Field-circuit combined transient simulation method based on ADE dispersion model
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI JIUTONGFANG TECHNOLOGY CO LTD
- Filing Date
- 2026-03-13
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies are complex and computationally inefficient in modeling field-circuit joint transient simulation methods when dealing with complex high-speed, high-density integrated circuit designs. In particular, the applicability of existing methods is insufficient when dealing with dispersive media.
A field-circuit joint transient simulation method based on the ADE dispersion model is adopted. By introducing an auxiliary polarization vector, the frequency domain constitutive relation of the dispersive medium is transformed into an auxiliary differential equation in the time domain. Together with the second-order electric field wave equation, an electromagnetic equation system is constructed. The solution is performed by combining the central difference and Newmark-beta hybrid algorithms, and the field-circuit coupling problem is separated for joint simulation.
It improves the stability and accuracy of numerical calculations for dispersive media, simplifies model processing, enhances computational efficiency, is applicable to various dispersive media models, and has stronger versatility and simulation effects.
Smart Images
Figure CN122242416A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of field-path joint transient simulation technology for dispersive media, and particularly to a field-path joint transient simulation method based on the ADE dispersion model. Background Technology
[0002] The constitutive relations of dispersive media are typically given in the frequency domain. Simulating the electromagnetic response of dispersive media in the time domain usually involves time convolution terms, which are extremely time-consuming in long simulations. A more feasible approach is to apply auxiliary differential equations (ADEs). Furthermore, current field-circuit co-simulation methods typically rely on full-wave simulation to extract equivalent circuit or network parameters (such as S, Y, and Z parameters) of the electromagnetic structure, then cascade them with other circuit components and perform overall simulation using a circuit simulator. However, this method is clearly insufficient for complex high-speed, high-density integrated circuit designs. Therefore, those skilled in the art urgently need to propose a field-circuit joint transient simulation method based on the ADE dispersive model. Summary of the Invention
[0003] To address one or more of the above-mentioned defects or improvement needs in existing technologies, and to overcome the problems of complex modeling and computational efficiency in field-path joint transient simulation in existing technologies, this invention provides a field-path joint transient simulation method based on the ADE dispersion model. This method aims to more effectively solve the field-path coupling problem of specific types of dispersive media and improve the stability, accuracy, and efficiency of numerical calculations.
[0004] The aforementioned improved technical features can be combined with each other as long as they do not conflict with each other.
[0005] To achieve the above objectives, this invention proposes a field-path joint transient simulation method based on the ADE dispersion model, the method comprising the following steps: Obtain the electromagnetic model of the simulation target after mesh partitioning; Obtain the circuit model in the simulation, and the netlist file corresponding to the circuit model; The electromagnetic model includes a dispersive medium, and the frequency domain polarizability of the dispersive medium model can be expressed in a unified form in different dispersive materials; The dispersive medium model obtains the ADE formula for the time-domain constitutive relation by introducing polarization intensity into the frequency-domain constitutive relation; The circuit model is processed to obtain the differential algebraic equations of the circuit; Based on the electromagnetic model and the circuit model, a joint field-circuit transient simulation is performed.
[0006] Furthermore, the construction of the electromagnetic equations for the dispersive model includes the following steps: The frequency domain polarizability of different dispersive material models is rewritten into a unified form. By introducing the electric polarization intensity, the frequency domain constitutive relation of the dispersive medium is rewritten into the ADE formula of the time domain constitutive relation. Based on the first-order time-domain Maxwell equations and the constitutive relation of the ADE form, the second-order electric field wave equation describing the dispersive medium is obtained.
[0007] Furthermore, the specific steps for performing the field-circuit joint transient simulation are as follows: Field-circuit integration is performed, with the electric field and circuit connected through ports. Current is obtained from the circuit model, and the electromagnetic model is solved using FETD simulation. Then, the voltage obtained from the electric field is used to simulate the circuit model. Determine whether all time steps have been iterated. If the time step is less than the set time step, update the variables and perform the field-circuit joint transient simulation as described above. Otherwise, end the simulation.
[0008] Further, the step involves calculating and updating the electric field strength using the wave equation with time steps, and simultaneously calculating and updating the polarization intensity using the ADE equation, specifically as follows: The updated formula for the polarization intensity is obtained by using Newmark-beta integration on the time-domain constitutive relation of ADE form; The spatial discrete system equations are discretized in time using the central difference method to obtain time-updated equations; The updated electric field strength is obtained by substituting the updated formula of the polarization intensity into the time update equation.
[0009] Furthermore, the circuit model employs an improved node analysis method based on Kirchhoff's laws to establish differential algebraic equations, and uses Newmark-beta integration to obtain the circuit voltage update formula.
[0010] This invention also discloses a field-path joint transient simulation method based on the ADE dispersion model, the method comprising the following steps: Step 1: Obtain the electromagnetic model. Specifically, based on the full-wave solution requirements, perform structured modeling based on the target geometry, mark the dispersive material properties, and perform mesh generation to obtain the electromagnetic model; construct the circuit model by inputting the SPICE netlist file describing the circuit structure. Step 2: Rewrite the frequency domain polarizability of different dispersive material models into a unified form, introduce the electric polarization intensity, and use the conversion relationship from the frequency domain to the time domain to rewrite the frequency domain constitutive relation of the dispersive medium into the ADE formula of the time domain constitutive relation; Step 3: Using the time-domain finite element method, based on the first-order time-domain Maxwell equations and the time-domain constitutive relation in the form of ADE, the second-order vector wave equation describing the dispersive medium is obtained, and the time-domain finite element method is used to discretize the space to obtain the semi-discrete system equation. Step 4: Based on the improved node analysis method of Kirchhoff's laws, establish the differential algebraic equations of the circuit model; Step 5: Perform time stepping, update the electric field intensity in the electromagnetic field calculation domain using the central difference scheme, and update the electromagnetic field auxiliary polarization variable (electric polarization intensity) and the voltage of the circuit section using the Newmark-beta direct integration scheme; Step 6: Perform field-circuit coupling. Connect the field and the circuit through the port. Couple the field to the circuit, calculate the voltage on the circuit port, and use it as the equivalent driving source in the circuit simulator. Couple the circuit to the field, calculate the current in the circuit, and use it as the equivalent external current source in the full-wave simulation in the electromagnetic model. Step 7: Determine if all iteration time steps have been completed. If it is less than the set time step, return to step 3 to continue iterating; otherwise, end the iteration.
[0011] Furthermore, the unified form in step 2 is to express the polarizability of different dispersion models as rational fractions in order to obtain a general descriptive model. The second-order electric field wave equation avoids time-domain convolution calculation by introducing electric polarization intensity.
[0012] Furthermore, in step 5, the polarization intensity is updated using the Newmark-beta direct integration scheme, specifically by converting the time-domain constitutive relation containing the polarization intensity into a recursive form for updating.
[0013] Furthermore, step 5 involves updating the electric field strength using a central difference scheme, specifically including: The first and second derivatives of the electric field are constructed using the central difference of the electric field. These derivatives are then substituted into the spatial discrete equations. Based on the electric field values at the previous and current times, the electric field value at the next time step is estimated.
[0014] Furthermore, the dispersion model in step 2 includes the Drude model, the Debye model, and the Lorentz model.
[0015] In summary, the beneficial effects of the above-described technical solutions conceived by this invention compared with the prior art include: This invention presents a field-circuit joint simulation scheme for handling electromagnetic problems of different dispersive media models. As one aspect of this invention, an auxiliary polarization vector is introduced to transform the frequency domain constitutive relation of the dispersive medium into an auxiliary differential equation in the time domain concerning the polarization intensity. Together with the second-order electric field wave equation, this auxiliary polarization vector constructs a set of electromagnetic equations for handling dispersion problems. This method represents three common dispersion models in a unified form, has universality, and is simpler in theoretical model and code implementation than existing dispersion problem handling schemes (RC and SO), and has higher computational efficiency.
[0016] In another aspect, this invention divides the field-circuit coupling problem into two parts. The electromagnetic part uses a time-domain finite element method based on a central difference and Newmark-beta hybrid algorithm to solve for the port voltage, which serves as the equivalent driving source for the circuit model. The circuit part uses a co-simulation method based on Kirchhoff's laws and an improved node method to extract the circuit current, which serves as the equivalent external source for the electromagnetic model. The two parts achieve joint simulation of the field and the circuit through the port. This scheme is more versatile than the existing field-circuit joint simulation processing scheme that first extracts parameters and then cascades the circuit simulation. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0018] Figure 1 This is a flowchart illustrating the framework of the field-path joint transient simulation method for the ADE dispersion model implemented according to the present invention. Figure 2 This is a flowchart of one specific implementation of the field-path joint transient simulation method of the ADE dispersion model according to the present invention; Figure 3 This is a table of dispersive medium parameters in the field-path joint transient simulation method of the ADE dispersion model implemented according to the present invention; Figure 4 This is a field-path coupling diagram in the field-path joint transient simulation method of the ADE dispersion model implemented according to the present invention; Figure 5 This is a field-circuit joint simulation (circuit model) using a voltage excitation source with a Gauss pulse in the case of no metal modeling in the field-circuit joint transient simulation method of the ADE dispersion model implemented according to the present invention. Figure 6The field-circuit joint transient simulation method of the ADE dispersion model implemented according to the present invention performs field-circuit joint simulation (port voltage) using a voltage excitation source with Gauss pulses when the metal is not modeled. Figure 7 The field-circuit joint transient simulation method of the ADE dispersion model implemented according to the present invention uses the Drude dispersion model to perform field-circuit joint simulation (circuit model) using a voltage excitation source with a sinusoidal pulse. Figure 8 The field-circuit joint transient simulation method of the ADE dispersion model implemented according to the present invention uses the Drude dispersion model to perform field-circuit joint simulation (port voltage) using a voltage excitation source with a sinusoidal pulse. Figure 9 The field-circuit joint transient simulation method of the ADE dispersion model implemented according to the present invention uses Debye and a voltage excitation source with modulated Gauss pulse for field-circuit joint simulation (circuit model). Figure 10 The field-circuit joint transient simulation method of the ADE dispersion model implemented according to the present invention uses Debye and employs a voltage excitation source with modulated Gauss pulse for field-circuit joint simulation (port voltage). Detailed Implementation
[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0020] This invention proposes a field-circuit joint transient simulation method based on the ADE dispersion model. By utilizing auxiliary differential equations, the mathematical model of the dispersive medium is introduced into the FETD method, transforming the frequency-domain relationship between the polarization variable P and the electric field intensity E into a second-order differential equation in the time domain concerning P. The three dispersive medium models share a unified form, demonstrating universality. The Newmark-beta method is then used to solve this equation, yielding a time-domain recursive expression for E→P.
[0021] like Figure 1 As shown in the figure, this invention proposes a field-path joint transient simulation method based on the ADE dispersion model, which includes the following steps: Obtain the electromagnetic model of the simulation target after mesh partitioning; Obtain other circuit models in the simulation, and the corresponding netlist files of the circuit models; Netlist files are documents that primarily describe the specific requirements of a simulation circuit, including but not limited to SPICE netlists and their various formats. The electromagnetic model includes a dispersion model, and the frequency domain polarizability of the dispersion model can be expressed in a unified form for different dispersive materials. The dispersive medium model obtains the ADE formula for the time-domain constitutive relation by introducing polarization intensity into the frequency-domain constitutive relation; The circuit model is processed to obtain the differential algebraic equations of the circuit; Based on the electromagnetic model and the circuit model, a joint transient simulation of the field and circuit is performed.
[0022] The specific steps for performing a combined field-circuit transient simulation are as follows: The electric field strength calculated using the electromagnetic model is updated using time steps, and the polarization intensity is also updated. Field-circuit integration is performed, with the electric field and circuit connected through ports. Current is obtained from the circuit model, and the electromagnetic model is solved using FETD simulation. Then, the voltage obtained from the electric field is used to simulate the circuit model. Determine whether all time steps have been iterated. If the time step is less than the set time step, update all variables and perform the field-circuit joint transient simulation as described above. Otherwise, end the simulation.
[0023] The construction of the electromagnetic equations for the dispersive model includes the following steps: The frequency domain polarizability of different dispersive material models is rewritten into a unified form. By introducing electric polarization intensity, the frequency domain constitutive relations of different types of dispersive materials are rewritten into the ADE formula of time domain constitutive relations. Based on the first-order time-domain Maxwell equations and the time-domain constitutive relation in the form of ADE, the second-order vector wave equation describing the dispersive medium is obtained, and it is solved using the time-domain finite element method.
[0024] like Figure 2 As shown in the figure, the present invention also discloses a field-path joint transient simulation method based on the ADE dispersion model, the method comprising the following steps: Step 1: Obtain the electromagnetic model, specifically: based on the full-wave solution requirements, perform structured modeling based on the target geometry, mark the dispersive material properties, and perform mesh generation; obtain the circuit model by inputting the SPICE netlist file describing the circuit structure; Step 2: Rewrite the frequency domain polarizability of different dispersive material models into a unified form, introduce the electric polarization intensity, and use the conversion relationship from the frequency domain to the time domain to rewrite the frequency domain constitutive relation of different dispersive materials into the ADE formula of the time domain constitutive relation; Step 3: Based on the first-order time-domain Maxwell equations and the time-domain constitutive relation in the form of ADE, the second-order electric field wave equation of the dispersive medium is obtained, and the time-domain finite element method is used to discretize the space to obtain the discrete system equation. Step 4: Based on Kirchhoff's laws, an improved nodal analysis method is used to establish the differential algebraic equations of the circuit model; Step 5: Perform time stepping, update the electric field intensity in the electromagnetic field calculation domain using the central difference scheme, and update the polarization intensity and voltage of the circuit section using the Newmark-beta direct integration scheme; Step 6: Perform field-circuit coupling. Connect the field and the circuit through the port. Couple the field to the circuit, calculate the voltage on the circuit port, and use it as the equivalent driving source in the circuit simulator. Couple the circuit to the field, calculate the current in the circuit, and use it as the equivalent external current source in the full-wave simulation in the electromagnetic model. Step 7: Determine if all iteration time steps have been completed. If it is less than the set time step, return to step 3 to continue iterating; otherwise, end the iteration.
[0025] The unified form in step 2 is to express the polarizability of different dispersion models as rational fractions in order to obtain a general descriptive model. The second-order electric field wave equation avoids time-domain convolution calculation by introducing the polarization intensity.
[0026] Step 5 uses the Newmark-beta direct integration scheme to update the polarization intensity, specifically by converting the time-domain constitutive relation containing the polarization intensity into a recursive form for updating.
[0027] Step 5 uses a central difference scheme to update the electric field strength, specifically including: The first and second derivatives of the electric field are constructed using the central difference of the electric field. These derivatives are then substituted into the spatial discrete equations. Based on the electric field values at the previous and current times, the electric field value at the next time step is estimated.
[0028] In one specific implementation, such as Figure 2 The specific process corresponding to the steps in is as follows: Step 1: According to the full-wave solution requirements, for the electromagnetic part, perform structured modeling of the target based on the target's geometry. For the dispersive material properties, mark the Drude, Debye, or Lorentz model and perform mesh generation. For the circuit part, build the circuit model as needed and input the SPICE netlist file describing the circuit structure. Step 2: Dispersive material processing. The frequency domain polarizability of the three common dispersion models is rewritten into a unified form. To avoid time domain convolution calculation, an auxiliary polarization vector P (also known as polarization intensity) is introduced. The frequency domain constitutive relation is rewritten into the ADE formula of the time domain constitutive relation using the frequency domain to time domain conversion relationship. Step 3: The electromagnetic part is calculated using the time-domain finite element method. To avoid time-domain convolution calculations, the polarization intensity vector P is introduced to handle dispersion. Based on the first-order time-domain Maxwell equations and constitutive relations, the second-order vector wave equation to be solved is obtained. Step 4: The circuit section uses an improved node analysis method based on Kirchhoff's laws to establish the differential algebraic equations of the circuit. Step 5: Time stepping, using the central difference scheme, update the electric field intensity in the electromagnetic field calculation domain. The Newmark-beta direct integration scheme is adopted and Recursive formula for updating polarization intensity variables ; Step 6: Field-circuit connection. The field and circuit are connected through ports. Field -> Circuit: Utilizing the port voltage of the electric field section. Update the driving voltage in the circuit model ; Path → Field: Utilizing the current in the circuit Update the applied current source J in the electromagnetic model. CKT ; Step 7: Determine whether all iteration time steps have been completed. If it is less than the set time step, return to step 3; otherwise, end.
[0029] Specifically, according to one specific embodiment of the present invention, the field-path joint transient simulation method based on the ADE dispersion model of the present invention mainly includes the following calculation steps: Step 1: Based on the full-wave solution requirements, for the electromagnetic part, perform structured modeling of the target based on its geometry. For the dispersive material model, label the properties as Drude, Debye, or Lorentz models. This needs to be done according to... Figure 1 The list provides the corresponding parameters and performs mesh generation; for the circuit section, select the required circuit model and input the SPICE netlist file describing the circuit structure. Step 2: Dispersive material processing. The frequency domain polarizability of the three common dispersive medium models is rewritten into a unified form. The electric polarization intensity P is introduced, and the frequency domain constitutive relation is rewritten into a second-order time domain differential equation using the frequency domain to time domain conversion relationship. S21: Frequency domain polarizability of three common dispersive medium models: Debye model, Drude model, and Lorentz model. It can be represented in the following form: (1) Where j represents the imaginary part, Represents angular frequency, and L is the number of poles. , It is the relative permittivity at zero frequency; The extreme relaxation time, For collision frequency, For Drude frequency, This is the natural frequency of the oscillator.
[0030] Assumption
[0031] The general model description for the above three dispersive media is as follows: (2) The parameters of each model can be seen in the table. Figure 3 As shown in the image.
[0032] S22: The frequency domain constitutive relation of a dispersive medium is given by the following form: (3) In the formula, These are the vacuum permittivity and the relative permittivity at infinite frequency, respectively. To represent the polarizability, and to avoid time-domain convolution calculations, an electric polarization intensity P is introduced, and an auxiliary differential equation is constructed. (4) The frequency domain ADE relation can be obtained. (5) (2) Substitute into (5) (6) Utilizing the transformation relationship from frequency domain to time domain The time-domain ADE equation is obtained. (7) Time domain constitutive relations (8) S3: The electromagnetic part is calculated using the time-domain finite element method. To avoid time-domain convolution calculations, an electric polarization intensity vector P is introduced to handle dispersion. Based on the first-order time-domain Maxwell equations and the time-domain constitutive relation, the second-order electric field wave equation describing the dispersive medium is obtained, and it is solved using the time-domain finite element method to obtain the spatial discrete system equations; S31: The first-order time-domain Maxwell equations and the time-domain constitutive relation of the dispersive medium are expressed as follows: (9) in, Represents the Hamiltonian operator. It is magnetic flux density. It is the magnetic field strength. It is the electric flux density. It is the electric field strength. Indicates current density, Indicates the magnetic permeability of the medium; By eliminating the magnetic field strength and magnetic flux density using constitutive relations, we can obtain the second-order vector wave equation describing the dispersive model. (10) in
[0033] Apply first-order absorbing boundary conditions to the boundaries of the electromagnetic model. (11) Spatial discretization is performed using the finite element method to obtain the matrix equations of the semi-discrete electromagnetic field system. (12) in
[0034] S4: The circuit section adopts an improved node analysis method based on Kirchhoff's laws to establish the differential algebraic equations of the circuit. The circuit simulation was performed using SPICE. Based on the circuit topology, an improved node analysis method was used to establish the control circuit equations (except for the reference node) by applying Kirchhoff's current law and Kirchhoff's voltage law to independent loops at all nodes. (13) in The admittance matrix describes a time-independent linear and time-invariant circuit element model. The vector representing the unknowns in the circuit includes node voltages and branch currents flowing through internal supply voltage sources (if any). Therefore, the overall size of the system in (13) is... This equals the number of non-reference nodes in the circuit network plus the number of independent voltage sources; the excitation vector. This indicates the power supply value.
[0035] S5: Time discretization In the electromagnetic field part, the Newmark-beta direct integration scheme is first applied to the second-order time-domain auxiliary differential equation of the dispersive model to obtain the polarization intensity at the (n+1)th step. The updated formula is as follows: (14) in
[0036] Then, central difference is applied to the discrete system matrix equations of the electromagnetic field. (15) The time update formula of equation (16) is described as follows: (16) The result obtained in (14) Substituting into equation (16), we can obtain the electric field value at step (n+1). Iterative update (17) In summary, a recursive relationship can be obtained, and the electric field strength in the electromagnetic field calculation domain can be updated by formula (17). Then, according to formula (14) Update polarization intensity .
[0037] S6: Field-Circuit Joint. The field and circuit are connected through ports. Field -> Circuit: Calculates the integral of the electromagnetic port as the equivalent driving source for the circuit simulator; Circuit -> Field: Calculates the current I in the circuit. CKT This is transformed into the applied current source term J in the full-wave simulation of the electromagnetic model. CKT ; like Figure 4 As shown, the coupling of the electric field to the circuit is achieved by introducing equivalent driving sources into the circuit model at the lumped ports. By introducing these equivalent driving sources, (13) can be rewritten as (18) Where vector Including the current of the equivalent driving source, its dimension is equal to the number of lumped ports.
[0038] Similarly, as Figure 5 As shown, the coupling from the circuit to the electric field is modeled by introducing an external current source into the electromagnetic model at the lumped port of the circuit network. These external current sources exist in (17) and are represented as follows: .
[0039] In summary, and in combination with Figure 5 The field-circuit joint simulation has the following update and iteration relationship: S61: Voltage at the lumped port, expressed as an integral equation along path C. (19) Using the electric field port voltage to update the driving voltage of the circuit
[0040] S62: Using the voltage-current relationship in the circuit equations, the current can be obtained. Then, based on the current value at the lumped port, update the applied current source, as shown below. Where l represents the port integration line length. S63, repeat the first two steps until the simulation ends.
[0041] The algorithm proposed in this invention was compared with the PSI solver of Ansys SIWave and the co-simulation of Ansys Circuit, and the port output voltages of the two methods showed good agreement. Figures 5-10 The circuit diagrams and port voltage comparison results are provided for three specific examples.
[0042] like Figure 6-7 As shown, Case 1 uses a Gauss pulse voltage source for excitation. Metals are not modeled, there is no loss, and the circuit model and port voltages are as follows: Figure 6-7 As shown in the image.
[0043] Case 2 uses sinusoidal excitation pulses for excitation. Metal modeling, using the Drude dispersion model, circuit model and port voltages, such as Figure 8-9 As shown in the image.
[0044] Case 3: Excitation using modulated Gauss pulses Metal modeling, using the Debye dispersion model, circuit model and port voltages, as shown Figure 9-10 As shown in the image.
[0045] The description in this specification is merely illustrative of the invention. Those skilled in the art can make various modifications or additions to the specific embodiments described or use similar methods to replace them, as long as they do not deviate from the content of this specification or exceed the scope defined in the claims, they should all fall within the protection scope of this invention.
Claims
1. A field-circuit joint transient simulation method based on the ADE dispersion model, characterized in that, The method includes the following steps: Obtain the electromagnetic model of the simulation target after mesh partitioning; Obtain the circuit model in the simulation, and the netlist file corresponding to the circuit model; The electromagnetic model includes a dispersive medium, and the polarizability of the dispersive medium model can be expressed in a uniform form in different dispersive materials; The dispersive medium model has an ADE constitutive relation in the time domain; The circuit model is processed to obtain the differential algebraic equations of the circuit; Based on the electromagnetic model and the circuit model, a joint field-circuit transient simulation is performed.
2. The field-path joint transient simulation method based on the ADE dispersion model as described in claim 1, characterized in that, The construction of the electric field wave equation of the dispersive model includes the following steps: The frequency domain polarizability of different dispersive material models is rewritten into a unified form. By introducing the electric polarization intensity, the frequency domain constitutive relation of the dispersive medium is rewritten into the ADE formula of the time domain constitutive relation. Based on the first-order time-domain Maxwell equations and the time-domain constitutive relation in the form of ADE, the second-order electric field wave equation describing the dispersive medium is obtained, and the finite-element time-domain (FETD) method is adopted.
3. The field-circuit joint transient simulation method based on the ADE dispersion model as described in claim 2, characterized in that, The specific steps for performing the field-circuit joint transient simulation are as follows: Field-circuit integration is performed, with the electric field and circuit connected through ports. Current is obtained from the circuit model, and the electromagnetic model is solved using FETD simulation. Then, the voltage obtained from the electric field is used to simulate the circuit model. Determine whether all time steps have been iterated. If the time step is less than the set time step, update the variables and perform the field-circuit joint transient simulation as described above. Otherwise, end the simulation.
4. The field-circuit joint transient simulation method based on the ADE dispersion model as described in claim 3, characterized in that, The aforementioned steps, using time steps and the wave equation, calculate and update the electric field strength, and simultaneously use the ADE equation to calculate and update the polarization intensity. Specifically: The updated formula for the polarization intensity is obtained by using Newmark-beta integration on the time-domain constitutive relation of ADE form; The second-order electric field wave equation is spatially discretized using the time-domain finite element method to obtain the discrete system equation, and then time-discretized using the central difference method to obtain the time-updating equation. The updated electric field strength is obtained by substituting the updated formula of the polarization intensity into the time update equation.
5. The field-circuit joint transient simulation method based on the ADE dispersion model as described in claim 2, characterized in that, The circuit model employs an improved nodal analysis method based on Kirchhoff's laws to establish differential algebraic equations, and uses Newmark-beta integration to obtain updated equations for the circuit voltage.
6. A field-circuit joint transient simulation method based on the ADE dispersion model, characterized in that, The method includes the following steps: Step 1: Obtain the electromagnetic model, specifically: based on the full-wave solution requirements, perform structured modeling based on the target geometry, mark the model properties of the dispersive medium, and perform mesh generation; obtain the circuit model by inputting the SPICE netlist file describing the circuit structure; Step 2: Rewrite the frequency domain polarizability of different dispersive medium models into a unified form, introduce the electric polarization intensity, and use the frequency domain to time domain conversion relationship to rewrite the frequency domain constitutive relation of the dispersive medium into the ADE formula of the time domain constitutive relation; Step 3: Based on the first-order time-domain Maxwell equations and the time-domain constitutive relation in the form of ADE, obtain the second-order electric field wave equation describing the dispersive medium, and solve it using the time-domain finite element method to obtain the spatial discrete system equation. Step 4: Based on the improved node analysis method of Kirchhoff's laws, establish the differential algebraic equations of the circuit model; Step 5: Perform time stepping, update the electric field intensity in the electromagnetic field calculation domain using the central difference scheme, and update the polarization intensity and voltage of the circuit part in the electromagnetic field calculation domain using the Newmark-beta direct integration scheme. Step 6: Perform field-circuit coupling, connect the field and the circuit through the port, couple from the field to the circuit, calculate the voltage on the circuit port, and use it as the equivalent driving source for the circuit simulator; The circuit is coupled to the field, the current is calculated in the circuit, and it is used as the equivalent external current source in the full-wave simulation of the electromagnetic model. Step 7: Determine if all iteration time steps have been completed. If it is less than the set time step, return to step 3 to continue iterating; otherwise, end the iteration.
7. The field-circuit joint transient simulation method based on the ADE dispersion model as described in claim 6, characterized in that, The unified form mentioned in step 2 is to express the polarizability of different dispersion models as a rational fraction to obtain a general description model. The second-order electric field wave equation avoids time-domain convolution calculation by introducing electric polarization intensity.
8. The field-path joint transient simulation method based on the ADE dispersion model as described in claim 7, characterized in that, Step 5 uses the Newmark-beta direct integration scheme to update the polarization intensity, specifically including: converting the time-domain constitutive relation containing the polarization intensity into a recursive form for updating.
9. The field-path joint transient simulation method based on the ADE dispersion model as described in claim 8, characterized in that, Step 5, which updates the electric field strength using a central difference scheme, specifically includes: The first and second derivatives of the electric field are constructed using the central difference of the electric field. These derivatives are then substituted into the spatial discrete equations. Based on the electric field values at the previous and current times, the electric field value at the next time step is estimated.
10. The field-circuit joint transient simulation method based on the ADE dispersion model as described in claim 9, characterized in that, The dispersion model mentioned in step 2 includes the Drude model, the Debye model, and the Lorentz model.