A time-domain finite difference simulation method for microwave ferrite intermodulation and harmonic effects

Abstract

The application discloses a time-domain finite difference simulation method for microwave ferrite intermodulation and harmonic effect, which comprises the following steps: obtaining a nonlinear mathematical expression f() of the relationship between the magnetization intensity and the magnetic field intensity of a ferrite material; obtaining differential equations satisfied by the magnetization intensity and the magnetic field intensity of the ferrite material based on Maxwell equations and a magnetic dipole moment motion equation in the ferrite; solving the differential equations satisfied by each field component by using an iterative method, converting into two groups of equations satisfied by the iterative initial values and the difference between the approximate solution and the respective iterative initial value; solving the equation groups by using a time-domain finite difference method to obtain time-domain numerical solutions of each field component, and obtaining the intermodulation and harmonic levels of the ferrite microwave device through post-processing. The application can simulate the intermodulation and harmonic effect of the ferrite microwave component caused by the nonlinear relationship between the magnetization intensity and the applied magnetic field intensity and the nonlinear product of the magnetization intensity and the magnetic field intensity.

Description

Technical Field

[0001] This invention belongs to the field of passive intermodulation and harmonic effects of microwave components, specifically relating to a time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects. Background Technology

[0002] Microwave ferrite materials are widely used in the fabrication of microwave devices such as circulators, isolators, switches, phase shifters, and modulators due to their gyromagnetic effect. The magnetization and magnetic field strength of microwave ferrites typically exhibit significant nonlinear characteristics, resulting in substantial nonlinear effects in microwave ferrite devices, namely, the generation of intermodulation and harmonic interference.

[0003] Nonlinear problems caused by magnetic materials, such as nickel plating, have attracted attention in applications like coaxial connectors and waveguide flange connections. Intermodulation and harmonic effects can typically be suppressed by reducing the magnetism of the plating material or avoiding exposure of the magnetic material to electromagnetic fields. However, unlike the hysteresis nonlinearity of plating materials, ferrite devices utilize their gyromagnetic properties to modulate the propagation of electromagnetic fields within them to achieve specific functions. Therefore, ferrite devices inevitably exhibit nonlinear effects such as intermodulation and harmonics during operation.

[0004] Because ferrite materials possess anisotropic permeability and are modulated by an applied magnetic field, the modeling and simulation methods for their intermodulation and harmonic effects differ significantly from those used in traditional nickel-plated hysteresis nonlinearity simulations. The finite-difference time-domain (FDTD) method is a well-known classic method for electromagnetic calculations in the microwave field. However, currently, there is no FDTD full-wave electromagnetic simulation method specifically for the intermodulation and harmonic effects of microwave ferrite materials. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects.

[0006] This invention is achieved using the following technical solution:

[0007] A finite-difference time-domain simulation method for microwave ferrite intermodulation and harmonic effects includes the following steps:

[0008] 1) Obtain the nonlinear mathematical expression f() of the relationship between magnetization and magnetic field strength of ferrite materials: Measure the magnetization M of the ferrite material. c With the applied magnetic field strength H c The changing relationship curve M c (H c The mathematical expression f(H) of the nonlinear functional relationship is obtained through numerical fitting. c );

[0009]

[0010] Where M s The saturation magnetization is Represents the applied magnetic field strength H c The direction is defined as the z-direction;

[0011] 2) Based on Maxwell's equations and the equations of motion of magnetic dipole moments in ferrites, obtain the differential equations satisfied by each component of magnetization and magnetic field strength in ferrite materials:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] Where M x M y and M z H represents the magnetization components in the x, y, and z directions, respectively. x H y and H z E represents the magnetic field strength components in the x, y, and z directions, respectively. x E y and E z denoted as electric field intensity components in the x, y, and z directions, respectively; t is time; μ0 is free permeability; γ is gyromagnetic ratio; ε is permittivity; and σ is conductivity.

[0022] 3) Use the iterative method to solve the set of differential equations satisfied by each field component in step 2), and convert it into two sets of equations satisfied by the initial iterative value and the difference between the approximate solution and the initial iterative value.

[0023] The initial values ​​for iteration are obtained through the following system of equations:

[0024]

[0025]

[0026] M z0 =0(13)

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Where M x0 M y0 and M z0 H represents the initial values ​​for the iteration of the magnetization components in the x, y, and z directions, respectively. x0 H y0 and H z0 E represents the initial values ​​for the iteration of the magnetic field intensity components in the x, y, and z directions, respectively. x0 E y0 and E z0 These are the initial values ​​for the iteration of the electric field intensity components in the x, y, and z directions, respectively.

[0034] The difference between the m-th order approximate solution of each field component and its respective initial value in the iteration, where m = 1, 2, 3…, satisfies the following system of equations:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] Where M xp,m M yp,m and M zp,mH represents the difference between the m-th approximate solution and the initial value of the magnetization components in the x, y, and z directions, respectively. xp,m H yp,m and H zp,m E represents the difference between the m-th approximate solution and the initial value of the magnetic field intensity components in the x, y, and z directions, respectively. xp,m E yp,m and E zp,m M represents the difference between the m-th order approximate solution and the initial value of the iteration for the electric field intensity components in the x, y, and z directions, respectively; x,m-1 M y,m-1 and M z,m-1 Let H be the (m-1)th order approximate solution for the magnetization components in the x, y, and z directions, respectively. When m = 1, this is the initial value for iteration. x,m-1 H y,m-1 and H z,m-1 These are the (m-1)th order approximate solutions for the magnetic field strength components in the x, y, and z directions, respectively. When m = 1, this is the initial value for iteration, E. x,m-1 E y,m-1 and E z,m-1 These are the (m-1)th order approximate solutions for the electric field intensity components in the x, y, and z directions, respectively. When m = 1, these are the initial values ​​for the iteration.

[0045] 4) Solve the equations in step 3) using the finite-difference time-domain method to obtain the time-domain numerical solutions of each field component, and obtain the intermodulation and harmonic levels of the ferrite microwave device through post-processing.

[0046] A further improvement of the present invention is that, in step 1), the mathematical relationship f() is used to describe the nonlinear relationship between the magnetization intensity of the ferrite material and the applied magnetic field intensity.

[0047] A further improvement of this invention is that step 2) considers the nonlinear characteristics of f(), and also considers factors including M. y ·H z M z ·H y M x ·H z M z ·H x M x ·H y and M y ·H x The nonlinearity resulting from the product of the magnetization and magnetic field strength is represented.

[0048] A further improvement of the present invention is that, in step 4), the time-domain excitation signal waveform of the finite-difference time-domain method can be set as a single tone, two tone, multiple tone, or modulation signal according to the requirements of intermodulation and harmonic effect analysis.

[0049] A further improvement of the present invention is that, in step 4), the finite-difference time-domain method uses Yee cells, the spatial positions of the values ​​of each component of magnetization intensity coincide with the spatial positions of the values ​​of each component of magnetic field intensity, and the values ​​are all at time n+1 / 2, while the electric field intensity is at time n.

[0050] A further improvement of the present invention is that the difference equations for each component of magnetization and magnetic field strength in step 4) of the finite-difference time-domain method are in the following form;

[0051] The recurrence relation for the initial values ​​of the iteration is:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] Where i, j, and k represent discrete coordinates of spatial location;

[0059]

[0060]

[0061]

[0062]

[0063] in:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Where Δt represents the time step, and Δx, Δy, and Δz represent the lengths of the discrete grids in the x, y, and z directions, respectively;

[0070] The recursive equation for the difference between the m-th order approximate solution and the initial value during iteration is as follows:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] in:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] A further improvement of this invention is that the intermodulation and harmonic levels are obtained by the difference between the m-th order approximate solution obtained in step 4) and the initial value of the iteration, that is, by adjusting H... xp,m H yp,m H zp,m E xp,m E yp,m and E zp,m The data is post-processed, and intermodulation and harmonic levels are extracted using FFT transformation.

[0093] A further improvement of this invention is that the intermodulation and harmonic levels are obtained by the difference between the m-th order approximate solution obtained in step 4) and the initial value of the iteration, that is, by adjusting H... xp,m H yp,m H zp,m E xp,m E yp,m and E zp,m The data is post-processed, and intermodulation and harmonic levels are extracted using the Prony algorithm.

[0094] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0095] This invention provides a finite-difference time-domain simulation method for microwave ferrite intermodulation and harmonic effects. It establishes a full-wave numerical simulation method for the intermodulation and harmonic levels of ferrite microwave devices based on the nonlinear relationship between magnetization and applied magnetic field strength. This method can be used to quantitatively evaluate the nonlinear characteristics of microwave devices such as circulators, isolators, switches, phase shifters, and modulators based on ferrite materials. This invention has the following advantages:

[0096] 1. The present invention provides a finite-difference time-domain simulation method for microwave ferrite intermodulation and harmonic effects, which not only considers the nonlinear characteristics f() of the relationship between magnetization and applied magnetic field strength, but also considers factors including M. y ·H z M z ·H y M x ·H z M z ·H x M x ·H y and M y ·H x The nonlinearity resulting from the product of the magnetization and magnetic field strength is represented.

[0097] 2. The present invention provides a time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects. By setting the time-domain excitation waveform, it can be used to quantitatively evaluate the intermodulation and harmonic characteristics of ferrite microwave devices under various excitation signal conditions such as single tone, two tone, multiple tone and modulation signal.

[0098] 3. This invention provides a time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects. It employs an iterative method to handle nonlinear equations and uses the solution obtained under the condition of neglecting nonlinear terms as the initial value for iteration. The intermodulation and harmonics are ultimately expressed as the field component H corresponding to the difference between the approximate solution stored in the simulation and the initial value for iteration. xp,m H yp,m H zp,m E xp,m E yp,m and Ezp,m This method avoids the problem of large solution errors caused by rounding when nonlinear components are much smaller than linear components, thus improving the simulation accuracy of intermodulation and harmonic levels. Attached Figure Description

[0099] Figure 1 This is a simulation flowchart of the present invention;

[0100] Figure 2 This is a simulation diagram of the parallel flat plate structure according to an embodiment of the present invention;

[0101] Figure 3 This is a waveform diagram of the dual-tone signal excitation source according to an embodiment of the present invention;

[0102] Figure 4 This is a waveform diagram of the linear portion of the voltage obtained at the resistor terminal in an embodiment of the present invention;

[0103] Figure 5 This is a waveform diagram of the nonlinear portion of the voltage obtained at the resistor terminal in an embodiment of the present invention;

[0104] Figure 6 This is an FFT transformation diagram of the linear portion voltage waveform obtained at the resistor terminal in an embodiment of the present invention;

[0105] Figure 7 This is an FFT transformation diagram of the nonlinear voltage waveform obtained at the resistor terminal in an embodiment of the present invention. Detailed Implementation

[0106] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0107] This invention provides a time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects, the simulation flowchart of which is shown below. Figure 1 As shown.

[0108] The following is based on Figure 2 Taking the solution of the third-order intermodulation of the parallel plate simulation structure shown as an example, this paper illustrates the beneficial effects of the time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects provided by this invention.

[0109] Figure 2In the parallel plate simulation structure shown, the parallel plate is located inside the ferrite material. Since the third-order intermodulation of microwave devices is typically related to the third-order nonlinear term, the nonlinear characteristics of the ferrite in this embodiment are expressed using mathematical relationships. Expression. A parallel plate is connected to a voltage source at one end and a resistive load at the other. The voltage source excitation waveform is as follows: Figure 3 The dual-tone carrier signals shown have frequencies of 1 GHz and 1.1 GHz, respectively. The initial values ​​of each calculated field component correspond to the linear portion of the solution results for each field component. Based on this, the linear portion voltage waveform at the load resistor can be obtained as shown in the figure. Figure 4 As shown. The obtained nonlinear voltage waveform is shown in the figure. Figure 5 As shown. For Figure 4 and Figure 5 The time-domain simulation results shown are subjected to FFT transformation, and the results are as follows: Figure 6 and Figure 7 As shown, the third-order intermodulation level amplitude can be extracted. It can be seen that although the calculated voltage value of the nonlinear part is 12 orders of magnitude smaller than that of the linear part, it can still be accurately separated, indicating that the simulation method provided by this invention has high simulation accuracy for intermodulation and harmonic levels.

[0110] In summary, this invention provides a finite-difference time-domain simulation method for microwave ferrite intermodulation and harmonic effects. This method can simulate the intermodulation and harmonic effects of ferrite microwave components caused by the nonlinear relationship between magnetization and applied magnetic field strength, as well as the nonlinearity of the product of magnetization and magnetic field strength. Depending on the applied excitation signal, it can be used to evaluate the intermodulation and harmonic characteristics under various excitation signal conditions, including single-tone, two-tone, multi-tone, and modulated signals. Furthermore, this invention utilizes an iterative method in the numerical solution, avoiding the problem of large solution errors caused by rounding when nonlinear components are much smaller than linear components, thus improving the simulation accuracy of intermodulation and harmonic levels. This invention provides a reliable method for simulating the intermodulation and harmonic effects of microwave devices such as ferrite-based circulators, isolators, switches, phase shifters, and modulators.

[0111] The above description is a further detailed explanation of the present invention in conjunction with specific embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the patent protection scope defined by the claims submitted by the present invention.

Claims

1. A time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects, characterized in that, Includes the following steps: 1) Obtaining a nonlinear mathematical expression for the relationship between magnetization and magnetic field strength of ferrite materials: Measuring the magnetization of ferrite materials M c With the strength of the applied magnetic field H c The changing relationship curve M c ( H c The mathematical expression of the nonlinear functional relationship is obtained through numerical fitting. f ( H c ); （1） in M s The saturation magnetization is Represents the strength of the applied magnetic field H c The direction is defined as the z-direction; 2) Based on Maxwell's equations and the equations of motion of magnetic dipole moments in ferrites, obtain the differential equations satisfied by each component of magnetization and magnetic field strength in ferrite materials: （2） （3） （4） （5） （6） （7） （8） （9） （10） in M x , M y and M z These are the magnetization components in the x, y, and z directions, respectively. H x , H y and H z These are the magnetic field intensity components in the x, y, and z directions, respectively. E x , E y and E z These are the electric field intensity components in the x, y, and z directions, respectively. t For time, μ 0 is the permeability of free space. γ It is the gyromagnetic ratio. ε Where is the dielectric constant. σ Electrical conductivity; 3) Use the iterative method to solve the set of differential equations satisfied by each field component in step 2), and convert it into two sets of equations satisfied by the initial iterative value and the difference between the approximate solution and the initial iterative value. The initial values ​​for iteration are obtained through the following system of equations: （11） （12） （13） （14） （15） （16） （17） （18） （19） in M x0 , M y0 and M z0 Let be the initial values ​​for the iteration of the magnetization components in the x, y, and z directions, respectively. H x0 , H y0 and H z0 These are the initial values ​​for the iteration of the magnetic field intensity components in the x, y, and z directions, respectively. E x0 , E y0 and E z0 These are the initial values ​​for the iteration of the electric field intensity components in the x, y, and z directions, respectively; The difference between the m-th order approximate solution of each field component and its respective initial value in the iteration. m =1,2,3…, satisfying the following system of equations: （20） （21） （22） （23） （24） （25） （26） （27） （28） in M xp,m , M yp,m and M zp,m Let be the differences between the m-th order approximate solutions of the magnetization components in the x, y, and z directions and the initial values ​​of the iterations. H xp,m , H yp,m and H zp,m Let be the differences between the m-th order approximate solution and the initial value of the iteration for the magnetic field intensity components in the x, y, and z directions, respectively. E xp,m , E yp,m and E zp,m These are the differences between the m-th order approximate solutions and the initial values ​​of the iteration for the electric field intensity components in the x, y, and z directions, respectively. M x,m-1 , M y,m-1 and M z,m-1 Let be the (m-1)th order approximate solutions of the magnetization components in the x, y, and z directions, respectively. m When =1, it is the initial value for iteration. H x,m-1 , H y,m-1 and H z,m-1 Let be the (m-1)th order approximate solutions of the magnetic field intensity components in the x, y, and z directions, respectively. m When =1, it is the initial value for iteration. E x,m-1 , E y,m-1 and E z,m-1 Let be the (m-1)th order approximate solutions of the electric field intensity components in the x, y, and z directions, respectively. m When =1, it is the initial value for iteration; 4) Solve the equations in step 3) using the finite-difference time-domain method to obtain the time-domain numerical solutions of each field component, and obtain the intermodulation and harmonic levels of the ferrite microwave device through post-processing.

2. The time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects according to claim 1, characterized in that, In step 4), the time-domain excitation signal waveform of the finite-difference time-domain method can be set as a single tone, two tone, multiple tone, or modulated signal according to the requirements of intermodulation and harmonic effect analysis.

3. The time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects according to claim 1, characterized in that, Step 4) The finite-difference time-domain method uses Yee cells. The spatial positions of the magnetization components coincide with the spatial positions of the magnetic field components, and the values ​​are all at time n+1 / 2, while the electric field value is at time n.

4. The time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects according to claim 3, characterized in that, Step 4) The difference equations for each component of magnetization and magnetic field strength in the finite-difference time-domain method are in the following form; The recurrence relation for the initial values ​​of the iteration is: （29） （30） （31） （32） （33） （34） in i , j , k Discrete coordinates representing spatial location; （35） （36） （37） （38） in: （39） （40） （41） （42） （43） Where Δ t Represents the time step, Δ x Δ y and Δ z These represent the lengths of the discrete grid in the x, y, and z directions, respectively. The recursive equation for the difference between the m-th order approximate solution and the initial value during iteration is as follows: （44） （45） （46） （47） （48） （49） in: （50） （51） （52） （53） （54） （55） （56） （57） （58） （59） （60） （61） （62） （63）。 5. The time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects according to claim 4, characterized in that, The intermodulation and harmonic levels are obtained by the difference between the m-th order approximate solution obtained in step 4) and the initial value of the iteration, i.e., by adjusting the initial value of the solution. H xp,m , H yp,m , H zp,m , E xp,m , E yp,m and E zp,m The data is post-processed, and intermodulation and harmonic levels are extracted using FFT transformation.

6. The time-domain finite-difference simulation method for microwave ferrite intermodulation and harmonic effects according to claim 4, characterized in that, The intermodulation and harmonic levels are obtained by the difference between the m-th order approximate solution obtained in step 4) and the initial value of the iteration, i.e., by adjusting the initial value of the solution. H xp,m , H yp,m , H zp,m , E xp,m , E yp,m and E zp,m The data is post-processed, and intermodulation and harmonic levels are extracted using the Prony algorithm.

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