Macro-modeling method for ensuring direct current precision

Abstract

The invention discloses a macro modeling method for ensuring direct current precision. The method comprises the following steps: reading n-port network parameters; initializing sampling points used for constructing a macro model; initializing the order of the macro model; initializing a pole of the macro model; establishing a weighted linear system according to the current order, the sampling point and the pole; solving the system of linear equations, judging convergence according to errors, and obtaining a macro model; the macro model is optimized by applying residue matrix disturbance, and the optimized macro model is output. According to the macro modeling method for guaranteeing the direct current precision, the direct current precision is controlled in two stages, in the first stage, a weighted least square method is adopted on the basis of establishing a linear system through a traditional vector fitting algorithm, and the direct current precision is preliminarily controlled; and in the second stage, tiny disturbance is applied to the residue matrix of the macro model, so that the disturbed macro model has accurate direct current characteristics.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated circuit design, and in particular to a macro modeling method for ensuring direct current accuracy. Background Art

[0002] In integrated circuit design, numerical modeling and simulation are core tools for ensuring chip functional reliability and optimized performance. They help designers proactively identify and resolve potential issues, effectively reducing chip design cycles and manufacturing costs. However, actual physical systems are complex, and modeling and simulating the entire system is a challenging task. Macromodeling is a common technique in integrated circuit simulation. By reducing the order of complex circuit modules, it can simulate large-scale circuits within limited computing resources, significantly improving simulation efficiency.

[0003] Macromodels can be identified from the frequency response, resulting in a reduced-order representation of the physical system. Once macromodels for individual physical modules are obtained, they can be embedded into the overall system for simulation using a circuit simulator. Vector fitting has become a standard technique for macromodeling due to its well-known robustness.

[0004] During macromodeling, the DC accuracy of the macromodel is typically required, meaning that the macromodel H(s) at frequency s = 0 fully matches the original data. This is because any DC error can cause a change in the system's steady-state operating point, leading to a change in the system solution under steady-state conditions. Furthermore, the steady-state operating point serves as the initial value for other simulation analyses. For example, transient simulations are all based on the system's steady-state operating point, making transient simulations of integrated circuits highly dependent on the accuracy of the steady-state operating point. Transient simulations are often used in the verification phase of system-level circuits to ensure the correctness and reliability of module functionality. Therefore, ensuring the DC accuracy of the macromodel is crucial. However, traditional vector fitting algorithms lack a DC error control mechanism, resulting in inherent DC deviations in the constructed macromodel, which can cause the steady-state operating point to drift.

[0005] Therefore, how to ensure DC accuracy is a technical problem that needs to be solved urgently. Summary of the Invention

[0006] In order to address the shortcomings of the existing technology, the present invention provides a macro modeling method that ensures DC accuracy. Through the dual control mechanism of the weighted linear system and the perturbation macro model residue matrix, it ensures the generation of a macro model with strict matching DC characteristics, thereby obtaining a correct and reliable steady-state operating point.

[0007] The embodiments of the present invention provide the following solutions:

[0008] An embodiment of the present invention provides a macro modeling method for ensuring DC accuracy, the method comprising:

[0009] S1, read n-port network parameters;

[0010] S2, initialize the sampling points used to build the macro model;

[0011] S3. Initialize the order N of the macro model int ;

[0012] S4, initialize the poles of the macro model;

[0013] S5. Establish a weighted linear system based on the current order, sampling points and poles;

[0014] S6. Solve the linear equations, judge convergence based on the error, and obtain the macro model;

[0015] S7. Optimize the macro model by applying residue matrix perturbation, and output the optimized macro model.

[0016] In an optional embodiment, the n-port network parameters in step S1 include an S parameter matrix and frequency information.

[0017] In an optional embodiment, step S2 is initialized using an adaptive strategy of low-frequency encrypted sampling and wide-band uniform sampling to construct a sampling frequency point set.

[0018] In an optional embodiment, step S3 uses a peak estimation method to estimate the macromodel order N int , N int =max(4,2N peaks ), N peaks is the number of resonance peaks in the network parameters.

[0019] In an optional embodiment, the weighted linear system described in step S5 is expressed as:

[0020]

[0021] in, s k =j2πw k , j is the imaginary unit, w k is the frequency corresponding to the kth sampling point, p n represents the nth extreme point; represents a (2Ns×1) column vector, f v =diag([Re(f′ v )Im(f′ v )]) is represented by the vector [Re(f′ v )Im(f′ v )], Re(f′ v ) and Im(f′v ) are f′ v The real and imaginary parts, f′ v =[f v (s1) … f v (s Ns )] represents the vector composed of all sampling points of the vth S-parameter curve; V = n 2 Or V = n; C v represents the residue vector of the vth S-parameter curve, represents the coefficient of the auxiliary function σ(s) in vector fitting; Λ=diag([λ1,λ2,…,λ Ns ]) represents the weight of the i-th sampling point.

[0022] In an optional embodiment, step S6 includes the following steps:

[0023] S6.1. Solve for the zero point of σ(s) and obtain the vector set consisting of the poles of the macro model Among them A σ represents the pole matrix of σ(s), B σ represents the state matrix of σ(s), C σ represents the residue matrix of σ(s), D σ A constant matrix representing σ(s);

[0024] S6.2. Update the residue and constant terms of the S-parameter curve using the following formula:

[0025]

[0026] where p n =α n +jβ n For curve S ij The nth extreme point, c n For p n The corresponding residue, d ij For curve S ij The constant term of ;

[0027] S6.3. Determine whether If yes, the convergence condition is met and the macro model is saved; otherwise, the process goes to step S6.4;

[0028] S6.4. Determine whether the current number of sampling points is greater than the macro model order. If so, increase the number of uniform sampling points and return to step S5 to re-establish the weighted linear system. Otherwise, increase the macro model order and return to step S5 to re-establish the weighted linear system.

[0029] In an optional embodiment, applying the residue matrix perturbation in step S7 includes the following process:

[0030] S7.1. For the saved macromodel H(s)=C(sI-A) -1 The residue matrix C in B+D is perturbed and expressed as:

[0031]

[0032] S7.2. After sorting out the constraints, we get:

[0033] ΔC(-A -1 B)=H dc -D+CA -1 B

[0034] S7.3. Transpose the formula to obtain:

[0035] (-A -1 B) T ΔC T =(H dc -D+CA -1 B) T

[0036] This is the optimized macro model.

[0037] The beneficial effects of the present invention based on its technical solution are:

[0038] The present invention provides a macro modeling method for ensuring DC accuracy, which controls DC accuracy in two stages. In the first stage, a weighted least squares method is used to establish a linear system based on a traditional vector fitting algorithm to preliminarily control the DC accuracy. In the second stage, a small perturbation is applied to the residue matrix of the macro model so that the perturbed macro model has accurate DC characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 A schematic flow chart of a macro modeling method for ensuring DC accuracy provided by the present invention.

[0041] Figure 2 Schematic diagram of S parameter comparison in this embodiment.

[0042] Figure 3 This is a partial enlarged view of the DC approach characteristics. DETAILED DESCRIPTION

[0043] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field fall within the scope of protection of the embodiments of the present invention.

[0044] This embodiment provides a macro modeling method for ensuring DC accuracy, the method comprising:

[0045] S1. Read n-port network parameters. This embodiment takes S parameters as an example, and the processing of Y parameters and Z parameters is similar.

[0046] A Touchstone file (also called a SnP file) is an ASCII text file used to record n-port network parameter data of an active device or a passive network. k (k = 1, 2, 3, ..., K), the form of the n-port S parameter matrix is:

[0047]

[0048] Assume that the S parameter has a total of K uniform frequency point data, including the DC frequency point, that is,

[0049]

[0050] The Touchstone file contains not only the S parameter matrix but also the frequency information. The highest frequency is defined as w max , the lowest frequency is w min = 0. The Touchstone file of this embodiment contains the frequency 0.

[0051] S2. Adopting the adaptive sampling strategy of low-frequency encrypted sampling and broadband uniform sampling to initialize the sampling points used to construct the macro model.

[0052] Since the accuracy of the macro model at DC needs to be guaranteed, r0 consecutive frequency points near DC must be added as sampling points. The S parameter of the highest frequency must also be used as the initial sampling point to ensure that the macro model has accurate behavior at high frequencies. In this embodiment, the number of initial sampling frequency points r can be set to 5, and the number of consecutive frequency points r0 selected near DC also needs to be adjusted according to the number of frequency points K in the Touchstone file. Generally, it can be calculated according to the formula In addition, in order to obtain an accurate macro model of the S parameters, the accuracy within the band must be guaranteed. Therefore, within the band [0,w max ]Uniformly select r u frequency points, and includes DC and w max, so the number of initial sampling frequency points r=r0+r u , r u Indicates the band [0, w max ] Uniformly select the number of frequency points. Since the number of sampling points must be greater than the order of the macro model, it may be necessary to dynamically increase the number of sampling points during the fitting process. Therefore, the number of sampling points for the current fitting is set to Ns = r.

[0053] S3. Initialize the order N of the macro model using the peak estimation method int .

[0054] Generally speaking, the true order of the macro model cannot be accurately predicted. In practice, the order of the macro model is usually determined by increasing the order and judging whether the error is within an acceptable range. It is well known that real poles appear as attenuation in the transfer function, while pairs of complex conjugate poles appear as oscillation in the transfer function. Therefore, in order to ensure that each resonance peak is represented by at least a pair of complex conjugate poles, the initial order of the macro model is set to the number of network parameter resonance peaks N. peaks 2 times, that is, N int =max(4,2N peaks ). In order to avoid taking too low an order, N is forced to be set. int The minimum is 4th order.

[0055] S4. Initialize the poles of the macro model so that the initial poles are evenly and linearly distributed.

[0056] Since the frequency range of S parameters is [0,w max ], so the imaginary part of the initial pole of the complex conjugate is evenly distributed in [0,w max ], that is:

[0057] p n =-α n +jβ n ,p n+1 =-α n -jβ n

[0058] N represents the order used in the current fitting. Initially, N=N int , and α n <0.

[0059] In addition, The purpose of this initialization is:

[0060] (1) The extreme points are evenly distributed in [0,w max ] can reduce the number of pole relocations so as to converge to the real poles quickly.

[0061] (2) Using weakly attenuated complex conjugate poles can avoid generating severely ill-conditioned systems and can also capture resonance peaks.

[0062] S5. Establish a weighted linear system based on the current order, sampling points and poles.

[0063] For the traditional vector fitting algorithm, the established linear system is as follows

[0064]

[0065] in And s k =j2πw k , j is the imaginary unit, w k is the frequency corresponding to the kth sampling point, p n represents the nth extreme point. In addition, represents a (2Ns×1) column vector, f v =diag([Re(f′ v ) Im(f′ v )]) is represented by the vector [Re(f′ v ) Im(f′ v )], Re(f′ v ) and Im(f′ v ) are f′ v The real and imaginary parts, f′ v =[f v (s1) … f v (s Ns )] represents the vector composed of all sampling points of the vth S-parameter curve. If matrix fitting is used, then V = n 2 ; If column fitting is used, V = n. C v represents the residue vector of the vth S-parameter curve, Represents the coefficient of the auxiliary function σ(s) in vector fitting.

[0066] Furthermore, if a fast algorithm is used, we have:

[0067]

[0068] Among them, the matrix [Xf v X] performs QR decomposition, and

[0069] This step transforms the traditional linear system into a weighted linear system, and the problem changes from the original least squares problem to a weighted least squares problem. Specifically, this is achieved through a weighting matrix Λ, where:

[0070] Λ=diag([λ1,λ2,…,λ Ns ])

[0071] λ i Represents the weight of the i-th sampling point.

[0072] Then, a new weighted linear system is

[0073]

[0074] In order to ensure the DC accuracy of the macro model, a large weight can be given to the DC frequency data. In this embodiment, λ1 is set to 10 3 , and the weights of the remaining frequencies are set to 1.

[0075] S6. Solve the linear equations, determine convergence based on the error, and obtain the macro model. This includes the following steps:

[0076] S6.1. Solve for the zeros of σ(s) to obtain the poles of the macromodel. This can be easily obtained through the state space model of σ(s), that is:

[0077]

[0078] Among them, {p n} represents the vector set composed of the poles of the macro model, A σ represents the pole matrix of σ(s), B σ represents the state matrix of σ(s), C σ represents the residue matrix of σ(s), D σ A constant matrix representing σ(s).

[0079] S6.2, according to the new extreme {p n}Update the residue and constant terms of the S parameter curve. For any S parameter curve S ij ,have

[0080]

[0081] where p n =α n +jβ n For curve S ij The nth extreme point, c n For p n The corresponding residue, d ij For curve S ij The constant term of ;

[0082] S6.3. Determine whether the convergence threshold is met according to the error. In this invention, the Root Mean Square Error (RMSE) is used to measure the accuracy between the macro model and the original S-parameters. Determine whether it meets If so, the convergence condition is reached and the macro model is saved; otherwise, go to step S6.4. In this embodiment, the convergence threshold ∈ = 0.001 is set.

[0083] S6.4. Determine whether the current number of sampling points is greater than the order of the macro model:

[0084] (a) If the current number of sampling points is greater than or equal to the order of the macro model, that is, Ns ≥ N, then increase the number of uniformly sampled points r u , reselect r u + 0.5r u sampling points, and let r u = 1.5r u , return to step S5 to re - establish the weighted linear system;

[0085] (b) If the current number of sampling points is less than the order of the macro model, that is, Ns < N, then continue to increase the order of the macro model, return to step S5 to re - establish the weighted linear system.

[0086] S7. Second - stage optimization, optimize the macro model by applying residue matrix perturbation, and output the optimized macro model. The process includes the following:

[0087] S7.1. Apply perturbation to the residue matrix C in the saved macro model H(s) = C(sI - A) -1 B + D, which is expressed as: <00003~30>

[0088]

[0089] S7.2. After organizing the constraints, we get:

[0090] ΔC(-A -1 B) = H dc - D + CA -1 B

[0091] S7.3. Transpose the formula to get:

[0092] (-A -1 B) T ΔC T = (H dc - D + CA -1 B) T

[0093] This is the optimized macro model.

[0094] Figure 2Input reflection coefficient curves of the S-parameters of a three-port voltage-controlled oscillator (VCO) provided by an embodiment of the present invention. For ease of illustration, only the amplitude of the S(1,1) curve is provided. The blue solid line represents the original S-parameter data, the orange dotted line represents the traditional vector fitting results, and the yellow dashed line represents the results of this embodiment. Because the same convergence threshold is used, both macromodels achieve good accuracy across the entire bandwidth. Figure 3 This is a partial enlarged diagram of the DC near-field characteristics. It can be clearly found that the traditional vector fitting has an error of 0.12% in DC, while the present invention can provide accurate DC characteristics.

[0095] The following table shows the circuit simulation results of macro models generated by two different macro modeling methods for the VCO, using the linear interpolation simulation result of 28.245mA as the standard. Since interpolation does not change the original data, linear interpolation has the most reliable steady-state operating point. Among them, Idc_vco represents the DC supply current, which is a key parameter for measuring VCO power consumption and power supply design. As shown in the table below, the results of the macro model generated by the traditional vector fitting algorithm produced an error of 0.120%, with a deviation of 0.033mA from the standard value. However, the simulation indicator Idc_vco of the solution provided by the present invention has a deviation of 0 from the standard, which shows the superiority of the solution provided by the present invention.

[0096]

[0097] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] The present invention is described with reference to flowcharts and / or block diagrams of methods, apparatus (modules, systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0099] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0101] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0102] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A macro modeling method for ensuring DC accuracy, characterized in that: The method comprises: S1, read n-port network parameters; S2, initialize the sampling points used to build the macro model; S3. Initialize the order N of the macro model int ; S4, initialize the poles of the macro model; S5. Establish a weighted linear system based on the current order, sampling points and poles; S6. Solve the linear equations, judge convergence based on the error, and obtain the macro model; S7. Optimize the macro model by applying residue matrix perturbation, and output the optimized macro model.

2. The macro modeling method for ensuring DC accuracy according to claim 1, characterized in that: The n-port network parameters described in step S1 include an S parameter matrix and frequency information.

3. The macro modeling method for ensuring DC accuracy according to claim 1, characterized in that: Step S2 uses an adaptive strategy of low-frequency encrypted sampling and broadband uniform sampling to initialize and construct a sampling frequency point set.

4. The macro modeling method for ensuring DC accuracy according to claim 1, wherein: Step S3 uses the peak estimation method to estimate the macro model order N int , N int =max(4,2N peaks ), N peaks is the number of resonance peaks in the network parameters.

5. The macro modeling method for ensuring DC accuracy according to claim 1, wherein: The weighted linear system described in step S5 is expressed as: in, s k =j2πw k , j is the imaginary unit, w k is the frequency corresponding to the kth sampling point, p n represents the nth extreme point; represents a (2Ns×1) column vector, f v =diag([Re(f′ v ) Im(f′ v )]) is represented by the vector [Re(f′ v ) Im(f′ v )], Re(f′ v ) and Im(f′ v ) are f′ v The real and imaginary parts, f′ v =[f v (s1) … f v (s Ns )] represents the vector composed of all sampling points of the vth S-parameter curve; V = n 2 Or V = n; C v represents the residue vector of the vth S-parameter curve, represents the coefficient of the auxiliary function σ(s) in vector fitting; Λ=diag([λ1,λ2,…,λ Ns ]) represents the weight of the i-th sampling point.

6. The macro modeling method for ensuring DC accuracy according to claim 5, characterized in that: Step S6 includes the following steps: S6.

1. Solve for the zero point of σ(s) and obtain the vector set consisting of the poles of the macro model Among them A σ represents the pole matrix of σ(s), B σ represents the state matrix of σ(s), C σ represents the residue matrix of σ(s), D σ A constant matrix representing σ(s); S6.

2. Update the residue and constant terms of the S-parameter curve using the following formula: where p n =α n +jβ n For curve S ij The nth extreme point, c n For p n The corresponding residue, d ij For curve S ij The constant term of ; S6.

3. Determine whether If yes, the convergence condition is met and the macro model is saved; otherwise, the process goes to step S6.4; S6.

4. Determine whether the current number of sampling points is greater than the macro model order. If so, increase the number of uniform sampling points and return to step S5 to re-establish the weighted linear system. Otherwise, increase the macro model order and return to step S5 to re-establish the weighted linear system.

7. The macro modeling method for ensuring DC accuracy according to claim 1, wherein: Applying the residue matrix perturbation in step S7 includes the following process: S7.

1. For the saved macromodel H(s)=C(sI-A) -1 The residue matrix C in B+D is perturbed and expressed as: S7.

2. After sorting out the constraints, we get: ΔC(-A -1 B)=H dc -D+CA -1 B S7.

3. Transpose the formula to obtain: (-A -1 B) T ΔC T =(H dc -D+CA -1 B) T This is the optimized macro model.

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