CN115146573A - Simulation method for small signal frequency response characteristic in analog circuit and related product - Google Patents
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Abstract
The embodiment of the application provides a simulation method for small signal frequency response characteristics in an analog circuit and a related product. Constructing a Krylov subspace and determining an orthogonal basis vector therein and generating a Heisenberg matrix based on the selected real number, static matrix, dynamic matrix and complex representation of an AC excitation source by establishing a mathematical model of an analog circuit; constructing a new Heisenberg matrix according to the orthogonal basis vector of the Krylov subspace and the Heisenberg matrix; constructing a right-end term of a Heisenberg equation; constructing a Heisenberg equation according to the right-end term and the Heisenberg matrix; givens rotation is carried out on the Heisenberg matrix and the right-end item so as to carry out upper triangularization on the Heisenberg equation, and whether the Heisenberg equation is converged is judged based on the right-end item after the upper triangularization; solving the Heisenberg equation after the upper triangulation according to the converged Heisenberg equation to obtain a solution of the Heisenberg equation; and combining the solution of the Heisenberg equation with the orthogonal basis vector of the Krylov subspace to obtain the solution of the mathematical model so as to generate a simulation result of the frequency response of the small signal in the analog circuit.
Description
Technical Field
The present application relates to the field of circuit processing technologies, and in particular, to a simulation method for small signal frequency response characteristics in an analog circuit and a related product.
Background
The AC (Alternating Current, abbreviated AC) analysis of a circuit finds the frequency domain response of the circuit. Currently, in AC analysis, the commonly used method is LU decomposition: since the complex matrix G + j ω C is different for different frequencies ω, LU decomposition and back substitution of the complex matrix G + j ω C are required at each frequency point, so the LU decomposition factor of the matrix cannot be reused, and a large amount of time is consumed for matrix LU decomposition, which greatly reduces the efficiency of AC analysis.
Disclosure of Invention
The embodiment of the application provides a simulation method for small signal frequency response characteristics in an analog circuit and a related product, so as to overcome or alleviate the technical problems in the prior art.
The technical scheme adopted by the application is as follows:
a simulation method for simulating small signal frequency response characteristics in a circuit comprises the following steps:
establishing a mathematical model of the analog circuit, wherein the mathematical model is (G + j ω C) X = r, G is a static matrix, and elements in the static matrix are resistance values and/or conductance values of the analog circuit; c is a dynamic matrix, elements in the dynamic matrix are capacitance values and/or inductance values of the analog circuit, and omega is an angular frequency value of the AC excitation source; r is a complex representation of the AC excitation source;
based on the selected real number alpha 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source, determining orthogonal basis vectors in the Krylov subspace and generating a Heisenberg matrix;
constructing a new Heisenberg matrix according to the orthogonal basis vector of the Krylov subspace and the Heisenberg matrix;
constructing a right-end term of a Heisenberg equation;
constructing a Heisenberg equation according to the right-end term and the new Heisenberg matrix;
givens rotation is carried out on the Heisenberg matrix and the right-end term to carry out upper triangulation on the Heisenberg equation, and whether the Heisenberg equation is converged is judged based on the right-end term after the upper triangulation;
solving the Heisenberg equation after the upper triangularization according to the converged Heisenberg equation to obtain a solution of the Heisenberg equation;
the solution of the Heisenberg equation and the orthogonal basis vector V of the Krylov subspace m Merging to obtain a solution of the mathematical model;
and generating a frequency response curve according to the solution of the corresponding mathematical model under the condition of a plurality of frequency points so as to generate a simulation result of the frequency response of the small signal in the simulation circuit.
Optionally, the method further comprises: if the imaginary parts of the r are all 0, directly jumping to the real number alpha based on selection 0 And constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source and determining an orthogonal basis vector in the Krylov subspace.
Optionally, the method further comprises: if the r has only one non-zero element with an imaginary part different from zero, or two non-zero elements added to zero, the method further comprises: and carrying out vector normalization processing on the r.
Optionally, the selecting is based on a real number α 0 Constructing a Krylov subspace through the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source comprises the following steps: based on the selected real number alpha 0 The static matrix G, the dynamic matrix C and the normalized complex representation r of the AC excitation source construct a Krylov subspace and determine an orthogonal basis vector therein.
Optionally, the method further comprises: if r does not satisfy: the imaginary parts of r are all 0, and if the imaginary part of r has only one non-zero element with non-zero imaginary part or two non-zero elements added to zero, the method further comprises: splitting the r into real and imaginary parts.
Optionally, said is based on selectionReal number alpha 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source comprises the following steps: based on a selected real number alpha 0 The static matrix G and the dynamic matrix C respectively construct different Krylov subspace base vectors with the real part and the imaginary part.
An apparatus for simulating the frequency response characteristics of a small signal in an analog circuit, comprising:
a first program unit, configured to create a mathematical model of the analog circuit, where the mathematical model is (G + j ω C) X = r, where G is a static matrix, and elements in the static matrix are resistance values and/or conductance values of the analog circuit; c is a dynamic matrix, elements in the dynamic matrix are capacitance values and/or inductance values of the analog circuit, and omega is an angular frequency value of the AC excitation source; r is a complex representation of the AC excitation source;
a second program element for, based on the selected real number alpha 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source, determining orthogonal basis vectors in the Krylov subspace and generating a Heisenberg matrix;
a third program unit, configured to construct a new Heisenberg matrix according to the orthogonal basis vector of the Krylov subspace and the Heisenberg matrix;
the fourth program unit is used for constructing a right-end term of a Heisenberg equation;
a fifth program unit, configured to construct a Heisenberg equation according to the right-end term and the new Heisenberg matrix;
a sixth program unit, configured to perform Givens rotation on the Heisenberg matrix and the right-end term to perform upper triangulation on the Heisenberg equation, and determine whether the Heisenberg equation converges based on the upper-triangulated right-end term;
a seventh program unit, configured to solve the triangulated Heisenberg equation according to the converged Heisenberg equation, so as to obtain a solution to the Heisenberg equation;
an eighth program element for solving the Heisenberg equation with the orthogonal basis vector V of the Krylov subspace m Merging to obtain a solution of the mathematical model;
and the ninth program unit is used for generating a frequency response curve according to the solutions of the mathematical models corresponding to the plurality of frequency points so as to generate a simulation result of the frequency response of the small signal in the analog circuit.
A computer program product, comprising: having stored thereon computer-executable instructions for performing any of the methods described above in the embodiments of the present application.
A computer device comprising a storage medium having computer-executable instructions thereon and a processor configured to execute the executable instructions to perform the method of any of the embodiments of the present application.
A simulation system comprises an analog circuit and a test host, wherein the test host is used for executing the method of any one of the embodiments of the application to simulate the small-signal frequency response characteristic of the analog circuit.
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Fig. 1 is a schematic flow chart of a simulation method for simulating a small signal frequency response characteristic in a circuit according to an embodiment of the present application.
Detailed Description
To make the technical problems, technical solutions and advantages to be solved by the present application clearer, the following detailed description is made with reference to the accompanying drawings and specific embodiments.
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description of the present invention, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the subject matter of the present disclosure can be practiced without one or more of the specific details, or with other methods, apparatus, steps, etc. In other instances, well-known structures, methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the disclosure.
Furthermore, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present disclosure, "plurality" means at least two, e.g., two, three, etc., unless explicitly defined otherwise. The symbol "/" generally indicates that the former and latter associated objects are in an "or" relationship.
In the present disclosure, unless otherwise expressly specified or limited, the terms "connected" and the like are to be construed broadly, e.g., as meaning electrically connected or in communication with each other; may be directly connected or indirectly connected through an intermediate. The specific meaning of the above terms in the present disclosure can be understood by those of ordinary skill in the art as appropriate.
In the simulation method for the small signal frequency response characteristic in the analog circuit provided in the embodiment of the present application, a mathematical model of the analog circuit is established, where the mathematical model is (G + j ω C) X = r, and G is a static matrix, and elements in the static matrix are resistance values and/or conductance values of the analog circuit; c is a dynamic matrix, elements in the dynamic matrix are capacitance values and/or inductance values of the analog circuit, and omega is an angular frequency value of the AC excitation source; r is a complex representation of the AC excitation source; based on the selected real number alpha 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source, determining orthogonal basis vectors in the Krylov subspace and generating a Heisenberg matrix; constructing a new Heisenberg matrix according to the orthogonal basis vector of the Krylov subspace and the Heisenberg matrix; constructing a right-end term of a Heisenberg equation according to the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source; constructing a Heisenberg equation according to the right end item and the new Heisenberg matrix; givens rotation of the Heisenberg matrix and right-hand terms to align the Heisenberg matrix with the right-hand termsCarrying out upper triangularization on a Heisenberg equation, and judging whether the Heisenberg equation is converged or not based on a right-end item after the upper triangularization; solving the Heisenberg equation after the upper triangularization according to the converged Heisenberg equation to obtain a solution of the Heisenberg equation; the solution of the Heisenberg equation and the orthogonal basis vector V of the Krylov subspace m Merging to obtain a solution of the mathematical model; and generating a frequency response curve according to the corresponding solution of the mathematical model under the condition of a plurality of frequency points to generate a simulation result of the frequency response of the small signal in the analog circuit, thereby realizing that the Krylov subspace can be shared for a plurality of angular frequencies needing to be measured, and improving the efficiency of AC analysis.
Fig. 1 is a schematic flowchart of a simulation method for simulating a small signal frequency response characteristic in a circuit according to an embodiment of the present disclosure; as shown in fig. 1, it includes:
s101, establishing a mathematical model of the analog circuit;
in this embodiment, the mathematical model is (G + j ω C) X = r, where G is a static matrix, and elements in the static matrix are resistance values and/or conductance values of the analog circuit; c is a dynamic matrix, elements in the dynamic matrix are capacitance values and/or inductance values of the analog circuit, and omega is an angular frequency value of the AC excitation source; r is a complex representation of the AC excitation source;
specifically, the analog circuit may be analyzed by an MNA functional module in the SPICE simulation component based on kirchhoff voltage law and kirchhoff current law to obtain values in the static matrix and the dynamic matrix.
S102, based on the selected real number alpha 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source, determining orthogonal basis vectors in the Krylov subspace and generating a Heisenberg matrix;
wherein,
wherein, A = (G + α) 0 C) -1 C; k is an integer greater than 0, k is a dimension of the Krylov subspace,H k representing the kth Heisenberg matrix,
representing a row vector with the dimension of k, wherein the kth element is 1, and the rest elements are 0; alpha (alpha) ("alpha") 0 For selected real numbers, h k+1,k Represents the 2 norm of the k +1 th vector (also called residual vector) in Krylov subspace; v. of k+1 Represents the unit vector corresponding to the k +1 th vector (also called residual vector) in Krylov subspace.
Specifically, for the analog circuit represented by (G + j ω c) X = r, the equation is applied to a real number α 0 Unfolding to obtain (I + (j omega-alpha) 0 )(Gα 0 C) -1 C)X＝(G+α 0 C) -1 r, let A = (G + α) 0 C) -1 C，b＝(G+α 0 C) -1 r, then is
Is the Krylov subspace, wherein, b, ab, \ 8230;, A k-1 b is a group of vectors of the Krylov subspace respectively, and the group of base vectors are subjected to orthogonalization treatment, so that an orthogonal base vector is obtained and is marked as V k Its dimension is k. Thereby, (G + j ω C) X = r is transformed into (I + α a) V k ＝V k+1 (I k+1,k + αH k+1,k ). Due to the fact that
Is actually V k+1 H k+1,k ，H k+1,k Denotes the kth Heisenberg matrix, where V k+1 ＝[V k ,v k+1 ]Its dimension is k +1. Thus, AV k ＝V k+1 H k+1,k 。
S103, according to the orthogonal basis vector V of the Krylov subspace k And Heisenberg matrix H n+1,n Constructing a new Heisenberg matrix as H n+1,n ＝I n+1,n +αH n+1,n ；
Wherein let α = j ω - α 0 ，
Where I is an identity matrix, n =1,2, \ 8230;, k, for which k Heisenberg matrices total; it can be seen that in the simulation process, only H needs to be changed when taking a different ω n+1,n ＝I n+1,n + αH n+1,n α of (1) is sufficient. And wherein for the orthogonal basis vector V k And, by extension, namely:
n =1,2, \ 8230;, k, AV, will be present n ＝V n+1 H n+1,n 。(I+αA)V n ＝V n+1 (I n+1,n +αH n+1,n )。 AV n ＝V n+ 1 H n+1,n Thus, brought into (I + α A) V n In (b) to obtain V n +αV n+1 H n+1,n ＝V n+1 (I n+1,n + αH n+1,n ) Thus, it can be seen that AV n ＝V n+1 H n+1,n And (I + alpha A) V n ＝V n+1 (I n+1,n +αH n+1,n ) The orthogonal base V can be shared n And V n+1 I.e. using the Krylov subspace of Ax = b, can also be used to find a solution of the algebraic equation (I + α a) x = b.
S104, constructing a right-end term beta e of a Heisenberg equation according to the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source 1 ；
Wherein β = | (G + α) 0 C) -1 r||，e 1 ＝[1,0,0..,0] T ；
S105, according to the right end item beta e 1 Constructing a Heisenberg equation by the Heisenberg matrix;
specifically, the Heisenberg equation was constructed as: (I) n+1,n +αH n+1,n )y＝βe 1 (ii) a y represents the solution of the Heisenberg equation;
s106, givens rotation is carried out on the Heisenberg matrix and the right-end term to carry out upper triangulation on the Heisenberg equation, and whether the Heisenberg equation is converged is judged based on the right-end term after the upper triangulation is carried out; executing step S107 according to the converged Heisenberg equation;
considering that the subsequent steps may be solved based on the Heisenberg equation after the upper triangulation, whether convergence is judged through the result of the rotation.
Specifically, since the dimension n +1 × n of the Heisenberg matrix is rotated by Givens and reaches convergence, the last row of the Heisenberg matrix is 0, for this reason, the right-end term has n elements, which correspond to the last action 0 in the Heisenberg matrix, and the last element is also as close to 0 as possible (a threshold value which is as close to 0 as possible is set in the actual engineering and is marked as epsilon), it can be determined that the Heisenberg equation converges, otherwise, it is determined that the Heisenberg equation does not converge.
In this embodiment, for any angular frequency ω, since n =1,2, \8230;, k, there will be a total of k said Heisenberg equations, i.e. it is determined by the above step S106 whether each Heisenberg equation converges one by one until a converged Heisenberg equation is found; if the corresponding Heisenberg equation does not converge until n = k, increasing the Krylov subspace V k Until said Heisenberg equation is found to converge, to perform the following step S107.
Specifically, when Givens rotation is performed, the Givens factor right-hand term, the Heisenberg equation, may be used. The Givens factor may be determined in particular depending on the application scenario.
Here, it should be noted that, in some embodiments, the corresponding influence when the convergence is not achieved is accumulated on the right-end term, heisenberg equation, corresponding to the convergence by means of an influence factor, so as to improve the accuracy of the operation. The specific use of the impact factor may be determined according to the application scenario.
S107, solving the triangulated Heisenberg equation to obtain a solution of the Heisenberg equation;
because Givens rotation is needed to be carried out on the right-hand term when convergence is judged, in order to save operation resources and improve operation speed, and meanwhile, the Heisenberg equation is rotated, therefore, the Heisenberg equation and the right-hand term are rotated, so that the upper triangulation of the Heisenberg equation is realized, and the Heisenberg equation after the upper triangulation is solved with the Heisenberg equation before the upper triangulation, when the step S107 is executed, the solution can be directly solved based on the Heisenberg equation after the upper triangulation, and the obtained solution is directly used as the solution of the Heisenberg equation.
The last row of the upper triangulated Heisenberg matrix is 0, and the last element of the right end term after the upper triangularization can be regarded as 0, so that the upper triangularized Heisenberg matrix can be directly adjusted into a matrix of m x m, the right end term is a column vector with dimension of m, and accordingly, y can be directly solved, and is the column vector with dimension of m. Wherein m is an orthogonal basis vector V corresponding to the converged Heisenberg equation m The serial number of (c).
S108, solving the Heisenberg equation and orthogonal basis vector V of the Krylov subspace m Merging to obtain a solution of the mathematical model;
specifically, X = V may be passed m *Y m Solving the Heisenberg equation with the orthogonal basis vector V of the Krylov subspace m And combining to obtain the solution of the mathematical model.
Specifically, for example, when n =3, the Heisenberg equation converges, then
V m = (v 1 v2 v 3), then
Where x0 is the guess of the solution, set according to the application scenario. The elements of v1, v2 and v3 are the same as the number of elements of the row vector or the column vector of A.
When the execution of the above steps is completed for one of the angular frequencies S102-S106, when for the next angular frequency value, it is only necessary to bring the next angular frequency value into α = j ω - α 0 In (b), new alpha is obtained, and then I is added n+1,n +αH n+1,n And (4) changing the alpha in the test table into a new alpha, and repeating the steps S102-S106, and so on until the solutions of the mathematical models corresponding to all angular frequencies to be tested are obtained.
S109, generating a frequency response curve according to the solution of the corresponding mathematical model under the condition of a plurality of frequency points;
in this embodiment, specifically, the multiple frequency points are used as abscissa, and the solution corresponding to the mathematical model is used as ordinate, so as to complete generation of the frequency response curve, and reflect the influence relationship of the node voltage and the node current by the frequency of the excitation source.
And S110, generating a simulation result of the frequency response of the small signal in the analog circuit according to the frequency response curve.
In this embodiment, the frequency response curve may be directly used as a simulation result of the small signal frequency response in the analog circuit. Of course, in other embodiments, data statistics may be performed based on the frequency response curve, so that the statistical result is used as a simulation result of the small signal frequency response in the analog circuit, thereby reflecting the trend relationship of the voltage and current of each node in the analog circuit along with the change of the frequency, such as the relationship that the amplitude and the phase are affected by the frequency.
Alternatively, in an embodiment, there may be one of the following:
if the imaginary parts of the r are all 0, directly jumping to the real number alpha based on selection 0 The static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source construct a Krylov subspace and determine an orthogonal basis vector V therein k The step (2). The imaginary parts of the r are all 0, indicating that there is no AC excitation source in the analog circuit.
If the r has only one non-zero element with non-zero imaginary component, or two non-zero elements with zero added, the method further comprises: carrying out vector normalization processing on the r; the r has only one non-zero element with non-zero imaginary part or two non-zero elements which are added to be zero, and the fact that only one AC excitation source or AC excitation sources with differential input exist in the analog circuit is indicated.
The selection based on the real number alpha 0 Constructing a Krylov subspace V by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source k The method comprises the following steps: based on the selected real number alpha 0 The static matrix G, the dynamic matrix C and the normalized complex representation r of the AC excitation source construct a Krylov subspace and determine an orthogonal basis vector V therein k 。
Through the vector normalization processing, the obtained normalized complex number representation r of the AC excitation source has 2 norms of 1, so that the situation that the imaginary part of r is 0 is eliminated.
If r does not satisfy: the imaginary parts of r are all 0, and if there is only one non-zero element with an imaginary part of non-zero, or there are two non-zero elements with an imaginary part of zero added, the method further comprises: splitting the r into a real part and an imaginary part;
the selection based on the real number alpha 0 Constructing a Krylov subspace V by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source k The method comprises the following steps: based on a selected real number alpha 0 The static matrix G and the dynamic matrix C respectively construct different Krylov subspace base vectors V together with the real part and the imaginary part k Therefore, based on the real-time processing of the steps S102-S106 for the real part and the imaginary part of the excitation source, finally, the solutions corresponding to the mathematical model under each angular frequency value are obtained by combination.
The above-mentioned embodiments are only specific embodiments of the present application, and are used for illustrating the technical solutions of the present application, but not limiting the same, and the scope of the present application is not limited thereto, and although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope disclosed in the present application; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present application and are intended to be covered by the appended claims. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (10)
1. A method for simulating the frequency response characteristics of small signals in an analog circuit is characterized by comprising the following steps:
establishing a mathematical model of the analog circuit, wherein the mathematical model is (G + j ω C) X = r, G is a static matrix, and elements in the static matrix are resistance values and/or conductance values of the analog circuit; c is a dynamic matrix, elements in the dynamic matrix are capacitance values and/or inductance values of the analog circuit, and omega is an angular frequency value of the AC excitation source; r is a complex representation of the AC excitation source;
based on the selected real number alpha 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source, determining an orthogonal basis vector in the Krylov subspace, and generating a Heisenberg matrix;
constructing a new Heisenberg matrix according to the orthogonal basis vector of the Krylov subspace and the Heisenberg matrix;
constructing a right-end term of a Heisenberg equation;
constructing a Heisenberg equation according to the right-end term and the new Heisenberg matrix;
givens rotation is carried out on the Heisenberg matrix and the right-end term to carry out upper triangulation on the Heisenberg equation, and whether the Heisenberg equation is converged is judged based on the right-end term after the upper triangulation;
solving the Heisenberg equation after the upper triangularization according to the converged Heisenberg equation to obtain a solution of the Heisenberg equation;
the solution of the Heisenberg equation and the orthogonal basis vector V of the Krylov subspace m Merging to obtain a solution of the mathematical model;
and generating a frequency response curve according to the solution of the corresponding mathematical model under the condition of a plurality of frequency points so as to generate a simulation result of the frequency response of the small signal in the simulation circuit.
2. The method of claim 1, further comprising: if the imaginary parts of the r are all 0, directly jumping to the real number alpha based on selection 0 And constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source, and determining an orthogonal basis vector in the Krylov subspace.
3. The method of claim 1, further comprising: if the r has only one non-zero element with an imaginary part different from zero, or two non-zero elements added to zero, the method further comprises: and carrying out vector normalization processing on the r.
4. The method of claim 3, wherein a is based on the selected real number 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source comprises the following steps: based on a selected real number alpha 0 The static matrix G, the dynamic matrix C and the normalized complex representation r of the AC excitation source construct a Krylov subspace and determine an orthogonal basis vector therein.
5. The method of claim 3, further comprising: if r does not satisfy: the imaginary parts of r are all 0, and if the imaginary part of r has only one non-zero element with non-zero imaginary part or two non-zero elements added to zero, the method further comprises: splitting the r into real and imaginary parts.
6. The method of claim 5, wherein a is based on the selected real number 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source comprises the following steps: based on a selected real number alpha 0 And the static matrix G and the dynamic matrix C respectively construct different Krylov subspace basis vectors with the real part and the imaginary part.
7. An apparatus for simulating a frequency response characteristic of a small signal in an analog circuit, comprising:
a first program unit, configured to create a mathematical model of the analog circuit, where the mathematical model is (G + j ω C) X = r, where G is a static matrix, and elements in the static matrix are resistance values and/or conductance values of the analog circuit; c is a dynamic matrix, elements in the dynamic matrix are capacitance values and/or inductance values of the analog circuit, and omega is an angular frequency value of the AC excitation source; r is a complex representation of the AC excitation source;
a second program element for, based on the selected real number α 0 Constructing a Krylov subspace by the static matrix G, the dynamic matrix C and the complex representation r of the AC excitation source, determining an orthogonal basis vector in the Krylov subspace, and generating a Heisenberg matrix;
a third program unit, configured to construct a new Heisenberg matrix according to the orthogonal basis vector of the Krylov subspace and the Heisenberg matrix;
the fourth program unit is used for constructing a right-end term of a Heisenberg equation;
a fifth program unit, configured to construct a Heisenberg equation according to the right-end term and the new Heisenberg matrix;
a sixth program unit, configured to perform Givens rotation on the Heisenberg matrix and the right-end term to perform upper triangulation on the Heisenberg equation, and determine whether the Heisenberg equation converges based on the upper-triangulated right-end term;
a seventh program unit, which solves the Heisenberg equation after the upper triangularization according to the converged Heisenberg equation to obtain the solution of the Heisenberg equation;
an eighth program element for solving the Heisenberg equation with the orthogonal basis vector V of the Krylov subspace m Merging to obtain a solution of the mathematical model;
and the ninth program unit is used for generating a frequency response curve according to the solution of the corresponding mathematical model under the condition of a plurality of frequency points so as to generate a simulation result of the frequency response of the small signal in the analog circuit.
8. A computer program product, comprising: having stored thereon computer-executable instructions for performing the method of claims 1-6.
9. A computer device comprising a storage medium having computer-executable instructions thereon and a processor configured to execute the executable instructions to perform the method of any one of claims 1 to 6.
10. A simulation system comprising an analog circuit and a test host for performing the method of any of claims 1-6 to simulate a small signal frequency response characteristic of the analog circuit.
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| US20130124168A1 (en) * | 2005-11-04 | 2013-05-16 | Purdue Research Foundation | Computationally efficient modeling and simulation of large scale systems |
| CN113191105A (en) * | 2021-03-22 | 2021-07-30 | 梁文毅 | Electrical simulation method based on distributed parallel operation method |
| CN114547938A (en) * | 2022-02-22 | 2022-05-27 | 中南大学 | Three-dimensional multi-frequency controllable source electromagnetic inversion method and system based on rational Krylov subspace |
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| US20130124168A1 (en) * | 2005-11-04 | 2013-05-16 | Purdue Research Foundation | Computationally efficient modeling and simulation of large scale systems |
| CN113191105A (en) * | 2021-03-22 | 2021-07-30 | 梁文毅 | Electrical simulation method based on distributed parallel operation method |
| CN114547938A (en) * | 2022-02-22 | 2022-05-27 | 中南大学 | Three-dimensional multi-frequency controllable source electromagnetic inversion method and system based on rational Krylov subspace |
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| 梁英波 等: "MATLAB仿真在运算放大电路频率响应分析中的应用", 绵阳师范学院学报, vol. 33, no. 11, 30 November 2014 (2014-11-30), pages 158 - 159 * |
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