Fast modeling simulation method based on time domain hybrid finite element method and circuit simulator SPICE

Abstract

The invention provides a rapid modeling simulation method based on a time domain hybrid finite element method and a circuit simulator SPICE. The rapid modeling simulation method is used for analyzing transient linear / nonlinear and passive / active complex microwave network circuit models on a PCB. The method comprises the following steps of: constructing an electromagnetic module of a microwave network circuit in computer aided design software, writing an SPICE netlist of the circuit module, and realizing interaction between the electromagnetic module and the circuit module through voltage and current defined on a lumped port, so as to obtain a complete circuit structure; in the electromagnetic part, a modal order reduction technology based on a second-order Arnoldi algorithm is adopted to reduce the order of a wave equation to a low-dimensional Krylov subspace for solving, and the data interaction process of the electromagnetic part and the circuit part in each time step length is obviously accelerated; in the time domain hybrid finite element method, the tree-cotree technology is adopted to overcome the problem of low-frequency breakdown or high-density breakdown occurring in the time domain finite element method; a circuit simulator SPICE enables a joint simulation algorithm to be powerful, and a complex multi-port circuit can be simulated.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic field modeling and simulation, and in particular relates to a fast modeling and simulation method based on a time domain hybrid finite element method and a circuit simulator SPICE. Background Art

[0002] In the simulation of high-speed and high-density integrated circuits, due to the increasingly obvious electromagnetic wave effects such as electromagnetic radiation, signal delay and distortion, skin effect and proximity effect, the traditional equivalent circuit method is no longer accurate enough in complex applications. Therefore, the field-circuit joint simulation method is a very promising high-speed and high-density integrated circuit modeling method. Field-circuit joint simulation involves electromagnetic structures, circuit systems and their coupling interfaces. In the field-circuit joint simulation method, both electromagnetic algorithms and circuit algorithms need to meet the requirements of accuracy, efficiency and versatility.

[0003] The field-circuit joint simulation algorithm currently used by commercial software uses a full-wave simulation algorithm to extract the equivalent circuit or network parameters of the electromagnetic structure, such as S, Y, and Z parameters, and then cascades with other circuits, and then uses a circuit simulator for simulation. However, it is only applicable to linear electromagnetic structures and is not universal enough when simulating complex high-speed and high-density integrated circuits. Therefore, finding a new field-circuit joint simulation algorithm is an urgent problem to be solved.

[0004] In the field-circuit joint simulation algorithm, the electromagnetic algorithm uses a time-domain full-wave algorithm, which requires calculating the electric field in each time step and takes a lot of time to realize the interaction between the field and the circuit. Therefore, it is particularly important to improve the efficiency of the field-circuit joint simulation.

[0005] In view of this, a fast modeling and simulation method based on time-domain hybrid finite element method and circuit simulator SPICE is very meaningful. Summary of the invention

[0006] In order to solve the problems of excessive calculation amount, long field and circuit interaction time, low-frequency collapse, small simulation range of electromagnetic and circuit parts in the field-circuit collaborative simulation algorithm, the present invention provides a rapid modeling and simulation method based on time-domain hybrid finite element method and circuit simulator SPICE to solve the above-mentioned technical defects.

[0007] In a first aspect, the present invention proposes a fast modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE, the method comprising the following steps:

[0008] In response to building a microwave network circuit, including geometric modeling of an electromagnetic module of the microwave network circuit and writing a SPICE netlist of the circuit portion, the electromagnetic module interacts with the circuit module through the voltage and current of the lumped port.

[0009] The electromagnetic part of the microwave network circuit model is calculated by using a hybrid finite element method to obtain a matrix equation of the electromagnetic part.

[0010] The modal reduction technique based on the second-order Arnoldi algorithm can be used to convert the electromagnetic matrix equation into a low-dimensional Krylov subspace Q m , and then use Qm to reduce the order of the matrix equation.

[0011] The interaction process between the electromagnetic and circuit modules is based on the equations of the electromagnetic part. The equivalent current method and the equivalent voltage method convert the hybrid system composed of the electromagnetic module and the circuit module into an equivalent circuit, and use SPICE to solve it to obtain the voltage and current information in the circuit; and use the current at the lumped port of the SPICE circuit as the excitation of the electromagnetic module to accurately describe the wave effect in the microwave network circuit.

[0012] This method first builds a geometric model of the hybrid system, and then numerically simulates the hybrid system based on the hybrid finite element method and SPICE simulator. This field-circuit collaborative simulation algorithm based on the hybrid finite element method and SPICE simulator can improve the stability of the calculation process, speed up the interaction process between the electric field and the circuit, and expand the simulation range of the electromagnetic and circuit parts.

[0013] Preferably, the time domain wave equation of the electromagnetic part of the field-circuit collaborative simulation is:

[0014]

[0015] in, represents the Hamiltonian operator, μ represents the relative magnetic permeability, and E represents the electric field intensity. In the formula, J i is the applied current density, J c is the current density introduced by the SPICE port, ∈ represents the dielectric constant, and σ is the conductivity.

[0016] Further preferably, the hybrid finite element method includes jointly expanding the electric field E by the edge basis function on the cotree edge and the gradient of the node basis function of the free nodes excluding the PEC nodes through the tree-cotree algorithm, which is expressed as follows:

[0017]

[0018] Among them, N c and N t are the number of cotree edges and tree edges in the model mesh, respectively. Φ represents the vector edge basis function used to expand the cotree edges and maintain the consistent curl. is the gradient of the scalar nodal basis function for the free nodes, and e represents the unknown coefficient to be solved.

[0019] Preferably, the ABC boundary is substituted into the second-order wave equation of the electric field to obtain the final system matrix equation

[0020]

[0021] Among them, the mass matrix M, the damping matrix C, the stiffness matrix S, the external excitation input matrix b and the SPICE excitation input matrix b CKT The expression is as follows:

[0022]

[0023] in,<A,B> Ω Indicates that A and B are inner products within the range of Ω, the superscript t indicates the transpose of the matrix, N is the total number of circuit ports, I s (t) is the current at port s, C s and are the paths to port s respectively.

[0024] Preferably, the implicit Newmark-β method (β=1 / 4) is used to time discretize the wave equation to be solved to obtain the time step equation:

[0025]

[0026] Further preferably, the discretized second-order matrix equation to be solved is reduced in order. The equation to be solved can be expressed in the frequency domain as:

[0027] s 2 Me+sCe+Se=-sb-sb CKT

[0028] Where s = jw, j refers to the imaginary unit, and ω is the angular frequency. The low-dimensional Krylov subspace Q of the above equation can be obtained by using the modal reduction technique based on the second-order Arnoldi algorithm. m Multiply both sides of the discretized second-order matrix equation by Q m Transpose The coefficients to be solved are expressed in the low-dimensional Krylov subspace Q m Expand, that is, e = Q m x,x are expansion coefficient vectors. The discretized second-order matrix equation to be solved is transformed into

[0029]

[0030] Further preferably, when solving a hybrid system consisting of distributed and lumped components, the computational domain needs to be divided into two modules: an electromagnetic module and a circuit module. At the lumped port s: the electromagnetic module and the circuit module satisfy the following relationship:

[0031]

[0032] The electromagnetic module interacts with the circuit part through the voltage and current of the lumped port. The interaction process between electromagnetic and circuit is to convert the electromagnetic part into an equivalent circuit and solve it using SPI CE.

[0033] The voltage on path C is as follows:

[0034]

[0035] Substituting the electric field expansion equation into the above formula, the voltage at the lumped port can be expressed as

[0036]

[0037] Among them, F and H represent the number of edge basis functions and node basis functions related to port s respectively, and the matrix with subscript s is a new matrix that recombines the rows related to SPICE port s in the original matrix.

[0038] From the reduced matrix equation, we can know that the expansion coefficient x can be expressed as

[0039]

[0040] Substituting the expression of the expansion coefficient x into the expression of the lumped port voltage, the relationship between the voltage V and the current I of the SPICE port s at the n+1 time step can be expressed as

[0041]

[0042] At time step n+1, and R(s,j) are known. According to the relationship between voltage and current in the above equation, the hybrid system composed of electromagnetic modules and circuit modules can be equivalent to a SPICE circuit. When all the parameters of the hybrid system's equivalent circuit are input into SPICE, the port voltage V at the n+1 time step s and I s can be solved. The port current calculated by the SPICE simulator is It is then used as an excitation for the electromagnetic module to accurately describe the wave effects in microwave network circuits.

[0043] Compared with the prior art, the beneficial results of the present invention are:

[0044] Building a microwave network circuit includes geometric modeling of the electromagnetic module of the microwave network circuit, writing a SPICE netlist of the circuit part, coupling the electromagnetic module with the circuit module using the voltage and current of the lumped port; meshing the electromagnetic module of the microwave network circuit simulation model, and then solving it using a hybrid finite element algorithm; the modal order reduction technology based on the second-order Arnoldi algorithm can reduce the order of the electromagnetic module matrix equation, which can improve the coupling process of the electromagnetic module and the circuit module; according to the matrix equation of the electromagnetic module, the equivalent current method and the equivalent voltage method can be used to equate the hybrid system composed of the electromagnetic module and the circuit module into a circuit, and SPICE is used to solve the equivalent circuit to obtain the port voltage and current; the port current solved by the SPICE circuit is used as the excitation of the electromagnetic part to accurately describe the wave effect in the microwave network circuit. The present invention proposes a field-circuit collaborative rapid modeling and simulation algorithm based on the time-domain hybrid finite element method and the circuit simulator SPICE, which can greatly improve the solution efficiency and solution range of the microwave network circuit, and increase the stability of the simulation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate the embodiments and are used together with the description to explain the principles of the present invention. It will be easy to recognize other embodiments and many expected advantages of the embodiments because they become better understood by reference to the following detailed description. The elements of the drawings are not necessarily to scale with each other. The same reference numerals refer to corresponding similar parts.

[0046] Figure 1 A schematic flow chart of a fast modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE according to an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of coupling between an electromagnetic part and a circuit part of a microwave circuit model in a fast modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE according to an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of an equivalent circuit of a microwave circuit model of a fast modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE according to an embodiment of the present invention;

[0049] Figure 4 A schematic diagram of an electromagnetic part of a model structure of a fast modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE according to an embodiment of the present invention;

[0050] Figure 5A schematic diagram of an electromagnetic part amplifier of a model structure of a fast modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE according to an embodiment of the present invention;

[0051] Figure 6 A schematic diagram of a circuit schematic diagram of a model structure of a fast modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE according to an embodiment of the present invention;

[0052] Figure 7 A comparison diagram of the voltage at the input end (lumped port 1) obtained by using the microwave circuit model in the embodiment of the present invention based on the time domain hybrid finite element and SPICE simulator fast algorithm and the commercial software CST;

[0053] Figure 8 A comparison diagram of the voltage at the output end (lumped port 2) obtained by using the microwave circuit model in an embodiment of the present invention based on the time domain hybrid finite element and SPICE simulator fast algorithm and the commercial software CST; DETAILED DESCRIPTION

[0054] In the following detailed description, reference is made to the accompanying drawings, which form a part of the detailed description and are shown by illustrative specific embodiments in which the present invention can be put into practice. To this end, directional terms, such as "top", "bottom", "left", "right", "up", "down", etc., are used with reference to the orientation of the figures described. Because the parts of the embodiments can be positioned in several different orientations, directional terms are used for the purpose of illustration and are by no means limiting. It should be understood that other embodiments may be utilized or logical changes may be made without departing from the scope of the present invention. Therefore, the following detailed description should not be adopted in a limiting sense, and the scope of the present invention is defined by the appended claims.

[0055] Figure 1 It is shown that the embodiment of the present invention discloses a fast modeling and simulation method based on the time domain hybrid finite element method and the circuit simulator SPICE, such as Figure 1 As shown, the method comprises the following steps:

[0056] S1. Perform geometric modeling of the electromagnetic module of the microwave network circuit, write the SPICE netlist of the circuit part, and couple the electromagnetic module with the circuit module using the voltage and current of the lumped port;

[0057] S2, meshing the electromagnetic module of the microwave network circuit, and calculating using a time-domain hybrid finite element method to obtain a time-domain second-order electric field wave equation to be solved;

[0058] S3. The modal reduction technique based on the second-order Arnoldi algorithm can obtain the low-dimensional Krylov subspace Q of the electromagnetic matrix equation.m , and then use Q m Reduce the order of the matrix equations of the electromagnetic part;

[0059] S4. According to the matrix equation of the electromagnetic module, the equivalent current method and the equivalent voltage method are used to equate the hybrid system composed of the electromagnetic module and the circuit module into a circuit, and SPICE is used to solve the equivalent circuit to obtain the port voltage and current; the port current solved by the SPICE circuit is used as the excitation of the electromagnetic part to accurately describe the wave effect in the microwave network circuit.

[0060] Based on the differential form of Maxwell's equations, the electric field wave equation to be solved in the time domain of the electromagnetic part of the microwave circuit model is obtained:

[0061]

[0062] in, represents the Hamiltonian operator, μ represents the relative magnetic permeability, and E represents the electric field intensity. In the formula, J i is the applied current density, J c is the current density introduced by the SPICE port, ∈ represents the dielectric constant, and σ is the conductivity.

[0063] The hybrid finite element method includes the expansion of the electric field E by the edge basis function on the cotree edge and the gradient of the node basis function of the free nodes except the PEC nodes through the tree-cotree algorithm, which is expressed as follows:

[0064]

[0065] N c and N t are the number of cotree edges and tree edges in the model mesh, respectively. Φ represents the vector edge basis function used to expand the cotree edges and maintain the consistent curl. is the gradient of the scalar nodal basis function for the free nodes, and e represents the unknown coefficient to be solved.

[0066] Substituting the ABC boundary into the second-order wave equation of the electric field, we obtain the final system matrix equation

[0067]

[0068] Among them, the mass matrix M, the damping matrix C, the stiffness matrix S, the external excitation input matrix b and the SPICE excitation input matrix b CKT The expression is as follows:

[0069]

[0070] in,<A,B> ΩIndicates that A and B are inner products within the range of Ω, the superscript t indicates the transpose of the matrix, N is the total number of circuit ports, I s (t) is the current at port s, C s and are the paths to port s respectively.

[0071] The implicit Newmark-β method (β = 1 / 4) is used to time discretize the wave equation to be solved, and the time step equation is obtained:

[0072]

[0073] The discretized second-order matrix equation to be solved is reduced in order. The equation to be solved can be expressed in the frequency domain as:

[0074] s 2 Me+sCe+Se=-sb-sb CKT

[0075] Where s = jw, j refers to the imaginary unit, and ω is the angular frequency. The low-dimensional Krylov subspace Q of the above equation can be obtained by using the modal reduction technique based on the second-order Arnoldi algorithm. m Multiply both sides of the discretized second-order matrix equation by Q m Transpose The coefficients to be solved are expressed in the low-dimensional Krylov subspace Q m Expand, that is, e = Q m x,x are expansion coefficient vectors. The discretized second-order matrix equation to be solved is transformed into

[0076]

[0077] like Figure 2 As shown in the figure, when solving a hybrid system consisting of distributed and lumped components, the computational domain needs to be divided into two modules: the electromagnetic module and the circuit module. At the lumped port s: the electromagnetic module and the circuit module satisfy the following relationship:

[0078]

[0079] The electromagnetic module interacts with the circuit part through the voltage and current of the lumped port. The interaction process between electromagnetic and circuit is to convert the electromagnetic part into an equivalent circuit and solve it using SPI CE.

[0080] The voltage on path C is as follows:

[0081]

[0082] Substituting the electric field expansion equation into the above formula, the voltage at the lumped port can be expressed as

[0083]

[0084] Wherein, F and H represent the number of edge basis functions and node basis functions associated with port s, respectively. The matrix with subscript s is a new matrix in which the rows associated with SPI CE port s in the original matrix are recombined.

[0085] From the reduced matrix equation, we can know that the expansion coefficient x can be expressed as

[0086]

[0087] Substituting the expression of the expansion coefficient x into the expression of the lumped port voltage, the relationship between the voltage V and the current I of the SPICE port s at the n+1 time step can be expressed as

[0088]

[0089] At time step n+1, and R(s,j) are known. According to the relationship between voltage and current in the above equation, the hybrid system composed of electromagnetic module and circuit module can be equivalent to Figure 3 When all the parameters of the hybrid system's equivalent circuit are input into SPICE, the port voltage V at the n+1 time step s and I s can be solved. The port current calculated by the SPICE simulator is It is then used as an excitation for the electromagnetic module to accurately describe the wave effects in microwave network circuits.

[0090] In this embodiment, the microwave network circuit is constructed, including geometric modeling of the electromagnetic module of the microwave network circuit, such as Figure 4 As shown in Figure 2, each branch of the model has two identical amplifiers, two Wilkinson dividers and two quarter-wavelength microstrip lines. The details of the amplifier are shown in Figure 2. Figure 5 The entire electromagnetic device consists of three 3D projects, an SMD component (representing a hybrid model of a resistor or capacitor), a transistor package and a complete PCB layout; write a SPICE netlist for the circuit part, and the electromagnetic module interacts with the circuit module through the voltage and current of the lumped port, as shown in Figure 6 As shown, port 1 is excited by a 100MHZ sinusoidal signal, and port 2 is connected to a 50Ω resistor as a load. Ports 17, 18 and 19, 20 are connected to two identical transistors, represented by a SPICE circuit. The connections between the other ports of the electromagnetic module and the circuit can be seen in Figure 6In order to verify the accuracy of the results of the present invention, a microwave circuit model, a balanced amplifier, is used to verify the high accuracy and efficiency of the developed fast algorithm. The same model is also established in the commercial software CST, and the simulation results are used as reference values.

[0091] Compare the calculation results of the algorithm proposed in the present invention with those of CST, as shown in Figure 7 ,8, the voltages of the input ports and output ports of the two are in good agreement; in addition, the calculation parameters of the algorithm proposed in the present invention are compared with those of CST, as shown in Table 1; CST uses an explicit time stepping scheme, which requires a large time step, and the present invention uses an implicit time stepping scheme, which speeds up the coupling of the electromagnetic module and the circuit module; from the results, it can be seen that the algorithm studied in the present invention has the same accuracy as the commercial software, but the simulation time of the algorithm is shorter than that of the commercial software, which verifies the stability and efficiency of the hybrid finite element fast algorithm.

[0092] Table 1

[0093]

[0094] In a specific embodiment, the electromagnetic part of the model is solved by the time-domain finite element method. The tree-cotree algorithm based on the finite element method can effectively overcome the low-frequency collapse problem and realize electromagnetic simulation from low frequency to high frequency. The modal reduction technology of the second-order Arnoldi algorithm can reduce the time-stepping equation of the electromagnetic part to a low-dimensional Krylov subspace, speeding up the solution process. According to the matrix equation of the electromagnetic module, the equivalent current method and the equivalent voltage method can be used to convert the hybrid system composed of the electromagnetic module and the circuit module into a circuit, and SPICE is used to solve the equivalent circuit to obtain the port voltage and current. Compared with the traditional field-circuit synergy method - using the full-wave simulation algorithm to extract the equivalent circuit or network parameters of the electromagnetic structure, such as S, Y, Z parameters, etc., cascade with other circuits, and then use the circuit simulator for simulation, although this method is efficient, it is only applicable to linear electromagnetic structures and is not universal enough when simulating complex high-speed and high-density integrated circuits; this method uses hybrid finite elements to solve the electromagnetic part and uses SPICE to solve the equivalent circuit, which increases the simulation range of the electromagnetic and circuit parts. This field-circuit collaborative simulation algorithm based on the hybrid finite element method and SPICE simulator can improve the stability of the calculation process, accelerate the interaction process between the electric field and the circuit, and expand the simulation range of the electromagnetic and circuit parts.

[0095] The present invention proposes a rapid modeling and simulation method based on a time-domain hybrid finite element method and a circuit simulator SPICE, and builds a microwave network circuit, including geometric modeling of the electromagnetic module of the microwave network circuit, writing a SPICE netlist of the circuit part, and coupling the electromagnetic module with the circuit module using the voltage and current of the lumped port; meshing the electromagnetic module of the microwave network circuit simulation model, and then solving it using a hybrid finite element algorithm; the modal order reduction technology based on the second-order Arnoldi algorithm can reduce the order of the electromagnetic module matrix equation, which can improve the coupling process of the electromagnetic module and the circuit module; according to the matrix equation of the electromagnetic module, the equivalent current method and the equivalent voltage method can be used to equate the hybrid system composed of the electromagnetic module and the circuit module into a circuit, and SPICE is used to solve the equivalent circuit to obtain the port voltage and current; the port current solved by the SPICE circuit is used as the excitation of the electromagnetic part to accurately describe the wave effect in the microwave network circuit. The present invention proposes a field-circuit collaborative rapid modeling and simulation algorithm based on the time-domain hybrid finite element method and the circuit simulator SPICE, which can greatly improve the solution efficiency and solution range of the microwave network circuit, and increase the stability of the simulation process.

[0096] The above description is only a preferred embodiment of the present invention and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the present invention is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the above features are replaced with the technical features with similar functions disclosed in the present invention (but not limited to) to form a technical solution.

Claims

1. A fast modeling and simulation method based on time domain hybrid finite element method and circuit simulator SPICE, characterized in that: The method comprises the following steps: In response to building a microwave network circuit; including geometric modeling of the electromagnetic module of the microwave network circuit, writing a SPICE netlist of the circuit module, and the electromagnetic module interacting with the circuit module through the voltage and current of the lumped port; The electromagnetic module of the microwave network circuit is calculated by using a time-domain hybrid finite element method to obtain a time-domain second-order electric field wave equation to be solved; The implicit Newmark-β method (β=1 / 4) is used to time discretize the wave equation to be solved, and the time-stepping equation is obtained; and the modal reduction technique of the second-order Arnoldi algorithm is used to reduce the time-stepping equation to a low-dimensional Krylov subspace; The interaction process between the electromagnetic and circuit modules is to convert the hybrid system composed of the electromagnetic module and the circuit module into an equivalent circuit according to the time-stepping equation to be solved, and use SPICE to solve it to obtain the voltage and current information in the circuit; and use the current at the lumped port of the SPICE circuit as the excitation of the electromagnetic module to accurately describe the wave effect in the microwave network circuit.

2. The rapid modeling and simulation method based on the time-domain hybrid finite element method and the circuit simulator SPICE according to claim 1 is characterized in that: The wave equation to be solved is: in, represents the Hamiltonian operator, μ represents the relative magnetic permeability, and E represents the electric field intensity. In the formula, J i is the applied current density, J c is the current density introduced by the SPICE port, ∈ represents the dielectric constant, and σ is the conductivity.

3. The rapid modeling and simulation method based on time-domain hybrid finite element method and circuit simulator SPICE according to claim 2 is characterized in that: The hybrid finite element method includes jointly expanding the electric field E by the edge basis function on the cotree edge and the gradient of the node basis function of the free nodes except the PEC node through the tree-cotree algorithm, which is expressed as follows: Among them, N c and N t are the number of cotree edges and tree edges in the model mesh, respectively. φ represents the vector edge basis function used to expand the cotree edges and maintain the consistent curl. is the gradient of the scalar nodal basis function for the free nodes, and e represents the unknown coefficient to be solved.

4. The rapid modeling and simulation method based on the time domain hybrid finite element method and the circuit simulator SPICE according to claim 3 is characterized in that: Substituting the ABC boundary into the second-order wave equation of the electric field, we obtain the final system matrix equation Among them, the mass matrix M, the damping matrix C, the stiffness matrix S, the external excitation input matrix b and the SPICE excitation input matrix b CKT The expression is as follows: in,<A,B> Ω Indicates that A and B are inner products within the range of Ω, the superscript t indicates the transpose of the matrix, N is the total number of circuit ports, I s (t) is the current at port s, C s and are the paths to port s respectively.

5. The rapid modeling and simulation method based on the time-domain hybrid finite element method and the circuit simulator SPICE according to claim 4 is characterized in that: The implicit Newmark-β method (β = 1 / 4) is used to time discretize the wave equation to be solved, and the time step equation is obtained:

6. The rapid modeling and simulation method based on the time domain hybrid finite element method and the circuit simulator SPICE according to claim 5 is characterized in that: The discretized second-order matrix equation to be solved is reduced in order, and the equation to be solved can be expressed in the frequency domain as follows: s 2 Me+sCe+Se=-sb-sb CKT Where s = jw, j refers to the imaginary unit, ω is the angular frequency, and the low-dimensional Krylov subspace Q of the above equation can be obtained by using the modal reduction technique based on the second-order Arnoldi algorithm. m , multiply both sides of the discretized second-order matrix equation to be solved by Q m Transpose The coefficients to be solved are expressed in the low-dimensional Krylov subspace Q m Expand, that is, e = Q m x, x is the expansion coefficient vector, and the discretized second-order matrix equation to be solved is transformed into 7. The rapid modeling and simulation method based on the time-domain hybrid finite element method and the circuit simulator SPICE according to claim 6 is characterized in that: When solving a hybrid system consisting of distributed and lumped components, the computational domain needs to be divided into two modules: the electromagnetic module and the circuit module. The electromagnetic module and the circuit module satisfy the following relationship: The electromagnetic module interacts with the circuit part through the voltage and current of the lumped port. The interaction process between the electromagnetic and the circuit is to convert the electromagnetic part into an equivalent circuit and solve it using SPICE. The voltage on path C is as follows: Substituting the electric field expansion equation into the above formula, the voltage at the lumped port can be expressed as From the reduced matrix equation, we can know that the expansion coefficient x can be expressed as Substituting the expression of the expansion coefficient x into the expression of the lumped port voltage, the relationship between the voltage V and the current I of the SPICE port s at the n+1 time step can be expressed as At time step n+1, and R(s,j) are known. According to the relationship between voltage and current in the above equation, the hybrid system composed of electromagnetic modules and circuit modules can be equivalent to a SPICE circuit. When all the parameters of the equivalent circuit of the hybrid system are input into SPICE, the port voltage V at the n+1 time step is s and I s can be solved, and the port current calculated by the SPICE simulator It is then used as an excitation for the electromagnetic module to accurately describe the wave effects in microwave network circuits.

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