CN112232001B - Self-adaptive determination method and system for ultra-wideband resonance response of integrated circuit - Google Patents

Self-adaptive determination method and system for ultra-wideband resonance response of integrated circuit Download PDF

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CN112232001B
CN112232001B CN202011425185.2A CN202011425185A CN112232001B CN 112232001 B CN112232001 B CN 112232001B CN 202011425185 A CN202011425185 A CN 202011425185A CN 112232001 B CN112232001 B CN 112232001B
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simulation
cubic spline
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CN112232001A (en
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唐章宏
邹军
黄承清
汲亚飞
王芬
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Beijing Wisechip Simulation Technology Co Ltd
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/32—Circuit design at the digital level
    • G06F30/33—Design verification, e.g. functional simulation or model checking
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2115/00—Details relating to the type of the circuit
    • G06F2115/12—Printed circuit boards [PCB] or multi-chip modules [MCM]

Abstract

The invention relates to a self-adaptive determination method and a self-adaptive determination system for an ultra-wideband resonance response of an integrated circuit. The method comprises the following steps: dividing the resonance frequency point into a plurality of simulation sub-frequency bands by taking the resonance frequency point as a division point, and determining an initial frequency point of each simulation sub-frequency band range; calculating the electromagnetic response of the initial frequency point of each simulation sub-frequency range by using a coarse grain parallel method, and determining an electromagnetic response sequence; determining the sampling step length of a third cubic spline interpolation curve of each simulation sub-frequency band according to the two cubic spline interpolation curves in each simulation sub-frequency band; determining newly inserted frequency points between initial frequency points in each simulation sub-frequency band according to the sampling step length; determining the electromagnetic response of all newly inserted frequency points by using a coarse particle parallel computing method, and determining a resonance response curve of each simulation sub-frequency band; and combining the resonance response curves of all the simulated sub-bands to generate an ultra-wideband resonance response curve of the integrated circuit. The invention accurately calculates the ultra-wideband resonance response of the integrated circuit and reduces the calculation time cost.

Description

Self-adaptive determination method and system for ultra-wideband resonance response of integrated circuit
Technical Field
The invention relates to the field of integrated circuit design, in particular to a method and a system for adaptively determining ultra-wideband resonance electromagnetic response of an integrated circuit.
Background
Aiming at the problem of calculating the ultra-wideband electromagnetic field of a multilayer ultra-large scale integrated circuit, the frequency range needing to be calculated comprises a wide frequency range from a few kHz to a few GHz, the working frequency of the integrated circuit reaches a few GHz along with the reduction of the minimum characteristic dimension of the multilayer ultra-large scale integrated circuit to a nanometer level, the problems of crosstalk, voltage drop, signal delay, noise and the like caused by parasitic effects generated among layers, through holes, interconnecting lines and the like are more and more serious, and the analysis of the electromagnetic response of the multilayer ultra-large scale integrated circuit in the wide frequency range is very necessary. Because the minimum characteristic dimension of the multilayer VLSI is a multi-scale structure from nano-scale to centimeter-scale, the traditional analytic methods such as transmission line method can not accurately calculate the frequency response of the multilayer VLSI, and an electromagnetic field numerical calculation method with higher precision is needed. Because the multilayer ultra-large scale integrated circuit has a multi-scale complex structure from centimeter to nanometer, when the broadband electromagnetic response of the multilayer ultra-large scale integrated circuit is calculated by adopting a numerical calculation method, dense unstructured grid subdivision is caused by a large number of small-scale structures, which needs to solve tens of millions of unknown ultra-large scale sparse matrices, so that the calculation time is very long for the electromagnetic response characteristics of each frequency point, and in order to obtain an electromagnetic response curve of a wide frequency band, when the electromagnetic response of the integrated circuit is calculated by adopting a traditional method such as uniform frequency point sampling, thousands of sampling points of frequency need to be obtained to obtain certain calculation precision, otherwise some important frequency information can be lost. For a very large scale integrated circuit comprising a plurality of resonant frequencies, even if the electromagnetic response of the integrated circuit is fitted through interpolation, the selection of discrete frequency points greatly influences the electromagnetic response curve of the interpolation fitting, so that how to select proper discrete frequency points to carry out correct interpolation fitting to extract the resonant characteristics of the very large scale integrated circuit is a problem which needs to be focused. On one hand, the number of the calculated sampling frequency points determines the precision of the calculated frequency response curve, and the number of the sampling frequency points is too small, so that the precision of the calculated frequency response curve is low, and some important frequency information can be lost; on the other hand, too much sampling frequency is calculated at a significant calculation time cost, which is not acceptable for chip design.
Disclosure of Invention
The invention aims to provide a method and a system for adaptively determining the ultra-wideband resonance electromagnetic response of an integrated circuit, which aim to solve the problems of low calculation precision and high calculation time cost caused by the fact that the number of sampling points for frequency is less than thousands when the electromagnetic response of the integrated circuit is calculated by adopting the traditional method such as uniform frequency point sampling.
In order to achieve the purpose, the invention provides the following scheme:
a method for adaptive determination of an ultra-wideband resonant electromagnetic response of an integrated circuit, comprising:
calculating a resonance frequency point in a simulation frequency band range of the integrated circuit, and dividing the simulation frequency band range into a plurality of simulation sub-frequency bands by taking the resonance frequency point as a dividing point;
determining an initial frequency point of each simulation sub-frequency range; the simulation sub-frequency band range is a frequency interval formed by two adjacent resonance frequency points which are arranged from small to large;
calculating the electromagnetic response of the initial frequency point of each simulation sub-frequency band range by using a coarse grain parallel method, respectively sampling the electromagnetic response of each simulation sub-frequency band at a first sampling interval and a second sampling interval, and determining a first electromagnetic response sequence and a second electromagnetic response sequence;
performing interpolation processing on the first electromagnetic response sequence and the second electromagnetic response sequence to determine a first cubic spline interpolation curve and a second cubic spline interpolation curve;
acquiring the maximum allowable error of the simulation curve, and determining the sampling step length of a third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that the maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve;
determining newly inserted frequency points between the initial frequency points in each simulation sub-frequency band according to the sampling step length of the third cubic spline interpolation curve in each simulation sub-frequency band;
determining the electromagnetic response of all newly inserted frequency points by using a coarse particle parallel computing method, performing cubic spline interpolation on the electromagnetic response of all the frequency points of each simulation sub-band, and determining a resonance response curve of each simulation sub-band;
and combining the resonance response curves of all the simulated sub-bands to generate an ultra-wideband resonance response curve of the integrated circuit.
Optionally, the obtaining a maximum allowable error of the simulation curve, and determining a sampling step size of a third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that a maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve, specifically includes:
according to the formula
Figure DEST_PATH_IMAGE001
Is determined to beiSampling step length of a third cubic spline interpolation curve of each simulation sub-frequency band; wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE002
，N i is as followsiThe number of final sampling points in the range of the simulation sub-frequency bands;ithe serial number of the simulation sub-frequency band;
Figure DEST_PATH_IMAGE003
is to round up upwards; ln () represents taking the natural logarithm;f i,minis as followsiThe lowest frequency of the sub-bands;f i,maxis as followsiThe highest frequency of the sub-band;E maxthe maximum allowable error of the simulation curve is obtained;T i (f) Is as followsiCubic spline interpolation curves of the sub-bands;T i1,(f) Is as followsiA first cubic spline interpolation curve of the sub-band;T i2,(f) Is as followsiA second cubic spline interpolation curve of the sub-band;h i2,is as followsiSampling step length of a second cubic spline interpolation curve of the sub-frequency band;h i3,is as followsiSampling step length of a third cubic spline interpolation curve of the sub-frequency band;v i is as followsiThe sub-bands replace the approximation coefficients of the fourth derivative of the electromagnetic response curve truth values with the difference between the first cubic spline interpolation curve and the second cubic spline interpolation curve,v i ≥1；rto presetThe fixed frequency is compared with a threshold value,r>1。
optionally, the determining, according to the sampling step size of the third cubic spline interpolation curve in each simulation sub-band, a newly inserted frequency point between the initial frequency points in each simulation sub-band specifically includes:
according to the formula
Figure DEST_PATH_IMAGE004
Is determined to beiThe number of frequency points to be inserted in each sub-band; wherein the content of the first and second substances,n i,new is as followsiThe number of frequency points to be inserted in each sub-band;
Figure 100002_DEST_PATH_IMAGE005
is to round up upwards;
according to the firstiCalculating the number of frequency points to be inserted in each sub-bandiNewly inserted frequency points between the initial frequency points in each sub-band.
Optionally, the method according toiCalculating the number of frequency points to be inserted in each sub-bandiThe newly inserted frequency points between the initial frequency points in each sub-band specifically include:
according to the formula
Figure DEST_PATH_IMAGE006
Determine insertion toiNewly inserted frequency points among the initial frequency points in each sub-frequency band; wherein exp () represents a power function of a natural logarithmic base;f i,k is as followsiSub-band ofkA second sampling frequency point;f i,k+1is as followsiSub-band ofk+1 second sampling frequency points of the first sampling frequency,f i,k,j is as followsiSub-band ofkA second sampling frequency point andka number one between +1 second sampling frequency pointsjA newly inserted frequency point;m i to sample at a second sampling interval, aiThe number of the simulation sub-bands is divided into equal parts;l i for the first sampling interval and the second samplingMultiple of sample spacing.
An adaptive determination system for an ultra-wideband resonant electromagnetic response of an integrated circuit, comprising:
the resonance frequency point calculating module is used for calculating resonance frequency points in a simulation frequency band range of the integrated circuit, taking the resonance frequency points as dividing points and dividing the simulation frequency band range into a plurality of simulation sub-frequency bands;
the initial frequency point determining module is used for determining the initial frequency point of each simulation sub-frequency range; the simulation sub-frequency band range is a frequency interval formed by two adjacent resonance frequency points which are arranged from small to large;
the electromagnetic response sequence determining module is used for calculating the electromagnetic response of the initial frequency point of each simulation sub-frequency band range by using a coarse grain parallel method, respectively sampling the electromagnetic response of each simulation sub-frequency band at a first sampling interval and a second sampling interval, and determining a first electromagnetic response sequence and a second electromagnetic response sequence;
the interpolation processing module is used for carrying out interpolation processing on the first electromagnetic response sequence and the second electromagnetic response sequence to determine a first cubic spline interpolation curve and a second cubic spline interpolation curve;
the sampling step length determining module is used for acquiring the maximum allowable error of the simulation curve, and determining the sampling step length of the third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that the maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve;
a newly inserted frequency point determining module, configured to determine, according to the sampling step size of the third cubic spline interpolation curve in each simulation sub-band, a newly inserted frequency point between the initial frequency points in each simulation sub-band;
the simulation sub-band resonance response curve determining module is used for determining the electromagnetic response of all newly inserted frequency points by using a coarse particle parallel computing method, performing cubic spline interpolation on the electromagnetic response of all the frequency points of each simulation sub-band, and determining the resonance response curve of each simulation sub-band;
and the integrated circuit ultra-wideband resonance response curve generation module is used for combining the resonance response curves of all the simulated sub-frequency bands to generate an integrated circuit ultra-wideband resonance response curve.
Optionally, the sampling step determining module specifically includes:
a sampling step size determining unit for determining a sampling step size according to a formula
Figure DEST_PATH_IMAGE007
Is determined to beiSampling step length of a third cubic spline interpolation curve of each simulation sub-frequency band; wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE008
，N i is as followsiThe number of final sampling points in the range of the simulation sub-frequency bands;ithe serial number of the simulation sub-frequency band;
Figure 93420DEST_PATH_IMAGE005
is to round up upwards; ln () represents taking the natural logarithm;f i,minis as followsiThe lowest frequency of the sub-bands;f i,maxis as followsiThe highest frequency of the sub-band;E maxthe maximum allowable error of the simulation curve is obtained;T i (f) Is as followsiCubic spline interpolation curves of the sub-bands;T i1,(f) Is as followsiA first cubic spline interpolation curve of the sub-band;T i2,(f) Is as followsiA second cubic spline interpolation curve of the sub-band;h i2,is as followsiSampling step length of a second cubic spline interpolation curve of the sub-frequency band;h i3,is as followsiSampling step length of a third cubic spline interpolation curve of the sub-frequency band;v i is as followsiBetween the first cubic spline interpolation curve and the second cubic spline interpolation curve for sub-bandsThe difference value replaces the approximation coefficient of the fourth derivative of the electromagnetic response curve truth,v i ≥1；ris a preset frequency ratio threshold value,r>1。
optionally, the newly inserted frequency point determining module specifically includes:
a unit for determining the number of frequency points to be inserted, for determining the number of frequency points to be inserted according to a formula
Figure 100002_DEST_PATH_IMAGE009
Is determined to beiThe number of frequency points to be inserted in each sub-band; wherein the content of the first and second substances,n i,new is as followsiThe number of frequency points to be inserted in each sub-band;
Figure 701731DEST_PATH_IMAGE005
is to round up upwards;
a newly inserted frequency point determination unit for determining a frequency point according toiCalculating the number of frequency points to be inserted in each sub-bandiNewly inserted frequency points between the initial frequency points in each sub-band.
Optionally, the newly inserted frequency point determining unit specifically includes:
a newly inserted frequency point determination subunit for determining the frequency point according to the formula
Figure 697369DEST_PATH_IMAGE006
Determine insertion toiNewly inserted frequency points among the initial frequency points in each sub-frequency band; wherein exp () represents a power function of a natural logarithmic base;f i,k is as followsiSub-band ofkA second sampling frequency point;f i,k+1is as followsiSub-band ofk+1 second sampling frequency points of the first sampling frequency,f i , k,j is as followsiSub-band ofkA second sampling frequency point andka number one between +1 second sampling frequency pointsjA newly inserted frequency point;m i to sample at a second sampling interval, aiThe artificial sub-bands being equally dividedParts (b);l i is a multiple of the first sampling interval and the second sampling interval.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a method and a system for adaptively determining ultra-wideband resonance electromagnetic response of an integrated circuit, which comprises the steps of firstly adopting a resonance calculation mode, calculating a resonance frequency point and frequency response of a super-large scale integrated circuit in a preset frequency range, and dividing the frequency range to be measured into a plurality of sub-frequency ranges to be measured by taking the resonance frequency point as a dividing point, so that the divided sub-frequency ranges to be measured do not comprise any resonance frequency point, the influence of the resonance frequency point on the electromagnetic response can be avoided, and the calculation efficiency of the electromagnetic response is improved; secondly, calculating an even number of uniformly distributed sampling frequency points by a coarse particle parallel calculation method, then respectively carrying out cubic spline interpolation twice based on the sampling frequency points, determining the calculation error of a maximum electromagnetic response curve based on two cubic spline interpolation curves, determining the sampling step length of a frequency point, determining the number of the frequency points to be inserted according to the sampling step length of the frequency point, and determining all inserted frequency points in the frequency band range; the electromagnetic response of all the interpolated frequency points is determined simultaneously according to a coarse grain parallel method. Therefore, the sampling frequency point which needs to be newly added can be calculated in a self-adaptive manner only by one time; the frequency response of the newly added sampling frequency points can be calculated by a coarse particle parallel calculation method at one time, and the electromagnetic response of the multilayer super-large-scale integrated circuit can be obtained by performing spline interpolation on all the calculated sampling frequency points for three times. The invention obtains the preassigned calculation precision through the minimum sampling frequency points, further, aiming at the newly added sampling frequency points, the frequency response of all the newly added sampling frequency points is calculated at one time by adopting a parallel calculation method, the electromagnetic response of the integrated circuit can be accurately calculated by a small number of sampling frequency points, the calculation time cost is reduced, and the finally determined electromagnetic response curve is used for determining an impedance matrix so as to adjust the real-time impedance in the circuit and avoid the resonance in the circuit, thereby designing the optimal circuit.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a method for adaptively determining an ultra-wideband resonant electromagnetic response of an integrated circuit in accordance with the present invention;
FIG. 2 is a block diagram of an adaptive determination system for the ultra-wideband resonant electromagnetic response of an integrated circuit provided in accordance with the present invention;
FIG. 3 is a schematic diagram of the distribution of discrete frequency points of a first cubic spline interpolation curve and a second cubic spline interpolation curve in different sub-bands provided by the present invention;
fig. 4 is a distribution diagram of a discrete frequency point response and a finally fitted cubic spline interpolation curve (fitting curve) provided by the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for adaptively determining the ultra-wideband resonance electromagnetic response of an integrated circuit, which can accurately calculate the electromagnetic response of the integrated circuit and reduce the calculation time cost.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Interpolation is an important method for discrete data approximation, and by using the method, the approximate value of a function at other points can be estimated under the condition that the function takes values at a limited number of points. In electromagnetic calculation of a multilayer very large scale integrated circuit, in order to obtain electromagnetic response of a wide frequency band, it is impossible to calculate frequency response of all frequency points, and frequency response of other frequency points can only be estimated by calculating frequency response of a limited point and then by interpolation. Common interpolation methods are piecewise linear interpolation, polynomial interpolation and cubic spline interpolation. The piecewise linear interpolation method is simple, has good stability and accuracy, but has poor overall smoothness; the polynomial interpolation has good smoothness as a whole, but the problem of oscillation easily occurs under the high-order condition; the cubic spline interpolation has the advantages of piecewise linear interpolation and polynomial interpolation, has good stability and accuracy, and has the advantage of overall smoothness, so that the cubic spline interpolation is a widely adopted interpolation method.
The invention is realized by a self-adaptive frequency point sampling technology based on cubic spline interpolation:
the cubic spline function is a piecewise cubic polynomial in each cellf g,f g+1]Can be written as
Figure DEST_PATH_IMAGE010
Wherein the content of the first and second substances,a g, b g, c g, d gis the undetermined coefficient. Due to the fact thatnEach interpolation node divides an interpolation interval intonSegment-1, therefore, having 4: (n-1) undetermined coefficients. If at the same time satisfy
Figure 100002_DEST_PATH_IMAGE011
Then callT(f) Is composed ofF(f) At a nodef g(g=1,2,…,n) Cubic spline interpolation function above. In this connection, it is possible to use,F(f) The ultra-wideband electromagnetic response of the multilayer ultra-large scale integrated circuit.
If the ultra-wideband electromagnetic response curve of the multilayer VLSI is smooth in the whole frequency band range, the cubic spline interpolation function can be considered to be at the nodes except the end pointsf g(g=2,…,n-1) first and second derivativesThe numbers being all continuous, i.e.
Figure DEST_PATH_IMAGE012
This equation can form n equations, form 3: (n-2) equations, 2 more equations being required for determining the pending coefficients. Usually, a boundary condition is added to the interpolation interval, and there are several boundary conditions:
knowing the first derivative value of the interpolation interval endpoint:
Figure DEST_PATH_IMAGE013
knowing the second derivative value of the interpolation interval endpoint:
Figure DEST_PATH_IMAGE014
periodic boundary conditions:
Figure DEST_PATH_IMAGE015
non-kinking boundary conditions:
Figure DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE017
presentation pair
Figure DEST_PATH_IMAGE018
GetqA first derivative;
the first three boundary conditions are used on the premise that the interpolated curve has one of the known properties or has a periodic property at the end point, but for the ultra-wideband electromagnetic response curve of the multi-layer VLSI, the response characteristic of the response curve at the end point of the frequency band is not clear in advance, and the frequency response does not have a periodic property, so that the last non-kinking boundary condition is adopted, which means that the interpolated curve is smooth enough because it represents that the three derivatives of the response curve at the end point of the frequency band are continuous, and the condition conforms to the ultra-wideband electromagnetic response characteristic of the multi-layer VLSI.
According to the non-kinking boundary condition, the coefficient shown by the formula can be solved, and then the cubic spline interpolation function of the electromagnetic response curve of the multilayer super-large-scale integrated circuit in the frequency band range is determined.
If the electromagnetic response curve of the multilayer VLSIF(f) In the first placeiThe range of simulated sub-bands is smooth, then based on the error estimation theorem,F(f) In the first placeiThe interpolation error in the range of the simulated sub-bands can be given by the following equation
Figure DEST_PATH_IMAGE019
In the formula
Figure DEST_PATH_IMAGE020
Is as followsiThe maximum spacing of adjacent discrete frequency points within a sub-band,
Figure DEST_PATH_IMAGE021
presentation pairF(f) Take the 4 th derivative. Obviously, if
Figure DEST_PATH_IMAGE022
The electromagnetic response curve of the multilayer VLSI can be accurately interpolated by the electromagnetic response of at most 4 frequency pointsF(f)。
Conversely, if the accuracy of the required fit is given in advance, it is possible to controlh i I.e. the interval of the sampling points, once obtains the frequency points to be simulated.
Maximum value of absolute value of derivative in 4 th order of electromagnetic response curve
Figure DEST_PATH_IMAGE023
Unknown, it can be approximated by two interpolations.
Fig. 1 is a flowchart of a method for adaptively determining an ultra-wideband resonant electromagnetic response of an integrated circuit according to the present invention, and as shown in fig. 1, a method for adaptively determining an ultra-wideband resonant electromagnetic response of an integrated circuit includes:
step 101: calculating a resonance frequency point in a simulation frequency band range of the integrated circuit, and dividing the simulation frequency band range into a plurality of simulation sub-frequency bands by taking the resonance frequency point as a dividing point.
Adopting a resonance calculation mode to calculate the resonance frequency point and the frequency response of the super-large-scale integrated circuit within a preset frequency range, comprising the following steps: the method comprises the steps of writing a generalized eigenvalue equation of a continuity equation of a super-large-scale integrated circuit field through a region discretization column by adopting a resonance calculation mode, solving the generalized eigenvalue equation to obtain a plurality of eigenvalues and eigenvectors, wherein the eigenvalues correspond to resonance frequency points of electromagnetic waves propagated in a dielectric layer of the integrated circuit under the passive condition of the super-large-scale integrated circuit, the eigenvectors corresponding to each resonance frequency point correspond to the distribution of the field under the resonance frequency point, and the frequency response corresponding to the resonance frequency point is obtained according to the distribution of the field.
For the alternating electromagnetic field model, the three-dimensional model of the multilayer integrated circuit refers to the dielectric constant in the three-dimensional model of the electromagnetic response characteristic in the frequency domain simulation of the multilayer VLSI
Figure DEST_PATH_IMAGE024
Magnetic permeability of
Figure DEST_PATH_IMAGE025
The distribution of the electric field strength E and the magnetic field strength H is a function of the three-dimensional space coordinates (x, y, z), i.e.:
Figure DEST_PATH_IMAGE026
，
Figure DEST_PATH_IMAGE027
，
Figure DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE029
. The function of the three-dimensional model satisfies the following equation:
Figure DEST_PATH_IMAGE030
（1）；
in the formulaJFor the purpose of the applied current density distribution,
Figure DEST_PATH_IMAGE031
for the angular frequency simulated for the integrated circuit,
Figure DEST_PATH_IMAGE032
is the intensity of a magnetic fieldHThe degree of rotation of the screw is reduced,
Figure DEST_PATH_IMAGE033
is the electric field strengthEThe degree of rotation of the screw is reduced,jis the unit of an imaginary number,j 2=-1。
when the actual PCB or chip package size in the multilayer VLSI is far larger than the metal layer, the three-dimensional model of the electromagnetic response characteristic of a frequency point in the frequency domain simulation of the multilayer VLSI can be simplified into a two-dimensional model, and the dielectric constant in the model is at the moment
Figure DEST_PATH_IMAGE034
Magnetic permeability of
Figure DEST_PATH_IMAGE035
Electric field intensityEMagnetic field intensityHAll the distributions are two-dimensional plane coordinates (x, y) I.e.:
Figure DEST_PATH_IMAGE036
，
Figure DEST_PATH_IMAGE037
，
Figure DEST_PATH_IMAGE038
，
Figure DEST_PATH_IMAGE039
the distribution is independent of z. And the potential u and the surface current density J in the fieldsSatisfies the following conditions:
Figure DEST_PATH_IMAGE040
（2）；
in the formula
Figure DEST_PATH_IMAGE041
Respectively representx，y，zThe unit vector of the direction is,E zof electric field strengthzThe direction component of the light beam is,H xandH yrespectively of magnetic field strengthxAndythe direction component of the light beam is,tis the metal layer spacing.
Through the equivalence from the three-dimensional model to the two-dimensional model, the two-dimensional finite element functional extreme value formula corresponding to the two-dimensional model is obtained as follows:
Figure DEST_PATH_IMAGE042
（3）；
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE043
the functional is a functional, the minimum value of the functional is corresponding to the variation of the functional as 0,
Figure DEST_PATH_IMAGE044
the variation of the functional is represented by the functional,
Figure DEST_PATH_IMAGE045
as a grid cell
Figure DEST_PATH_IMAGE046
The surface admittance of the first and second electrodes,pis referred to aspThe number of the boundaries is such that,
Figure DEST_PATH_IMAGE047
is a boundary
Figure DEST_PATH_IMAGE048
Opening boundary condition of (u)pIs a boundary
Figure 182944DEST_PATH_IMAGE048
The distribution of the electric potential on the upper side,
Figure DEST_PATH_IMAGE049
indicating a position to the right of the boundary and infinitely close to the boundary,
Figure DEST_PATH_IMAGE050
indicating a position to the left of the boundary and infinitely close to the boundary,
Figure DEST_PATH_IMAGE051
presentation unit
Figure 861794DEST_PATH_IMAGE046
The area of (a) is,
Figure DEST_PATH_IMAGE052
as a grid cell
Figure 944019DEST_PATH_IMAGE046
The current density of (a) is,
Figure DEST_PATH_IMAGE053
as a grid cell
Figure 759660DEST_PATH_IMAGE046
The surface resistance of the glass substrate is higher than the surface resistance of the glass substrate,
Figure DEST_PATH_IMAGE054
as a grid cell
Figure 627253DEST_PATH_IMAGE046
The potential of (2).
With the extreme condition of the above equation, a system of eigenvalue equations for the resonant modes can be formed. Solving the characteristic value equation set to obtain a plurality of characteristic values and characteristic vectors, wherein the characteristic values correspond to resonant frequency points of electromagnetic waves propagated in a dielectric layer of the integrated circuit under the passive condition of the ultra-large scale integrated circuit, the characteristic vector corresponding to each resonant frequency point corresponds to the distribution of fields under the resonant frequency points, and the frequency response corresponding to the resonant frequency points is obtained according to the distribution of the fields.
Step 102: determining an initial frequency point of each simulation sub-frequency range; the simulation sub-frequency band range is a frequency interval formed by two adjacent resonance frequency points which are arranged from small to large.
Calculated as requirediSub-band range [ 2 ]f i,min, f i,max]Determiningl i m i +1 (l i >=2, m i >=4) uniformly distributed initial frequency points if
Figure DEST_PATH_IMAGE055
Then, take the initial frequency points evenly distributed logarithmically:
Figure DEST_PATH_IMAGE056
otherwise, take the conventional uniformly distributed initial frequency points:
Figure DEST_PATH_IMAGE057
in the formula (I), the compound is shown in the specification,f i,min, f i,maxrespectively representing the lowest frequency and the highest frequency to be calculated;r>1 is a preset frequency ratio threshold; ln () represents taking the natural logarithm, exp () represents the power function of the natural logarithm base;f i,k is as followsiWithin a simulation sub-bandkAn initial frequency point;l i ，m i is a positive integer andl i ≥2，m i ≥4，m i to sample at a second sampling interval, aiThe number of the simulation sub-bands is divided into equal parts;l i for the first sampling interval and the second samplingMultiple of sample spacing.
Step 103: and calculating the electromagnetic response of the initial frequency point of each simulation sub-frequency range by using a coarse grain parallel method, respectively sampling the electromagnetic response of each simulation sub-frequency range at a first sampling interval and a second sampling interval, and determining a first electromagnetic response sequence and a second electromagnetic response sequence.
The coarse grain parallel method in step 103 is a parallel coarse grain technique for calculating and screening out parallel coarse grains according to the weighted CPU time, and specifically comprises the following steps:
step 1, according to problem calculation characteristics, defining calculation programs for executing all independent calculations of the same type in the whole calculation process as calculation particles, dividing the whole calculation program for executing the whole calculation process into a plurality of non-overlapping calculation particles, and taking an independent calculation executed by the calculation particles as a calculation task;
step 2, realizing serial calculation including single calculation of all the calculation particles, and counting the CPU time required by single classical calculation task calculation according to the calculation result;
step 3, calculating the weighted CPU time of each calculation particle and the total CPU time of the whole calculation process, wherein the weighted CPU time of each calculation particle is the time for multiplying the classical calculation times of each calculation particle in the whole calculation process by the CPU time required by the single classical calculation task calculation of each calculation particle;
step 4, sorting the calculation particles according to the weighted CPU time, selecting a plurality of calculation particles with the weighted CPU time sum being more than 99% of the total CPU time from large to small, and taking each selected calculation particle as a parallel coarse particle;
step 5, before executing the parallel coarse grains, executing the calculation grains except the parallel coarse grains by adopting a main process;
step 6, when a parallel coarse grain is executed, randomly disordering the sequence of all the calculation tasks executed by the parallel coarse grain by the main process based on a random distribution strategy according to all the calculation tasks required to be executed by the parallel coarse grain to form a new calculation task sequence;
the implementation method of the random allocation strategy comprises the following steps:
step 6-1, correspondingly generating a random number sequence { Rn }, wherein the sequence List0 of the calculation task is { N }, and N is 1,2,3, …, N;
step 6-2, sequencing the sequence { Rn } from small to large, wherein the sequence after sequencing is { On };
step 6-3, generating a new non-repeated calculation task sequence List which is { Ln }, wherein Ln is the position of the On in Rn, and the distribution sequence of the actual task is distributed according to the new non-repeated calculation task sequence List;
step 7, based on the file marking technology and the first application and first allocation strategy, the main process dynamically allocates all the calculation tasks executed by the parallel coarse grains to all the processes including the main process according to the new calculation task sequence, and completes the parallel calculation of the calculation tasks;
the file marking technology comprises the following steps: if a certain calculation task in the parallel coarse grains is distributed to a process, generating a state file of the calculation task; when applying for distributing a certain calculation task, another process will try to generate a state file of the calculation task, if the state file exists, the calculation task is indicated to be distributed, and then the other process will automatically try to apply for distributing the next calculation task;
the implementation method of the file marking technology comprises the following steps:
step 7-1, a process applies for allocationbA computing task;
step 7-2, judgmentbStatus file for a computing taskF b If the current state does not exist, jumping to the step 7-5, and if the current state does not exist, jumping to the step 7-3;
step 7-3, generating a state fileF b ；
Step 7-4, completing the first stepbCalculating a calculation task;
7-5, judging whether all calculation tasks executed by the parallel coarse grains are completely finished or not, and if not, judging whether all calculation tasks executed by the parallel coarse grains are completely finished or noti＝i+1, and returning to step 7-1, if finished, jumping to step 7-6;
7-6, finishing;
step 8, repeating the step 6 to the step 7, and sequentially completing parallel calculation of all calculation tasks to be executed by each parallel coarse particle;
and 9, after the parallel computation of all computation tasks to be executed by all the parallel coarse grains is completed, collecting computation results by the main process and performing post-processing to complete the whole computation process.
The coarse grain parallel scheme is adopted for one-time calculationl i m i +1(l i >=2，m i >=4) electromagnetic response of uniformly distributed frequency points.
Step 104: and performing interpolation processing on the first electromagnetic response sequence and the second electromagnetic response sequence to determine a first cubic spline interpolation curve and a second cubic spline interpolation curve.
Respectively to the first electromagnetic response sequence
Figure DEST_PATH_IMAGE058
And a second electromagnetic response sequence
Figure DEST_PATH_IMAGE059
And (3) carrying out interpolation to obtain a cubic spline interpolation curve: first cubic spline interpolation curveT 1(f) And a second cubic spline interpolation curveT 2(f)。
Step 105: and obtaining the maximum allowable error of the simulation curve, and determining the sampling step length of the third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that the maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve.
Due to the fact that
Figure DEST_PATH_IMAGE060
First sampling interval ofh 1Is composed of
Figure DEST_PATH_IMAGE061
Second sampling interval ofh 2Is/are as followsl i Multiple, then
Figure DEST_PATH_IMAGE062
。
In thatl i >Can be approximately considered when =2
Figure DEST_PATH_IMAGE063
。
Namely T2(f) Approximated as the true value of the electromagnetic response curve of a multilayer very large scale integrated circuit:
Figure DEST_PATH_IMAGE064
。
when in usel i >=2, using electromagnetic response sequences according to formula
Figure DEST_PATH_IMAGE065
Cubic spline interpolation function ofT 1(f) And electromagnetic response sequence
Figure DEST_PATH_IMAGE066
Cubic spline interpolation function ofT 2(f) Error determination of
Figure DEST_PATH_IMAGE067
：
Figure DEST_PATH_IMAGE068
。
In general, the maximum allowable electromagnetic response curve calculates the errorE maxFor a given one, then
Figure DEST_PATH_IMAGE069
In the formula
Figure DEST_PATH_IMAGE070
Is as followsiThe maximum distance between adjacent discrete frequency points in the sub-frequency band. Can obtain the producth i The value taking conditions are as follows:
Figure DEST_PATH_IMAGE071
。
i.e. atiSampling step length of frequency point in sub-frequency bandh i The calculation accuracy of the electromagnetic response of the designated layer of the very large scale integrated circuit can be obtained.
Step 106: and determining newly inserted frequency points between the initial frequency points in each simulation sub-frequency band according to the sampling step length of the third cubic spline interpolation curve in each simulation sub-frequency band.
Based onh i The value taking condition of (1) directly taking
Figure DEST_PATH_IMAGE072
Wherein, in the step (A),
Figure DEST_PATH_IMAGE073
，
Figure DEST_PATH_IMAGE074
which means that the rounding is made up,f i , min, f i , maxrespectively the lowest frequency and the highest frequency of the whole frequency band range; ln () represents taking the natural logarithm;N i is as followsiThe number of final sampling points in the range of the simulation sub-frequency bands;ithe serial number of the simulation sub-frequency band;E maxthe maximum allowable error of the simulation curve is obtained;T i (f) Is as followsiCubic spline interpolation curves of the sub-bands;T i1,(f) Is as followsiA first cubic spline interpolation curve of the sub-band;T i2,(f) Is as followsiA second cubic spline interpolation curve of the sub-band;h i2,is as followsiSampling step length of a second cubic spline interpolation curve of the sub-frequency band;h i3,is as followsiSub-unitSampling step length of a third cubic spline interpolation curve of the frequency band;v i is as followsiThe sub-bands replace the approximation coefficients of the fourth derivative of the electromagnetic response curve truth values with the difference between the first cubic spline interpolation curve and the second cubic spline interpolation curve,v i ≥1；ris a preset frequency ratio threshold value,r>1。
step 107: and determining the electromagnetic response of all newly inserted frequency points by using a coarse particle parallel computing method, performing cubic spline interpolation on the electromagnetic response of all the frequency points of each simulation sub-band, and determining a resonance response curve of each simulation sub-band.
Step 108: and combining the resonance response curves of all the simulated sub-bands to generate an ultra-wideband resonance response curve of the integrated circuit.
In each frequency point interval
Figure DEST_PATH_IMAGE075
Inserting new frequency point to be calculated in one time, and taking
Figure DEST_PATH_IMAGE076
。
Each frequency point interval
Figure DEST_PATH_IMAGE077
The new frequency point to be calculated is inserted into the system at one time
Figure 54167DEST_PATH_IMAGE006
。
Finally, the newly inserted frequency points to be calculated are as
Figure DEST_PATH_IMAGE078
This can be calculated simultaneously using a coarse grain parallel calculation method
Figure DEST_PATH_IMAGE079
Electromagnetic response of individual frequency points.
Fig. 2 is a structural diagram of an adaptive determination system for an ultra-wideband resonant electromagnetic response of an integrated circuit provided by the present invention, and as shown in fig. 2, an adaptive determination system for an ultra-wideband resonant electromagnetic response of an integrated circuit includes:
the resonant frequency point calculating module 201 is configured to calculate a resonant frequency point in a simulation frequency band range of the integrated circuit, and divide the simulation frequency band range into a plurality of simulation sub-frequency bands by using the resonant frequency point as a division point.
An initial frequency point determining module 202, configured to determine an initial frequency point of each simulation sub-band range; the simulation sub-frequency band range is a frequency interval formed by two adjacent resonance frequency points which are arranged from small to large.
The electromagnetic response sequence determining module 203 is configured to calculate an electromagnetic response of an initial frequency point of each simulation sub-band range by using a coarse grain parallel method, sample the electromagnetic response at a first sampling interval and a second sampling interval for each simulation sub-band, and determine a first electromagnetic response sequence and a second electromagnetic response sequence.
And the interpolation processing module 204 is configured to perform interpolation processing on the first electromagnetic response sequence and the second electromagnetic response sequence, and determine a first cubic spline interpolation curve and a second cubic spline interpolation curve.
And the sampling step size determining module 205 is configured to obtain a maximum allowable error of the simulation curve, and determine a sampling step size of a third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that the maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve.
The sampling step determining module 205 specifically includes:
a sampling step size determining unit for determining a sampling step size according to a formula
Figure DEST_PATH_IMAGE080
Is determined to beiThird cubic spline interpolation curve of simulation sub-frequency bandA sampling step length of the line; wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE081
，N i is as followsiThe number of final sampling points in the range of the simulation sub-frequency bands;ithe serial number of the simulation sub-frequency band;
Figure DEST_PATH_IMAGE082
is to round up upwards;f i i,mnis as followsiThe lowest frequency of the sub-bands;f i,maxis as followsiThe highest frequency of the sub-band; ln () represents taking the natural logarithm;E maxthe maximum allowable error of the simulation curve is obtained;T i (f) Is as followsiCubic spline interpolation curves of the sub-bands;T i1,(f) Is as followsiA first cubic spline interpolation curve of the sub-band;T i2,(f) Is as followsiA second cubic spline interpolation curve of the sub-band;h i2,is as followsiSampling step length of a second cubic spline interpolation curve of the sub-frequency band;h i3,is as followsiSampling step length of a third cubic spline interpolation curve of the sub-frequency band;v i is as followsiThe sub-bands replace the approximation coefficients of the fourth derivative of the electromagnetic response curve truth values with the difference between the first cubic spline interpolation curve and the second cubic spline interpolation curve, v i ≥1；ris a preset frequency ratio threshold value,r>1。
a newly inserted frequency point determining module 206, configured to determine, according to the sampling step size of the third cubic spline interpolation curve in each simulated sub-band, a newly inserted frequency point between the initial frequency points in each simulated sub-band.
The newly inserted frequency point determining module 206 specifically includes:
a unit for determining the number of frequency points to be inserted, for determining the number of frequency points to be inserted according to a formula
Figure DEST_PATH_IMAGE083
Is determined to beiThe number of frequency points to be inserted in each sub-band; wherein the content of the first and second substances,n i,new is as followsiThe number of frequency points to be inserted in each sub-band;
Figure 309175DEST_PATH_IMAGE082
is to round up upwards;
a newly inserted frequency point determination unit for determining a frequency point according toiCalculating the number of frequency points to be inserted in each sub-bandiNewly inserted frequency points between the initial frequency points in each sub-band.
The newly inserted frequency point determining unit specifically includes:
a newly inserted frequency point determination subunit for determining the frequency point according to the formula
Figure 381036DEST_PATH_IMAGE006
Determine insertion toiNewly inserted frequency points among the initial frequency points in each sub-frequency band; wherein ln () represents taking the natural logarithm, exp () represents the power function of the natural logarithm base;f i,k is as followsiSub-band ofkA second sampling frequency point;f i,k+1is as followsiSub-band ofk+1 second sampling frequency points of the first sampling frequency,f i , k,j is as followsiSub-band ofkA second sampling frequency point andka number one between +1 second sampling frequency pointsjA newly inserted frequency point;m i to sample at a second sampling interval, aiThe number of the simulation sub-bands is divided into equal parts;l i is a multiple of the first sampling interval and the second sampling interval.
And the simulation sub-band resonance response curve determining module 207 is configured to determine electromagnetic responses of all newly inserted frequency points by using a coarse grain parallel computing method, perform cubic spline interpolation on the electromagnetic responses of all frequency points of each simulation sub-band, and determine a resonance response curve of each simulation sub-band.
An integrated circuit ultra-wideband resonance response curve generating module 208, configured to combine the resonance response curves of all the simulated sub-bands to generate an integrated circuit ultra-wideband resonance response curve.
Assuming that the frequency range of electromagnetic response to be calculated of a certain multilayer super large scale integrated circuit is 10 Hz-10 GHz, calculating a single-ended signal S response curve of the multilayer super large scale integrated circuit in the frequency range by adopting an adaptive frequency point sampling technology, and calculating the single-ended signal S response curve by S11The curves are illustrated as examples.
Firstly, a resonance calculation mode is adopted to calculate the resonance frequency point and the electromagnetic response of the super-large scale integrated circuit within a preset frequency range, and the resonance frequency and the S of a certain multilayer super-large scale integrated circuit are shown in table 111The results of the parameter calculations are shown schematically in table 1.
TABLE 1
Figure DEST_PATH_IMAGE084
Dividing the whole frequency range of 10 Hz-10 GHz into 5 sub-frequency bands based on the calculated resonant frequency, wherein the frequency bands are respectively as follows:
10 Hz~998.2 Hz, 998.2 Hz~20.05 kHz, 20.05 kHz~10.02 MHz, 10.02 MHz~0.898 GHz, 0.898GHz~10 GHz。
thirdly, accurately fitting an electromagnetic response curve of each sub-frequency band by using a twice interpolation method for each sub-frequency band, wherein the specific process is as follows:
1) is provided withl=2, mAnd =4, the responses of 9 frequency points are calculated once for each frequency sub-band, the frequency points repeated by adjacent frequency sub-bands only need to be calculated once, and the total number of the frequency points to be calculated is 41.
2) For each sub-band, respectively for the electromagnetic response sequence
Figure DEST_PATH_IMAGE085
And
Figure DEST_PATH_IMAGE086
interpolation is carried out to obtain a cubic spline interpolation functionT 1(f) AndT 2(f). Of all sub-bands within the entire range of the calculated bandT 1(f) AndT 2(f) The curve of (a) is shown in fig. 3.
3) Assuming that the allowable maximum electromagnetic response curve calculation error is 5%, in each frequency band, firstly, according to the calculated interpolation functionT 1(f) AndT 2(f) Each sub-band is available
Figure DEST_PATH_IMAGE087
Substituting the formula into the formula, calculating
Figure DEST_PATH_IMAGE088
Substituting the formula to calculatehWill behCan be calculated by substitutingn newTable 2 is a schematic table of calculation results of different amounts for each sub-band, and as shown in table 2, it can be seen that new frequency points (0 +8+8+8+8= 32) need to be inserted on the basis of the originally calculated 41 frequency points. Finally, the number of the calculated discrete frequency point responses is 73 (41+32=73), and a cubic spline interpolation curve of the discrete frequency point responses is shown in fig. 4.
TABLE 2
Figure DEST_PATH_IMAGE089
The method and the device adaptively determine newly added sampling frequency points based on twice cubic spline interpolation curve errors, obtain pre-designated calculation precision through the minimum sampling frequency points, and further calculate the frequency response of all newly added sampling frequency points at one time by adopting a parallel calculation method aiming at the newly added sampling frequency points, thereby improving the calculation efficiency and solving the calculation time cost.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (4)

1. A method for adaptively determining an ultra-wideband resonant electromagnetic response of an integrated circuit, comprising:
calculating a resonance frequency point in a simulation frequency band range of the integrated circuit, and dividing the simulation frequency band range into a plurality of simulation sub-frequency bands by taking the resonance frequency point as a dividing point;
determining an initial frequency point of each simulation sub-frequency range; the simulation sub-frequency band range is a frequency interval formed by two adjacent resonance frequency points which are arranged from small to large;
calculating the electromagnetic response of the initial frequency point of each simulation sub-frequency band range by using a coarse grain parallel method, respectively sampling the electromagnetic response of each simulation sub-frequency band at a first sampling interval and a second sampling interval, and determining a first electromagnetic response sequence and a second electromagnetic response sequence;
performing interpolation processing on the first electromagnetic response sequence and the second electromagnetic response sequence to determine a first cubic spline interpolation curve and a second cubic spline interpolation curve;
acquiring the maximum allowable error of the simulation curve, and determining the sampling step length of a third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that the maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve;
determining newly inserted frequency points between the initial frequency points in each simulation sub-frequency band according to the sampling step length of the third cubic spline interpolation curve in each simulation sub-frequency band;
determining the electromagnetic response of all newly inserted frequency points by using a coarse particle parallel computing method, performing cubic spline interpolation on the electromagnetic response of all the frequency points of each simulation sub-band, and determining a resonance response curve of each simulation sub-band;
combining the resonance response curves of all the simulated sub-bands to generate an ultra-wideband resonance response curve of the integrated circuit;
the obtaining of the maximum allowable error of the simulation curve, and determining the sampling step size of the third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that the maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve specifically includes:
according to the formula
Figure 987332DEST_PATH_IMAGE002
Is determined to beiSampling step length of a third cubic spline interpolation curve of each simulation sub-frequency band; wherein the content of the first and second substances,
Figure 983101DEST_PATH_IMAGE004
，N i is as followsiThe number of final sampling points in the range of the simulation sub-frequency bands;ithe serial number of the simulation sub-frequency band;
Figure DEST_PATH_IMAGE005
is to round up upwards;f i,minis as followsiThe lowest frequency of the sub-bands;f i,maxis as followsiThe highest frequency of the sub-band; ln () represents taking the natural logarithm;E maxthe maximum allowable error of the simulation curve is obtained;T i (f) Is as followsiCubic spline interpolation curves of the sub-bands;T i1,(f) Is as followsiSub-band ofA cubic spline interpolation curve;T i2,(f) Is as followsiA second cubic spline interpolation curve of the sub-band;h i2,is as followsiSampling step length of a second cubic spline interpolation curve of the sub-frequency band;h i3,is as followsiSampling step length of a third cubic spline interpolation curve of the sub-frequency band;v i is as followsiThe sub-bands replace the approximation coefficients of the fourth derivative of the electromagnetic response curve truth values with the difference between the first cubic spline interpolation curve and the second cubic spline interpolation curve,v i ≥1；ris a preset frequency ratio threshold value,r>1；
wherein, the determining of the newly inserted frequency point between the initial frequency points in each simulation sub-band according to the sampling step length of the third cubic spline interpolation curve in each simulation sub-band specifically includes:
according to the formula
Figure 903783DEST_PATH_IMAGE006
Is determined to beiThe number of frequency points to be inserted in each sub-band; wherein the content of the first and second substances,n i,new is as followsiThe number of frequency points to be inserted in each sub-band;
Figure 830151DEST_PATH_IMAGE005
is to round up upwards;
according to the firstiCalculating the number of frequency points to be inserted in each sub-bandiNewly inserted frequency points between the initial frequency points in each sub-band.
2. The method of adaptively determining an ultra-wideband resonant electromagnetic response of an integrated circuit of claim 1, wherein said determining is based oniCalculating the number of frequency points to be inserted in each sub-bandiThe newly inserted frequency points between the initial frequency points in each sub-band specifically include:
according to the formula
Figure 926414DEST_PATH_IMAGE008
Determine insertion toiNewly inserted frequency points among the initial frequency points in each sub-frequency band; wherein ln () represents taking the natural logarithm, exp () represents the power function of the natural logarithm base;f i,k is as followsiSub-band ofkA second sampling frequency point;f i,k+1is as followsiSub-band ofk+1 second sampling frequency points of the first sampling frequency,f i , k,j is as followsiSub-band ofkA second sampling frequency point andka number one between +1 second sampling frequency pointsjA newly inserted frequency point;m i to sample at a second sampling interval, aiThe number of the simulation sub-bands is divided into equal parts;l i is a multiple of the first sampling interval and the second sampling interval.
3. An adaptive determination system for an ultra-wideband resonant electromagnetic response of an integrated circuit, comprising:
the resonance frequency point calculating module is used for calculating resonance frequency points in a simulation frequency band range of the integrated circuit, taking the resonance frequency points as dividing points and dividing the simulation frequency band range into a plurality of simulation sub-frequency bands;
the initial frequency point determining module is used for determining the initial frequency point of each simulation sub-frequency range; the simulation sub-frequency band range is a frequency interval formed by two adjacent resonance frequency points which are arranged from small to large;
the electromagnetic response sequence determining module is used for calculating the electromagnetic response of the initial frequency point of each simulation sub-frequency band range by using a coarse grain parallel method, respectively sampling the electromagnetic response of each simulation sub-frequency band at a first sampling interval and a second sampling interval, and determining a first electromagnetic response sequence and a second electromagnetic response sequence;
the interpolation processing module is used for carrying out interpolation processing on the first electromagnetic response sequence and the second electromagnetic response sequence to determine a first cubic spline interpolation curve and a second cubic spline interpolation curve;
the sampling step length determining module is used for acquiring the maximum allowable error of the simulation curve, and determining the sampling step length of the third cubic spline interpolation curve of each simulation sub-band according to the first cubic spline interpolation curve in each simulation sub-band and the second cubic spline interpolation curve in each simulation sub-band, so that the maximum error estimation of the third cubic spline interpolation curve of each simulation sub-band is smaller than the maximum allowable error of the simulation curve;
a newly inserted frequency point determining module, configured to determine, according to the sampling step size of the third cubic spline interpolation curve in each simulation sub-band, a newly inserted frequency point between the initial frequency points in each simulation sub-band;
the simulation sub-band resonance response curve determining module is used for determining the electromagnetic response of all newly inserted frequency points by using a coarse particle parallel computing method, performing cubic spline interpolation on the electromagnetic response of all the frequency points of each simulation sub-band, and determining the resonance response curve of each simulation sub-band;
the integrated circuit ultra-wideband resonance response curve generation module is used for combining the resonance response curves of all the simulated sub-frequency bands to generate an integrated circuit ultra-wideband resonance response curve;
the sampling step determining module specifically includes:
a sampling step size determining unit for determining a sampling step size according to a formula
Figure DEST_PATH_IMAGE009
Is determined to beiSampling step length of a third cubic spline interpolation curve of each simulation sub-frequency band; wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE011
，N i is as followsiThe number of final sampling points in the range of the simulation sub-frequency bands;ithe serial number of the simulation sub-frequency band;
Figure 342352DEST_PATH_IMAGE005
is to round up upwards; ln () represents taking the natural logarithm;f i,minis as followsiThe lowest frequency of the sub-bands;f i,maxis as followsiThe highest frequency of the sub-band;E maxthe maximum allowable error of the simulation curve is obtained;T i (f) Is as followsiCubic spline interpolation curves of the sub-bands;T i1,(f) Is as followsiA first cubic spline interpolation curve of the sub-band;T i2,(f) Is as followsiA second cubic spline interpolation curve of the sub-band;h i2,is as followsiSampling step length of a second cubic spline interpolation curve of the sub-frequency band;h i3,is as followsiSampling step length of a third cubic spline interpolation curve of the sub-frequency band;v i is as followsiThe sub-bands replace the approximation coefficients of the fourth derivative of the electromagnetic response curve truth values with the difference between the first cubic spline interpolation curve and the second cubic spline interpolation curve,v i ≥1；ris a preset frequency ratio threshold value,r>1；
the newly inserted frequency point determining module specifically includes:
a unit for determining the number of frequency points to be inserted, for determining the number of frequency points to be inserted according to a formula
Figure 153925DEST_PATH_IMAGE012
Is determined to beiThe number of frequency points to be inserted in each sub-band; wherein the content of the first and second substances,n i,new is as followsiThe number of frequency points to be inserted in each sub-band;
Figure 883984DEST_PATH_IMAGE005
is to round up upwards;
a newly inserted frequency point determination unit for determining a frequency point according toiCalculating the number of frequency points to be inserted in each sub-bandiNewly inserted frequency points between the initial frequency points in each sub-band.
4. The system of claim 3, wherein the newly inserted frequency point determination unit comprises:
a newly inserted frequency point determination subunit for determining the frequency point according to the formula
Figure 84021DEST_PATH_IMAGE014
Determine insertion toiNewly inserted frequency points among the initial frequency points in each sub-frequency band; wherein ln () represents taking the natural logarithm, exp () represents the power function of the natural logarithm base;f i,k is as followsiSub-band ofkA second sampling frequency point;f i,k+1is as followsiSub-band ofk+1 second sampling frequency points of the first sampling frequency,f i , k,j is as followsiSub-band ofkA second sampling frequency point andka number one between +1 second sampling frequency pointsjA newly inserted frequency point;m i to sample at a second sampling interval, aiThe number of the simulation sub-bands is divided into equal parts;l i is a multiple of the first sampling interval and the second sampling interval.
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