CN115993485A - Estimation Method of Equivalent Relative Permittivity of Parallel Pair Multi-Core Cables - Google Patents

Abstract

The parallel-to-multi-core cable equivalent relative dielectric constant estimation method solves the problem of how to realize non-invasive rapid nondestructive detection of the cable equivalent dielectric constant, and belongs to the technical field of cable parameter measurement. The invention comprises the following steps: step 1, manufacturing a cable sample with the length of l; step 2, measuring crosstalk spectrum of the cable sample by using a vector network analyzer; step 3, identifying maximum points or minimum points in the crosstalk spectrum, calculating average frequency difference delta f between the maximum points or the minimum points, and obtaining an estimated value of the equivalent relative dielectric constant of the cable sample according to the average frequency difference

c represents the speed of light in vacuum. The invention calculates the relative dielectric constant by measuring the crosstalk amplitude frequency spectrum between the shielded parallel pair cable core wires without damaging the cable structureThe sample of the cable insulating material is manufactured, and the non-invasive rapid nondestructive detection of the equivalent dielectric constant of the cable can be realized.

Description

Estimation method of equivalent relative dielectric constant of parallel multi-core cables

Technical Field

The invention relates to a method for estimating the equivalent relative dielectric constant of a parallel multi-core cable, belonging to the technical field of cable parameter measurement.

Background Art

The equivalent relative dielectric constant of high-speed data cables is an important parameter that directly determines the size of the wave velocity and time delay in the cable. In addition, the equivalent relative dielectric constant also plays an important role in estimating the quality consistency and performance degradation of cables. On the one hand, the equivalent relative dielectric constant of newly produced cables is mainly affected by the quality of cable materials and the process steps in the processing process. Therefore, the equivalent relative dielectric constant can be used as a basis for judging the quality consistency between different batches of cables; on the other hand, the cable may be affected by mechanical shock, excessive temperature rise and other factors during use, and its mechanical structure and material properties may change, resulting in the degradation of its performance parameters including the equivalent relative dielectric constant. Therefore, the equivalent relative dielectric constant can also be used as an important parameter to characterize the performance degradation of cables in service. The traditional low-frequency dielectric constant measurement method is the flat plate capacitor method, which requires the material to be tested to be made into a cylindrical sample, inserted into a fixture composed of parallel plates, and the relative dielectric constant is calculated by measuring the capacitance of the capacitor; the high frequency can use the transmission line method, which also requires the cylindrical sample to be inserted into a coaxial fixture, and the relative dielectric constant is calculated by measuring the scattering parameters after the sample is inserted. When these methods are used to detect the dielectric constant of cable insulation materials, the material to be tested needs to be made into a sample of a specific shape, which will not only cause irreversible damage to the cable to be tested, making it impossible for it to work normally, but also the process of processing the sample may 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 be to use 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, but this method is not suitable for non-coaxial cables with poor uniformity.

Summary of the invention

In order to solve the problem of how to realize non-invasive rapid non-destructive detection of equivalent dielectric constant of cables, the present invention provides a method for estimating equivalent relative dielectric constant of multi-core cables in parallel.

A method for estimating the equivalent relative dielectric constant of a multi-core cable in parallel of the present invention comprises:

Step 1, making a cable sample with a length of l;

Step 2: Use a vector network analyzer to measure the crosstalk spectrum of the cable sample;

Step 3: Identify the maximum or minimum points in the crosstalk spectrum, calculate the average frequency difference Δf between the maximum or minimum points, and obtain an estimated value of the equivalent relative dielectric constant of the cable sample based on the average frequency difference.

c is the speed of light in vacuum.

Preferably, in step 3, the average frequency difference is:

Arrange the identified s maximum or minimum points from small to large into a frequency point sequence _fi , i = 1, 2, ..., s, s represents the number of maximum or minimum points;

Preferably, in step 3, a maximum point n _max or a minimum point n _min in the crosstalk spectrum is identified that satisfies:

A(n _max )≥max{A(n _max -t:n _max +t)}

A(n _min )≤min{A(n _min -t:n _min +t)}

Wherein, A(n ₁ :n ₂ ) represents the set of crosstalk amplitudes from the n _1th to the n _2th frequency points, t represents the extreme point search range threshold, A(n _max ) represents the crosstalk amplitude of the maximum point n _max , and A(n _min ) represents the crosstalk amplitude of the minimum point n _min .

Preferably, 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, _fM represents the upper limit of the frequency range to be estimated, _fm represents the lower limit of the frequency range to be estimated, and _εrM represents the upper limit of the equivalent dielectric constant.

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

Preferably, in step 1, the length l is:

f _m represents the lower limit of the frequency range to be estimated, ε _rM represents the upper limit of the equivalent dielectric constant, and ε _rm represents the lower limit of the equivalent dielectric constant.

The beneficial effects of the present invention are as follows: the method for measuring the average equivalent relative dielectric constant within a certain frequency range of the present invention calculates the relative dielectric constant by measuring the crosstalk amplitude spectrum between the shielded parallel cable cores, and there is no need to destroy the cable structure to prepare samples of the cable insulation material, thereby realizing non-invasive, rapid and non-destructive detection of the equivalent dielectric constant of the cable.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a measuring circuit of the present invention;

Figure 2 is an example of a connector between a vector network and a cable;

FIG3 is a schematic diagram of a local disturbance in a crosstalk spectrum, where the abscissa is the frequency and the ordinate is the crosstalk amplitude;

FIG4 is a crosstalk spectrum diagram measured at 25°C and a distribution diagram of the identified maximum points, where the horizontal axis is the frequency and the vertical axis is the crosstalk amplitude;

FIG5 is a scatter plot of the equivalent relative dielectric constant calculated at different temperatures, where the abscissa is temperature and the ordinate is the equivalent relative dielectric constant.

DETAILED DESCRIPTION

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

This implementation method calculates the equivalent relative dielectric constant of parallel cables based on the crosstalk spectrum: a certain length of parallel cables with a shielding layer can be regarded as a typical three-conductor transmission line system, and its crosstalk amplitude is affected by the 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 near-end crosstalk signal of the crosstalk-affected line is affected by the superposition of the waves on the cable, showing an approximate periodic change with the frequency, which is manifested as a periodic change of the crosstalk amplitude with the frequency. The frequency period of the change is directly related to the wavelength of the electromagnetic wave on the cable and the equivalent relative dielectric constant. Affected by the attenuation and layout of the cable, the spectrum of the crosstalk amplitude is not a perfect periodic spectrum line. The frequency period of the crosstalk spectrum can be estimated by the average interval between the maximum or minimum points of the crosstalk spectrum in a certain frequency range, and then the average equivalent relative dielectric constant of the cable in a certain frequency range can be estimated.

Proof of the periodic variation of the amplitude of the three-conductor near-end crosstalk spectrum with frequency under lossless conditions, ignoring the dispersion effect:

Consider a lossless uniform three-conductor transmission line problem and define:

L、C分别表示传输线电流向量、传输线电压向量、传输线单位长度电感参数矩阵、传输线单位长度电容参数矩阵；

分别表示串扰发射线和串扰接收线上位置z处的电流相量；

分别表示串扰发射线和串扰接收线上位置z处的电压相量；l_G、l_m、l_R分别表示串扰发射线的自电感、串扰接收线的自电感、串扰发射线与串扰接收线之间的互电感；c_G、c_m、c_R分别表示串扰发射线的自电容、串扰接收线的自电容、串扰发射线与串扰接收线之间的互电容；

L and C represent the transmission line current vector, the transmission line voltage vector, the transmission line unit length inductance parameter matrix, and the transmission line unit length capacitance parameter matrix respectively;

represent the current phasors at position z on the crosstalk transmitting line and the crosstalk receiving line respectively;

Respectively represent the voltage phasors at position z on the crosstalk transmitting line and the crosstalk receiving line; l _G , l _m , l _R 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; c _G , _cm , c _R 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;

Then there is a lossless three-conductor transmission line equation in the frequency domain:

The terminal source and impedance matrix are defined as follows:

R_S、R_NE、R_L、R_FE分别表示串扰发射线源端电压、串扰发射线源端输出电阻、串扰接收线源端输出电阻、串扰发射线负载端输入电阻、串扰接收线负载端输入电阻。V _S , R _S , and _RL represent the source terminal voltage vector, source terminal resistance vector, and load terminal resistance vector, respectively;

R _S , R _NE , R _L , and R _FE represent the voltage at the source end of the crosstalk transmission line, the output resistance at the source end of the crosstalk transmission line, the output resistance at the source end of the crosstalk receiving line, the input resistance at the load end of the crosstalk transmission line, and the input resistance at the load end of the crosstalk receiving line, respectively.

Then the solution for a transmission line of length L satisfies the terminal condition:

The transmission line equation is decoupled at this time, and the chain parameter matrix can be solved by (5) (6):

in:

Φ ₁₁ ＝cos(βL)1 ₂ (13)

Φ ₂₂ = cos(βL)1 ₂ (16)

β represents the propagation constant of the three-conductor transmission line system, and 1 ₂ represents the second-order unit matrix.

Combining the terminal conditions (10) and (11) we can obtain:

For (17), the resistance between the two load wires and the ground is equal, both R, then (17) becomes:

Dividing both sides by R, we get:

Let R tend to positive infinity, which is equivalent to the case where the load ends of the two wires are open circuited, and the above equation becomes:

Expands to:

利用Cramer法则，容易求出串扰接收端电流：Considering the wave speed

Using Cramer's law, it is easy to find the crosstalk receiving end current:

B＝c _m cos(βL)+jvsin(βL)(c _G +c _m )c _m ( _RS -R _NE ) (25)

为电缆的电角度，则：remember

is the electrical angle of the cable, then:

的以

为周期的函数。Ignoring the dispersion effect, _VR (0) is a periodic function with a period of π about θ, which is also a periodic function with a period of λ/2 about L.

of

is a function of the period.

The method for estimating the equivalent relative dielectric constant of a multi-core cable in parallel of this embodiment includes:

Step 1: Determine the length l of the cable sample according to the required estimated frequency band, and make the cable sample;

Step 2: Use a vector network analyzer to measure the crosstalk spectrum of the cable sample;

Step 3: Identify the maximum or minimum points in the crosstalk spectrum, calculate the average frequency difference Δf between the maximum or minimum points, and obtain an estimated value of the equivalent relative dielectric constant of the cable sample based on the average frequency difference.

In this implementation, based on the conclusion that the amplitude of the crosstalk spectrum changes periodically with frequency, the changing frequency period is directly related to the wavelength of the electromagnetic wave on the cable, that is, the equivalent relative dielectric constant. It can be determined that the average frequency difference between the extreme points of the crosstalk spectrum satisfies the following relationship:

Easy to get:

c is the speed of light in vacuum.

This embodiment calculates the relative dielectric constant of a shielded parallel pair of cables by measuring the crosstalk amplitude spectrum between the core wires. There is no need to destroy the cable structure to make samples of the cable insulation material, and non-invasive, rapid and non-destructive detection of the equivalent dielectric constant of the cable can be achieved.

In step 1 of this embodiment, a parallel pair cable sample is prepared. The parallel pair cable used needs to include a shielding layer to form a three-conductor system to generate crosstalk. Assuming the frequency range to be estimated is [f _m ,f _M ], then generally f _M <10f _m to ensure that there are uniform and sufficient frequency points between adjacent spectrum maxima or minima. The length of the cable sample is determined by the lower limit of the frequency range to be estimated, f _m , and is estimated using the following formula:

In the formula, l represents the length of the cable sample to be manufactured; c represents the speed of light in a vacuum, which is approximately 3×10 ⁸ m/s; ε _rM represents the upper limit of the equivalent dielectric constant; and ε _rm represents the lower limit of the equivalent dielectric constant. The upper and lower limits of the equivalent dielectric constant, ε _rM and ε _rm, can be estimated from the type of insulating material or the nominal wave velocity of the cable.

A cable sample was made based on the calculated cable length. One end was cut open by about 1 cm to separate the two single-core cables and the shielding layer. An appropriate length of insulation outside the single-core cable was removed to expose the conductor for easy connection to the vector network analyzer port.

In step 2 of this embodiment, the circuit diagram for measuring the crosstalk spectrum is shown in Figure 1. The two core wires C and V at one end of the cable are respectively connected to the signal wires of the two ports Port 1 and Port 2 of the vector network analyzer through the connector, the insulation layer G is connected to the ground wires of the two ports of the vector network analyzer through the connector, and the other end of the cable is completely open.

The connector completes the conversion of the coaxial port of the vector network analyzer to the shielded parallel pair port of the cable, and at the same time reduces the reflection of electromagnetic waves and enhances the accuracy of the crosstalk spectrum measurement results. The connector can be made of PCB board, and the two ends can use SMA sockets and terminal sockets respectively. The transmission line part can be designed as a 50Ω microstrip line as short as possible to match the vector network analyzer, as shown in Figure 2.

After the circuit is built, the crosstalk spectrum can be measured using a vector network analyzer. When configuring the vector network analyzer, set the upper and lower frequency limits to f _M and f _m , the number of sweep points should be as large as possible, the sweep mode should be set to linear sweep, and the signal power should be the maximum power within the optional range. If connected as shown in Figure 1, the S21 measured by the vector network analyzer is the crosstalk spectrum.

In step 3 of this embodiment, after measuring the S21 data and near-end crosstalk spectrum of the vector network analyzer, the equivalent relative dielectric constant of the cable can be obtained through data processing. First, the maximum (or minimum) value point in the crosstalk spectrum is 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 dielectric constant.

Step 31: Identify extreme points:

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

A(n _max -1)＜A(n _max )＞A(n _max +1) (32)

A(n _min -1)＞A(n _min )＜A(n _min +1) (33)

Where A(n) represents the crosstalk amplitude at the nth frequency point, n is the number of discrete frequency sweep points from small to large, n _max represents the number of the maximum point, and n _max represents the number of the minimum point.

In fact, due to the unevenness of the cable's own process level, reflections between connection points, external electromagnetic interference and other factors, the crosstalk spectrum may have slight jitter, as shown in the circle in Figure 3, resulting in the point that satisfies equation (32) or (33) is not necessarily the point expected to be identified.

Considering that such jitter points are local maximum (minimum) value points in a small range nearby, and the extreme value points to be identified are nearby, the methods of equations (32) and (33) can be improved, and the extreme value points satisfy:

A(n _max )≥max{A(n _max -t:n _max +t)} (34)

A(n _min )≤min{A(n _min -t:n _min +t)} (35)

Wherein, A(n ₁ :n ₂ ) represents the set of crosstalk amplitudes from the n _1th to the n _2th frequency points; t represents the extreme point search range.

The selection of the search range t is very important for the successful identification of extreme points: if t is selected too small, the interference of jitter points cannot be effectively eliminated; if t is selected too large and larger than the frequency interval between some adjacent extreme points, some extreme points expected to be identified may be missed. Both of these situations will lead to errors in the estimated equivalent dielectric constant. t can be selected according to the following formula:

Where N represents the total number of frequency points sampled by the vector network analyzer.

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

Step 32, calculate the equivalent relative dielectric constant:

Arrange the identified s maximum or minimum points from small to large into a frequency point sequence _fi :

f ₁ ＜f ₂ ＜...＜f _s-1 ＜f _s (37)

i＝1,2,…,s, s represents the number of maximum or minimum points;

The index i is the independent variable and the frequency point _fi is the dependent variable. Consider fitting it as:

_fi = ai + b (38)

This is a typical linear regression problem. The result of least squares fitting is:

in:

Obviously, the average frequency difference to be calculated is:

get:

According to Δf, the estimated value of the equivalent relative dielectric constant of the cable sample is calculated using formula (30):

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

It was placed in a constant temperature box, connected to the crosstalk measurement circuit, and the near-end crosstalk spectrum of the cable was measured at some discrete temperature points from 25 to 140°C. The near-end crosstalk spectrum at t=20, 25°C and the identified crosstalk maximum point position are shown in Figure 4.

The same method is used to analyze and calculate the equivalent relative dielectric constant at each temperature, and the relationship curve between the equivalent relative dielectric constant of the cable used and temperature is shown in Figure 5. The result is consistent with the known temperature variation characteristics of the ePTFE dielectric constant.

Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims (10)

1. A method for estimating the equivalent relative dielectric constant of a multi-core cable in parallel, characterized in that the method comprises: Step 1, making a cable sample with a length of l; Step 2: Use a vector network analyzer to measure the crosstalk spectrum of the cable sample; Step 3: Identify the maximum or minimum points in the crosstalk spectrum, calculate the average frequency difference Δf between the maximum or minimum points, and obtain an estimated value of the equivalent relative dielectric constant of the cable sample based on the average frequency difference.

c is the speed of light in vacuum. 2. The method for estimating the equivalent relative dielectric constant of a parallel multi-core cable according to claim 1, wherein in step 3, the average frequency difference is:

Arrange the identified s maximum or minimum points from small to large into a frequency point sequence _fi , i = 1, 2, ..., s, s represents the number of maximum or minimum points;

3. The method for estimating the equivalent relative dielectric constant of a parallel pair of multi-core cables according to claim 1, characterized in that in step 3, the maximum point n _max or the minimum point n _min in the crosstalk spectrum is identified to satisfy: A(n _max )≥max{A(n _max -t:n _max +t)} A(n _min )≤min{A(n _min -t:n _min +t)} Wherein, A(n ₁ :n ₂ ) represents the set of crosstalk amplitudes from the n _1th to the n _2th frequency points, t represents the extreme point search range threshold, A(n _max ) represents the crosstalk amplitude of the maximum point n _max , and A(n _min ) represents the crosstalk amplitude of the minimum point n _min . 4. The method for estimating the equivalent relative dielectric constant of a parallel multi-core cable according to claim 3, 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, _fM represents the upper limit of the frequency range to be estimated, _fm represents the lower limit of the frequency range to be estimated, and _εrM represents the upper limit of the equivalent dielectric constant. 5. The method for estimating the equivalent relative dielectric constant of a parallel multi-core cable according to claim 4 is characterized in that, in step 3, if the number s of maximum points or minimum points in the crosstalk spectrum identified according to the extreme point search range threshold t does not meet expectations, the total number of frequency points N sampled by the vector network analyzer is increased. 6. The method for estimating the equivalent relative dielectric constant of a parallel pair of multi-core cables according to claim 1, characterized in that in step 1, the length l is:

f _m represents the lower limit of the frequency range to be estimated, ε _rM represents the upper limit of the equivalent dielectric constant, and ε _rm represents the lower limit of the equivalent dielectric constant. 7. The method for estimating the equivalent relative dielectric constant of a parallel multi-core cable according to claim 6 is characterized in that, in step 1, the shielding layer and two single-core cables are separated at one end of the cable sample, and an appropriate length of the insulation layer outside the single-core cable is removed to expose the conductor for connecting to a vector network analyzer. 8. The method for estimating the equivalent relative dielectric constant of a parallel multi-core cable according to claim 7 is 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 respectively connected to the signal lines of port Port 1 and port Port 2 of the vector network analyzer through a connector, and the insulation layers G of the two single-core cables C and V are respectively connected to the ground wires of port Port 1 and port Port 2 of the vector network analyzer through a connector, and the other end of the cable sample is completely open. 9. The method for estimating the equivalent relative dielectric constant of a parallel multi-core cable according to claim 8, characterized in that the connector is made of a PCB board, the two ends are respectively an SMA socket and a wiring socket, and the transmission line is a 50Ω microstrip line. 10. The method for estimating the equivalent relative dielectric constant of a parallel multi-core cable according to claim 1, characterized in that, in step 2, the upper and lower limits of the frequency when the vector network analyzer is measured are f _M and f _m respectively, the frequency sweep mode is set to linear sweep, and the signal power selects the maximum power; The frequency range to be estimated is [f _m ,f _M ], where f _M represents the upper limit of the frequency range to be estimated, and f _m represents the lower limit of the frequency range to be estimated; S21 measured by a vector network analyzer is the crosstalk spectrum.

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