A broadband electromagnetic simulation method using efficient adaptive frequency sweeping

Abstract

The present invention discloses a broadband electromagnetic simulation method using efficient adaptive frequency scanning. The present invention proposes to use an error formula to judge the convergence of frequency response, thereby being able to obtain appropriate frequency sampling points, which reduces the required sampling points and speeds up the simulation compared to other methods. The present invention proposes to convert a nonlinear problem into two linear problems, iteratively calculate the precise pole and residue values, solve the linear equation, obtain an accurate frequency response fitting value, speed up the calculation rate, and improve the accuracy.

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 frequency scanning. 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 using efficient adaptive frequency scanning. The method adopts a novel adaptive frequency scanning technology, integrates frequency fitting technology and dichotomy, and can obtain the response results within the frequency band more quickly and accurately, thereby realizing efficient adaptive frequency scanning. Summary of the invention

[0005] An object of the present invention is to provide a broadband electromagnetic simulation method with efficient adaptive frequency scanning 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 is the dielectric constant, μ is the magnetic permeability;

[0008] Step (2): According to the frequency range [f1, f2] set by the antenna, initialize the endpoints and the middle value f of the selected frequency range. min , f mid , fmax As the frequency sampling point, where f min =f1,f mid =(f1+f2) / 2, f max =f2; 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 fitting values ​​corresponding to all frequency points within the frequency range;

[0010] Step (4), determine whether all frequency response fitting values ​​in the current iteration meet the convergence standard, if so, output all frequency response fitting 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 frequency scanning.

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

[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 the 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 convert a nonlinear problem into two linear problems, calculate the precise pole and residue values ​​through iteration, solve the linear equation, obtain the accurate frequency response fitting value, speed up the calculation rate and improve the accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0018] Figure 2 It is a butterfly patch antenna model used for testing in the present invention;

[0019] Figure 3 It is the result of the test of the present invention. DETAILED DESCRIPTION

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

[0021] like Figure 1 An efficient adaptive frequency-sweeping broadband electromagnetic simulation method employs a rational function approximation to fit the measured or computed frequency domain response, which is achieved by a scaling procedure replacing a starting set of poles with a refined set of poles.

[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 is the dielectric constant, μ is the magnetic permeability;

[0024] Step (2): According to the frequency range [f1, f2] set by the antenna, initialize the endpoints and the middle value f of the selected frequency range. min , f mid , f max As the frequency sampling point, where f min =f1,f mid =(f1+f2) / 2, f max =f2; then the moment method is used to solve the electromagnetic field inside the conductor and the corresponding actual value of the frequency response S(f min ), S(f mid ), S(f max );

[0025] The method of moments used to solve the electromagnetic field inside the conductor is specifically as follows:

[0026] 2-1 Use the moment method to solve the electric field inside the conductor:

[0027] The integral equation of the electric field inside a conductor is:

[0028]

[0029] 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;

[0030] 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;

[0031] The definition of the RWG basis function is:

[0032]

[0033] 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;

[0034] The unknown current on the conductor surface can be expanded using the RWG basis function into the following form:

[0035]

[0036] Where I n represents the unknown current expansion coefficient (unknown quantity), and N represents the number of unknown quantities;

[0037] Substituting formula (3) into formula (1) yields:

[0038]

[0039] Where L(f n (r)) represents the RWG basis function f n (r) linear equation;

[0040] Using the RWG basis function as the test function, the electric field integral equation can be tested to obtain:

[0041] where f m (r) represents the mth RWG basis function in the field region;

[0042] Because f m (r) is always tangential to the conductor surface, so it can be rewritten as follows:

[0043]

[0044] Further, formula (6) can be written in matrix form:

[0045] ZI=V Formula (7)

[0046] 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;

[0047] The elements of the mth row and nth column of the matrix Z are expressed as follows:

[0048]

[0049]

[0050] 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;

[0051] Substitute formulas (8)-(9) into the matrix equation (7) 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.

[0052] 2-2 Use the moment method to solve the magnetic field inside the conductor:

[0053] The integral equation of the magnetic field inside the conductor is as follows:

[0054]

[0055] Where K represents a linear operator, H inc represents the incident magnetic field;

[0056] 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:

[0057]

[0058] Written in matrix form: ZI = V;

[0059] Among them, the matrix elements of Z and V are expressed as:

[0060]

[0061]

[0062] 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);

[0063] Substitute formula (12)-(13) 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 theoretical value of the frequency response;

[0064] Step (3), obtaining frequency response fitting values ​​corresponding to all frequency points within the frequency range;

[0065] 3-1 Find an approximate value for a given value by fitting the ratio of two polynomials:

[0066]

[0067] where d1-d N Both represent the coefficients of the numerator polynomial, b1-b N denote the coefficients of the denominator polynomial, Represents the fitted value of the frequency response at frequency f.

[0068] Due to the rational function approximation, formula (14) can be rewritten as:

[0069]

[0070] Where a n represents the extreme point, c n represents the residue, d and h represent linear constants.

[0071] Known residue c n and the extreme point a n Either a real quantity or a complex conjugate pair, and d and h are real quantities. Since the unknown a n Appears in the denominator, which will be a nonlinear problem, so in the process of vector fitting, a n Solve as known poles, and then convert the nonlinear problem into two linear problems;

[0072] 3-2 Simplify formula (15) and solve for the poles and residues; the details are as follows:

[0073] 1) Initialize randomly defined pole estimate values ​​and residue estimate values ​​(1 in this embodiment), and the number of iterations i=1;

[0074]

[0075] Formula (17)

[0076] Simplifying the above formula (16) we get:

[0077]

[0078] Formula (18) can be expressed in the form of Ax=b:

[0079]

[0080] Where x represents the number of frequency sampling points;

[0081] Solving formula (19) yields c1…c N ,d,h,

[0082] 3) constructing a matrix A-BC based on the known pole estimate values ​​and the residue estimate values ​​obtained in step 2); solving the eigenvalues ​​of the matrix A-BC to obtain pole values;

[0083]

[0084] 4) Update the pole estimate value to the pole value obtained in step 2), return to step 2), update the number of iterations i=i+1, until the number of iterations i reaches the maximum number of iterations, and obtain the accurate value of the pole;

[0085] 5) Update iterative residues to obtain more accurate residues;

[0086] The exact value of the pole obtained in step 4) is used as the estimated value of the pole, and formula (15) is rewritten into a matrix form:

[0087]

[0088] Solve to get the exact residue value c1…c N , d, h.

[0089] 6) Substitute the exact value of the poles and the exact value of the residue obtained in steps 4) and 5) and the value obtained by solving formula (21) into formula (15) to obtain the frequency response fitting value.

[0090] Step (4), determine whether all frequency response fitting values ​​in the current iteration meet the convergence standard, if so, output all frequency response fitting values, if not, use the binary search method to add new frequency sampling points, and return to step (2).

[0091] The method of using binary division to add new frequency sampling points specifically divides the frequency range into [f min ,f mid ] and [f mid ,f max], take the endpoints and the middle value of each newly divided frequency range as frequency sampling points, and repeat step (2) to obtain the corresponding frequency response theoretical values ​​of all frequency sampling points;

[0092] The convergence criterion described uses the error formula Where S(f) represents the theoretical value of frequency response, Represents the frequency response fitting value; if err < threshold, convergence is achieved, otherwise convergence is not achieved.

[0093] This example is about Figure 2 The frequency response of the butterfly patch antenna is simulated and analyzed. In practice, the frequency band of 8-12 GHz needs to be analyzed. The traditional analysis method is to calculate at an average interval of 0.1 GHz. The method proposed in the present invention can fit the frequency response of the entire frequency band using fewer frequency sampling points.

[0094] First, the first iteration process selects three sampling points: f min =8GHz,f mid =10GHz,f max =12GHz, through the frequency response S(f min ), S(f mid ), S(f max ).

[0095] Through step 3-2, the pole estimate value is initially set to 1, and a set of solutions is obtained by solving formula (15): c1…c N ,d,h,

[0096] By using the above results and formula (16) to solve the eigenvalue of (A-BC), the eigenvalue is the extreme point

[0097] The more accurate pole value calculated above is used to replace the initial pole estimate value. The calculation is repeated 4-5 times, and the obtained pole accurate value is more accurate.

[0098] Substitute the exact value of the pole calculated above into formula (12);

[0099] Calculate a more accurate c1…c N , d, h.

[0100] In summary, all unknowns have been solved in the first iteration, so any frequency response fitting value can be calculated by formula (6);

[0101] For the frequency band response fitting values ​​calculated above, it is determined whether the error is within the error range. The result of the first iteration in this example is not convergent.

[0102] Therefore, the original frequency band is divided into [f min ,f mid ] and [f mid ,f max ];

[0103] In the second iteration, the frequency point is increased: f1 = (f mid -f min ) / 2, f2=(f max -f mid ) / 2;

[0104] Calculate the responses S(f1) and S(f2) at this frequency point;

[0105] Repeat the above steps. This example converges after three iterations.

[0106] Figure 3 This is the test result of this embodiment.

[0107] 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 frequency scanning, 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 is the dielectric constant, μ is the magnetic permeability; Step (2): According to the frequency range [f1, f2] set by the antenna, initialize the endpoints and the middle value f of the selected frequency range. min , f mid , f max As the frequency sampling point, where f min =f1,f mid =(f1+f2) / 2, f max =f2; 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 ); Step (3), obtaining frequency response fitting values ​​corresponding to all frequency points within the frequency range; 3-1 By fitting the ratio of two polynomials, the frequency response fitting value of frequency f is obtained where d0…d N All represent the coefficients of the numerator polynomial, b0…b N All represent the coefficients of the denominator polynomial; Due to the rational function approximation, formula (14) can be rewritten as: Where a n represents the extreme point, c n represents the residue, d and h represent linear constants; 3-2 Simplify formula (15) and solve for the poles and residues; the details are as follows: 1) Initialize the randomly defined pole estimate and residue estimate, and the number of iterations i = 1; 2) Introduce function σ(f) into formula (15): In the formula represents the extreme point estimate, represents the estimated value of residues; Simplifying the above formula (16) we get: Further, formula (18) is expressed in the form of Ax=b: Where x represents the number of frequency sampling points; Solving formula (19) yields c1…c N ,d,h, 3) constructing a matrix A-BC based on the known pole estimate values ​​and the residue estimate values ​​obtained in step 2); solving the eigenvalues ​​of the matrix A-BC to obtain pole values; 4) Update the pole estimate value to the pole value obtained in step 2), return to step 2), update the number of iterations i=i+1, until the number of iterations i reaches the maximum number of iterations, and obtain the accurate value of the pole; 5) Update the iterative residues to obtain the accurate values ​​of the residues; the details are as follows: The exact value of the pole obtained in step 4) is used as the estimated value of the pole, and formula (15) is rewritten into a matrix form: Solve to obtain the exact residue values ​​c1~c N , d, h; 6) Substitute the pole accurate value and the residue accurate value obtained by solving steps 4) and 5) and d and h obtained by solving formula (21) into formula (15) to obtain the frequency response fitting value; Step (4), determine whether all frequency response fitting values ​​in the current iteration meet the convergence standard, if so, output all frequency response fitting values, if not, use the binary search method to add new frequency sampling points, and return to step (2); The method of moments used in step (2) to solve the electromagnetic field inside the conductor is as follows: 2-1 Use the moment method 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 using the RWG basis function into the following form: Where I n represents the unknown current expansion coefficient, and N represents the unknown quantity; Substituting formula (3) into formula (1) yields: Where L(f n (r)) represents the RWG basis function f n (r) linear equation; Using the RWG basis function as the test function, the electric field integral equation can be tested to obtain: where f m (r) represents the mth RWG basis function in the field region; Because f m (r) is always tangential to the conductor surface, so it can be rewritten as follows: Formula (6) is further written in matrix form: ZI=V Formula (7) 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, (uniform unbounded space), R = |rr′|, 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; Substitute formulas (8)-(9) into the matrix equation (7) 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. 2-2 Use the moment method to solve the magnetic field inside the conductor: The integral equation of the magnetic field inside the conductor is as follows: Where K represents a linear operator, H inc represents the incident magnetic field; Using the RWG basis function as the expansion function and the Galerkin method to test, we get the following: Written in matrix form: 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)-(13) 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 theoretical value of the frequency response.

2. A broadband electromagnetic simulation method using efficient adaptive frequency scanning as claimed in claim 1, characterized in that The use of the binary method to add new frequency sampling points in step (4) specifically divides the frequency range into [f min ,f mid ] and [f mid ,f max ], take the endpoints and the middle value of each newly divided frequency range as the frequency sampling points, and repeat step (2) to obtain the theoretical frequency response values ​​of all frequency sampling points.

3. A broadband electromagnetic simulation method using efficient adaptive frequency scanning as claimed in claim 1, characterized in that The convergence criterion described in step (4) uses the error formula Where S(f) represents the theoretical value of frequency response, Represents the frequency response fitting value; if err < threshold, convergence is achieved, otherwise convergence is not achieved.

4. An electronic device, characterized in that: It comprises 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 frequency scanning as described in any one of claims 1 to 3.

5. A machine-readable storage medium, characterized in that: The machine-readable storage medium stores machine-executable instructions. 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 frequency scanning as described in any one of claims 1-3.

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