A broadband electromagnetic simulation method using efficient adaptive interpolation

Abstract

The present invention discloses a broadband electromagnetic simulation method using efficient adaptive interpolation, adopting an improved frequency sweeping method based on Lagrange matrix rational interpolation, and a new convergence criterion, taking into account the slope between two adjacent frequency points between the previous interpolation and the current interpolation of S parameters and Y parameters. By combining matrix rational interpolation and dichotomy frequency scanning, not only can the entire frequency range be interpolated using a few sampling frequency points and frequency responses, but also the result will be more accurate due to the adoption of a new convergence criterion, especially for the problem of rapidly changing frequency response.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic field numerical calculation, and in particular is a broadband electromagnetic simulation method using efficient adaptive interpolation. Background Art

[0002] Full-wave simulation of electromagnetic problems is one of the most challenging problems in modern computing technology. The method of moments based on integral equations is widely used as an effective solution method. For many practical applications, electromagnetic problems need to be solved in a wide frequency band. However, for frequency domain solvers, many frequency points need to be calculated to describe the frequency response, especially for problems where the frequency response changes rapidly in a wide frequency band.

[0003] To overcome this problem, many scanning techniques have been developed, such as the adaptive multi-point (AMP) method and the asymptotic waveform evaluation (AWE). One of the most popular methods is the adaptive frequency scanning method, which can greatly reduce the number of frequency points in direct calculation in electromagnetic simulation by using interpolation-based frequency scanning. However, for fast-changing frequency responses, the error threshold should be set to a very small value, so the number of frequency points calculated by the original adaptive frequency scanning may still be very large, and the time consumed will be longer.

[0004] The present invention proposes a broadband electromagnetic simulation method with efficient adaptive interpolation, which adopts an improved frequency sweeping method based on Lagrange matrix rational interpolation and a new convergence criterion, and takes into account the slope between two adjacent frequency points between the previous interpolation and the current interpolation of the S parameter and the Y parameter. By combining matrix rational interpolation and dichotomy frequency scanning, not only can the entire frequency range be interpolated using very few sampling frequency points and frequency responses, but also the results will be more accurate due to the use of a new convergence criterion, especially for rapidly changing frequency response problems. In order to verify this method, a traditional fifth-order hairpin antenna is used for verification. Summary of the invention

[0005] An object of the present invention is to provide a broadband electromagnetic simulation method with efficient adaptive interpolation in order to address the deficiencies of the existing technology.

[0006] The method of the present invention comprises the following steps:

[0007] Step (1), consider the antenna as being in the incident field (E inc ,H inc ) is an ideal conductor under the irradiation of the electromagnetic parameter (ε (e) ,μ (e) ) in the medium space; the electric field and magnetic field in the outer area of ​​the conductor are E e , H e , the electric field and magnetic field inside the conductor are both 0; ε(e) is the dielectric constant, μ (e) is the magnetic permeability;

[0008] Step (2), according to the frequency range [f0,f N ], initialize the endpoints of the selected frequency range and the middle value f min , f mid , f max As the frequency sampling point, where f min =f0,f mid =(f0+f N ) / 2,f max =f N ; Then the moment method is used to solve the electromagnetic field inside the conductor and the corresponding frequency response theoretical value S(f min ), S(f mid ), S(f max );

[0009] Step (3), obtaining frequency response interpolation values ​​corresponding to all frequency points within the frequency range;

[0010] Step (4), determine whether all frequency response interpolation values ​​in the current iteration meet the new convergence standard, if so, output all frequency response interpolation values, if not, use the binary search method to add new frequency sampling points, and return to step (2).

[0011] Another object of the present invention is to provide an electronic device, comprising a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the above-mentioned broadband electromagnetic simulation method using efficient adaptive interpolation.

[0012] Another object of the present invention is to provide a machine-readable storage medium storing machine-executable instructions, which, when called and executed by a processor, prompt the processor to implement the above-mentioned broadband electromagnetic simulation method using efficient adaptive interpolation.

[0013] The beneficial effects of the present invention are:

[0014] Compared with the traditional method, this method can obtain the frequency response of a frequency band more quickly and accurately.

[0015] The present invention proposes to use a new error formula to perform frequency response convergence judgment, thereby being able to obtain appropriate frequency sampling points. Compared with other methods, the required sampling points are reduced and the simulation speed is accelerated.

[0016] The present invention proposes to interpolate more data using less sampled data through Lagrange complex matrix rational interpolation, and realize adaptive interpolation in combination with a binary algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a broadband electromagnetic simulation method for realizing efficient adaptive interpolation according to the present invention;

[0018] Figure 2 It is a traditional fifth-order hairpin antenna model used for testing in the present invention;

[0019] Figure 3 and Figure 4 They are the simulation comparison results of parameters S11 and S12 of the present invention and the traditional method respectively. DETAILED DESCRIPTION

[0020] The present invention is described in detail below in conjunction with the accompanying drawings.

[0021] like Figure 1 An efficient adaptive interpolation broadband electromagnetic simulation method uses a few frequencies and frequency responses as sampling data and uses matrix rational interpolation to interpolate frequency responses corresponding to more frequencies.

[0022] The method of the present invention comprises the following steps:

[0023] Step (1), consider the antenna as being in the incident field (E inc ,H inc ) is an ideal conductor under the irradiation of the electromagnetic parameter (ε (e) ,μ (e) ) in the medium space; the electric field and magnetic field in the outer area of ​​the conductor are E e , H e , the electric field and magnetic field inside the conductor are both 0; ε (e) is the dielectric constant, μ (e) is the magnetic permeability;

[0024] Step (2), initialize the antenna frequency range [f0,f N ], the number of iterations k = 1;

[0025] Step (3), select the minimum value f in the frequency range min Maximum value f max and the intermediate value f mid As the frequency sampling point, the moment method is used to solve the electromagnetic field inside the conductor, and the actual frequency response value S(f min ), S(f mid ), S(f max );

[0026] The method of moments used to solve the electromagnetic field inside the conductor is specifically as follows:

[0027] 3-1 Use the moment method to solve the electric field inside the conductor:

[0028] The integral equation of the electric field inside a conductor is:

[0029]

[0030] In the formula represents the normal unit vector outside the conductor, η represents the wave impedance of the medium space, L represents the linear operator, J represents the current density, E inc represents the incident electric field;

[0031] The RWG basis function is defined on two adjacent triangles with common edges, which can simulate the surface electric and magnetic current distribution of objects of arbitrary shapes;

[0032] The definition of the RWG basis function is:

[0033]

[0034] Where l n represents the length of the common side of the nth pair of adjacent triangles, and The adjacent triangles and The area of It is a triangle The vertex of is the vector pointing to point r, It is a triangle The vertex of the vector points to point r; f n (r) represents the nth RWG basis function in the field region;

[0035] The unknown current on the conductor surface can be expanded using the RWG basis function into the following form:

[0036]

[0037] Where I n represents the unknown current expansion coefficient (unknown quantity), and N represents the number of unknown quantities;

[0038] Substituting formula (3) into formula (1) yields:

[0039]

[0040] Where L(f n (r)) represents the RWG basis function f n (r) linear equation;

[0041] Using the RWG basis function as the test function, the electric field integral equation can be tested to obtain:

[0042] where f m (r) represents the mth RWG basis function in the field region;

[0043] Because f m (r) is always tangential to the conductor surface, so it can be rewritten as follows:

[0044]

[0045] Further, formula (6) can be written in matrix form:

[0046] ZI=V Formula (6)

[0047] Where Z represents the N×N moment method "impedance" matrix, I and V are both N×1 column vectors, which represent the "current" vector and "voltage" vector of the moment method respectively;

[0048] The elements of the mth row and nth column of the matrix Z are expressed as follows:

[0049]

[0050]

[0051] In the formula ω=2πf, f represents frequency; r represents field point, r′ represents source point, G(R) represents Green’s function, (uniform unbounded space), R = |rr′|, which represents the distance from the field point to the source point, represents the gradient operator, represents the divergence operator, ds represents the surface vector element of the field region, and ds′ represents the surface vector element of the source region; f n (r′) represents the nth RWG basis function in the source region, j represents an imaginary number, V m represents the "voltage" vector of the mth row;

[0052] Substitute formula (7)-(8) into matrix equation (6) and solve the matrix equation to obtain the current I. The current I at a fixed voltage is expressed as the Y admittance parameter. The Y admittance parameter is converted into the S parameter, i.e., the theoretical value of the frequency response.

[0053] 3-2 Use the moment method to solve the magnetic field inside the conductor:

[0054] The integral equation of the magnetic field inside the conductor is as follows:

[0055]

[0056] Where K(J) represents the linear operator of the current in the magnetic field, H inc represents the incident magnetic field;

[0057] Taking the smooth surface model as an example, the RWG basis function is used as the expansion function, and the Galerkin method is used to test, and the following formula is obtained:

[0058]

[0059] Written in matrix form: ZI = V;

[0060] Among them, the matrix elements of Z and V are expressed as:

[0061]

[0062]

[0063] in, is the nth basis function f n The triangle pair where (r′) is located (source triangle pair), is the mth basis function f m (r) The triangle pair where it is located (source triangle pair);

[0064] Substitute formula (12)-(11) into the matrix equation ZI=V, and solve the matrix equation to obtain the current I; the current I under a fixed voltage is expressed as the Y admittance parameter; the Y admittance parameter is converted into the S parameter, that is, the actual value of the frequency response;

[0065] Step (4), based on the frequency sampling point f min 、f max 、f mid The corresponding actual value of the frequency response S(f min )、S(f mid )、S(f max ), using the Lagrange matrix interpolation method, obtain all frequencies f within the frequency range i The corresponding frequency response estimate The details are as follows:

[0066] By using matrix rational interpolation, we can traverse all frequencies in the frequency range in turn and obtain the frequency f i The corresponding frequency response estimate is:

[0067] Through the matrix rational function of formula (14), the frequency f is interpolated i The corresponding frequency response estimate

[0068] R(f i )=P(f i ) / q(f i ) Formula (13)

[0069]

[0070] Where R(f i ) represents the interpolation result, P(f i ) represents the matrix polynomial, q(f i ) represents a complex polynomial;

[0071] Let the Lagrange basis function l i (f i )for:

[0072]

[0073] f t =[f min ,f max ]

[0074] in:

[0075]

[0076] Among them l i ′(f i ) means l i (f i )

[0077]

[0078] in:

[0079] Indicates the actual value of the frequency response S(f t ),S(f m ) in the .

[0080] Step (5), determine all frequencies f in the current iteration i The corresponding frequency response estimate Whether it meets the convergence requirements, if so, the final frequency f is obtained i The corresponding frequency response estimate If it does not meet the requirement, the current frequency range is divided into two frequency ranges by using the binary method, and the number of iterations k=k+1 is updated, and the process returns to step (3) to obtain the actual value and estimated value of the frequency response for the frequency in the new divided frequency range;

[0081] The convergence criteria are as follows:

[0082] 1) Error formula for the frequency response estimate under adjacent iterations:

[0083]

[0084] in Indicates the frequency point f in the current iterationi+1 The corresponding frequency response estimate, f i+1 、f i Indicates two adjacent frequency points;

[0085] 2) Convert the above S parameters (i.e., frequency response estimates) into Y parameters by parameter type conversion, where the Y parameters are Further error formula of Y parameter under adjacent iterations:

[0086]

[0087] If err1∈[e1,e2]; err2∈[e3,e4], the embodiment of the present invention adopts e1=e2=0.8, e3=e4=1.0; if the adjustment is satisfied, convergence is achieved, otherwise convergence is not achieved.

[0088] The conversion process of S parameters into Y parameters is as follows:

[0089] In a two-port network, the relationship between the various parameters is expressed as:

[0090] The S parameter (scattering) relationship is as follows:

[0091]

[0092] The Y parameter (admittance) relationship is as follows:

[0093]

[0094] The Z parameter (impedance) relationship is as follows:

[0095]

[0096] The conversion relationship between Z parameters and S parameters is as follows:

[0097]

[0098] The conversion relationship between Y parameters and S parameters is as follows:

[0099]

[0100] The conversion relationship between Z parameters and Y parameters is as follows:

[0101]

[0102] The following example Figure 2The frequency response of the traditional fifth-order hairpin antenna is simulated and analyzed. In fact, the frequency band of 4-12GHz needs to be analyzed. The traditional analysis method is to calculate the average 0.1GHz interval. The method proposed in the present invention can fit the frequency response estimation value of the entire frequency band with fewer frequency sampling points.

[0103] First, the first iteration process selects three sampling points: f min =4GHz,f mid =8GHz,f max =12GHz, the actual value of the frequency response S(f min ), S(f mid ), S(f max ).

[0104] Then, through the Lagrange matrix rational interpolation in step (3), each frequency point f in the entire frequency band range of 4GHz-12GHz is interpolated. i The corresponding frequency response estimate

[0105] Use the convergence error formulas err1 and err2 to determine the interpolation results above Whether it meets the requirements, if it meets the convergence error requirements, then the value of each frequency point f in the entire frequency band range of 4GHz-12GHz is directly returned. i The corresponding interpolation value

[0106] If the convergence requirements are not met, the binary algorithm is used to increase the sampling points. At this time, it is divided into two segments, namely 4GHz-8GHz and 8GHz-12GHz. At this time, the three sampling frequency points of 4GHz, 6GHz and 8GHz are used to interpolate the frequency band 4GHz-8GHz; the three sampling frequency points of 8GHz, 10GHz and 12GHz are used to interpolate the frequency band 8GHz-12GHz.

[0107] After 4 iterations, the error convergence requirement is met and the result is returned.

[0108] Figure 3 and Figure 4 They are the simulation comparison results of parameters S11 and S12 of the present invention and the traditional method respectively.

[0109] The above embodiments are not limitations of the present invention, and the present invention is not limited to the above embodiments. As long as the requirements of the present invention are met, they belong to the protection scope of the present invention.

Claims

1. A broadband electromagnetic simulation method using efficient adaptive interpolation, characterized in that The following steps are involved: Step (1), consider the antenna as being in the incident field (E inc ,H inc ) is an ideal conductor under the irradiation of the electromagnetic parameter (ε (e) ,μ (e) ) in the medium space; the electric field and magnetic field in the outer area of ​​the conductor are E e , H e , the electric field and magnetic field inside the conductor are both 0; ε (e) is the dielectric constant, μ (e) is the magnetic permeability; E inc represents the incident electric field, H inc represents the incident magnetic field; Step (2), initialize the antenna frequency range [f0,f N ], the number of iterations k = 1; Step (3), select the minimum value f in the frequency range min , maximum value f max and the intermediate value f mid As the frequency sampling point, the moment method is used to solve the electromagnetic field inside the conductor, and the actual frequency response value S(f min ), S(f mid ), S(f max ); Step (4), based on the frequency sampling point f min 、f max 、f mid The corresponding actual value of the frequency response S(f min )、S(f mid )、S(f max ), using the Lagrange matrix interpolation method, obtain all frequencies f within the frequency range i The corresponding frequency response estimate Step (5), determine all frequencies f in the current iteration i The corresponding frequency response estimate Whether it meets the convergence requirements, if so, the final frequency f is obtained i The corresponding frequency response estimate If it does not meet the requirement, the current frequency range is divided into two frequency ranges using the binary search method, and the number of iterations k=k+1 is updated, and the process returns to step (3) to obtain the actual value and estimated value of the frequency response for the frequency within the new divided frequency range.

2. A broadband electromagnetic simulation method using efficient adaptive interpolation as claimed in claim 1, characterized in that In step (3), the method of moments is used to solve the electric field inside the conductor: The integral equation of the electric field inside a conductor is: In the formula represents the normal unit vector outside the conductor, η represents the wave impedance of the medium space, L represents the linear operator, J represents the current density, E inc represents the incident electric field; The RWG basis function is defined on two adjacent triangles with common edges, which can simulate the surface electric and magnetic current distribution of objects of arbitrary shapes; The definition of the RWG basis function is: Where l n represents the length of the common side of the nth pair of adjacent triangles, and The adjacent triangles and The area of It is a triangle The vertex of is the vector pointing to point r, It is a triangle The vertex of the vector points to point r; f n (r) represents the nth RWG basis function in the field region; The unknown current on the conductor surface can be expanded into the following form using the RWG basis function: Where I n represents the unknown current expansion coefficient; Substituting formula (3) into formula (1) yields: Where L(f n (r)) represents the RWG basis function f n (r) linear equation; The RWG basis function is used as the test function, and because f m (r) is always tangential to the conductor surface, so the electric field integral equation is as follows: where f m (r) represents the mth RWG basis function in the field region; Further, formula (5) is rewritten into matrix form: ZI=V Formula (6) Where Z represents the N×N moment method "impedance" matrix, I and V are both N×1 column vectors, which represent the "current" vector and "voltage" vector of the moment method respectively; The elements of the mth row and nth column of the matrix Z are expressed as follows: In the formula ω=2πf, f represents frequency; r represents field point, r′ represents source point, G(R) represents Green’s function, R = |rr′|, which represents the distance from the field point to the source point, ▽ represents the gradient operator, ▽′ represents the divergence operator, ds represents the surface vector element of the field region, and ds′ represents the surface vector element of the source region; f n (r′) represents the nth RWG basis function in the source region, j represents an imaginary number, V m represents the "voltage" vector of the mth row; and is the mth basis function f m (r) The adjacent triangle; Substitute formulas (7)-(8) into matrix equation (6) and solve the matrix equation to obtain the current I. The current I at a fixed voltage is expressed as the Y admittance parameter. The Y admittance parameter is converted into the S parameter, that is, the theoretical value of the frequency response.

3. A broadband electromagnetic simulation method using efficient adaptive interpolation as claimed in claim 2, characterized in that In step (3), the moment method is used to solve the magnetic field inside the conductor: The integral equation of the magnetic field inside the conductor is as follows: Where K(J) represents the linear operator of the current in the magnetic field, H inc represents the incident magnetic field; Using RWG basis function as the expansion function and Galerkin method to test, we get: Formula (10) is written in matrix form as ZI=V; Among them, the matrix elements of Z and V are expressed as: in, is the nth basis function f n (r′) is located in the triangle pair, is the mth basis function f m (r) The triangle pair where it is located; Substitute formula (12)-(11) into the matrix equation ZI=V, and solve the matrix equation to obtain the current I; the current I at a fixed voltage is expressed as the Y admittance parameter; the Y admittance parameter is converted into the S parameter, that is, the actual value of the frequency response.

4. A broadband electromagnetic simulation method using efficient adaptive interpolation as claimed in claim 3, characterized in that Step (4) is as follows: By using matrix rational interpolation, we can traverse all frequencies in the frequency range in turn and obtain the frequency f i The corresponding frequency response estimate is: Through the matrix rational function of formula (14), the frequency f is interpolated i The corresponding frequency response estimate R(f i )=P(f i ) / q(f i ) Formula (13) Where R(f i ) represents the interpolation result, P(f i ) represents the matrix polynomial, q(f i ) represents a complex polynomial; Let the Lagrange basis function l i (f i )for: Where: f t =[f min ,f max ]; where l′ i (f i ) indicates l i (f i ) in: Indicates the actual value of the frequency response S(f t ),S(f m ) in the .

5. An electronic device comprising a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement a broadband electromagnetic simulation method using efficient adaptive interpolation as described in any one of claims 1 to 4.

6. A machine-readable storage medium storing machine-executable instructions, wherein when the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement a broadband electromagnetic simulation method using efficient adaptive interpolation as described in any one of claims 1 to 4.

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