CN106484946B - PDN capacitor optimization method based on lossless resonant cavity power ground planar hull modelling - Google Patents
PDN capacitor optimization method based on lossless resonant cavity power ground planar hull modelling Download PDFInfo
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Abstract
The invention discloses a kind of PDN capacitor optimization methods based on lossless resonant cavity power ground planar hull modelling.Implementation step is: 1) designing the relevant parameter inputted in power distribution network；2) initial power distribution network impedance value is calculated according to result 1)；3) decoupling capacitor number is calculated according to the parameter of 1) design；4) according to 2-3) result calculate actual power distribution network impedance value Z；5) judge discrete point in frequency fnWith maximum target frequency fmaxRelationship: if fn< fmax, then follow the steps 6), if fn=fmax, then the result of step 3) is exported；6) the target impedance Z designed by Z and 1)tIt makes comparisons: if Z > Zt, return step 3), otherwise, 1 is added to the subscript n of discrete point in frequency, return step 4).The present invention has expanded target frequency bands, and capacitor number is reduced under conditions of meeting power distribution network design requirement, can be used for the design analysis of High Speed System.
Description
Technical field
The invention belongs to technical field of circuit design, in particular to a kind of capacitor optimization method of power distribution network PDN,
It can be used for the optimization design of decoupling network in power distribution network in high speed circuit.
Background technique
As working frequency of chip is higher and higher and devices switch speed is getting faster, power distribution network PDN is designed not
Only need to provide pure power supply for circuit, also act as and provide low noise circuit for high speed signal, between multi-chip noise isolation with
And ensure the effect of electromagnetic compatibility characteristic.Power distribution network mainly includes DC power supply, and voltage control module VRM is also DC-
DC converter, printing board PCB plate grade decoupling capacitor, pcb board level power supply/ground level, the connectors such as socket, package level electricity
Source/ground level, package level decoupling capacitor, connecting line, on piece PDN and on piece decoupling capacitor etc..It is for high speed in summary
The design and analysis of PDN is vital in system.
The design of power distribution network, typically from frequency domain, application target impedance is as reference standard, and nearly 20 years
It is all mainly using Larry D.Smith et al. in " Power Distribution System Design Methodology
Mention in and Capacitor Selection for Modern CMOS Technology " article based on target impedance
PDN design method makes PDN impedance be lower than target impedance in target frequency bands by adding different types of decoupling capacitor, this
The key problem of one process is the determination of decoupling capacitor capacitance and number.
" the Comparison of Power Distribution Network Design that Istvan Novak is delivered
Methods:Bypass Capacitor Selection Based on Time Domain and Frequency Domain
The decoupling capacitor selection method in power distribution network design process is summarized and has been compared in Performances ",
It is related to 4 kinds of common methods: (1) " Big-V " in text；(2)"Distributed Matched Bypassing"(DMB)；(3)
"Capacitors-by-the-decade"(CBD)；(4)"Multi-pole"(MP).Wherein:
Big " V " method is to reduce PDN impedance using the Low ESR of the identical multiple capacitor parallel connections generations of capacitance,
Therefore PDN impedance curve shows as deep " V " shape in shape.The disadvantages of the method are as follows entire design process only uses a kind of decoupling
Capacitor, though being easily achieved, the capacitor number generally required is more, and redundancy is larger.
Distributed Matched Bypassing method be by entire target frequency bands carry out discrete partition,
Matched decoupling capacitor is chosen in each discrete frequency range.The disadvantages of the method are as follows the ununified frequency range criteria for classifying, no
Conducive to the Automation Design.
Latter two method then suggests choosing decoupling capacitor in the band limits of each order of magnitude when carrying out PDN design
Device.The difference of the two is that Capacitors-by-the-decade method is to choose a kind of capacitor in each order of magnitude frequency range
And Multi-pole is then to choose a variety of capacitors.Latter two method is disadvantageous in that used on each order of magnitude
Capacitor number and type are limited, but might not can be met in actual design, while the decoupling electricity designed
Container number is also not least.
Another critical issue of PDN design process is exactly parameter extraction and the modeling for product systems, wherein most core
The part of the heart is the modeling of power supply ground level, works " Power Integrity of the Madhavan Swaminathan at him
Phase has been carried out to power ground planar hull modelling in Modeling and Design for Semiconductors and Systems "
When it is detailed classification compare, be totally segmented into two classes: lump modeling method and distributed modeling method, the former the advantages of be to build
Mould is convenient, and the circuit system for being suitble to working frequency not high, the disadvantage is that its simulation accuracy will be far short of what is expected for High Speed System.Just
Elegant qin, Li Weizhe etc. is in its patent of invention " the power distribution network design method based on flying capacitor selection algorithm "
(CN201210001643) local element equivalent circuit PEEC modeling method used by just belongs to one kind of lump modeling method,
This is also the common method of PDN power ground planar hull modelling.
However as being continuously increased for circuit system frequency, this modeling pattern has its limitation, therefore high speed is
More accurate design method of uniting is using distributed modeling method.Existing distributed modeling is according to using different mathematics works
Tool method can be divided into again: Green Function Method, finite difference calculus, transfer matrix method, multi layer finite difference method, has Resonant-cavity Method
Limit FD―TD method, Fast solution method and FInite Element, macromodel method etc..These distributed modeling method advantages are high frequency systems
Simulation accuracy is higher in system, the disadvantage is that calculation amount is huge, modeling process is more complex.
Summary of the invention
It is an object of the invention to overcome above-mentioned the deficiencies in the prior art, propose a kind of based on lossless resonant cavity power supply Horizon
The PDN capacitor optimization method of face modeling simplifies modeling process, improves the high frequency simulation accuracy of system to reduce calculation amount.
To achieve the above object, the present invention is based on the PDN capacitor optimization method of lossless resonant cavity power ground planar hull modelling,
Technical solution includes the following:
(1) parameter pre-treatment step:
1a) according to integrated chip IC maximum operating currenbt Imax, regulated power supply voltage Vo, ripple factor r, calculate power supply point
The target impedance Z of distribution networkt, while determining the range of target frequencies f for needing to meet target impedancemin~fmax；
The equivalent resistance R of regulated power supply 1b) is determined by software emulation or instrument and equipmentoWith equivalent inductance LoParameter with
And the equivalent resistance R of the big capacity electrolyte capacitor in voltage regulator circuitb, equivalent inductance Lb, equivalent capacity Cb；
1c) the corresponding dead resistance of the package lead of integrated chip IC, via hole is successively extracted using FastHenry software
RpWith parasitic inductance Lp；
Unit grids segmentation 1d) is carried out to printing board PCB, determines the port I (x of regulated power supplyi,yi) and it is integrated
Chip port J (xj,yj), wherein (xi,yi) indicate position coordinates of the regulated power supply on pcb board, (xj,yj) indicate integrated chip
Position coordinates on pcb board；
1e) type of the decoupling capacitor used required in design is marked, is denoted as 1,2,3 ... ..., m, every kind
The parameter of type mark includes the capacitance C [m], equivalent resistance R [m], equivalent inductance value L [m] of capacitor, according to these ginsengs
Number calculates the self-resonant frequency of decoupling capacitor:
(2) it calculates primary power and distributes network impedance step:
2a) according to 1b), 1c) in extract determination regulated power supply equivalent resistance Ro, equivalent inductance Lo, large capacity electrolysis
The equivalent resistance R of capacitorb, equivalent inductance Lb, equivalent capacity Cb, the dead resistance R of IC package lead, via holep, parasitic inductance Lp,
Calculate separately regulated power supply equivalent impedance Zo(f), big capacity electrolyte capacitor equivalent impedance Zb(f), IC package via hole equivalent impedance Zp
(f), wherein f is frequency；
2b) according to lossless resonant cavity power ground planar hull modelling method, the self-impedance coefficient of regulated power supply port I is calculated separately
Zii(f), the self-impedance coefficient Z of integrated chip port Jjj(f), regulated power supply is to the transfger impedance coefficient Z between integrated chipij
(f), integrated chip is to the transfger impedance coefficient Z between regulated power supplyji(f)；By these impedance factors Zii(f)、Zjj(f)、Zij(f)、
Zji(f) it substitutes into conversion formula, corresponding equivalent parallel impedance Z in T-type impedance network is calculatedpc(f) and the first equivalent string
Join impedance Zsc1(f), the second equivalent series resistance Zsc2(f)；In conjunction with 2a) in regulated power supply equivalent impedance Zo(f), large capacity electricity
Solve capacitor equivalent impedance Zb(f), IC package via hole equivalent impedance Zp(f), the equivalent impedance of primary power distribution network is calculated
Zi(f)；
(3) power distribution network impedance value and target impedance step under more each discrete point in frequency:
Sliding-model control 3a) is carried out to given target frequency bands, is obtained with minimum frequency fminFor initial frequency point f0, maximum
Frequency fmaxTo terminate Frequency point fNDiscrete point in frequency set: f0、f1…fn…fN-1、fN；
3b) be according to the impedance value of power distribution network frequency function Z (f), in discrete point in frequency fnLess than or equal to most
Big frequency fmaxUnder the premise of, calculate discrete point in frequency fnEquivalent impedance Z (the f of corresponding power distribution networkn), and by itself and mesh
Mark impedance ZtIt is compared, if Z (fn) > Zt, then Frequency point F=f is markedn, execute step (4)；Otherwise, step 3c is executed)；
Discrete point in frequency subscript n=n+1 3c) is enabled, new discrete point in frequency f is obtainedn, return step 3b)；
(4) decoupling capacitor step is added:
4a) with the self-resonant frequency value f of all available decoupling capacitors in 1e)rStep 3b is individually subtracted in [m]) label
The value F of Frequency point obtains decoupling capacitor corresponding to the smallest self-resonant frequency value of value F difference with the Frequency point, and will
The decoupling capacitor is labeled as capacitance present device C [u]；
4b) calculate the minimum use number N of capacitance present device C [u] in current power distribution networko[u], it is basic herein
On recalculate power distribution network impedance value Z (fn), if Z (fn) > Zt, enable N [u]=No[u], and execute step 4c)；It is no
Then, return step 3c)；
Number N 4c) is used to the minimum of capacitance present device C [u]o[u] is finely adjusted processing, recalculates power distribution net
Network impedance value Z (fn), until meeting condition Z (fn) < Zt, and the capacitor after being finely tuned uses number N [u], return step
3c)；
(5) optimum results step is exported:
5a) the corresponding primary power distribution network impedance value Z of discrete frequency obtained according to step (2)i(fn), utilize work
Journey software for calculation MATLAB exports range of target frequencies fmin~fmaxPrimary power distribution network impedance curve Q1；
5b) the corresponding power distribution network impedance value Z (f of discrete frequency obtained according to step 3b)n), utilizing works meter
It calculates software MATLAB and exports range of target frequencies fmin~fmaxPower distribution network impedance curve Q2；
5c) according to the type C [u] of selected decoupling capacitor in step 4b) and using number N [u], utilizing works are calculated
Software MATLAB exports range of target frequencies fmin~fmaxThe impedance curve Q3 for having selected shunt capacitor.
Compared with the prior art, the invention has the following advantages:
1. the present invention due to during power ground planar hull modelling use lossless Resonant-cavity Method, in conventional method by power supply
Ground level is equivalent to be compared at plane capacitance, and this method has preferably emulation fitting precision, experimental data table in high-frequency range
It is bright, although two methods suffer from relatively good degree of fitting in the frequency range of 100MHz, when test frequency be increased to GHz it
Afterwards, there is better degree of fitting using lossless Resonant-cavity Method.
2. the present invention, can be by complicated lossless resonant cavity impedometer due to carrying out sliding-model control to target frequency bands
It is equivalent at simple discretization Two-port Network Parameters to calculate formula, and by conversion formula, is calculated corresponding discrete
Change T-type impedance network parameter, to achieve the purpose that simplify whole power distribution network circuit modeling.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is that two-port network is converted to the power distribution network circuit original obtained after T-type impedance network in the present invention
Reason figure；
Fig. 3 is the PDN impedance curve result schematic diagram emulated with the method for the present invention.
Specific embodiment
Referring to Fig.1, the present invention includes following realization step:
Step 1: parameter pretreatment.
Integrated chip IC maximum operating currenbt I is setmax=2A, regulated power supply voltage Vo=3V, ripple factor r=0.05,
Calculate the target impedance of power distribution network: Zt=Vo×r/(Imax/ 2)=3V × 0.05/ (2A/2)=0.15 Ω；
The equivalent resistance R of regulated power supply is seto=2m Ω and equivalent inductance Lo=30nH, big capacity electrolyte capacitor it is equivalent
Resistance Rb=0.06 Ω, equivalent inductance Lb=2.3nH, equivalent capacity Cb=47 μ F；
The overall parasitic resistance R of IC package lead and via hole is setp=0.05 Ω, parasitic inductance Lp=20pH；
Determine range of target frequencies: 0~0.5GHz, i.e. fmin=0, fmax=0.5GHz.
Step 2: the port parameter of setting power ground planar dimension parameter, regulated power supply and integrated chip.
The related physical dimensional parameters of power supply layer plane in multilayer printed circuit board PCB and formation plane: power supply are set
The long w of layer plane and formation planex=0.127m, width wy=0.127m, the medium thickness between power supply layer plane and formation plane
Spend h=2.5 × 10-4M, and unit grids processing is carried out to power supply ground level, i.e., power supply ground level is divided into 5 × 5 unit
Lattice point, the size of each unit grids unit are as follows: 0.0254m × 0.0254m；
Port I (the x of regulated power supply is seti,yi), wherein xi=1, yi=1；
Integrated chip port J (x is setj,yj), wherein xj=2.5, yj=2.5.
Step 3: input capacitor parameter.
This simulation example has selected 16 kinds of decoupling capacitors, and the parameter of each type label includes the capacitance C of capacitor
[m], equivalent resistance R [m], equivalent inductance value L [m], m are the label of capacitor type, m ∈ 1-16；
The self-resonant frequency of every a kind of decoupling capacitor is calculated according to these parameters:
Step 4: the impedance value of primary power distribution network is calculated.
(4.1) sliding-model control is carried out to target frequency bands:
Logarithm operation first is taken to 0~0.5GHz of target frequency bands, then equably chooses the Frequency point of 10000 discretizations, is obtained
To the set of discrete point in frequency: f0、f1…fn…f9999、f10000；
(4.2) Two-port Network Parameters are converted into T-type impedance network parameter, it is public using lossless resonant cavity impedance computation
Formula calculates separately the self-impedance coefficient Z of the regulated power supply port I of target frequency bands sliding-model controlii(fn), target frequency bands discretization
The self-impedance coefficient Z of the integrated chip port J of processingjj(fn), the regulated power supply of target frequency bands sliding-model control to integrated chip
Between transfger impedance coefficient Zij(fn), the integrated chip of target frequency bands sliding-model control to the transfger impedance coefficient between regulated power supply
Zji(fn) it is as follows:
Wherein j is imaginary number, and f is frequency, and μ is the magnetic permeability magnetic conductivity of dielectric material, wx, wy, h is respectively power supply ground level
Length and width, thickness, m, n are corresponding subscript variables in cumulative summation operation, and M is the cumulative upper limit of the first order:
N is the cumulative upper limit in the second level:fM、fNRespectively first order cutoff frequency and second level cutoff frequency,
M=N and meet fM=fM=fmax=0.5GHz；ConstantεrFor the dielectric constant of medium, c is the light velocity；
kxm=(m π)/wxFor intermediate variable relevant to x, kyn=(n π)/wyFor intermediate variable relevant to y；χmnFor conditional-variable: when
When m=0 and n=0, χmn 2=1；As m=0 or n=0, χmn 2=2；When m ≠ 0 and n ≠ 0, χmn 2=4.
Since the regulated power supply of target frequency bands sliding-model control is to the transfger impedance coefficient Z between integrated chipij(fn) and mesh
The integrated chip of frequency range sliding-model control is marked to the transfger impedance coefficient Z between regulated power supplyji(fn) it is equal, therefore can by this two
Port network is equivalent at T-type impedance network, by T-type impedance network conversion formula, calculates separately target frequency in T-type impedance network
Corresponding equivalent parallel impedance Z after section sliding-model controlpc(fn) and the first equivalent series resistance Zsc1(fn), the second equivalent series
Impedance Zsc2(fn) it is as follows:
Zpc(fn)=Zij(fn),
Zsc1(fn)=Zii(fn)-Zij(fn),
Zsc2(fn)=Zjj(fn)-Zij(fn),
With the power supply ground level equivalent capacity in the equivalent T-type impedance network replacement existing method of power supply ground level, this is obtained
The power distribution network equivalent-circuit model of invention, as shown in Fig. 2, containing power module of voltage regulation part, Voltage stabilizing module in Fig. 2
Equivalent impedance part, power supply ground level equivalent T-type impedance network part, capacitor decoupling network portion, integrated chip part, IC envelope
Fill lead and the total spurious impedance part of via hole；
(4.3) primary power for calculating target frequency bands sliding-model control distributes network impedance:
(4.3a) is according to the equivalent resistance R of the regulated power supply being arranged in step 1o=2m Ω and equivalent inductance Lo=30nH,
Calculate Voltage stabilizing module impedance: Zo(fn)=Ro+j2πfnLo=2 × 10-3+6π×10-8fnj
(4.3b) is according to the equivalent resistance R of the big capacity electrolyte capacitor being arranged in step 1b=0.06 Ω, equivalent inductance Lb
=2.3nH, equivalent capacity Cb=47 μ F calculate the impedance of big capacity electrolyte capacitor device:
(4.3c) is according to the overall parasitic resistance R that IC package lead and via hole are arranged in step 1p=0.05 Ω, parasitic electricity
Feel Lp=20pH calculates the total impedance of IC package lead and via hole: Zp(fn)=Rp+j2πfnLpπ × 10=0.05+4-11fnj；
(4.3d) is according to Voltage stabilizing module impedance Z in step (4.3a)o(fn) and step (4.3b) in big capacity electrolyte capacitor device
Impedance Zb(fn), calculate First Transition electric conductivity value: Y1(fn)=1/Zo(fn)+1/Zb(fn)；
(4.3e) according in step (4.2) in T-type impedance network after target frequency bands sliding-model control it is corresponding first equivalent
Series impedance Zsc1(fn), calculate the second transition electric conductivity value: Y2(fn(the Z of)=1/sc1(fn)+1/Y1(fn))；
(4.3f) is according to corresponding equivalent parallel after target frequency bands sliding-model control in T-type impedance network in step (4.2)
Impedance Zpc(fn), calculate third transition electric conductivity value: Y3(fn)=1/Zpc(fn)+Y2(fn)；
(4.3g) according in step (4.2) in T-type impedance network after target frequency bands sliding-model control it is corresponding second equivalent
Series impedance Zsc2(fn), calculate the 4th transition electric conductivity value: Y4(fn(the Z of)=1/sc2(fn)+1/Y3(fn))；
(4.3h) is according to the total impedance Z of IC package lead and via hole in step (4.3c)p(fn), calculate power distribution network
Initial impedance: Z (fn)=Zp(fn)+1/Y4(fn)。
Step 5: decoupling capacitor number is added.
(5.1) it calculates current decoupling capacitor and at least uses number:
Minimum use number N of the currently selected capacitor with marked as u in current power distribution network0[u]=R
[u]/Zt, wherein R [u] is the current equivalent resistance for selecting capacitor of the capacitor marked as u, and to No[u] is taken upwards
Whole operation, to guarantee that the number of every kind of capacitor is greater than 0；
(5.2) processing is finely adjusted to the capacitor number currently selected:
Calculating power distribution network impedance value Z (fn) during, if Z (fn) > Zt, then N is enabledo[u]=No[u]+1, and
The process is repeated until meeting Z (fn) < Zt, finally obtain the use number N [u] after capacitance present device is finely tuned.
Step 6: the impedance value of the practical power distribution network after addition decoupling capacitor is calculated.
(6.1) 16 kinds of capacitors are selected, the capacitor decoupling network admittance value after calculation optimization:
Wherein C [u] is the current capacitance for selecting capacitor of the capacitor marked as u, and R [u] is currently to select capacitor
The equivalent resistance of capacitor marked as u, L [u] are the current equivalent inductance value for selecting capacitor of the capacitor marked as u, N
[u] is the current use number for selecting capacitor of the capacitor marked as u；
(6.2) according to the total impedance Z of IC package lead and via hole in step (4.3c)p(fn), the 4th mistake in step (4.3g)
Cross electric conductivity value Y4(fn) and step (6.1) in optimization after capacitor decoupling network admittance value Ycap(fn), calculate power distribution network
Practical impedance: Z (fn)=Zp(fn)+1/(Ycap(fn)+Y4(fn))。
Step 7: according to discrete point in frequency fnSize determine final output.
As discrete point in frequency fnLess than maximum target frequency fmaxWhen=0.5GHz, practical power in step 6 is distributed to net
Impedance value Z (the f of networkn) and target impedance ZtIt is compared, if Z (fn) > Zt, then return step five；Otherwise discrete point in frequency is enabled
Subscript n=n+1 obtains new discrete point in frequency fn, and return step six；
As discrete point in frequency fnEqual to maximum target frequency fmaxWhen=0.5GHz, output such as lower curve and parameter:
The corresponding primary power distribution network impedance value Z of discrete frequency obtained according to step 4i(fn), utilizing works meter
Calculate the impedance curve Q1 of the primary power distribution network of software MATLAB output 0~0.5GHz of range of target frequencies；
The corresponding power distribution network impedance value Z (f of discrete frequency obtained according to step (6.2)n), utilizing works calculate
Software MATLAB exports the impedance curve Q2 of the practical power distribution network of 0~0.5GHz of range of target frequencies；
According to the type C [u] of selected decoupling capacitor in step (6.1) and using number N [u], utilizing works are calculated
The impedance curve Q3 for having selected shunt capacitor of software MATLAB output 0~0.5GHz of range of target frequencies；
Utilizing works software for calculation MATLAB calculates and exports the summation that selected 16 kinds of capacitors use number:
The primary power distributes network impedance curve Q1, practical power distribution network impedance curve Q2, has selected simultaneously
Join the impedance curve Q3 of capacitor, as shown in Figure 3.From the figure 3, it may be seen that the power distribution network impedance value Z (f after optimizationn) in mesh
It marks within the scope of 0~0.5GHz of frequency range, meets Z (fn) < ZtRelationship meets the design requirement of power distribution network；And the present invention
19 number of capacitors used are fewer than existing method, to have the function that reduce design cost and optimization layout resource.
Claims (4)
1. a kind of PDN capacitor optimization method based on lossless resonant cavity power ground planar hull modelling, comprising:
(1) parameter pre-treatment step:
1a) according to integrated chip IC maximum operating currenbt Imax, regulated power supply voltage Vo, ripple factor r, calculate power distribution network
Target impedance Zt, while determining the range of target frequencies f for needing to meet target impedancemin~fmax；
The equivalent resistance R of regulated power supply 1b) is determined by software emulation or instrument and equipmentoWith equivalent inductance LoParameter and steady
The equivalent resistance R of big capacity electrolyte capacitor in volt circuitb, equivalent inductance Lb, equivalent capacity Cb；
1c) the corresponding dead resistance R of the package lead of integrated chip IC, via hole is successively extracted using FastHenry softwarepWith
Parasitic inductance Lp；
Unit grids segmentation 1d) is carried out to printing board PCB, determines the port I (x of regulated power supplyi,yi) and integrated chip
Port J (xj,yj), wherein (xi,yi) indicate position coordinates of the regulated power supply on pcb board, (xj,yj) indicate that integrated chip exists
Position coordinates on pcb board；
1e) type of the decoupling capacitor used required in design is marked, is denoted as 1,2,3 ... ..., m, each type
The parameter of label includes the capacitance C [m], equivalent resistance R [m], equivalent inductance value L [m] of capacitor, according to these parameter meters
Calculate the self-resonant frequency of decoupling capacitor:
(2) it calculates primary power and distributes network impedance step:
2a) according to 1b), 1c) in extract determination regulated power supply equivalent resistance Ro, equivalent inductance Lo, big capacity electrolyte capacitor
Equivalent resistance Rb, equivalent inductance Lb, equivalent capacity Cb, the dead resistance R of IC package lead, via holep, parasitic inductance Lp, respectively
Calculate regulated power supply equivalent impedance Zo(f), big capacity electrolyte capacitor equivalent impedance Zb(f), IC package via hole equivalent impedance Zp(f),
Wherein f is frequency；
2b) according to lossless resonant cavity power ground planar hull modelling method, the self-impedance coefficient Z of regulated power supply port I is calculated separatelyii
(f), the self-impedance coefficient Z of integrated chip port Jjj(f), regulated power supply is to the transfger impedance coefficient Z between integrated chipij(f)、
Integrated chip is to the transfger impedance coefficient Z between regulated power supplyji(f)；By these impedance factors Zii(f)、Zjj(f)、Zij(f)、Zji
(f) it substitutes into conversion formula, corresponding equivalent parallel impedance Z in T-type impedance network is calculatedpc(f) and the first equivalent series
Impedance Zsc1(f), the second equivalent series resistance Zsc2(f)；In conjunction with 2a) in regulated power supply equivalent impedance Zo(f), large capacity is electrolysed
Capacitor equivalent impedance Zb(f), IC package via hole equivalent impedance Zp(f), the equivalent impedance Z of primary power distribution network is calculatedi
(f)；
(3) power distribution network impedance value and target impedance step under more each discrete point in frequency:
Sliding-model control 3a) is carried out to given target frequency bands, is obtained with minimum frequency fminFor initial frequency point f0, maximum frequency
fmaxTo terminate Frequency point fNDiscrete point in frequency set: f0、f1…fn…fN-1、fN；
3b) be according to the impedance value of power distribution network frequency function Z (f), in discrete point in frequency fnLess than or equal to maximum frequency
fmaxUnder the premise of, calculate discrete point in frequency fnEquivalent impedance Z (the f of corresponding power distribution networkn), and by itself and target impedance
ZtIt is compared, if Z (fn) > Zt, then Frequency point F=f is markedn, execute step (4)；Otherwise, step 3c is executed)；
Discrete point in frequency subscript n=n+1 3c) is enabled, new discrete point in frequency f is obtainedn, return step 3b)；
(4) decoupling capacitor step is added:
4a) with the self-resonant frequency value f of all available decoupling capacitors in 1e)rStep 3b is individually subtracted in [m]) label Frequency point
Value F, obtain with decoupling capacitor corresponding to the smallest self-resonant frequency value of value F difference of the Frequency point, and by the decoupling
Capacitor is labeled as capacitance present device C [u]；
4b) calculate the minimum use number N of capacitance present device C [u] in current power distribution networko[u], weighs on this basis
It is new to calculate power distribution network impedance value Z (fn), if Z (fn) > Zt, enable N [u]=No[u], and execute step 4c)；Otherwise, it returns
Return step 3c)；
Number N 4c) is used to the minimum of capacitance present device C [u]o[u] is finely adjusted processing, recalculates power distribution network resistance
Anti- value Z (fn), until meeting condition Z (fn) < Zt, and the capacitor after being finely tuned uses number N [u], return step 3c)；
(5) optimum results step is exported:
5a) the corresponding primary power distribution network impedance value Z of discrete frequency obtained according to step (2)i(fn), utilizing works meter
It calculates software MATLAB and exports range of target frequencies fmin~fmaxPrimary power distribution network impedance curve Q1；
5b) the corresponding power distribution network impedance value Z (f of discrete frequency obtained according to step 3b)n), utilizing works software for calculation
MATLAB exports range of target frequencies fmin~fmaxPower distribution network impedance curve Q2；
5c) the type C [u] according to selected decoupling capacitor in step 4b) and use number N [u], utilizing works software for calculation
MATLAB exports range of target frequencies fmin~fmaxThe impedance curve Q3 for having selected shunt capacitor.
2. according to claim 1 based on the PDN capacitor optimization method of lossless resonant cavity power ground planar hull modelling, wherein step
2b) calculate the self-impedance coefficient Z of regulated power supply port Iii(f), the self-impedance coefficient Z of integrated chip port Jjj(f), pressure stabilizing electricity
Source is to the transfger impedance coefficient Z between integrated chipij(f), integrated chip is to the transfger impedance coefficient Z between regulated power supplyji(f), lead to
Following formula is crossed to calculate:
Wherein j is imaginary number, and f is frequency, and μ is the magnetic conductivity of dielectric material, wx, wy, h is respectively the length and width of power supply ground level, thickness
Degree, m, n are corresponding subscript variables in cumulative summation operation, and the first order adds up the upper limitThe second level is tired
In addition limitfM、fNRespectively first order cutoff frequency and second level cutoff frequency, M=N and meet fM
=fN=fmax；ConstantεrFor the dielectric constant of medium, c is the light velocity；kxm=(m π)/wxIt is related to x
Intermediate variable, kyn=(n π)/wyFor intermediate variable relevant to y；χmnFor conditional-variable: as m=0 and n=0, χmn 2=1；
As m=0 or n=0, χmn 2=2；When m ≠ 0 and n ≠ 0, χmn 2=4.
3. according to claim 1 based on the PDN capacitor optimization method of lossless resonant cavity power ground planar hull modelling, wherein step
Corresponding equivalent parallel impedance Z in T-type impedance network is calculated in 2b)pc(f) and the first equivalent series resistance Zsc1(f),
Two equivalent series resistance Zsc2(f), it is expressed as follows:
Zpc(f)=Zij(f)
Zsc1(f)=Zii(f)-Zij(f)
Zsc2(f)=Zjj(f)-Zij(f)
Wherein ZijIt (f) is regulated power supply that frequency is f to the transfger impedance coefficient between integrated chip, Zii(f) be frequency be f it is steady
Self-impedance coefficient, the Z of piezoelectricity source port Ijj(f) be frequency be f integrated chip port J self-impedance coefficient.
4. the PDN capacitor optimization method according to claim 1 based on lossless resonant cavity power ground planar hull modelling, feature
Be, step 3b) in calculate discrete point in frequency fnEquivalent impedance Z (the f of corresponding power distribution networkn), as follows into
Row:
3b1) calculate First Transition electric conductivity value: Y1(fn)=1/Zo(fn)+1/Zb(fn), wherein Zo(fn)、Zb(fn) it is respectively target
Regulated power supply equivalent impedance and big capacity electrolyte capacitor equivalent impedance after frequency range sliding-model control；
3b2) calculate the second transition electric conductivity value: Y2(fn(the Z of)=1/sc1(fn)+1/Y1(fn)), wherein Zsc1(fn) be target frequency bands from
Corresponding first equivalent series resistance in dispersion treated T-type impedance network；
3b3) calculate third transition electric conductivity value: Y3(fn)=1/Zpc(fn)+Y2(fn), wherein Zpc(fn) it is at target frequency bands discretization
Corresponding equivalent parallel impedance in T-type impedance network after reason；
3b4) calculate the 4th transition electric conductivity value: Y4(fn(the Z of)=1/sc2(fn)+1/Y3(fn)), wherein Zsc2(fn) be target frequency bands from
Corresponding second equivalent series resistance in dispersion treated T-type impedance network；
3b5) calculate the equivalent impedance of power distribution network: Z (fn)=Zp(fn)+1/(Ycap(fn)+Y4(fn)), wherein Zp(fn) be
IC package via hole equivalent impedance after target frequency bands sliding-model control, Ycap(fn) gone to be selected after target frequency bands sliding-model control
The equivalent conductance value of coupling capacitor.
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