CN108037389A - A kind of hole coupling analysis method based on equivalent field principle - Google Patents
A kind of hole coupling analysis method based on equivalent field principle Download PDFInfo
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses a kind of hole coupling analysis method based on equivalent field principle, this method includes：Equivalent surface currcnt, structure subdivision, basic function selection, model inference and the content of parameter calculating and model solution.Cable of the present invention for various wirings form, by the way that cable is equivalent to corresponding circuit model, and the model contains the Kelvin effect and kindred effect characteristic that cable occurs when frequency transmission signal raises, coupling between cable is described with the parameter in circuit model, so as to obtain the voltage and current distribution under certain input along cable, in the case where not doing the test case of complexity, whether the wiring for analyzing cable is reasonable, whether coupled between cable influences signal transmission, since wiring configuration is various, this kind of method reduces the manpower and materials and time needed for substantial amounts of test, this method covers the Kelvin effect and kindred effect that cable occurs, acquired results are closer to actual conditions.
Description
Technical field
The present invention relates to the coupling measurement technical field of airborne cable, more particularly to a kind of cable based on equivalent field principle
Coupling analytical method.
Background technology
Modern aircraft is equipped with the electronic system of large amount of complex, they are very sensitive to electromagnetic interference, system easily occur
Inexactness and malfunction, even system collapse, cause serious accident, and the coupling between cable is electromagnetic interference
Main source, as shown in Figure 1.Need to carry out airborne cable coupling analysis and test, guarantee does not interfere with electronic system
Energy.But there are the following problems for the prior art.Only hole coupling situation is investigated by experiment test, can only indicate that system is current
State, can not reflect the work behavior of system in different situations comprehensively, in addition since the cable wiring of system equipment has been difficult to
Full fixation and specification, cause test result often to have very big uncertainty, and be difficult to reappear.Traditional analysis method then without
Method accurately analyzes the coupling of small-signal, and is deteriorated for the lifting of signal frequency, effect.
The content of the invention
In view of this, the present invention provides a kind of hole coupling analysis method based on equivalent field principle, having realized can
Coupling analysis carrying out cable to the cable of arbitrary placement, can obtain the voltage and current point under known input along cable
Cloth.
To achieve the above object, there is provided following scheme：A kind of hole coupling analysis method based on equivalent field principle, is used for
Coupling analysis is carried out to airborne cable, is included the following steps：
Step 1, the principle of equal effects by field, the body CURRENT DISTRIBUTION of cylindrical type cable cross section is equivalent to only on surface point
The surface current of cloth, and be distributed using cylindrical conductive mode current by equivalent surface current single order modified Bessel function and triangle
Function is indicated；
Step 2, the structure of cable and the frequency range of transmission signal according to required analysis, determine to exist for cable
Structure subdivision size shape under cylindrical coordinate, determines the node of subdivision, according to the pass of current unit and electric charge element and node
System divides different units；
The selection of step 3, electric current basic function is divided into three kinds of basic functions according to the obtained equivalent surface currcnt of step 1：Become skin
Effective pattern, kindred effect sinusoidal model, kindred effect cosine mode, different electric currents is had for different electric current basic functions
With the relational expression of electric field.Electric charge basic function is equally divided into three kinds according to trigonometrical number：Kelvin effect pattern, kindred effect sine mould
Formula, kindred effect cosine mode；
Step 4, using PEEC methods, obtain equivalent circuit model, the basic function obtained by step 3 be updated to circuit ginseng
In several calculating formulas, parameter is calculated；
Step 5, for the circuit by node division, circuit equation group is changed into matrix equation with MNA methods, according to step 4
The circuit parameter of calculating can solve the Current Voltage distribution on egress.
Wherein, this method obtains basic function by normallized current density and charge density, and basic function describes electric current
With the distribution situation of electric charge, for CURRENT DISTRIBUTION, the loop integral of the electric current for passing through itself divided by its section, i.e. surface current is taken
It is normalized to obtain basic function；For distribution of charges, represented in the form of trigonometrical number, because of the loop integral of trigonometric function
It is zero, therefore actual normalized is to ask the loop integral of absolute value trigonometric function in distribution of charges divided by distribution function
Electric charge basic function under to different mode, while basic function is obtained, since current density and electric field strength are unsatisfactory for ratio
For this relation of electrical conductivity, it is necessary to retain the relation of electric current and electric field under different mode.
Wherein, during model inference, conductivity relation is unsatisfactory in current density and electric field strength, is obtained first in model
Item is handled as self-impedance, which is not real number, in partial inductance and the coefficient of potential calculate, since basic function is distributed in
Conductive surface, therefore calculating therein is related to quad-slope integration, processing method is first with integral transformation by two of which integration variable
It is changed into one, then calculates an integration variable and reduce by a multiple integral, two multiple integrals can be handled using Some Integral Identities, wherein
Have one be each parameter generic items.
The present invention having the beneficial effect that compared with prior art：
Airborne number of cables is more and complicated, if cannot accomplish that reasonable line arrangement can produce the coupling of cable signal, may lead
The error or failure of equipment are caused, this kind of method can analyze the coupling of cable in the case of various wirings, thus need not carry out big
Amount object test just can carry out reasonable line arrangement planning, save manpower and material resources, and compared to other analysis methods, this method tool
Standby result closer to it is actual the advantages of.Airborne number of cables is more and complex distribution, if cannot accomplish reasonable line arrangement, cable passes
Coupling between defeated signal may cause equipment to malfunction or fail.This kind of method can be analyzed to be obtained in the case of various wirings
Voltage and current along the lower cable of certain input, analyzes the coupling between cable, thus need not carry out a large amount of object tests with regard to energy
Reasonable line arrangement planning is carried out, saves a large amount of manpower and materials；If this method is special (parallel, vertical) for cable distribution situation,
Calculative parameter will be reduced in its parameter matrix, so as to save computing resource；This method is for cable in transmission signal
The Kelvin effect and kindred effect that frequency occurs when raising all are taken into account, so that compared to other analysis methods, possess more
The characteristics of close to actual effect.
Brief description of the drawings
Fig. 1 is hole coupling schematic diagram；
Fig. 2 is the face source equivalent schematic of cable, wherein, Fig. 2 (a) is original distribution schematic diagram, and Fig. 2 (b) is equivalent
Model schematic；
Fig. 3 is cable subdivision schematic diagram；
Fig. 4 is complete schematic equivalent circuit；
Fig. 5 is equivalent circuit (example) schematic diagram that three nodes add input signal.
Embodiment
Below in conjunction with the accompanying drawings and embodiment further illustrates the present invention.
A kind of hole coupling analysis method based on equivalent field principle of the present invention, for carrying out coupling point to airborne cable
Analysis, including：Equivalent surface currcnt model, cable subdivision and basic function derive, model parameter calculation and model solution.
Equivalent surface currcnt model is the model by body current equivalence for surface current based on equivalent field principle, and current source is for line
Cable exterior space is equivalent, i.e., does not change the field strength distribution of the external space.See a space for including conductor, as shown in Fig. 2 left sides,
Space is divided into inside and outside two parts, and inside is conductor, and outside is medium, conductor space V1Dielectric constant, magnetic conductivity, electrical conductivity point
Wei not be ε, μ, σ, dielectric constant, the magnetic conductivity of dielectric space are εout,μ.Its CURRENT DISTRIBUTION of the conductor of cylinder is in conductor
Portion, its equivalent surface currcnt model, in equivalent model space, original body CURRENT DISTRIBUTION is without the substitute is in original
Surface current on conductor and dielectric interface, and original conductor space is filled by external agency, as shown in Fig. 2 right sides.Pass through
Field boundary condition can obtain the relational expression of equivalent surface current and original body electric current：
Complicated body CURRENT DISTRIBUTION is become simple surface current and is distributed by the step, J in formulasRepresent surface current, ω is angle
Frequency, E, E1It is equivalent front and rear internal electric field.
By the way that conduction mode CURRENT DISTRIBUTION expression formula and formula (1) are combined, the expression formula of equivalent surface currcnt is obtained：
J in formulaSFor surface current, ω is angular frequency, and R is conductor radius, InIt is first kind modified Bessel function, k and k0Meter
Formula isThe formula combines the kindred effect produced at high frequencies on cable and becomes
Skin effect influences, and is integrated into surface current expression formula, simplifies the complexity of analysis.
PEEC methods are built using Helmholtz equation electricity scalar potential and magnetic vector potential and the relation of current source and Charge Source
Vertical equivalent circuit model to the object analyzed, it is necessary to carry out structure subdivision.For cable, due to length of cable much
More than the cross sectional radius of cable, a point with respect to cable major axis is regarded as in cross section in actual division, for cable
Only need along major axis subdivision.Division condition is：Element length be no more than cable transmission signal wavelength 1/20, i.e., no more than λ/
20；Node selection is along major axis；Cable is divided into current unit between two adjacent nodes；Electric charge element length and current unit phase
Together, stagger half-space, and node is included among unit.It is specific as shown in Figure 3.
Basic function is the function for describing power distribution situation in division unit, is the core of PEEC methods.Based on equivalent
It is as follows that power source model chooses basic function：
Since Kelvin effect, at this time due to the interference between no cable, it is believed that CURRENT DISTRIBUTION is constant along angle, at this time by
Then surface current, so basic function performance is its distribution situation along circumferential direction.In the case of only Kelvin effect, its edge
It is equally distributed circumferential direction.
Above formula is the electric current basic function under Kelvin effect pattern, R is Cable radius, the electricity involved in solve afterwards
Field is, it is necessary to which the relation of electric field and electric current, as follows
Js=EY0
For kindred effect, by taking sine basic function as an example：
The relation of electric current and electric field is at this time：
Js=EYn,
Equally there is cosine-basis function：
Equivalent charge model be in the case where interacting between considering cable, electric charge cable surface distribution just
No longer it is uniform.Because charge density distribution is related to angle, therefore consider to represent the distribution feelings of electric charge using trigonometric function
Condition.
It assume that electric charge only exists the surface with cable.In the case where interacting between considering cable, electric charge is online
The distribution on cable surface is no longer just uniform.Because charge density distribution is related to angle, therefore consider to carry out table using trigonometric function
Show the distribution situation of electric charge.It is similar：
From Fourier space, which can represent any distribution of charges situation.Equally, when actual use
Higher order term will not be used, is equally divided into three kinds of basic functions.
The situation for having Kelvin effect is only considered, because distribution of charges, only on surface, so-called Kelvin effect is to its distribution situation
Do not influence, it is believed that electric charge lists equally distributed in electric charge element in this case.I.e.：
ρ=c0 (9)
By normalization, what is obtained is basic function：
R is the radius of cable in formula, liIt is the length of electric charge element, substantial denominator is the area of electric charge element.
Consider the situation for thering is kindred effect to influence.By taking SIN function as an example, in order not to allow integral term to be zero, processing is as follows：
The result is that：
Same processing obtains cosine term basic function：
Formula (3), (5), (7) are the electric current basic functions under different mode, and (4) and (6) are electric current and electric field under different mode
Relation, (10), (12), (13) are the electric charge basic functions under different mode.Basic function describes the electric current in division unit
And distribution of charges, rather than size, this kind of basic function contain electric current when cable is subject to Kelvin effect and kindred effect well
Distribution of charges situation, and the basic function form is simple, beneficial to application.
Establish model：
Using PEEC methods, derive that node potential eikonal equation and node current equation are as follows, complete equivalent circuit is such as
Fig. 4 (plus the equivalent capacitance of dielectric layer)：
Can be seen that the equivalent circuit between two nodes is impedance, inductance and the multiple flow control voltage sources of series connection, and node is over the ground
It is equivalent to the capacitance of parallel connection and multiple flow control current sources.
The parameter calculating formula of an element in PEEC models is derived with reference to obtained basic function：
Formula (14) is the calculating formula of self-impedance, describes division unit middle impedance, and (15) and (16) are induced electricity respectively
Sense and the coefficient of potential, describe intercoupling between different current units.
Parameter is calculated according to calculating formula and subdivision model as follows：
Calculating section inductance first, the basic function of partial inductance are divided into two kinds, have trigonometric function and no trigonometric function, do not have
The basic function for having trigonometric function is exactly that surface current is uniformly distributed basic function, is calculated as follows：
For formula (4.6), two multiple integrals can be solved according to the method for calculating z-axis integration used before, utilizing phase
Two angle variables, are become one, then reduce by a multiple integral by same integral transformation.As a result it is as follows：
For formula (17), using integral transformation, two angle variables are become one, then reduce by a multiple integral.As a result such as
Under：
There is situation existing for trigonometric function, calculated by taking single order trigonometric function as an example：
It equally can first reduce by two multiple integrals, for two angle integration variables, utilize product to sum formula：
The calculating formula is only needed to θ+Integration, has obtained final expression formula：
Wherein fz(θ-) in the l that includes2(2 points of square distances in cross section projection of integration) processing method is identical, as follows：
(23) first formula included is used for the current unit calculating section inductance on identical cable, and second formula is used
Mutual inductance between the current unit on different cables is calculated, wherein to meet the much bigger bar of cable gap ratio Cable radius
Part.Above-mentioned various middle F is electric current basic function, θ-=θi-θj, R is conductor radius, l2It is 2 points of current unit on cross section
Projector distance, μ are magnetic conductivities, and d is cable spacing.
The coefficient of potential is calculated and is described below：
Next the coefficient of potential is calculated, since the calculating formula of the coefficient of potential is also defined on double plane integration, and its base
Function has suitable similitude with electric current basic function, directly gives result.
L in formula (24) and (25)i,ljIt is the length of two electric charge elements, ε is dielectric constant.Wherein (24) are Kelvin effects
Basic function result of calculation, (25) are the result of calculation of single order sine basic function.
Which part inductance and coefficient of potential calculating formula have the common item as follows：
A and b is the length coordinate of different demarcation unit in formula, l2It is as defined above.
Part impedance computation is described below：
On the calculating of part impedance, the Differential Properties of first kind modified Bessel function are make use of.
For Kelvin effect pattern, according to the basic function result of calculation of a upper chapter, have：
For approach effect pattern, there is trigonometric function, processing is as follows：
Above-mentioned three formulas liIt is the length of unit, R is conductor radius, and μ is magnetic conductivity.
Equivalent capacity is calculated and is described below：
In practical applications, cable always has one layer of medium, and this layer of medium is nonconducting, when considering its influence,
Equivalence element is a dielectric capacitance in parallel, and calculating formula is as follows：
ε in formula0Represent the dielectric constant of free space, εrRepresent the relative dielectric constant of medium,Represent current unit
Cross-sectional area, liRepresent element length.
The part gives the calculating formula according to parameter in circuit model equivalent in the case of corresponding basic function and subdivision, extremely
This gives whole equivalent models required work.According to obtained model and parameter therein, in the elevated feelings of frequency
Under condition, although Kelvin effect and kindred effect occurs in cable, all in the model by comprising that is, the model is examined well
The coupling between cable is considered.
Model use example
In order to analyze the Current Voltage situation of cable in transmitting procedure thereon, given an input Vs, at the same time
It is assumed that the internal resistance of source and load resistance (only need to know the situation of the extraneous input voltage or electric current of cable in the analysis process
), the input and output situation of the circuit is then solved using nodal method, as shown in Figure 5.
Two node potential eikonal equations and three node current equations are included in the equivalent circuit of three nodes, if plus defeated
Enter the equation of voltage and output voltage, then a total of seven equations, so unknown number should also be seven.This seven unknown numbers
It is：Φ1,Φ2,Φ3, the current potential of three nodes of expression；I1,I2, represent the electric current from node-flow to next node, I1It is from section
Point 1 flows to the electric current of node 2, I2It is the electric current that node 3 is flowed to from node 2；IS,IL, represent to flow to node 1 from power supply respectively
Electric current on electric current and load resistance.
Using Kirchhoff's second law, two node potential eikonal equations are write out, using Kirchhoff's current law (KCL), are write out
Three node current equations, plus input source and two equations of load resistance, share 7 equations, 7 unknown numbers, just may be used
Solution.
For convenience, the form of matrix multiple is organized into, matrix is write successively by equation order.
(31) it is complete matrix equation, programmed algorithm is the construction based on matrix, coefficient matrix can be divided into seven
It is a, such as following formula：
According to (31), M1It is 3 × 3 diagonal matrix；M2It is 3 × 2 matrix；M3It is 3 × 2
Matrix；M4It is 2 × 3 diagonal matrix；M5It is 2 × 3 matrix；M6It is 2 × 2 matrix；M7It is 2 × 7 matrix.Post analysis
Assuming that number of cables NL, current unit quantity NJ, electric charge element quantity Nρ.According to division before, meet such as between these three amounts
Lower relation NL+NJ=Nρ, number of nodes is equal to electric charge element quantity, and electric charge element is more than current unit during the division of each cable
One.
Carefully analyze each matrix.Matrix M1It is diagonal matrix, the value of matrix, the size of matrix is determined by self-potential coefficient
Determined by the quantity of node, be Nρ×Nρ；Matrix M2What is characterized is the shadow of the electric current for the electric charge element on remaining node flow direction ground
Ring, so size is Nρ×(Nρ- 1), it is characterized in that the worth denominator per a line is the self-potential coefficient of the unit, molecule is to connect
The difference for the coefficient of potential that continuous two and the unit are coupled；Matrix M3It is to describe input source and the presence loaded for a certain electric charge
The characteristics of influence of unit, the matrix value is that denominator is self-potential coefficient, and molecule is initial current unit and electric current most respectively
Unit determines the mutual coefficient of potential of the unit, its size by electric charge element and number of cables, and each cable is active and load
Brightness, therefore size is Nρ×2NL；Matrix M4It is the matrix for the potential difference for defining a certain current unit both ends, the node of electric current outflow
Assignment -1, flows into node valuation 1, unrelated node valuation 0, matrix size NJ×Nρ；Matrix M5It is impedance matrix, is considered as
Two matrixes are added, and one of matrix is diagonal matrix, characterizes the parallel value of the impedance of each current unit part and dielectric capacitance,
Another describes partial inductance value, and matrix size is NJ×NJ；Matrix M6It is null matrix, because the section of each current unit
Point current potential eikonal equation is not related to external source and load, is a Nρ×2NLNull matrix；Matrix M7It is to describe external source and bear
The influence that galvanic electricity pressure is powered on for two end nodes is carried, size is 2NL×(NJ+Nρ+2NL), which is generally the largest, actual
Very simple is handled, because equation is extremely succinct.
It this example illustrate in the case of given input signal, can analyze to obtain the voltage and current distribution feelings along cable
Condition, to different installation scenarios, whether can judging the wiring, that interfering with each other between cable can be allowed not influence its is normal
Signal transmission.
Claims (3)
- A kind of 1. hole coupling analysis method based on equivalent field principle, for carrying out coupling analysis, its feature to airborne cable It is：Include the following steps：Step 1, the principle of equal effects by field, the body CURRENT DISTRIBUTION of cylindrical type cable cross section is equivalent to only in surface distribution Surface current, and be distributed using cylindrical conductive mode current by equivalent surface current single order modified Bessel function and trigonometric function It is indicated；Step 2, the structure of cable and the frequency range of transmission signal according to required analysis, determine to sit in column for cable Structure subdivision size shape under mark system, determines the node of subdivision, is drawn according to the relation of current unit and electric charge element and node Divide different units；The selection of step 3, electric current basic function is divided into three kinds of basic functions according to the obtained equivalent surface currcnt of step 1：Kelvin effect Pattern, kindred effect sinusoidal model, kindred effect cosine mode, different electric currents and electricity are had for different electric current basic functions The relational expression of field, electric charge basic function are equally divided into three kinds according to trigonometrical number：Kelvin effect pattern, kindred effect sinusoidal model, Kindred effect cosine mode；Step 4, using PEEC methods, obtain equivalent circuit model, the basic function obtained by step 3 be updated to circuit parameter In calculating formula, parameter is calculated；Step 5, for the circuit by node division, circuit equation group is changed into matrix equation with MNA methods, is calculated according to step 4 Circuit parameter can solve on egress Current Voltage distribution.
- A kind of 2. hole coupling analysis method based on equivalent field principle according to claim 1, it is characterised in that：The party Method obtains basic function by normallized current density and charge density, and basic function describes the distribution situation of electric current and electric charge, For CURRENT DISTRIBUTION, the electric current for passing through itself divided by its section is taken, i.e. the loop integral of surface current is normalized to obtain base Function；For distribution of charges, represented in the form of trigonometrical number, because the loop integral of trigonometric function is zero, therefore actual normalizing Change processing is that the loop integral of absolute value is sought trigonometric function in distribution of charges divided by distribution function to obtain under different mode Electric charge basic function, while basic function is obtained, it is this pass of electrical conductivity to be unsatisfactory for ratio due to current density and electric field strength System is, it is necessary to retain the relation of electric current and electric field under different mode.
- A kind of 3. hole coupling analysis method based on equivalent field principle according to claim 1, it is characterised in that：Model During derivation, conductivity relation is unsatisfactory in current density and electric field strength, obtains handling Section 1 as self-impedance in model, The Section 1 is not real number, in partial inductance and the coefficient of potential calculate, since basic function is distributed in conductive surface, thus it is therein Calculating is related to quad-slope integration, and two of which integration variable is changed into one by processing method first with integral transformation, then calculates one Item integration variable reduces by a multiple integral, and two multiple integrals can be handled using Some Integral Identities, wherein it is each parameter to have one Generic items.
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| CN114048661A (en) * | 2021-11-29 | 2022-02-15 | 中南大学 | Method and device for treating DC point source potential and electric field under laminar medium |
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