A method for quadratic response surface optimization of circulator insertion loss
By using Plackett-Burman screening of significant factors and a quadratic response surface surrogate model to optimize circulator insertion loss, the problems of long circulator design cycle and deteriorating insertion loss were solved, achieving fast, low-loss design cycle and optimization effect.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- LANZHOU UNIV
- Filing Date
- 2025-09-29
- Publication Date
- 2026-07-10
AI Technical Summary
Existing circulator designs are large in size and weight, and assembly tolerances and temperature drift are difficult to guarantee. Traditional optimization methods are time-consuming and computationally intensive, making it difficult to meet the needs of rapid iteration. Furthermore, size reduction can easily lead to problems such as deterioration of insertion loss and decrease in isolation.
Plackett-Burman screening of significant factors was adopted to construct a quadratic response surface surrogate model. Rapid optimization was performed with IL minimization as the objective, reducing the number of experiments and computational load, and optimizing the ferrite polarization characteristics. This model is suitable for determining the low-loss process window of self-biased circulators.
Significantly shortens the design cycle, reduces insertion loss, is applicable to self-biased circulators in any band, reduces experimental workload by 70%, achieves verification error of less than 5%, and compresses the design cycle from several weeks to 2-3 days. It is also suitable for the rapid optimization of other ferrite passive devices.
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Figure CN121328089B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of microwave passive device technology, and more specifically to a method for optimizing the secondary response surface of circulator insertion loss. Background Technology
[0002] In microwave and radio frequency front-ends, circulators, as non-reciprocal three-port devices, undertake critical functions such as transmit-receive isolation, power protection, and signal routing, and have been widely used in radar, satellite communications, electronic warfare, and 5G base stations. As systems evolve to higher frequency bands, comprehensive requirements are placed on circulators for miniaturization, low insertion loss, high isolation, and wide bandwidth.
[0003] Traditional circulators often employ external permanent magnet bias structures, resulting in large overall size and weight. Furthermore, assembly tolerances and temperature drift make it difficult to guarantee consistency. In addition, existing designs generally rely on global optimization methods such as genetic algorithms and particle swarm optimization, requiring full-wave simulations for each iteration. This often involves hundreds of sets of experiments, and the design cycle is measured in weeks, making it difficult to meet the needs of rapid iteration.
[0004] To reduce size, the industry has begun to use ferrite sheets with high saturation magnetization in conjunction with self-biased topologies. However, the magnetic parameters of ferrite are strongly coupled with the geometry of the microstrip, and existing empirical formulas cannot provide the optimal solution in one go. If only the size is reduced without simultaneous optimization of materials and structure, problems such as deterioration of insertion loss and decrease in isolation are likely to occur.
[0005] Therefore, there is an urgent need for a rapid optimization method that requires fewer experiments, lowers computational cost, and can fully utilize the polarization characteristics of ferrite. Summary of the Invention
[0006] In view of this, the present invention provides a method for optimizing the second-order response surface of circulator insertion loss. By screening significant factors through Plackett-Burman and constructing a surrogate model of the second-order response surface, the method achieves rapid optimization within the constraint space with the goal of minimizing IL. The total number of experiments is reduced by 70%, the verification error is less than 5%, the design cycle is significantly shortened and the insertion loss is reduced. It is suitable for the accurate determination of the low-loss process window of self-biased circulators in any band.
[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for optimizing the quadratic response surface of circulator insertion loss, comprising:
[0008] Step 1: Obtain the target performance of the circulator, and determine the set of adjustable factors of the circulator based on the target performance;
[0009] Step 2: Use experimental design to screen significant factors from the set of adjustable factors;
[0010] Step 3: Construct a quadratic response surface surrogate model based on significant factors, and train the model with the goal of minimizing insertion loss;
[0011] Step 4: Use the trained model to perform constrained multi-objective optimization to obtain the optimal parameter combination;
[0012] Step 5: After verifying the optimal parameter combination, the output is the final design parameters.
[0013] Preferably, the circulator includes a ferrite disc, a dielectric substrate, a ground plane, and microstrip lines, with the ferrite disc embedded in the dielectric substrate and the microstrip lines distributed on the substrate.
[0014] The set of adjustable factors includes: ferrite saturation magnetization, ferromagnetic resonance linewidth, dielectric constant, ferrite radius, and ferrite thickness.
[0015] Preferably, the process of screening significant factors includes
[0016] The adjustable factor set is initialized, and the Plackett-Burman algorithm is called in the Design-Expert software to automatically generate n sets of low-high level matrices, and the running order is randomized to balance the system error.
[0017] Write n sets of parameters into the HFSS script in sequence, keeping the mesh, boundary, and port settings unchanged, and perform batch simulations to obtain the raw data of insertion loss IL;
[0018] Import the raw insertion loss (IL) data into the ANOVA module to calculate the main effects of the adjustable factor and its p-value.
[0019] Based on the p-value, non-significant factors are eliminated to form a simplified factor set.
[0020] Preferably, the set of simplified factors includes ferromagnetic resonance linewidth, ferrite radius, and thickness.
[0021] Preferably, the process of constructing a quadratic response surface proxy model includes:
[0022] The simplified factor set is divided into three levels: low, medium, and high. The Box-Behnken design method is used to generate m sets of experimental matrices. The experiments are run in batches in HFSS, and the insertion loss IL is recorded as the response.
[0023] Import the experimental data into Design-Expert software, select the quadratic polynomial model, perform analysis of variance, and confirm the model's reliability.
[0024] The output includes the insertion loss surrogate equation containing quadratic and interaction terms, expressed as follows: IL=β0+β1ΔH+β2H+β3R+β4ΔH 2 +β5H2 +β6R 2 +β7ΔH*H+β8ΔH*R+β9H*R where IL represents the insertion loss, β0-β9 are the fitting coefficients, ΔH is the ferromagnetic resonance linewidth, H is the thickness of the ferrite disc, and R is the radius of the ferrite disc.
[0025] Preferably, confirming the reliability of the model requires simultaneously satisfying the Adj-R equation in the effective domain. 2 >0.7, Pred-R 2 With Adj-R 2 A difference < 0.2 and a Lack-of-Fitp > 0.05 indicate that the model has strong explanatory power, reliable prediction, and no significant model mismatch, respectively.
[0026] Preferably, the multi-objective optimization process includes:
[0027] The objective function is to minimize the insertion loss IL, and the range of variables is taken from the effective domain of the quadratic response surface surrogate model.
[0028] Import the range of significant factors into the Design-Expert software, select Numerical optimization, and the software will automatically solve and output the optimal parameter combination and its predicted insertion loss value.
[0029] Preferably, the optimal parameter combination is imported into high-frequency structural simulation software for verification. If the verification error is less than a preset threshold, the output is the final design parameters.
[0030] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for optimizing the quadratic response surface of circulator insertion loss, with the following beneficial effects:
[0031] 1. The design method provided by this invention requires dozens or even hundreds of full-wave simulations for traditional Ka-band circulator optimization. This invention, through Plackett-Burman + Box-Behnken two-stage DOE, completes the key factor locking and secondary response surface construction with only 31 sets of experiments, compressing the overall cycle from several weeks to 2-3 days and reducing the amount of experiments by more than 70%.
[0032] 2. The design method provided by this invention does not depend on specific dimensions or materials. It can be smoothly migrated to Ku, K, Ka and even higher frequency bands by simply replacing the significant factor range, or it can be applied to the rapid optimization of other ferrite passive devices (isolators, phase shifters).
[0033] 3. In the design method of the present invention, the proxy model can be reused multiple times after being trained once, and subsequent size fine-tuning can be completed in milliseconds, avoiding repeated calls to large electromagnetic software. Attached Figure Description
[0034] 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 only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0035] Figure 1 The method flowchart provided by the present invention.
[0036] Figure 2 A structural diagram of a circulator provided in an embodiment of the present invention. Detailed Implementation
[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0038] like Figure 1 As shown, this embodiment of the invention discloses a quadratic response surface optimization method for circulator insertion loss, comprising:
[0039] Step 1: Obtain the target performance of the circulator, and determine the set of adjustable factors of the circulator based on the target performance;
[0040] Step 2: Use experimental design to screen significant factors from the set of adjustable factors;
[0041] Step 3: Construct a quadratic response surface surrogate model based on significant factors, and train the model with the goal of minimizing insertion loss;
[0042] Step 4: Use the trained model to perform constrained multi-objective optimization to obtain the optimal parameter combination;
[0043] Step 5: After verifying the optimal parameter combination, the output is the final design parameters.
[0044] Specifically, the circulator includes a ferrite disc, a dielectric substrate, a ground plane, and microstrip lines. The ferrite disc is embedded in the dielectric substrate, and the microstrip lines are distributed on the substrate.
[0045] The set of adjustable factors includes: ferrite saturation magnetization, ferromagnetic resonance linewidth, dielectric constant, ferrite radius, and ferrite thickness.
[0046] In a specific embodiment of the present invention, such as Figure 2As shown, the circulator used is a single Y-type self-biased Ka-band circulator, which consists of a ferrite disc, a dielectric substrate, a ground plane, and microstrip lines. The ferrite disc is embedded in the dielectric substrate, and the microstrip lines are distributed on the substrate.
[0047] The microstrip circuit is a single Y-junction structure, comprising a central circular junction and three Y-shaped stubs, with the angles between the three stubs being 120°. Each Y-shaped junction consists of two 1 / 4 wavelength matching stubs. The three ports are connected to the second Y-shaped stub, respectively. A circular ferrite sheet (radius 1.15–1.25 mm, thickness 0.77–0.80 mm, 4πMs 3550–3850 G, ΔH 70–110 Oe) is embedded in a two-stage dielectric substrate. The microstrip Y-junction extends symmetrically at 120° to the three ports, with an overall thickness of 0.6 mm. The structure requires no external magnet.
[0048] Furthermore, the ferrite disc has a dielectric constant of 15, a saturation magnetization of 3700 Gs, and a linewidth of 90 Oe.
[0049] Specifically, the process of screening significant factors includes:
[0050] The adjustable factor set is initialized, and the Plackett-Burman algorithm is called in the Design-Expert software to automatically generate n sets of low-high level matrices, and the running order is randomized to balance the system error.
[0051] Write n sets of parameters into the HFSS script in sequence, keeping the mesh, boundary, and port settings unchanged, and perform batch simulations to obtain the raw data of insertion loss IL;
[0052] Import the raw insertion loss (IL) data into the ANOVA module to calculate the main effects of the adjustable factor and its p-value.
[0053] Based on the p-value, non-significant factors are eliminated, resulting in a simplified factor set. (The p-value is a statistical concept, referring to the probability of a more extreme outcome than the observed sample results when the null hypothesis is true. In the scenario used in this embodiment, the p-value = the probability of observing the current (or larger) effect under the assumption that 'the factor has no effect.' That is, the smaller the p-value, the less tenable the null hypothesis, and the more likely the factor is to have an impact on insertion loss, thus it is retained; a large p-value is judged as 'possibly just random fluctuation' and needs to be eliminated. All p-values mentioned in this text have this meaning.)
[0054] In a specific embodiment of the present invention, the experimental matrix is initialized based on the set of adjustable factors output. The Plackett-Burman algorithm is called in the Design-Expert software to automatically generate 8 sets of low-high level matrices and randomize the running order to balance the system error.
[0055] Response data acquisition: Write 8 sets of parameters into the HFSS script in sequence, keeping the mesh, boundary and port settings unchanged, and obtain the raw data of insertion loss IL through batch simulation.
[0056] Significance factor determination: Import the original data into the analysis of variance module, calculate the main effects of each factor and their p-values; based on the p-values, eliminate non-significant factors to form a simplified factor set of ferromagnetic resonance linewidth, ferrite radius and thickness for use in secondary response surface modeling.
[0057] In one approach, the determination of significant factors includes two parts: screening and validation.
[0058] The coarse screening process is as follows: select five factors, namely saturation magnetization, linewidth, dielectric constant, radius, and thickness, and establish eight Plackett-Burman matrices at two levels, low to high; after completing the simulation, calculate the p-value of each factor for insertion loss, and remove the two factors with the largest p-values.
[0059] The verification process is as follows: Eight sets of experiments are regenerated with three significant factors. The remaining two factors retain their central values. The simulation is repeated and the p-values are calculated. When two of the factors have p < 0.1 and one factor has p ≈ 0.4, these three factors are determined to be significant factors, thus completing the final determination of the set of significant factors.
[0060] Specifically, the set of simplified factors includes ferromagnetic resonance linewidth, ferrite radius, and thickness.
[0061] Specifically, the process of constructing a quadratic response surface proxy model includes:
[0062] The simplified factor set is divided into three levels: low, medium, and high. The Box-Behnken design method is used to generate m sets of experimental matrices. The experiments are run in batches in HFSS, and the insertion loss IL is recorded as the response.
[0063] Import the experimental data into Design-Expert software, select the quadratic polynomial model, perform analysis of variance, and confirm the model's reliability.
[0064] The output includes the insertion loss surrogate equation containing quadratic and interaction terms, expressed as follows: IL=β0+β1ΔH+β2H+β3R+β4ΔH 2 +β5H 2 +β6R 2 +β7ΔH*H+β8ΔH*R+β9H*R where IL represents the insertion loss, β0-β9 are the fitting coefficients, ΔH is the ferromagnetic resonance linewidth, H is the thickness of the ferrite disc, and R is the radius of the ferrite disc.
[0065] Specifically, confirming the model's credibility requires simultaneously satisfying the Adj-R equation in the effective domain. 2>0.7, Pred-R 2 With Adj-R 2 A difference < 0.2 and a Lack-of-Fitp > 0.05 indicate that the model has strong explanatory power, reliable prediction, and no significant model mismatch, respectively.
[0066] In a specific embodiment of the present invention, the model is constructed as follows: the significance factor is set to three levels: low, medium and high, and the Box-Behnken design method is called to generate 15 sets of experimental matrices; the model is run in batches in HFSS and the insertion loss IL is recorded as the response.
[0067] Model fitting: Import experimental data into Design-Expert software, select a quadratic polynomial model and perform analysis of variance; validate Adj-R. 2 >0.7: This indicates strong model explanatory power; Pred-R 2 With Adj-R 2 A difference < 0.2 indicates reliable prediction; a Lack-of-Fitp > 0.05 indicates no significant model mismatch. If all three conditions are met, the quadratic response surface is considered valid, confirming the model's reliability.
[0068] Specifically, the multi-objective optimization process includes:
[0069] The objective function is to minimize the insertion loss IL, and the range of variables is taken from the effective domain of the quadratic response surface surrogate model.
[0070] Import the range of significant factors into the Design-Expert software, select Numerical optimization, and the software will automatically solve and output the optimal parameter combination and its predicted insertion loss value.
[0071] Specifically, the optimal parameter combination is imported into high-frequency structural simulation software for verification. If the verification error is less than a preset threshold, the output is the final design parameters.
[0072] In another specific embodiment of the present invention, the obtained optimal parameter combination is written into the HFSS script, while keeping other parameters unchanged, and the simulation is run to extract IL_sim. If the relative error with the predicted value is less than 5%, it is locked as the final design parameter; otherwise, return to step 3 to supplement the experiment.
[0073] In another specific embodiment of the present invention, the device used in this embodiment is a single Y-type self-biased Ka-band circulator: a circular ferrite sheet (radius 1.15–1.25 mm, thickness 0.77–0.80 mm, 4πMs 3550–3850 G, ΔH 70–110 Oe) is embedded in a two-stage dielectric substrate, and the microstrip Y junction extends symmetrically at 120° to the three ports, with an overall thickness of 0.6 mm. The structure does not require an external magnet.
[0074] The experimental procedure for applying the method provided in the embodiments of the present invention is as follows:
[0075] a) Set the significance factors: retain the three factors of radius R, thickness H, and line width ΔH, and take three levels of low-medium-high for each;
[0076] b) Design matrix: Generate 15 sets of experimental points using Box-Behnken;
[0077] c) Simulation: Extracting insertion loss IL at the HFSS25GHz center frequency;
[0078] d) Modeling: Quadratic Response Surface Adj-R 2 =0.986, Pred-R 2 =0.974, Lack-of-Fit p=0.03;
[0079] e) Optimization: The software provides the optimal combination ΔH = 89Oe, H = 0.72mm, R = 0.97mm with one click, and predicts IL = 0.238dB.
[0080] Experimental conclusions
[0081] The HFSS retest IL was 0.245dB with an error of 2.9% < 5%, meeting the constraints of isolation ≥ 20dB and bandwidth ≥ 2.5GHz. The process window was locked in with 15 sets of experiments, and the design cycle was reduced from weeks to 2–3 days, which can be directly promoted.
[0082] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0083] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for optimizing the quadratic response surface of circulator insertion loss, characterized in that, include: Step 1: Obtain the target performance of the circulator, and determine the set of adjustable factors of the circulator based on the target performance; Step 2: Use experimental design to screen significant factors from the set of adjustable factors; Step 3: Construct a quadratic response surface surrogate model based on significant factors, and train the model with the goal of minimizing insertion loss; Step 4: Use the trained model to perform constrained multi-objective optimization to obtain the optimal parameter combination; Step 5: After verifying the optimal parameter combination, the output is the final design parameters; The circulator includes a ferrite disc, a dielectric substrate, a ground plane, and microstrip lines. The ferrite disc is embedded in the dielectric substrate, and the microstrip lines are distributed on the substrate. The set of adjustable factors includes: ferrite saturation magnetization, ferromagnetic resonance linewidth, dielectric constant, ferrite radius, and ferrite thickness. The circulator used is a single Y-type self-biased Ka-band circulator, which consists of a ferrite disc, a dielectric substrate, a ground plane, and microstrip lines. The ferrite disc is embedded in the dielectric substrate, and the microstrip lines are distributed on the substrate. The microstrip circuit is a single Y-junction structure, including a central circular junction and three Y-shaped stubs, with the angle between the three stubs being 120°. Each Y-shaped stub consists of two 1 / 4 wavelength matching stubs, and the three ports are connected to the second Y-shaped stub respectively. A circular ferrite sheet is embedded in a two-stage dielectric substrate, and the microstrip Y-junction extends symmetrically to the three ports at 120° intervals. The overall thickness is 0.6 mm, and the structure does not require an external magnet.
2. The method for optimizing the quadratic response surface of circulator insertion loss according to claim 1, characterized in that, The process of screening significant factors includes The adjustable factor set is initialized, and the Plackett-Burman algorithm is called in the Design-Expert software to automatically generate n sets of low-high level matrices, and the running order is randomized to balance the system error. Write n sets of parameters into the HFSS script in sequence, keeping the mesh, boundary, and port settings unchanged, and perform batch simulations to obtain the raw data of insertion loss IL; Import the raw insertion loss (IL) data into the ANOVA module to calculate the main effects of the adjustable factor and its p-value. Based on the p-value, non-significant factors are eliminated to form a simplified factor set.
3. The method for optimizing the quadratic response surface of circulator insertion loss according to claim 2, characterized in that, The set of simplified factors includes ferromagnetic resonance linewidth, ferrite radius, and thickness.
4. The method for optimizing the quadratic response surface of circulator insertion loss according to claim 3, characterized in that, The process of constructing a quadratic response surface proxy model includes: The simplified factor set is divided into three levels: low, medium, and high. The Box-Behnken design method is used to generate m sets of experimental matrices. The experiments are run in batches in HFSS, and the insertion loss IL is recorded as the response. Import the experimental data into Design-Expert software, select the quadratic polynomial model, perform analysis of variance, and confirm the model's reliability. The output includes the insertion loss surrogate equation containing quadratic and interaction terms, expressed as follows: Where IL represents the insertion loss, β0-β9 are the fitting coefficients, ΔH is the ferromagnetic resonance linewidth, H is the thickness of the ferrite disc, and R is the radius of the ferrite disc.
5. The method for optimizing the quadratic response surface of circulator insertion loss according to claim 4, characterized in that, To confirm the reliability of a model, it is necessary to simultaneously satisfy the following conditions: Adj-R² > 0.7 in the effective domain, the difference between Pred-R² and Adj-R² < 0.2, and Lack-of-Fit p > 0.05; these respectively indicate that the model has strong explanatory power, reliable prediction, and no significant model mismatch.
6. The method for optimizing the quadratic response surface of circulator insertion loss according to claim 5, characterized in that, The multi-objective optimization process includes: The objective function is to minimize the insertion loss IL, and the range of variables is taken from the effective domain of the quadratic response surface surrogate model. Import the range of significant factors into the Design-Expert software, select Numerical optimization, and the software will automatically solve and output the optimal parameter combination and its predicted insertion loss value.
7. The method for optimizing the quadratic response surface of circulator insertion loss according to claim 6, characterized in that, The optimal parameter combination is imported into high-frequency structural simulation software for verification. If the verification error is less than a preset threshold, the output is the final design parameter.