CN108829963B - Method for extracting parasitic capacitance and conductance of twisted pair in conductive shell - Google Patents

Method for extracting parasitic capacitance and conductance of twisted pair in conductive shell Download PDF

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CN108829963B
CN108829963B CN201810566383.7A CN201810566383A CN108829963B CN 108829963 B CN108829963 B CN 108829963B CN 201810566383 A CN201810566383 A CN 201810566383A CN 108829963 B CN108829963 B CN 108829963B
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孙亚秀
王建丽
钱军竹
林蒙
张铭
宋文良
梁非
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Harbin Engineering University
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Abstract

A method for extracting the parasitic capacitance and conductance of a twisted pair in a conductive shell relates to the field of extracting parasitic parameters in the prediction and elimination of crosstalk of a transmission line, in particular to a method for extracting the parasitic capacitance and conductance of the twisted pair in the conductive shell. The method comprises the following steps: s1, obtaining the change of the distance h between the single wire and the central axis of the twisted pair at the cross part by establishing the approximate periodic alternate transmission model of the twisted pair, and further obtaining the distance d between the lead and the conductive shelli(ii) a change; s2, obtaining single length inductance matrix L (FS) in free space of each layer of dielectric, single length inductance matrix L (INSUL) in insulating layer, single length complex (real) capacitance matrix C (FS) in free space, and single length complex (real) capacitance matrix C (FS) in insulating layer by establishing image displacement and extracting parasitic inductance schematic diagram
Figure DDA0001684617920000011
S3, obtaining the total composite capacitance matrix by the series idea
Figure DDA0001684617920000012
And obtaining a parasitic net capacitance C and a net conductance matrix G. The invention adopts the idea of medium layering to extract, and the extracted parasitic parameters are more accurate.

Description

Method for extracting parasitic capacitance and conductance of twisted pair in conductive shell
Technical Field
The invention relates to the field of extraction of parasitic parameters in transmission line crosstalk prediction and elimination, in particular to a method for extracting parasitic capacitance and conductance of a twisted pair in a conductive shell.
Background
The electromagnetic coupling of the transmission line is embodied in the form of parasitic parameters, and in order to realize the crosstalk prediction and crosstalk elimination of the transmission line, the parasitic parameters must be obtained firstly, and the extraction problem of the parasitic parameters of the unit length of the transmission line is the basis of crosstalk analysis of the transmission line. The extraction of parasitic parameters is difficult to extract parasitic capacitance and parasitic conductance.
The electrical parameter per unit length of the classical transmission line is only a simple value in practice and can be obtained by well-established formulas. The common electrical parameters of unit length are extracted mainly by a numerical calculation method such as a moment method. A scholars, represented by professor Paul c.r, has systematically analyzed conductor electrical parameter extraction using the moment method (MoM) and proposed many effective solutions, but wiring structures are generally considered to be uniform and lossless and are generally placed on an ideal ground. When the influence of an insulating coating on crosstalk in the non-uniform transmission line is analyzed, the Sergio A. Pignari and the Giordano Spadacini adopt MoM simulation, and a direct solution of parasitic parameters under the non-uniform medium condition is not obtained. When studying the near-end crosstalk (NEXT) and far-end crosstalk (FEXT) of twisted pairs, the abbolhamid Shoory et al considers the twisted pair cross distance as zero, does not consider the non-uniformity of parasitic parameters caused by the line distance change, and considers the medium as uniform without loss, i.e., the extraction of the parasitic parameters is idealized.
Many models are established on the basis of the conditions that the distance of the cross part of the twisted pair is considered to be zero, the conductors are ideal, the surrounding medium is free of consumption and uniform, and the like, however, in practical situations, the conditions are often not met, and the extracted parasitic parameters are not accurate enough, so that the crosstalk cannot be accurately predicted and eliminated. For twisted-pair lines, the wire spacing at the crossed part is approximately linearly changed along with the position, under the condition that the medium is consumed and is non-uniform, the calculation of parasitic parameters is complex and difficult, the classical transmission line analysis method is not suitable any more, and numerical methods such as a moment method, a finite element method and the like cannot effectively solve the problem of the non-uniform multi-conductor transmission line because the calculated amount is too large. The present invention has been made in view of such circumstances, and provides a method for solving these problems. Can meet various requirements under the actual production condition. But also for any transmission line situation.
In summary, the existing literature reports that the direct extraction problem of the parasitic capacitance and conductance of the lossy non-uniform twisted pair is not researched, and the extraction method still needs to be solved.
Disclosure of Invention
The invention aims to provide a method for extracting the parasitic capacitance and conductance of a twisted pair in a non-uniform dielectric conductive shell.
A method for extracting the parasitic capacitance and conductance of twisted pair in conductive shell includes following steps:
(1) by establishing an approximate periodic alternate transmission model of the twisted pair, the change of the distance h from the single wire to the central axis of the twisted pair at the cross part is obtained, and the change of the distance di from the lead to the conductive shell is further obtained;
(2) by establishing a mirror image replacement to extract a parasitic inductance schematic diagram, a unit length self-inductance lii (FS) in a free space and a unit length mutual inductance l in the free space are obtainedij(FS), self-inductance per unit length l in insulating mediumii(INSUL), mutual inductance per unit length l in insulating mediumij(INSUL), and obtaining a single length inductance matrix L (FS) in free space of each layer of dielectric, a single length inductance matrix L (INSUL) in insulating layer, a single length capacitance matrix C (FS) in free space, and a single length capacitance matrix in insulating layer
Figure BDA0001684617900000021
(3) Obtaining the total composite capacitance matrix by the series connection idea
Figure BDA0001684617900000022
And obtaining a parasitic net capacitance C and a net conductance matrix G.
In the step (1), the method comprises
Figure BDA0001684617900000023
L(FS)C(FS)＝μ0ε0E(n)
Obtaining the capacitance matrix per unit length C (FS) in each free space and the capacitance matrix per unit length in the insulating layer
Figure BDA0001684617900000024
Where μ is the permeability of the insulating layer, μ0Is a free space magnetic permeability,
Figure BDA0001684617900000025
Is a complex dielectric constant, epsilon, of the insulating layer0Is a free space dielectric constant, E (n) is an n-order identity matrix, L (FS) is a single-length-in-free-space inductance matrix, L (INSUL) is a single-length-in-insulation inductance matrix, C (FS) is a single-length-in-free-space capacitance matrix,
Figure BDA0001684617900000026
Is a single-unit length capacitor matrix in an insulating layer.
In the step (3), the method comprises
Figure BDA0001684617900000027
Deriving an overall composite capacitance matrix
Figure BDA0001684617900000028
Wherein C (FS) is a capacitance matrix per unit length in free space,
Figure BDA0001684617900000029
Is a single-unit length capacitor matrix in an insulating layer.
In the step (2), the unit length self-inductance in the insulating medium is as follows:
Figure BDA00016846179000000210
wherein lii(INSUL) is a unit length self-inductance, r, in an insulating mediumsIs the inner radius, mu, of the conductive shell0Is the free space permeability, rwIs the radius r of the inner conductor of the twisted pairmOuter radius of the insulating layer, diIs the distance between the center of the ith wire and the central axis of the shell.
In the step (2), the mutual inductance per unit length in the insulating medium is as follows:
Figure BDA00016846179000000211
wherein lij(INSUL) is the mutual inductance per unit length, s, in an insulating medium1The distance s from the center of the wire i to the point A on the outer layer of the insulation layer of the wire j2The distance s from the mirror image center of the wire i to the point A on the outer layer of the insulating layer of the wire jijIs the distance from the center of wire i to the center of wire j, s' is the distance from the mirror image center of wire i to the center of wire j, mu0Is the free space magnetic permeability and pi is the circumferential ratio.
In the step (2), the unit length self-inductance in the free space is as follows:
Figure BDA0001684617900000031
wherein lii(FS) is the unit length self-inductance, mu, in free space0Is free space magnetic permeability, pi is circumferential ratio, rsIs the inner radius of the conductive shell, diIs the distance r between the center of the ith wire and the central axis of the shellmThe outer radius of the insulating layer.
In the step (2), the capacitance matrix c (fs) per unit length in the free space is a real matrix when the dielectric constant is a real number, and is a complex matrix when the dielectric constant is a complex number; capacitance matrix per unit length in insulating layer
Figure BDA0001684617900000032
The dielectric constant is a real matrix when the dielectric constant is real, and is a complex matrix when the dielectric constant is complex.
From the total complex capacitance
Figure BDA0001684617900000033
The expression can directly derive the net capacitance per unit length and the net conductance matrix.
Figure BDA0001684617900000034
Figure BDA0001684617900000035
The invention has the beneficial effects that:
aiming at the non-uniform medium and the complex extraction of the parasitic parameters, the invention adopts the idea of medium layering for extraction, and the extracted parasitic parameters are more accurate.
Drawings
FIG. 1 is a detailed operation flowchart
FIG. 2 is a diagram illustrating parasitic inductance extraction using mirror replacement
FIG. 3 is a cross-sectional block diagram of the total cross-sectional structure of two twisted pairs (one pair connected by a dashed line) and a single twisted pair disposed in a conductive housing
FIG. 4 is a circuit model of twisted pair approximately periodic alternate transmission
Detailed Description
The invention is further described below with reference to the accompanying drawings.
In the third drawing, 1 is a conductive shell, 2 is a free space, 3 is an insulating layer, and 4 is a conductor of a wire.
The invention is explained in detail by taking the parasitic capacitance and conductance between two pairs of twisted-pair wires coupled with each other in a conductive shell as an example, and n is 4, thus forming a 4+1 non-uniform multi-conductor transmission line model. The cross-sectional configuration of two twisted pairs with insulation disposed in a conductive housing is shown in fig. 4. ThenIn the parallel part of the twisted pair
Figure BDA0001684617900000036
Cross section tan β ═ rm/l′，
Figure BDA0001684617900000037
Wherein (i ═ 1,2,3, 4). All twisted pair conductors are copper materials, and the parameters are set as follows:
μ0＝4π×10-7，ε0＝8.854187817×10-10，ε＝3.5ε0,tanδ＝0.02,l'＝0.25cm，rw＝0.4064mm，rs＝1.778mm，rm＝0.889mm
the parasitic capacitance and conductance of the twisted-pair cable are extracted by the method of the invention, the extraction results (frequency f is fixed to 1MHz) of the parasitic capacitance and conductance at different positions of the cross part of the twisted-pair cable are shown in table 1, and different values of x represent different line distances. As can be seen from the table, the method can directly extract the parasitic capacitance and the conductance matrix of any section of the twisted pair under different frequencies, accords with the actual situation and has great reference value.
The following table shows the parasitic capacitance and conductance extraction results at different positions of the twisted pair cross section (f is 1 MHz):
Figure BDA0001684617900000041
the invention aims to solve the extraction problem of the parasitic capacitance and conductance of a twisted pair surrounded by a plurality of layers of lossy non-uniform media in a conductive shell. Especially for non-uniform media, extraction of parasitic parameters is particularly complex, and the method adopts the idea of medium layering for extraction.
The parasitic inductance, capacitance and conductance parameter matrix extracted from the multi-conductor transmission line equation is as follows:
Figure BDA0001684617900000042
Figure BDA0001684617900000043
wherein n is the number of conductive lines.
The parasitic parameters are mainly influenced by two factors, namely the change of the distance from the center of the wire to the ideal conductive shell caused by the change of the wire spacing and the nonuniformity of the medium.
An approximate periodic alternating inversion model of twisted pair lines is established as shown in fig. 1, and comprises a parallel part and a cross part, wherein half of the distance of the cross part is l'. The spacing between the twisted pairs of conductors is not fixed. The wire spacing at the crossover section varies linearly with position, resulting in non-uniformity of parasitic parameters, each of which is related to its position at the crossover section. From fig. 1, the centerline spacing h in a twisted pair is x tan β.
Let the inner radius of the conductive shell be rsThe distance between the center of the ith wire and the central axis of the shell is diThe difference in h will result in diThe difference in (c). The wire is surrounded by two layers of different media, the first layer being an insulating layer and the second layer being a free space. The wire has a consumption inhomogeneous medium parameter of
Insulating layer: ε, μ, tan δ, rw<r<rm
Free space: epsilon0，μ0，rm<r<rs
Complex dielectric constant of insulating layer
Figure BDA0001684617900000051
Wherein epsilon and epsilon0Dielectric constant of insulating layer and free space, mu and mu respectively0The magnetic permeability of the insulating layer and the free space respectively, and delta is a loss angle of the lossy insulating layer. Let the radius of the inner conductor of the twisted pair be rwThe outer radius of the insulating layer is rm. The angle between the conductors is thetaijSetting the center of a cross-section wire as Oi。
The main idea of the invention is to extract the total net capacitance and conductance matrix by using the parasitic inductance matrix of each layer of dielectric area of different sections of the twisted pair, which is specifically explained as follows:
for the case where the wire is surrounded by a circular insulating medium, there is μ ═ μ0The inductance per unit length is therefore not affected by the inhomogeneous medium, i.e. as in the case of placement in a homogeneous medium (free space). The inductance matrices per unit length in the free space and in the insulating layer are defined as L (FS), L (INSUL), respectively. The parasitic inductance between the wires is obtained by using a mirror image method, and the conductive shell can be positioned in the central radius direction of the shell
Figure BDA0001684617900000052
The mirror current is replaced as shown in fig. 3. The specific solution is as follows.
The self inductance per unit length and the mutual inductance per unit length in the insulating medium are as follows:
Figure BDA0001684617900000053
Figure BDA0001684617900000054
wherein s is1Is the distance from the center of the wire i to the point A on the outer layer of the insulation layer of the wire j, s2Is the distance from the mirror center of the wire i to the point A on the outer layer of the insulation of the wire jijIs the distance from the center of wire i to the center of wire j, and s "is the distance from the center of the mirror image of wire i to the center of wire j.
The self-inductance per unit length and the mutual inductance per unit length in the free space are as follows:
Figure BDA0001684617900000055
Figure BDA0001684617900000056
wherein, s'1Is the distance, s ', from the center of wire i to the point B of the ideal conductive housing'1The distance from the mirror center of the wire i to the point B of the ideal conductive housing.
Figure BDA0001684617900000061
Figure BDA0001684617900000062
Figure BDA0001684617900000063
Figure BDA0001684617900000064
Figure BDA0001684617900000065
Figure BDA0001684617900000066
Inductance matrices per unit length l (insul) and l (fs) in the insulating layer and in free space are obtained.
The dielectric constant of the medium surrounding the conductor is non-uniform. Therefore, the capacitance and the conductance per unit length are influenced by the inhomogeneous medium. The unit length complex (real) capacitance matrix in the insulation layer and the free space are respectively defined as
Figure BDA0001684617900000067
C (fs) (capacitance is real if the dielectric constant is real, and complex otherwise).
Figure BDA0001684617900000068
L(FS)C(FS)＝μ0ε0E(n)
Wherein E (n) is an n-order identity matrix.
Because at the contact surface of two media, i.e. the surface r ═ rmIs an equipotential surface, so the total complex capacitance
Figure BDA0001684617900000069
Can be regarded as each area complex electricity
The capacitors are connected in series.
Figure BDA00016846179000000610
From the total complex capacitance
Figure BDA00016846179000000611
The expression (7) can directly obtain the net capacitance and the net conductance matrix per unit length.
Figure BDA00016846179000000612
Figure BDA00016846179000000613
From the above analysis, in view of the requirement of extracting the net capacitance and the net conductance per unit length, we must first obtain the complex capacitance matrix of each dielectric layer, and then must extract the parasitic inductance matrix of each dielectric layer.
A method for extracting the parasitic capacitance and conductance of twisted pair surrounded by lossy inhomogeneous medium in conductive shell.
The invention provides a method for extracting non-uniform parasitic capacitance and a conductance matrix of a lossy non-uniform twisted pair in a conductive shell, aiming at the practical problem that the parasitic parameter solution is complex in the crosstalk solution process of the non-uniform twisted pair and the conductive wire can only be regarded as lossless and uniform generally.
The invention establishes a twisted pair lineSimilar to the periodic alternating transmission model, the cross section of the twisted pair is no longer approximated to zero, and the line-to-line spacing changes according to different positions. The axial wire spacing schematic diagram of the twisted pair is further refined, and the result shows that the distance h from the single wire to the central axis of the twisted pair at the cross part is changed, so that the distance d from the wire to the conductive shell is causediAnd (6) changing.
Establishing a schematic diagram of extracting parasitic inductance by image replacement to obtain parasitic inductance parameter matrixes L (INSUL) and L (FS) of each layer of medium,
by
Figure BDA0001684617900000071
L(FS)C(FS)＝μ0ε0E(n)
Obtaining the capacitance matrix of each layer
Figure BDA0001684617900000072
And C (FS), obtaining the total composite capacitance matrix by the series idea
Figure BDA0001684617900000073
Figure BDA0001684617900000074
By
Figure BDA0001684617900000075
Figure BDA0001684617900000076
And obtaining a parasitic net capacitance and a net conductance matrix.
And according to a twisted pair model in a given conductive shell, carrying out specific operation according to given parameters to obtain the parasitic capacitance and the conductance matrix of different positions of the crossed part of the twisted pair at fixed frequency.

Claims (1)

1. The method for extracting the parasitic capacitance and the conductance of the twisted pair in the conductive shell is characterized by comprising the following steps of:
step 1: establishing an approximate periodic alternate reversal model of the twisted pair, wherein a lead is surrounded by two layers of different media, the first layer is an insulating layer, and the second layer is a free space; obtaining the radius r of the inner conductor of the twisted pairwThe outer radius of the insulating layer is rmThe inner radius of the conductive shell is rsPermeability of insulating layer, dielectric constant, loss angle of lossy insulating layer, angle between wires, thetaij；
Step 2: extracting inductance matrixes L (INSUL) and L (FS) of each dielectric area;
for the case where the wire is surrounded by a circular insulating medium, there is μ ═ μ0，μ0Is free space permeability, so the inductance per unit length is not affected by inhomogeneous media, i.e. as in the case of free space; defining inductance matrixes with single length in free space and insulating layer as L (FS) and L (INSUL), respectively, using a mirror image method to obtain parasitic inductance between leads, and positioning the conductive shell in the center radius direction of the shell
Figure FDA0003435415540000018
Mirror current substitution of (d)iThe distance between the center of the ith wire and the central axis of the shell;
the self inductance per unit length and the mutual inductance per unit length in the insulating medium are as follows:
Figure FDA0003435415540000011
Figure FDA0003435415540000012
wherein s is1The distance from the center of the wire i to the point A on the outer layer of the insulating layer of the wire j; s2Insulating a mirror image of wire i from center to wire jDistance of layer outer layer point A; sijThe distance from the center of the wire i to the center of the wire j; s "is the distance from the mirror center of wire i to the center of wire j;
the self-inductance per unit length and the mutual inductance per unit length in the free space are as follows:
Figure FDA0003435415540000013
Figure FDA0003435415540000014
wherein, s'1The distance from the center of the wire i to the point B of the ideal conductive shell; s'2The distance from the mirror image center of the wire i to the point B of the ideal conductive shell;
Figure FDA0003435415540000015
Figure FDA0003435415540000016
Figure FDA0003435415540000017
Figure FDA0003435415540000021
Figure FDA0003435415540000022
Figure FDA0003435415540000023
is prepared fromii(INSUL)、lij(INSUL) obtaining a single length inductance matrix L (INSUL) in the insulating layer; is prepared fromii(FS)、lij(FS) obtaining an inductance matrix L (FS) of unit length in free space;
and step 3: extracting complex capacitance matrix of each layer of dielectric region
Figure FDA0003435415540000024
And C (FS);
respectively defining the unit length complex capacitance matrix in the insulating layer and the free space as
Figure FDA0003435415540000025
C (FS); if the dielectric constant is real, the capacitance is real, otherwise, it is complex;
Figure FDA0003435415540000026
L(FS)C(FS)＝μ0ε0E(n)
wherein E (n) is an n-order identity matrix;
Figure FDA0003435415540000027
complex dielectric constant of the insulating layer; epsilon0Is the free space dielectric constant;
and 4, step 4: because at the contact surface of two media, i.e. the surface r ═ rmIs an equipotential surface, so the total complex capacitance
Figure FDA0003435415540000028
Can be viewed as a series connection of complex capacitances for each region; from the total complex capacitance
Figure FDA0003435415540000029
Extracting a net capacitance C and a net conductance matrix G of unit length;
Figure FDA00034354155400000210
Figure FDA00034354155400000211
Figure FDA00034354155400000212
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