalent permittivity of the cable.

[0090] In step 1 of this embodiment, a parallel-pair cable sample is fabricated. The parallel-pair cable used needs to include a shielding layer to form a three-conductor system, thus preventing crosstalk. Assume the frequency range to be estimated [f] m ,f M ], then generally f M <10f m This ensures a uniform and sufficient number of frequency points between adjacent spectral maxima or minima. The length of the cable sample is determined by the lower limit f of the frequency range to be estimated. m Determine, and estimate using the following formula:

[0091]

[0092] In the formula, l represents the length of the cable sample to be made; c represents the speed of light in a vacuum, approximately 3 × 10⁻⁶. 8 m / s; ε rM ε represents the upper limit of the equivalent dielectric constant; rm This represents the lower limit of the equivalent dielectric constant. The upper and lower limits of the equivalent dielectric constant are ε. rM and ε rm It can be estimated from the type of insulation material or the nominal wave velocity of the cable.

[0093] Based on the calculated cable length, a cable sample is made. One end is cut open by about 1cm to separate two single-core cables and the shielding layer. An appropriate length of insulation is removed from the single-core cables to expose the conductors, which facilitates connection to the vector network analyzer port.

[0094] In step 2 of this embodiment, the circuit diagram for crosstalk spectrum measurement is as follows: Figure 1 As shown in the diagram. At one end of the cable, the two core wires C and V are connected via connectors to the signal lines of the two ports, Port 1 and Port 2, of the vector network analyzer, respectively. The insulation layer G is connected via connectors to the ground wires of the two ports of the vector network analyzer, while the other end of the cable is completely open.

[0095] The connector serves to convert the coaxial port of the vector network analyzer to a shielded parallel port on the cable, while also reducing electromagnetic wave reflection and enhancing the accuracy of crosstalk spectrum measurement results. The connector can be fabricated using a PCB board, with SMA connectors and terminal blocks at both ends. The transmission line can be designed as a short 50Ω microstrip line to match the vector network analyzer. Figure 2 As shown.

[0096] After the circuit is built, the crosstalk spectrum can be measured using a vector network analyzer. When configuring the vector network analyzer, its upper and lower frequency limits are set to f. M and f m The number of frequency sweep points should be as large as possible, the frequency sweep mode should be set to linear sweep, and the signal power should be selected as the maximum power within the selectable range. If according to... Figure 1 If the connection is made in the manner shown, then S21 measured by the vector network analyzer is the crosstalk spectrum.

[0097] In step 3 of this embodiment, after measuring the S21 data and near-end crosstalk spectrum from the vector network analyzer, the equivalent relative permittivity of the cable can be obtained through data processing. First, the maximum (or minimum) points in the crosstalk spectrum are identified, and then the average frequency difference between these extreme points is calculated to estimate the wave velocity within a certain frequency range and then calculate the equivalent permittivity.

[0098] Step 31: Identify extreme points:

[0099] Ideally, the near-end crosstalk spectrum is monotonic between the maximum and minimum points to be identified. Considering that the crosstalk data measured by the vector network analyzer at different frequency points are not equal with a probability of 1, the condition satisfied by the maximum (minimum) point is that the crosstalk amplitude at this point is greater than (less than) the crosstalk amplitudes of the two points to its left and right, that is:

[0100] A(n max -1)<A(n max )>A(n max +1) (32)

[0101] A(n min -1)>A(n min )<A(n min +1) (33)

[0102] In the formula, A(n) represents the crosstalk amplitude at the nth frequency point, and n is the index of the discrete frequency sweep points from smallest to largest; n max Indicates the index of the maximum point; n max Indicates the index of the local minimum point.

[0103] In reality, due to factors such as unevenness caused by the cable's manufacturing process, reflections between connection points, and external electromagnetic interference, the crosstalk spectrum may exhibit slight fluctuations, such as... Figure 3 As shown in the circle, the point that causes the satisfaction of equation (32) or (33) is not necessarily the point that is expected to be identified.

[0104] Considering that such jitter points are local maximum (minimum) points within a very small surrounding area, and the extreme points to be identified are in the vicinity, the methods of equations (32) and (33) can be improved so that the extreme points satisfy:

[0105] A(n max )≥max{A(n max -t:n max +t)} (34)

[0106] A(n min )≤min{A(n min -t:n min +t)} (35)

[0107] In the formula, A(n1:n2) represents the set of crosstalk amplitudes at the n1 to n2 frequency points; t represents the search range for extreme points.

[0108] The selection of the search range t is crucial for the successful identification of extrema: if t is too small, interference from jittering points cannot be effectively eliminated; if t is too large, exceeding the frequency interval between some adjacent extrema, some expected extrema may be missed. Both situations will lead to errors in the estimated equivalent dielectric constant. t can be selected according to the following formula:

[0109]

[0110] In the formula, N represents the total number of frequency points sampled by the vector network analyzer.

[0111] The number of frequency points to be identified can be manually counted by observing the crosstalk spectrum. If the number of extreme points identified according to the t selected in (36) does not match the expectation, it indicates that the total number of sampling points N of the vector network analyzer is insufficient. The total number of frequency points N sampled by the vector network analyzer should be increased.

[0112] Step 32: Calculate the equivalent relative permittivity:

[0113] Arrange the identified s maximum or minimum points in ascending order to form a frequency point sequence f. i :

[0114] f1 < f2 < ... < f s-1 <f s (37)

[0115] i = 1, 2, ..., s, where s represents the number of local or minimum points;

[0116] The subscript i represents the independent variable, and the frequency point f represents the frequency point. i Let be the dependent variable, and consider fitting it as:

[0117] f i =ai+b (38)

[0118] This is a typical linear regression problem. The result of fitting using the least squares method is:

[0119]

[0120]

[0121] in:

[0122]

[0123]

[0124] Clearly, the average frequency difference to be determined is:

[0125]

[0126] get:

[0127]

[0128] Based on Δf, the estimated value of the equivalent relative permittivity of the cable sample is calculated using equation (30).

[0129] Experimental verification: Taking a parallel-pair cable insulated with ePTFE (expanded polytetrafluoroethylene) as an example, we want to estimate its average equivalent relative permittivity in the range of 200MHz to 1.2GHz. According to the parameter data provided by the manufacturer, its relative permittivity is in the range [1.0, 2.0]. After calculation according to (31), the length of the sample is selected as l = 5m, and the maximum number of sampling points of the vector network analyzer used is 4001.

[0130] The cable was placed in a constant temperature chamber, and the crosstalk measurement circuit was connected. The near-end crosstalk spectrum of the cable was measured at several discrete temperature points ranging from 25 to 140°C. The near-end crosstalk spectrum and the identified crosstalk maxima at t=20 and 25°C are shown below. Figure 4 As shown.

[0131] The equivalent relative permittivity at various temperatures was analyzed and calculated using the same method, resulting in the following curve showing the relationship between the equivalent relative permittivity of the cable and temperature: Figure 5 As shown, the results are consistent with the known temperature variation characteristics of the dielectric constant of ePTFE.

[0132] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for estimating the equivalent relative permittivity of parallel-pair multi-core cables, characterized in that, The method includes: Step 1: Make a piece with a length of... Cable samples; Step 2: Measure the crosstalk spectrum of the cable sample using a vector network analyzer; Step 3: Identify the maxima and minima in the crosstalk spectrum and calculate the average frequency difference between the maxima and minima. The estimated value of the equivalent relative permittivity of the cable sample is obtained based on the average frequency difference. : This represents the speed of light in a vacuum. In step 3, the average frequency difference is: The identified A sequence of frequency points, arranged from smallest to largest, consisting of maxima or minima. , , Indicates the number of maximum or minimum points; , .

2. The method for estimating the equivalent relative permittivity of a parallel-pair multi-core cable according to claim 1, characterized in that, In step 3, the maxima in the crosstalk spectrum are identified. or minimum point satisfy: Where A(n1:n2) represents the set of crosstalk amplitudes at the n1th to n2th frequency points, and t represents the threshold for the extreme point search range. Represents the maximum point The crosstalk amplitude, Represents the minimum point The crosstalk amplitude.

3. The method for estimating the equivalent relative permittivity of parallel-pair multi-core cables according to claim 2, characterized in that, In step 3, the extreme point search range threshold t satisfies: N represents the total number of frequency points sampled by the vector network analyzer, f M f represents the upper limit of the frequency range to be estimated. m This indicates the lower limit of the frequency range to be estimated. This represents the upper limit of the equivalent dielectric constant.

4. The method for estimating the equivalent relative permittivity of a parallel-pair multi-core cable according to claim 3, characterized in that, In step 3, if the number of maxima or minima in the crosstalk spectrum is identified according to the extreme point search range threshold t... If the result is not as expected, increase the total number of frequency points N sampled by the vector network analyzer.

5. The method for estimating the equivalent relative permittivity of a parallel-pair multi-core cable according to claim 1, characterized in that, In step 1, length : This indicates the lower limit of the frequency range to be estimated. This represents the upper limit of the equivalent dielectric constant. This represents the lower limit of the equivalent dielectric constant.

6. The method for estimating the equivalent relative permittivity of a parallel-pair multi-core cable according to claim 5, characterized in that, In step 1, the shielding layer and two single-core cables are separated at one end of the cable sample. An appropriate length of insulation layer is removed from the single-core cables to expose the conductors for connection to the vector network analyzer.

7. The method for estimating the equivalent relative permittivity of a parallel-pair multi-core cable according to claim 6, characterized in that, In step 2, the conductors of the two single-core cables C and V at one end of the cable sample are connected to the signal lines of Port 1 and Port 2 of the vector network analyzer via connectors. The insulation layer G of the two single-core cables C and V is connected to the ground wires of Port 1 and Port 2 of the vector network analyzer via connectors. The other end of the cable sample is completely open circuit.

8. The method for estimating the equivalent relative permittivity of a parallel-pair multi-core cable according to claim 7, characterized in that, The connector is made of PCB board, with SMA connector and terminal block at both ends, and the transmission line is 50 Ω microstrip line.

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