A macro modeling method for ensuring direct current precision

Abstract

The application discloses a macro modeling method for ensuring direct current precision, and the method comprises the following steps: reading n-port network parameters; initializing sampling points for constructing a macro model; initializing the order of the macro model; initializing the pole of the macro model; establishing a weighted linear system according to the current order, the sampling points and the pole; solving a linear equation set, judging convergence according to an error, and obtaining the macro model; and outputting the optimized macro model by applying a residue matrix disturbance to optimize the macro model. The macro modeling method for ensuring direct current precision provided by the application controls the direct current precision in two stages. In the first stage, a weighted least square method is adopted on the basis of a linear system established by a traditional vector fitting algorithm to preliminarily control the direct current precision. In the second stage, a small 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] This invention relates to the field of integrated circuit design technology, and in particular to a macro-modeling method that guarantees DC accuracy. Background Technology

[0002] In integrated circuit design, numerical modeling and simulation are core methods for ensuring chip functional reliability and performance optimization. They help designers identify and resolve potential problems in advance, effectively reducing chip design cycles and manufacturing costs. However, real-world physical systems are complex, making modeling and simulating the entire system a challenging task. Macro-modeling is a general 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] Macro-models can be identified from the frequency response, thus yielding a reduced-order representation of the physical system. Once the macro-models of each physical module are obtained, they can be embedded into the entire system for simulation by a circuit simulator. This technique has become the standard for macro-modeling due to the robustness of vector fitting.

[0004] In macro-modeling, it is typically required that the DC accuracy of the macro model be accurate, meaning that the macro model H(s) perfectly matches the original data at frequency s=0. This is because any error in the DC accuracy can cause a change in the system's steady-state operating point, thus altering 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 based on the system's steady-state operating point; therefore, the transient simulation of integrated circuits is highly dependent on the accuracy of the steady-state operating point. Transient simulations are commonly used in the verification phase of system-level circuits to ensure the correctness and reliability of module functions. Therefore, ensuring the DC accuracy of the macro model is crucial. However, traditional vector fitting algorithms do not establish a DC error control mechanism, resulting in inherent biases in the constructed macro model in terms of DC accuracy, which may lead to steady-state operating point drift.

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

[0006] To address the shortcomings of existing technologies, this invention provides a macro-modeling method that guarantees DC accuracy. By employing a dual control mechanism of a weighted linear system and a perturbation macro-model residue matrix, it ensures the generation of a macro-model that strictly matches DC characteristics, thereby obtaining a correct and reliable steady-state operating point.

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

[0008] This invention provides a macro-modeling method that guarantees DC accuracy, the method comprising:

[0009] S1. Read the network parameters of port n;

[0010] S2. Initialize the sampling points used to build the macro model;

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

[0012] S4. Initialize the poles of the macromodel;

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

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

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

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

[0017] In one optional embodiment, step S2 uses an adaptive strategy of low-frequency encrypted sampling and wideband uniform sampling to initialize and construct a set of sampling frequency points.

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

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

[0020]

[0021] in, s k =j2πw k j is the imaginary unit, w k p is the frequency corresponding to the kth sampling point. n Represents the nth pole; Let f represent a (2Ns×1) column vector. v =diag([Re(f′) v Im(f′) v )]) is represented by the vector [Re(f′ v Im(f′) v The diagonal matrix formed by )], Re(f′ v ) and Im(f′v ) are respectively f′ v The real and imaginary parts, f′ v =[f v (s1) … f v (s Ns [)] represents the vector consisting of all sampling points of the v-th S-parameter curve; V = n 2 Or V = n; C v This represents the residue vector of the v-th S-parameter curve. The coefficients of the auxiliary function σ(s) in vector fitting are represented by 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 zeros of σ(s) to obtain the vector set consisting of the poles of the macromodel. Where A σ Let B represent the pole matrix of σ(s). σ Let C represent the state matrix of σ(s). σ D represents the residue matrix of σ(s). σ The constant matrix representing σ(s);

[0024] S6.2 Update the residues and constants of the S-parameter curve using the following formula:

[0025]

[0026] Where p n =α n +jβ n For curve S ij The nth pole, c n For p n The corresponding residue, d ij For curve S ij The constant term;

[0027] S6.3, Determine if the condition is met. If so, the convergence condition has been met, and the macro model is saved; otherwise, proceed to step S6.4.

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

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

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

[0031]

[0032] S7.2, After simplifying 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 this invention based on its technical solution are as follows:

[0038] The present invention provides a macro-modeling method to ensure DC accuracy, which controls DC accuracy in two stages. The first stage uses weighted least squares method to initially control DC accuracy based on the establishment of a linear system by traditional vector fitting algorithm. The second stage applies a small perturbation to the residue matrix of the macro model so that the perturbated macro model has accurate DC characteristics. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating a macro-modeling method for ensuring DC accuracy provided by the present invention.

[0041] Figure 2 This is a schematic diagram comparing the S parameters in this embodiment.

[0042] Figure 3 This is a magnified view of the DC input field characteristics. Detailed Implementation

[0043] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the protection scope of the embodiments of the present invention.

[0044] This embodiment provides a macro-modeling method that guarantees DC accuracy, the method comprising:

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

[0046] Touchstone files (also known as SnP files) are ASCII text files used to record n-port network parameter data for active devices or passive networks. At frequency w k At (k = 1, 2, 3, ..., K), the form of the n-port S-parameter matrix is:

[0047]

[0048] Assume the S-parameters have a total of K uniform frequency points, including a DC frequency point, i.e.

[0049]

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

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

[0052] To ensure the macromodel's accuracy at DC, r0 consecutive frequency points near and around DC must be included as sampling points. The highest frequency S-parameter must also be used as an initial sampling point to ensure accurate behavior of the macromodel at high frequencies. In this embodiment, the initial number of sampling frequency points r can be set to 5, and the number r0 of consecutive frequency points near DC needs to be adjusted according to the number of frequency points K in the Touchstone file. Generally, this can be achieved using the formula... Settings. Furthermore, to obtain an accurate macromodel of the S-parameters, in-band accuracy must be guaranteed. Therefore, in-band accuracy is required within the [0, w] range. max Uniformly select r u Several frequency points, including DC and W maxTherefore, the initial number of sampling frequency points is r = r0 + r u r u Indicates the in-band [0, w max The number of frequency points is selected uniformly. Since the number of sampling points must be greater than the order of the macro model, the number of sampling points may need to be dynamically increased 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 macromodel using the peak prediction method. int .

[0054] Generally, the true order of a macromodel cannot be accurately predicted. In practice, an incremental order method is typically used, and the error is judged to be within an acceptable range to determine the order of the macromodel. It is well known that real poles exhibit decay in the transfer function, while paired complex conjugate poles exhibit oscillation. Therefore, to ensure that each resonance peak is characterized by at least one pair of complex conjugate poles, the initial order of the macromodel is set to the number of network parameter resonance peaks, N. peaks Twice that, that is, N int =max(4,2N) peaks To avoid taking an excessively low order, N is forcibly set here. int The minimum order is 4.

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

[0056] Since the frequency range of the S-parameters is [0, w max Therefore, the imaginary part of the initial poles of the complex conjugate is uniformly distributed in [0, w]. max Above, 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 process. Initially, N = N int , and α n <0.

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

[0060] (1) The poles are uniformly distributed in [0, w max This can reduce the number of pole relocations, allowing for faster convergence to the true pole.

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

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

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

[0064]

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

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

[0067]

[0068] Among them, the matrix [Xf] formed by the vth element v X] performs QR decomposition. and

[0069] This step transforms the traditional linear system into a weighted linear system, thus changing the problem from a simple least squares problem to a weighted least squares problem. Specifically, this is achieved using a weighting matrix Λ, where:

[0070] Λ=diag([λ1,λ2,…,λ Ns ])

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

[0072] Then, a new weighted linear system is:

[0073]

[0074] To ensure the DC accuracy of the macro model, a large weight can be assigned to the data at the DC frequency point. In this embodiment, λ1 = 10. 3 The weights of the remaining frequency points are set to 1.

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

[0076] S6.1 Solving for the zeros of σ(s) yields the poles of the macromodel. This is easily obtained through the state-space model of σ(s), i.e.:

[0077]

[0078] Among them, {p n} represents the vector set consisting of the poles of the macromodel, A σ Let B represent the pole matrix of σ(s). σ Let C represent the state matrix of σ(s). σ D represents the residue matrix of σ(s). σ The constant matrix representing σ(s).

[0079] S6.2, Based on the new pole {p n Update the residues 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 pole, c n For p n The corresponding residue, d ij For curve S ij The constant term;

[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 it is, 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 , and reselect r u + 0.5r u sampling points, and let r u = 1.5r u , and 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, and 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:

[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 2The S-parameter input reflection coefficient curve of a 3-port voltage-controlled oscillator (VCO) provided for an embodiment of the present invention is shown. For ease of illustration, only the amplitude of the S(1,1) curve is provided, where the blue solid line represents the original S-parameter data, the orange dotted line represents the traditional vector fitting result, and the yellow dashed line represents the result of this embodiment. Because the same convergence threshold is used, both macromodels exhibit good accuracy across the entire bandwidth. Figure 3 The magnified view of the DC near-field characteristics clearly shows that traditional vector fitting has an error of 0.12% in DC, while the present invention can provide accurate DC characteristics.

[0095] The table below shows the circuit simulation results of macromodels generated by two different macromodeling methods for VCOs, with the linear interpolation simulation result of 28.245mA used as the standard. Since interpolation does not change the original data, linear interpolation has the most reliable steady-state operating point. Here, Idc_vco represents the DC supply current, a key parameter for evaluating VCO power consumption and power supply design. As shown in the table, the macromodel generated by the traditional vector fitting algorithm produced an error of 0.120%, deviating from the standard value by 0.033mA. In contrast, the simulation index Idc_vco of the solution provided by this invention deviates from the standard by 0, demonstrating the superiority of the solution provided by this invention.

[0096]

[0097] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (modules, systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.

[0099] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0100] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0101] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0102] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A macro-modeling method that guarantees DC accuracy, characterized in that, The method includes: S1. Read the network parameters of port r; S2. Initialize the sampling points used to build the macro model; S3. Initialize the order of the macromodel N int ; S4. Initialize the poles of the macromodel; S5. Based on the current order, sampling points, and poles, establish a weighted linear system; the weighted linear system is expressed as: ； in, , , , j w is the imaginary unit. k p is the frequency corresponding to the kth sampling point. n Represents the nth pole; Represents a column vector of size (2Ns × 1). Represented by vector The diagonal matrix formed and They are respectively The real and imaginary parts, V represents the vector consisting of all sampling points of the v-th S-parameter curve; V=n 2 Or V=n; C v This represents the residue vector of the v-th S-parameter curve. Auxiliary function in vector fitting σ ( s The coefficient of ) Indicates the first i The weight of each sampling point; S6. Solve the system of linear equations, determine convergence based on the error, and obtain the macro model, including the following process: S6.1, Solve σ ( s The zeros of the macromodel are obtained, which form the vector set of the poles of the macromodel. A σ express σ ( s The pole matrix of B) σ express σ ( s The state matrix of C σ express σ ( s The residue matrix of D) σ express σ ( s The constant matrix of ). S6.2 Update the residues and constants of the S-parameter curve using the following formula: ； in For curve S ij The nth pole, c n For p n The corresponding residue, d ij For curve S ij The constant term; S6.3, Determine if the condition is met. If so, the convergence condition has been met, and the macro model is saved; otherwise, proceed to step S6.

4. S6.4 Determine whether the current number of sampling points is greater than the order of the macro model. If so, increase the number of uniform sampling points and return to step S5 to rebuild the weighted linear system; otherwise, increase the order of the macro model and return to step S5 to rebuild the weighted linear system. S7. Optimize the macro model by applying a residue matrix perturbation, and output the optimized macro model. The application of the residue matrix perturbation includes the following process: S7.1, For saved macro models The residue matrix C in the equation is perturbed and expressed as: ； S7.2, After simplifying the constraints, we get: ； S7.3, Transpose the formula to obtain: ； This is the optimized macro model.

2. The macro-modeling method for ensuring DC accuracy according to claim 1, characterized in that: The r-port network parameters mentioned in step S1 include the 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 set of sampling frequency points.

4. The macro-modeling method for ensuring DC accuracy according to claim 1, characterized in that: Step S3 uses the peak prediction method to predict the order of the macromodel. N int , , N peaks This represents the number of resonance peaks in the network parameters.

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