Power distribution network decoupling capacitor placement optimization method based on improved genetic algorithm
By improving the port removal and size change control strategies of the genetic algorithm, the search space is reduced, which solves the problem of excessively long optimization time for decoupling capacitors in power distribution networks and achieves the effect of finding the optimal solution quickly.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2023-08-29
- Publication Date
- 2026-05-19
AI Technical Summary
In power distribution networks, as complexity increases, the search space for decoupling capacitors grows exponentially, leading to excessively long optimization times for traditional algorithms and difficulty in finding the optimal solution.
An improved genetic algorithm based on port removal and size change control is adopted. An initial solution is obtained by introducing prior knowledge, and the improved genetic algorithm is used for iterative optimization to reduce the search space and improve search efficiency.
It accelerates the convergence speed of the algorithm, improves search efficiency and robustness, and can efficiently find the optimal capacitor configuration that meets the target impedance.
Smart Images
Figure CN117151013B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a decoupling capacitor arrangement optimization method in the field of power integrity and optimization methods, and more specifically to a decoupling capacitor arrangement optimization method in a power distribution network based on a genetic algorithm improved by port removal and size change control. Background Technology
[0002] Power integrity plays a crucial role in the reliability of high-frequency and high-speed circuits. Ensuring that the power distribution network meets the power requirements of the load chip is an important aspect of modern power integrity research.
[0003] Modern power integrity modeling methods require reducing the impedance of the power distribution network below a given target impedance by adding appropriate decoupling capacitors. This typically necessitates optimizing the selection and arrangement of decoupling capacitors, essentially a combinatorial optimization search problem. However, as the complexity of the power distribution network increases, the search space for decoupling capacitors grows exponentially, leading to excessively long optimization times for traditional algorithms and making it difficult to guarantee finding the optimal solution. Summary of the Invention
[0004] To address the issues of excessively long optimization time and difficulty in finding the optimal solution in the aforementioned capacitor optimization steps, this invention proposes an improved genetic algorithm based on port removal and size change control. This algorithm introduces prior knowledge to obtain an initial solution and then uses an improved genetic algorithm to enhance search efficiency.
[0005] The present invention adopts the following technical solution:
[0006] Step 1: Prioritize the ports of the power distribution network to obtain the port sorting sub-lists corresponding to various capacitors;
[0007] Step 2: Based on the port sorting sub-columns corresponding to various capacitors, select the optimal capacitor and its corresponding port from the capacitor library in sequence until the observed impedance is less than the target impedance at all frequency points, and obtain the initial decoupling capacitor arrangement.
[0008] Step 3: After iteratively optimizing the initial decoupling capacitor arrangement using an improved genetic algorithm, the optimal decoupling capacitor arrangement is obtained.
[0009] Step one specifically involves:
[0010] Based on the impedance parameter matrix of the power distribution network, the decoupling capacitor ports are short-circuited one by one. The port that minimizes the loop inductance at the observation port is designated as the highest priority port and fixed in a short-circuited state, completing one port sorting operation. This port sorting operation is repeated multiple times until all decoupling capacitor ports are short-circuited, obtaining the priority order of all ports. Based on the ports that different decoupling capacitors are matched with, the port sorting sub-sequences corresponding to different types of decoupling capacitors are determined based on the priority order of all ports.
[0011] Step two specifically involves:
[0012] 2.1) Based on the port sorting sub-column corresponding to various capacitors, place different decoupling capacitors in the capacitor library at the current highest priority port applicable to the corresponding capacitor, select the capacitor that reduces the amount of the observed impedance from the target impedance the most and record it as the optimal capacitor, and fix the current optimal capacitor at the corresponding current highest priority port.
[0013] 2.2) Repeat step 2.1) continuously select the optimal capacitor and fix it at the corresponding highest priority port until the observed impedance is less than the target impedance at all frequency points. This yields a set of initial solutions for decoupling capacitor types and corresponding ports, which are recorded as the initial decoupling capacitor arrangement.
[0014] Step three specifically involves:
[0015] 3.1) The length of the chromosome in the genetic algorithm is encoded as the number of capacitor ports in the initial decoupling capacitor arrangement. Each gene in the chromosome is the decoupling capacitor type corresponding to each port. After randomly changing the port position and capacitor type, the initial population of the genetic algorithm is generated.
[0016] 3.2) Remove ports from the current population group to obtain the population group after port removal;
[0017] 3.3) After removing the ports, the population group is subjected to genetic algorithms for inheritance, crossover, and mutation to obtain the next generation population group;
[0018] 3.4) Size variation control is applied to the next generation population to obtain a newer next generation population;
[0019] 3.5) Repeat steps 3.2)-3.4) to iterate and update the next generation population group until the preset iteration conditions are met and the optimal population group is obtained. The population with the fewest capacitor ports in the optimal population group is taken as the optimal decoupling capacitor arrangement.
[0020] The objective function of the genetic algorithm is set in the following manner:
[0021] When the impedance of the observed port does not meet the target impedance, the objective function is positive, and its size is the area of the portion of the observed port impedance that exceeds the target impedance; when the impedance of the observed port meets the target impedance, the objective function is negative, and its size is the number of ports without decoupling capacitors.
[0022] In the genetic algorithm, the chromosome encoding method is specifically as follows:
[0023] A chromosome is a sequence of the same length as the number of capacitor ports. If a capacitor port does not have a decoupling capacitor, the element corresponding to that capacitor port in the chromosome sequence is 0. If a capacitor port has a decoupling capacitor, the element corresponding to that capacitor port in the chromosome sequence is the number of the decoupling capacitor in the capacitor library.
[0024] The preset iteration condition is that the total number of iterations reaches the preset iteration limit or the number of iterations without improvement exceeds the limit of iterations without improvement.
[0025] Specifically, 3.2) refers to:
[0026] If the number of capacitors of the optimal population in the current population group is less than the number of capacitors of the optimal population in the previous iteration, then the ports with lower priority and without decoupling capacitors in the chromosomes of each population in the current population group are forcibly fixed to the open circuit state, and these ports are removed from the search space; otherwise, no operation is performed.
[0027] Specifically, 3.4) refers to:
[0028] In the current population group, count the number of ports where decoupling capacitors are placed in each population. If the number of ports in each population is greater than the number of decoupling capacitors in the optimal population in the current population group, then randomly remove some decoupling capacitors from each population, so that the remaining number of decoupling capacitors is equal to the number of decoupling capacitors in the optimal solution. If the number of ports in each population is less than or equal to the number of decoupling capacitors in the optimal population in the current population group, then calculate the difference between the number of ports in each population and the number of decoupling capacitors in the current optimal solution. If the difference is less than the change factor, then retain that population. Otherwise, randomly place some decoupling capacitors in the ports of each population, so that the difference between the number of capacitors in that population and the number of capacitors in the current optimal solution is equal to the change factor.
[0029] The beneficial effects of this invention are as follows:
[0030] This invention improves the genetic algorithm to further search for the optimal solution based on the initial solution, and accelerates the convergence speed of the algorithm through port removal and size change control strategies. The method of this invention has high search efficiency, fast convergence speed, and good robustness. The genetic algorithm has been specifically modified according to the application scenario of capacitor combination optimization, enabling it to efficiently find the optimal capacitor configuration that meets the target impedance. Attached Figure Description
[0031] Figure 1 This is a flowchart of an embodiment of the present invention;
[0032] Figure 2 This refers to the circuit board shape used in the embodiments of the present invention;
[0033] Figure 3 This refers to the stacked structure of the circuit board used in the embodiments of the present invention;
[0034] Figure 4 The self-impedance and target impedance of the circuit board used in this embodiment of the invention at the observation port;
[0035] Figure 5 Port priority distribution in this embodiment of the invention;
[0036] Figure 6 The capacitance position distribution of the initial solution in this embodiment of the invention;
[0037] Figure 7 The observation port self-impedance versus target impedance curves of the initial solution in this embodiment of the invention;
[0038] Figure 8 The capacitor location distribution is the optimal solution in this embodiment of the invention;
[0039] Figure 9 The observation port self-impedance and target impedance curves are the optimal solution in this embodiment of the invention. Detailed Implementation
[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.
[0041] like Figure 1 As shown, the embodiments and implementation steps of the present invention are as follows:
[0042] like Figure 2As shown, the circuit board used in this embodiment has an irregular, randomly closed curve shape. The board frame size is 150mm × 150mm. There are positions for placing decoupling capacitors on both the top and bottom layers of the board, which are marked with different symbols in the figure; there are a total of 100 positions for placing decoupling capacitors on the top and bottom layers of the board.
[0043] like Figure 3 As shown, the circuit board stack-up structure used in this embodiment is a four-layer structure, where the second layer is the power layer, and the first, third and fourth layers are ground plane layers. The thicknesses of the three dielectric layers are 0.2mm, 0.3mm and 0.2mm from top to bottom, respectively, and the copper used is 1oz copper.
[0044] In this embodiment, the observation port is located at Figure 2 At the chip location, before placing the decoupling capacitor, the self-impedance and target impedance of the circuit board used in this embodiment at the observation port are as follows: Figure 4 As shown in the figure. The target impedance used in this embodiment is an RL-type target impedance, that is, the target impedance can be regarded as a circuit impedance obtained by a resistor R and an inductor L connected in series, where the value of resistor R is 0.6mΩ and the value of inductor L is 90pH. The capacitor library used in this embodiment is an S-parameter model, with 10 different capacitor models, and their specific parameters are shown in Table 1.
[0045] Table 1 shows the capacitor library model used in this embodiment and its corresponding parasitic parameters.
[0046] serial number Capacitance (µF) Equivalent series inductance (nH) Equivalent series resistance (mΩ) 1 0.1 0.19 34.7 2 0.47 0.18 18.3 3 1 0.22 15.2 4 2.2 0.20 7.2 5 4.7 0.28 7.1 6 10 0.26 5.2 7 22 0.27 4.0 8 47 0.15 2.9 9 220 0.41 1.9 10 330 0.46 1.2
[0047] Step 1: Prioritize the ports of the power distribution network to obtain the port sorting sub-lists corresponding to various capacitors;
[0048] Step one is as follows:
[0049] Based on the impedance parameter matrix of the power distribution network, the decoupling capacitor ports are short-circuited sequentially. The port that minimizes the loop inductance at the observed port is designated as the highest priority port and fixed in a short-circuited state, completing one port sorting operation. The remaining decoupling capacitor ports are then short-circuited sequentially to obtain the next highest priority ports. This port sorting operation is repeated multiple times until all decoupling capacitor ports are short-circuited, obtaining the priority order of all ports. Based on the ports corresponding to different decoupling capacitors, port sorting sub-columns corresponding to different types of decoupling capacitors are determined according to the priority order of all ports. That is, for each type of decoupling capacitor package, the ports suitable for that decoupling capacitor are selected and arranged according to their priority order, resulting in the port sorting sub-column corresponding to each type of decoupling capacitor. The global priority order of all ports and the correspondence between port positions are as follows: Figure 5As shown in the figure, the numbers such as 1, 2, and 98 are all port numbers.
[0050] Step 2: Based on the port sorting sub-columns corresponding to various capacitors, select the optimal capacitor and its corresponding port from the capacitor library in sequence until the observed impedance is less than the target impedance at all frequency points, and obtain the initial decoupling capacitor arrangement.
[0051] Step two is as follows:
[0052] 2.1) Based on the port sorting sub-column corresponding to various capacitors, place different decoupling capacitors in the capacitor library at the current highest priority port applicable to the corresponding capacitor (the current highest priority port is unused), select the capacitor among the different decoupling capacitors that reduces the amount of the observed impedance from the target impedance by the most and record it as the optimal capacitor, and fix the current optimal capacitor at the corresponding current highest priority port.
[0053] 2.2) Repeat step 2.1), continuously selecting the optimal capacitor and fixing it at the corresponding highest priority port, until the observed impedance is less than the target impedance at all frequency points. This yields an initial solution for a set of decoupling capacitor types and corresponding ports, which is recorded as the initial decoupling capacitor arrangement. In this embodiment, the initial solution uses 25 capacitors, and the corresponding capacitor distribution is as follows: Figure 6 As shown, the comparison between the observation port self-impedance and the target impedance curves corresponding to the initial solution is as follows: Figure 7 As shown.
[0054] Step 3: After iteratively optimizing the initial decoupling capacitor arrangement using an improved genetic algorithm, the optimal decoupling capacitor arrangement is obtained.
[0055] Step three specifically involves:
[0056] 3.1) The length of the chromosome in the genetic algorithm is encoded as the number of capacitor ports in the initial decoupling capacitor arrangement. Each gene in the chromosome is the decoupling capacitor type corresponding to each port. After randomly changing the port position and capacitor type, the initial population of the genetic algorithm is generated.
[0057] In genetic algorithms, the specific encoding method for chromosomes is as follows:
[0058] A chromosome is a sequence of the same length as the number of capacitor ports. If a capacitor port does not have a decoupling capacitor, the element corresponding to that capacitor port in the chromosome sequence is 0. If a capacitor port has a decoupling capacitor, the element corresponding to that capacitor port in the chromosome sequence is the number of the decoupling capacitor in the capacitor library.
[0059] The objective function of a genetic algorithm is set in the following way:
[0060] When the impedance of the observed port does not meet the target impedance, the objective function is positive, and its size is the area of the portion of the observed port impedance that exceeds the target impedance; when the impedance of the observed port meets the target impedance, the objective function is negative, and its size is the number of ports without decoupling capacitors.
[0061] 3.2) Remove ports from the current population group to obtain the population group after port removal;
[0062] 3.2) Specifically:
[0063] If the number of capacitors of the optimal population in the current population group is less than the number of capacitors of the optimal population in the previous iteration, then the ports with lower priority and without decoupling capacitors in the chromosomes of each population in the current population group are forcibly fixed to the open circuit state, and these ports are removed from the search space. In the first iteration, the ports with lower priority and without decoupling capacitors in the chromosomes of each population are directly forcibly fixed to the open circuit state and removed from the search space; otherwise, no operation is performed.
[0064] 3.3) After removing the ports, the population group is subjected to genetic algorithms for inheritance, crossover, and mutation to obtain the next generation population group;
[0065] Genetic manipulation refers to a certain proportion of offspring inheriting all the genes from an equal number of parent generations with a smaller objective function.
[0066] Crossover refers to a process in which a certain proportion of offspring inherit some genes from one parent and others from another parent.
[0067] Mutation refers to the process by which some genes in a population are randomly transformed into another gene with a certain probability.
[0068] 3.4) Size variation control is applied to the next generation population to obtain a newer next generation population;
[0069] 3.4) Specifically:
[0070] In the current population group, count the number of ports where decoupling capacitors are placed in each population. If the number of ports in each population is greater than the number of decoupling capacitors in the optimal population in the current population group, then randomly remove some decoupling capacitors from each population, so that the remaining number of decoupling capacitors is equal to the number of decoupling capacitors in the optimal solution. If the number of ports in each population is less than or equal to the number of decoupling capacitors in the optimal population in the current population group, then calculate the difference between the number of ports in each population and the number of decoupling capacitors in the current optimal solution. If the difference is less than the change factor, then retain that population. Otherwise, randomly place some decoupling capacitors in the ports of each population, so that the difference between the number of capacitors in that population and the number of capacitors in the current optimal solution is equal to the change factor.
[0071] 3.5) Repeat steps 3.2)-3.4) to iterate and update the next generation population until the preset iteration conditions are met and the optimal population is obtained. The chromosome corresponding to the population with the fewest capacitor ports in the optimal population is taken as the optimal decoupling capacitor arrangement.
[0072] The preset iteration conditions are that the total number of iterations reaches the preset maximum number of iterations or the number of iterations without improvement exceeds the maximum number of iterations without improvement.
[0073] This invention reduces the search space and improves the search efficiency and convergence speed of the algorithm through improved strategies such as port removal and size change control.
[0074] For the initial solution obtained, a port removal strategy is adopted, placing lower-priority ports in an open-circuit state and forcibly setting the genes corresponding to these ports in all populations to 0, i.e., not placing any capacitors. Then, based on the initial solution, a genetic algorithm is used for multiple iterations to further find the optimal solution. After each iteration, a size change control strategy is implemented on all populations, and if a better solution is found, the port removal strategy is applied again to lower-priority ports. In this embodiment, the parameters of the genetic algorithm are selected as follows: population size 50, crossover probability 0.5, mutation probability 0.3, maximum number of iterations 100, and the change factor in the size change control strategy is 2.
[0075] In this embodiment, after 100 iterations, the optimal solution found by the algorithm uses 22 decoupling capacitors. The distribution of these capacitors on the circuit board is as follows: Figure 8 As shown. After placing these decoupling capacitors, observe the comparison between the impedance at the port and the target impedance. Figure 9 As shown, the optimal solution can reduce the PDN impedance to below the target impedance.
[0076] To further quantitatively illustrate the advantages of the proposed method, Table 2 compares the advantages of the proposed method with traditional genetic algorithms in terms of optimization efficiency and optimization quality. It can be seen that the proposed algorithm can find relatively high-quality feasible solutions in a very short time, greatly improving the optimization efficiency and optimization quality of capacitance optimization.
[0077] Table 2 compares the convergence quality and convergence speed of the method of the present invention with those of the traditional genetic algorithm.
[0078] Method of the present invention Genetic Algorithm Initial solution / 37 \ Optimal solution / 32 65 Time / second 80 3826
[0079] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for optimizing the decoupling capacitor arrangement in a power distribution network based on an improved genetic algorithm, characterized in that, Includes the following steps: Step 1: Prioritize the ports of the power distribution network to obtain the port sorting sub-lists corresponding to various capacitors; Step 2: Based on the port sorting sub-columns corresponding to various capacitors, select the optimal capacitor and its corresponding port from the capacitor library in sequence until the observed impedance is less than the target impedance at all frequency points, and obtain the initial decoupling capacitor arrangement. Step 3: After iteratively optimizing the initial decoupling capacitor arrangement using an improved genetic algorithm, the optimal decoupling capacitor arrangement is obtained; Step three specifically involves: 3.1) The length of the chromosome in the genetic algorithm is encoded as the number of capacitor ports in the initial decoupling capacitor arrangement. Each gene in the chromosome is the decoupling capacitor type corresponding to each port. After randomly changing the port position and capacitor type, the initial population of the genetic algorithm is generated. 3.2) Remove ports from the current population group to obtain the population group after port removal; Specifically, 3.2) refers to: If the number of capacitors of the best population in the current population group is less than the number of capacitors of the best population in the previous iteration, then the ports with lower priority and no decoupling capacitors in the chromosomes of each population in the current population group are forced to be fixed to the open circuit state, and these ports are removed from the search space; otherwise, no operation is performed. 3.3) After removing the ports, the population group is subjected to genetic algorithms for inheritance, crossover, and mutation to obtain the next generation population group; 3.4) Control the size change of the next generation population to obtain a newer next generation population; Specifically, 3.4) refers to: In the current population group, count the number of ports where decoupling capacitors are placed in each population; if the number of ports in each population is greater than the number of decoupling capacitors in the optimal population in the current population group, then randomly remove some decoupling capacitors from each population, so that the remaining number of decoupling capacitors is equal to the number of decoupling capacitors in the optimal solution. If the number of ports for each population is less than or equal to the number of decoupling capacitors for the optimal population in the current population group, then the difference between the number of ports for each population and the number of decoupling capacitors in the current optimal solution is obtained. If the difference is less than the change factor, then the population is retained; otherwise, some decoupling capacitors are randomly placed in the ports of each population so that the difference between the number of capacitors for that population and the number of capacitors in the current optimal solution is equal to the change factor. 3.5) Repeat steps 3.2)-3.4) to iterate and update the next generation population group until the preset iteration conditions are met and the optimal population group is obtained. The population with the fewest capacitor ports in the optimal population group is taken as the optimal decoupling capacitor arrangement.
2. The method for optimizing the decoupling capacitor arrangement in a power distribution network based on an improved genetic algorithm according to claim 1, characterized in that, Step one specifically involves: Based on the impedance parameter matrix of the power distribution network, the decoupling capacitor ports are short-circuited one by one. The port that minimizes the loop inductance at the observation port is designated as the highest priority port and fixed in a short-circuited state, completing one port sorting operation. This port sorting operation is repeated multiple times until all decoupling capacitor ports are short-circuited, obtaining the priority order of all ports. Based on the ports that different decoupling capacitors are matched with, the port sorting sub-sequences corresponding to different types of decoupling capacitors are determined based on the priority order of all ports.
3. The method for optimizing the decoupling capacitor arrangement in a power distribution network based on an improved genetic algorithm according to claim 1, characterized in that, Step two specifically involves: 2.1) Based on the port sorting sub-columns corresponding to various capacitors, place different decoupling capacitors in the capacitor library at the current highest priority port applicable to the corresponding capacitor, select the capacitor that reduces the amount of the observed impedance from the target impedance the most and record it as the optimal capacitor, and fix the current optimal capacitor at the corresponding current highest priority port. 2.2) Repeat 2.1) continuously select the optimal capacitor and fix it at the corresponding current highest priority port until the observed impedance is less than the target impedance at all frequency points. This yields a set of initial solutions for decoupling capacitor types and corresponding ports, which are recorded as the initial decoupling capacitor arrangement.
4. The method for optimizing the decoupling capacitor arrangement in a power distribution network based on an improved genetic algorithm according to claim 1, characterized in that, The objective function of the genetic algorithm is set in the following manner: When the impedance of the observed port does not meet the target impedance, the objective function is positive, and its size is the area of the portion of the observed port impedance that exceeds the target impedance; when the impedance of the observed port meets the target impedance, the objective function is negative, and its size is the number of ports without decoupling capacitors.
5. The method for optimizing the decoupling capacitor arrangement in a power distribution network based on an improved genetic algorithm according to claim 1, characterized in that, In the genetic algorithm, the chromosome encoding method is specifically as follows: A chromosome is a sequence of the same length as the number of capacitor ports. If a capacitor port does not have a decoupling capacitor, the element corresponding to that capacitor port in the chromosome sequence is 0. If a capacitor port has a decoupling capacitor, the element corresponding to that capacitor port in the chromosome sequence is the number of the decoupling capacitor in the capacitor library.
6. The method for optimizing the decoupling capacitor arrangement in a power distribution network based on an improved genetic algorithm according to claim 1, characterized in that, The preset iteration condition is that the total number of iterations reaches the preset iteration limit or the number of iterations without improvement exceeds the limit of iterations without improvement.