A method for designing a constant-thickness Vivaldi antenna scale model of a dielectric substrate and a method for measuring a low-frequency antenna

Abstract

A method for designing a scaled-down model of a Vivaldi antenna with a constant substrate thickness and a measurement method for low-frequency antennas are disclosed. This method solves the processing limitations of traditional scaled-down models, which prevent some antennas from achieving frequency conversion in engineering using traditional linear scaled-down models. The method includes: designing three Vivaldi antennas for different frequency bands based on antenna principles; processing the three Vivaldi antennas for different frequency bands through curve fitting to obtain the scaled-down relationship between antenna size and frequency; optimizing the scaled-down relationship between antenna size and frequency; and constructing a scaled-down model of the Vivaldi antenna based on the optimized scaled-down relationship. This invention is applied in the field of radar detection.

Description

Technical Field

[0001] This invention relates to the field of testing and design of low-frequency antennas, and more particularly to a method for designing a scaled-down model of a Vivaldi antenna with a constant dielectric substrate thickness. Background Technology

[0002] Monitoring and early warning technologies that primarily rely on surface deformation surveys cannot meet the precision requirements of highly concealed geological hazards such as underground cavities and collapses. Therefore, ground-penetrating radar (GPR), as a non-destructive electromagnetic detection method, has begun to be widely used for the refined detection of potential geological hazards, offering advantages such as high precision, high resolution, and high efficiency.

[0003] When targeting deep dispersive media, the antenna, as a crucial device for transmitting and receiving electromagnetic waves in ground-penetrating radar, ideally operates in the 10-100MHz frequency band. However, conventional far-field testing methods require test distances reaching kilometers, making direct far-field testing difficult. To address the measurement challenges of low-frequency antennas, compact-field far-field measurement methods based on optical reflectors and near-field measurement methods based on mathematical transformations are commonly used. However, both methods cannot avoid errors caused by edge warping. Besides measurement difficulties, low-frequency antenna simulation is limited by mesh generation, resulting in significant rounding errors between the geometric parameters of various parts and the design values, making direct acquisition using methods similar to those used for high-frequency antennas difficult.

[0004] Scaled-down models are based on similarity laws and establish a similarity relationship. Unlike the methods mentioned above, scaled-down models can evaluate low-frequency antennas by studying high-frequency antennas. Based on this relationship, prototype parameter performance can be predicted from the test data of the scaled-down model, enabling the measurement of large-size low-frequency antennas and simplifying the design of low-frequency antennas by working backward from the design of high-frequency antennas. Currently, this method has been applied in fields such as civil engineering, shipbuilding, aerospace, and even agriculture, becoming a fundamental measurement method. However, traditional linear scaled-down models are subject to manufacturing limitations in practical engineering. Taking the Vivaldi antenna as an example, according to the linear scaled-down model, when the frequency of an antenna from 10-100MHz is scaled down to 1-10GHz, the size needs to be reduced to 100 times its original size. However, in practical engineering, the thickness of the substrate for the Vivaldi antenna is limited; too large or too small a substrate will severely affect the antenna's radiation function, making testing impossible. Summary of the Invention

[0005] This invention addresses the manufacturing limitations of traditional scaled-down models, which prevent some antennas from achieving frequency conversions in engineering applications using traditional linear scaled-down models. It proposes a Vivaldi antenna scaled-down model design method with a constant dielectric substrate thickness. The method includes:

[0006] Design three Vivaldi antennas for different frequency bands based on antenna principles;

[0007] The Vivaldi antennas of the three different frequency bands were processed by curve fitting to obtain the scaling relationship between antenna size and frequency;

[0008] Optimize the scaling relationship between the antenna size and frequency;

[0009] A Vivaldi antenna scaling model is constructed based on the optimized scaling relationship between antenna size and frequency.

[0010] Furthermore, a preferred embodiment is provided, wherein the design of three Vivaldi antennas for different frequency bands based on antenna principles includes: designing the antenna exponential slot width, antenna length, circular resonant cavity, and the diameter and angle of the sector terminal.

[0011] Furthermore, a preferred method is provided, in which the Vivaldi antennas of the three different frequency bands are processed by curve fitting to obtain the scaling relationship between antenna size and frequency, including: the scaling relationship of antenna exponential slot width, the scaling relationship of antenna length, the scaling relationship of circular resonant cavity, the scaling relationship of sector terminal diameter, and the scaling relationship of sector terminal angle.

[0012] The scaling relationship of the antenna exponential slot linewidth is as follows:

[0013] w = ax b +cx 2 ,

[0014] w1 = ax b +cx,

[0015] w2 = ax b +cx,

[0016] The antenna length scaling relationship is as follows:

[0017] l = ax b +cx 2 ,

[0018] l1 = ax b +cx,

[0019] l2 = ax b +cx,

[0020] The scaling relationship of the circular resonant cavity is as follows:

[0021] r1 = ae -bx +c,

[0022] The scaling relationship of the diameter of the sector-shaped terminal is as follows:

[0023] r2=ae -bx +c,

[0024] The scaling ratio of the fan-shaped terminal angle is as follows:

[0025] deg = ax b +cx 2 ,

[0026] Where w is the width of the dielectric substrate, w1 is the maximum width of the slot opening, w2 is the minimum width of the slot opening, l is the length of the dielectric substrate, l1 is the length of the exponential curve slot, l2 is the distance from the center of the circular cavity to the edge of the antenna length, r1 is the circular resonant cavity, r2 is the diameter of the fan-shaped terminal, deg is the fan-shaped terminal angle, a, b, and c are all undetermined coefficients, and x is the center frequency of the antenna.

[0027] Furthermore, a preferred method is also provided, wherein optimizing the scaling relationship between the antenna size and frequency includes: filtering various possible relationships obtained by using the sum of squared errors (SSE).

[0028] Furthermore, a preferred embodiment is provided in which the relative bandwidth of the three different frequency bands of the Vivaldi antenna is 85.7%.

[0029] Furthermore, a preferred embodiment is provided in which the dielectric substrate thickness of the three Vivaldi antennas for different frequency bands is 1.6 mm.

[0030] Furthermore, a preferred embodiment is also provided, wherein the method further includes verifying the rationality of the Vivaldi antenna scaling model, including:

[0031] Simulation experiments were conducted on the scaled-down model of the constructed Vivaldi antenna using Vivaldi antennas with center frequencies of 2.1 GHz and 5.25 GHz, respectively, to obtain the bandwidth of the simulated 2.1 GHz and 5.25 GHz Vivaldi antennas.

[0032] The simulated bandwidth was compared with the bandwidth of the scaled-down Vivaldi antenna model.

[0033] Based on the same inventive concept, this invention also provides a measurement method for low-frequency antennas based on a scaled-down Vivaldi antenna model, the method comprising:

[0034] Extend the antenna frequency band to a higher frequency band and obtain a preset high-frequency antenna based on the basic principles of antenna design;

[0035] The dimensional parameters of each part of the proposed low-frequency antenna are obtained by inversion using a nonlinear scaled model.

[0036] Construct a corresponding high-frequency antenna model based on the dimensional parameters and scaled-down model of each part of the low-frequency antenna;

[0037] The performance of the high-frequency antenna model is used to indirectly evaluate the low-frequency antenna to be tested.

[0038] The advantages of this invention are:

[0039] This invention solves the processing limitations of traditional scaled-down models, which prevent some antennas from achieving frequency conversion in engineering using traditional linear scaled-down models due to processing limitations.

[0040] This invention proposes a Vivaldi antenna scaling model design method with a constant dielectric substrate thickness, overcoming the processing limitations of traditional scaling models. Traditional linear scaling models state that when the geometric dimensions of each part of the antenna are enlarged or reduced by a factor of N, its operating frequency also decreases or increases by a factor of N, while its electromagnetic performance remains unchanged within the operating frequency band. However, in practical engineering, due to processing limitations, some antennas cannot achieve frequency conversion through traditional linear scaling models. Taking the Vivaldi antenna as an example, according to the linear scaling model, when an antenna frequency of 10-100MHz is scaled down to 1-10GHz, the size needs to be reduced to 100 times its original size. However, in practical engineering, the thickness of the Vivaldi antenna dielectric substrate is limited; too large or too small a thickness will severely affect the antenna's radiation function. This invention maintains a constant Vivaldi antenna substrate thickness in the scaling model, establishing a qualitative nonlinear scaling model for the Vivaldi antenna where the dielectric substrate thickness does not need to be changed. This ensures that the antenna's electromagnetic performance meets the required qualitative performance indicators when the frequency is scaled. By constructing a scaled-down model of the Vivaldi antenna, frequency conversion can be achieved, and similar antenna designs can be used across multiple frequency bands. This expands the application range of the antenna, making it more versatile. The design method provided by this invention offers a new way to overcome the fabrication limitations of traditional scaled-down models, increasing the design flexibility and applicability of the antenna and helping to meet the needs of applications with different frequency requirements.

[0041] This invention proposes a scaled-down model design method for Vivaldi antennas with a constant dielectric substrate thickness, applicable to the design of low-frequency antennas. Since low-frequency antennas used for underground disaster identification and detection can reach kilometer-scale sizes, their excessive size leads to significant numerical errors when simulated using CST due to mesh generation limitations and rounding estimations when using theoretical calculations. Furthermore, at very low antenna frequencies, electromagnetic wave radiation is easily affected by interference, resulting in poor output stability and unsatisfactory simulation results. This invention solves the problem of difficult low-frequency antenna design by constructing a scaled-down model that allows the dimensions of various parts of the low-frequency antenna to be obtained through the design inversion of the high-frequency antenna.

[0042] This invention proposes a measurement method for low-frequency antennas based on a scaled-down Vivaldi antenna model, applicable to the measurement of low-frequency antennas. Existing antenna measurements often employ conventional far-field measurements. When dealing with low-frequency antennas, this method requires excessively large test distances, making it difficult to construct an ideal test environment. Compact far-field measurement methods based on optical reflectors and near-field measurement methods based on mathematical transformations cannot overcome the errors caused by edge warping due to the large size of low-frequency antennas. The nonlinear scaled-down model proposed in this invention can indirectly evaluate the low-frequency antenna to be tested by testing the performance of the scaled-down high-frequency antenna.

[0043] This invention is applied to the field of radar detection. Attached Figure Description

[0044] Figure 1 This is a flowchart of a Vivaldi antenna scaled-down model design method with constant dielectric substrate thickness as described in Embodiment 1.

[0045] Figure 2 This is a flowchart of a measurement method for a low-frequency antenna based on a scaled-down Vivaldi antenna model, as described in Embodiment 8. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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.

[0047] Implementation Method 1, see [link] Figure 1 This embodiment describes a method for designing a scaled-down model of a Vivaldi antenna with a constant dielectric substrate thickness. The method includes:

[0048] Design three Vivaldi antennas for different frequency bands based on antenna principles;

[0049] The Vivaldi antennas of the three different frequency bands were processed by curve fitting to obtain the scaling relationship between antenna size and frequency;

[0050] Optimize the scaling relationship between the antenna size and frequency;

[0051] A Vivaldi antenna scaling model is constructed based on the optimized scaling relationship between antenna size and frequency.

[0052] The design method provided in this embodiment, based on the working principle of the Vivaldi antenna, designs three Vivaldi antennas for different frequency bands. The Vivaldi antenna is a broadband antenna whose structure is based on a resonator design, enabling it to cover multiple frequency bands. By designing Vivaldi antennas for different frequency bands, frequency switching can be ensured across multiple frequency ranges, improving the antenna's versatility. This helps adapt to the frequency requirements of different applications. The three designed Vivaldi antennas are actually measured or simulated, and then the scaling relationship between antenna size and frequency is determined using curve fitting. These relationships describe how the antenna's geometric parameters change with frequency at different frequency bands. Curve fitting provides a way to describe the relationship between different frequency bands, allowing for a better understanding of the antenna's behavior at different frequencies. This helps establish a scaling model between frequencies. Furthermore, through optimization algorithms and parameter fine-tuning, the scaling relationship is ensured to meet design requirements, including maintaining a constant dielectric substrate thickness. This may require fine-tuning the antenna parameters to adapt the scaling model to actual manufacturing requirements. Optimization ensures the feasibility of the scaling relationship in practical applications. It helps solve problems caused by limitations in dielectric substrate thickness, thereby improving the antenna's manufacturing flexibility. Based on the optimized scaling relationship, a scaling model of the Vivaldi antenna is constructed. This model allows for the design of Vivaldi antennas in different frequency bands without being limited by the thickness of the dielectric substrate.

[0053] The design method provided in this embodiment solves the problem of fabrication limitations inherent in traditional linear scale-down models. By allowing the substrate thickness to remain constant, it improves antenna fabrication flexibility and allows for antenna design at different frequencies. By constructing a scaled-down Vivaldi antenna model, frequency conversion can be achieved, and similar antenna designs can be used across multiple frequency bands. This expands the application range of antennas, making them more versatile. The advantage of the design method provided in this embodiment lies in offering a new way to overcome the fabrication limitations of traditional scaled-down models, increasing antenna design flexibility and applicability, and helping to meet the needs of applications with different frequency requirements.

[0054] Implementation Method 2: This implementation method further defines the Vivaldi antenna scaled-down model design method with constant dielectric substrate thickness described in Implementation Method 1. The step of designing three Vivaldi antennas for different frequency bands based on antenna principles includes: designing the antenna exponential slot width, antenna length, circular resonant cavity, and the diameter and angle of the fan-shaped terminal.

[0055] This implementation optimizes the width of the exponential slot lines, the length of the antenna, the dimensions of the circular resonant cavity, and the diameter and angle of the fan-shaped terminals. These parameter optimizations ensure the Vivaldi antenna exhibits optimal performance within the desired frequency band. This allows the Vivaldi antenna to flexibly adapt to the frequency requirements of different applications, enabling its widespread use in various wireless communication and radar systems, thus improving its versatility. Furthermore, it expands the frequency coverage of the Vivaldi antenna, making it more multifunctional and capable of simultaneously meeting the communication needs of different frequency bands without altering the overall antenna structure.

[0056] The primary objective of this implementation is to optimize specific parameters to enable Vivaldi antennas to exhibit superior performance across different frequency bands while maintaining a constant substrate thickness. This enhances the antenna's versatility and applicability, allowing it to meet the demands of various frequency applications. By adjusting parameters such as the exponential slot linewidth, antenna length, circular resonator, and sector termination, specific frequency band requirements can be satisfied while achieving consistent performance across the entire frequency range. This further advances Vivaldi antenna technology and increases its flexibility in practical applications.

[0057] Implementation Method 3: This implementation method further defines the Vivaldi antenna scaling model design method with constant dielectric substrate thickness described in Implementation Method 2. The Vivaldi antennas of the three different frequency bands are processed by curve fitting to obtain the scaling relationship between antenna size and frequency, including: antenna exponential slot width scaling relationship, antenna length scaling relationship, circular resonant cavity scaling relationship, sector terminal diameter scaling relationship, and sector terminal angle scaling relationship.

[0058] The scaling relationship of the antenna exponential slot linewidth is as follows:

[0059] w = ax b +cx 2 ,

[0060] w1 = ax b +cx,

[0061] w2 = ax b +cx,

[0062] The antenna length scaling relationship is as follows:

[0063] l = ax b +cx 2 ,

[0064] l1 = ax b +cx,

[0065] l2 = ax b +cx,

[0066] The scaling relationship of the circular resonant cavity is as follows:

[0067] r1 = ae -bx +c,

[0068] The scaling relationship of the diameter of the sector-shaped terminal is as follows:

[0069] r2=ae -bx +c,

[0070] The scaling ratio of the fan-shaped terminal angle is as follows:

[0071] deg = ax b +cx 2 ,

[0072] Where w is the width of the dielectric substrate, w1 is the maximum width of the slot opening, w2 is the minimum width of the slot opening, l is the length of the dielectric substrate, l1 is the length of the exponential curve slot, l2 is the distance from the center of the circular cavity to the edge of the antenna length, r1 is the circular resonant cavity, r2 is the diameter of the fan-shaped terminal, deg is the fan-shaped terminal angle, a, b, and c are all undetermined coefficients, and x is the center frequency of the antenna.

[0073] This implementation method achieves better Vivaldi antenna performance through curve fitting and parameter scaling, ensuring excellent radiation characteristics and frequency response across different frequency bands. This approach allows the Vivaldi antenna to adapt to the needs of different frequency bands, thereby improving its versatility. The parameter scaling relationship of the antenna enables it to flexibly adapt to various applications. By obtaining the parameter scaling relationship, the frequency coverage range of the Vivaldi antenna can be expanded, thus meeting the needs of multi-band or broadband applications.

[0074] Implementation Method 4: This implementation method further defines the Vivaldi antenna scaling model design method with constant dielectric substrate thickness described in Implementation Method 1. The optimization of the scaling relationship between the antenna size and frequency includes: screening various possible relationships obtained by using the sum of squared errors (SSE).

[0075] This implementation uses SSE (Search-Screen Optimization) to screen different scaled-down formulas to determine the optimal formula that best suits the actual performance requirements. This helps to obtain an optimal Vivaldi antenna design to meet the performance requirements of a specific frequency band. The use of SSE helps to reduce the error between the design and actual performance because it takes into account the difference between the fitted curve and the actual data. This can improve the performance accuracy of the Vivaldi antenna.

[0076] Implementation Method 5: This implementation method further defines the Vivaldi antenna scaled-down model design method with constant dielectric substrate thickness described in Implementation Method 1. The relative bandwidth of the three different frequency bands of the Vivaldi antenna is 85.7%.

[0077] In this embodiment, relative bandwidth refers to the ratio of the antenna's bandwidth to its center frequency. In this case, a relative bandwidth of 85.7% means that the bandwidth of each antenna occupies 85.7% of its center frequency.

[0078] This implementation ensures similar bandgap performance across three different frequency bands by limiting the relative bandwidth of the Vivaldi antennas to 85.7%. This means they can provide broadband performance across multiple frequency bands, which is very useful for applications requiring coverage of multiple bands. Limiting the relative bandwidth simplifies the antenna design process because designers do not need to adjust antennas for different frequency bands to meet varying bandwidth requirements. This reduces design complexity and cost.

[0079] Implementation Method Six: This implementation method further defines the Vivaldi antenna scaled-down model design method with constant dielectric substrate thickness described in Implementation Method One. The dielectric substrate thickness of the three Vivaldi antennas with different frequency bands is 1.6 mm.

[0080] This embodiment ensures that the same substrate thickness is used for all three Vivaldi antennas operating at different frequency bands by limiting the substrate thickness to 1.6 mm. This contributes to consistent performance, especially across different frequency bands. Using the same substrate thickness simplifies the manufacturing process, as it eliminates the need to switch between different substrates for antennas operating at different frequency bands. Furthermore, other parameters can be focused on during design and tuning, as the substrate thickness is fixed. The substrate thickness refers to the thickness of the supporting material for the Vivaldi antenna, typically measured in millimeters. This parameter affects antenna performance, particularly across different frequency bands.

[0081] Implementation Method Seven: This implementation method further defines the Vivaldi antenna scale-down model design method with constant dielectric substrate thickness described in Implementation Method One. The method also includes verifying the rationality of the Vivaldi antenna scale-down model, including:

[0082] Simulation experiments were conducted on the scaled-down model of the constructed Vivaldi antenna using Vivaldi antennas with center frequencies of 2.1 GHz and 5.25 GHz, respectively, to obtain the bandwidth of the simulated 2.1 GHz and 5.25 GHz Vivaldi antennas.

[0083] The simulated bandwidth was compared with the bandwidth of the scaled-down Vivaldi antenna model.

[0084] This implementation verifies the accuracy of the model by simulating actual antennas (2.1 GHz and 5.25 GHz Vivaldi antennas) and then comparing the results with the model. This helps confirm whether the scaled-down model can reliably predict the performance of Vivaldi antennas at different frequency bands. By comparing the bandwidth of the model with that of the actual antennas, the performance prediction capability of the model can be evaluated. This is crucial for understanding the expected performance of the antenna during the design phase.

[0085] Implementation Method 8: A measurement method for a low-frequency antenna based on a scaled-down Vivaldi antenna model, the method comprising:

[0086] Extend the antenna frequency band to a higher frequency band and obtain a preset high-frequency antenna based on the basic principles of antenna design;

[0087] The dimensional parameters of each part of the proposed low-frequency antenna are obtained by inversion using a nonlinear scaled model.

[0088] Construct a corresponding high-frequency antenna model based on the dimensional parameters and scaled-down model of each part of the low-frequency antenna;

[0089] The performance of the high-frequency antenna model is used to indirectly evaluate the low-frequency antenna to be tested.

[0090] The measurement method provided in this embodiment overcomes the limitations of measurement distance. Traditional far-field measurement methods require large-distance test environments when dealing with low-frequency antennas, which are expensive and difficult to construct. This method indirectly evaluates the performance of low-frequency antennas to the high-frequency range through a scaled-down model, reducing the dependence on large test distances. Existing methods based on optical reflection and mathematical transformation may introduce errors when dealing with low-frequency antennas due to edge warping caused by their large size. This embodiment uses a scaled-down model, which can more accurately estimate the performance of low-frequency antennas and reduce errors. Furthermore, traditional methods require complex measurements and analyses in the far field, while this method can perform performance testing in the high-frequency range, saving time and resources.

[0091] The primary objective of the method provided in this embodiment is to overcome the challenges of low-frequency antenna measurement by indirectly evaluating the performance of low-frequency antennas using a scaled-down model. This allows designers to more easily evaluate and optimize low-frequency antennas without having to deal with far-field measurement issues. By conducting performance testing in the high-frequency range, errors associated with larger low-frequency antennas can be reduced, as the high-frequency range is generally unaffected by edge effects.

[0092] Implementation Method Nine: This implementation method provides a specific embodiment of the Vivaldi antenna scale-down model design method with constant dielectric substrate thickness described in Implementation Method One, and also serves to explain Implementation Methods Two through Nine. Specifically:

[0093] This invention addresses the testing and design of low-frequency antennas by proposing a nonlinear scaling model for a Vivaldi antenna with a constant dielectric substrate thickness. For example... Figure 1 As shown, based on antenna design theory, three Vivaldi antennas with impedance matching performance meeting the requirements of ultra-wideband were first designed. Based on the obtained antennas, the scaling relationship of each local size was obtained by curve fitting. Two antennas with different center frequencies than the original were selected to simulate and verify the scaling relationship. Finally, the feasibility of the scaling model in engineering was verified by physical testing.

[0094] In the design process of the Vivaldi antenna, based on the antenna principle, the theoretical values ​​of the antenna exponential slot linewidth, antenna length, circular resonant cavity and sector terminal diameter can be obtained. Then, combined with design experience, the parameters are continuously optimized during the simulation process to obtain the final dimensions of each part of the three antennas. In particular, considering that the present invention is based on overcoming the processing limitations of traditional scaled-down models, the thickness of the antenna dielectric substrate is kept at 1.6mm.

[0095] Based on three simulated antennas with a relative bandwidth of 85.7% and satisfactory impedance matching performance, the antenna frequency was used as the independent variable and the size as the dependent variable. The size-frequency scaling relationships of each part of the Vivaldi antenna with a constant substrate thickness were obtained through curve fitting. Simultaneously, to obtain a better model, the various possible relationships were screened using the sum of squared errors (SSE). The smaller the SSE, the better the fitting effect. The scaling relationships of the important geometric parameters of the antenna are shown in Table 1. Where deg is the fan-shaped terminal angle, r1 and r2 are the resonant cavity and fan-shaped terminal diameters, a is the slot curvature, l-l2 are the antenna length and slot length, and w-w2 are the antenna width and slot opening width.

[0096] Table 1. Scaling Relationships of Various Components of the Vivaldi Antenna

[0097]

[0098]

[0099] Among them, deg, a, l, l1, l2, w, w1, w2 have a power function relationship, and r1, r2 have an exponential relationship. In addition, the scaling relationship between l and w, which characterize the overall size of the antenna, is the same, and the fitted forms of l1, l2, w1, w2, which characterize the length and width of different segments of the slot are the same.

[0100] To verify the rationality of the established scaling model, Vivaldi antennas with center frequencies of 2.1 GHz and 5.25 GHz were selected for simulation verification. The dimensional parameters of the two frequency antennas were calculated using the scaling formulas in Table 1. Except for the geometric parameters obtained by fitting, all other geometric parameters adopted the traditional linear scaling relationship. Simulation results show that the impedance bandwidth of the two antennas is consistent with the original three antennas, all at 85.7%, proving that the scaling model can qualitatively achieve the expected electromagnetic performance when the antenna size is scaled up by frequency.

[0101] To verify the feasibility of the Vivaldi antenna nonlinear scaling model in engineering, physical tests were conducted on the five antennas mentioned above. The test results showed that, except for the 0.8-2 GHz range, the other antennas matched the simulation results well within the range of the vector network analyzer (0-7 GHz). The actual operating impedance bandwidth of 75.9% in the 0.8-2 GHz range differed from the simulation result by 9.8%. Analysis suggests that this difference is due to the antenna's overall size of 333mm*300mm, which is much larger than the antenna thickness, resulting in edge warping and substrate bending. This is attributed to manufacturing errors and also demonstrates the measurement difficulties associated with large-size antennas in practical engineering.

[0102] The scaled-down model constructed in this embodiment can assist in the design and measurement of low-frequency large-size antennas. When designing a low-frequency antenna, the antenna frequency band can be extended to the high-frequency band first. Based on the basic principles of antenna design, a high-frequency band antenna that meets the ideal requirements can be obtained. Then, the nonlinear scaled-down model is used to invert and obtain the dimensional parameters of each part of the low-frequency antenna to be designed. When measuring a low-frequency antenna, this nonlinear scaled-down model and the traditional linear scaled-down model can be combined. Based on the dimensions of the low-frequency antenna, the corresponding high-frequency band antenna model can be obtained based on the scaled-down model. Far-field tests can be performed on the high-frequency band antenna to evaluate the performance of the low-frequency antenna, such as return loss.

[0103] This embodiment proposes a Vivaldi antenna scaling model design method with a constant dielectric substrate thickness, overcoming the processing limitations of traditional scaling models. Traditional linear scaling models state that when the geometric dimensions of each part of the antenna are enlarged or reduced by a factor of N, its operating frequency also decreases or increases by a factor of N, while its electromagnetic performance remains unchanged within the operating frequency band. However, in practical engineering, due to processing limitations, some antennas cannot achieve frequency conversion through traditional linear scaling models. Taking the Vivaldi antenna as an example, according to the linear scaling model, when an antenna frequency of 10-100MHz is scaled down to 1-10GHz, the size needs to be reduced to 100 times its original size. However, in practical engineering, the thickness of the Vivaldi antenna dielectric substrate is limited; too large or too small a thickness will severely affect the antenna's radiation function. This embodiment maintains a constant Vivaldi antenna substrate thickness in the scaling model, establishing a qualitative nonlinear scaling model for the Vivaldi antenna where the dielectric substrate thickness does not need to be changed. This ensures that the antenna's electromagnetic performance meets the required qualitative performance indicators when the frequency is scaled.

[0104] This embodiment proposes a scaled-down model design method for Vivaldi antennas with a constant dielectric substrate thickness, applicable to low-frequency antenna design. Since low-frequency antennas used for underground disaster identification and detection can reach kilometer-scale sizes, their excessive size leads to significant numerical errors when simulated using CST due to mesh generation limitations and rounding estimations when using theoretical calculations. Furthermore, at very low antenna frequencies, electromagnetic wave radiation is susceptible to interference, resulting in poor output stability and unsatisfactory simulation results. This embodiment addresses the challenge of low-frequency antenna design by constructing a scaled-down model, which allows for the inversion of low-frequency antenna design dimensions to the low-frequency antenna, thus resolving the design difficulties associated with low-frequency antennas.

[0105] Based on the same inventive concept, this embodiment proposes a measurement method for low-frequency antennas based on a scaled-down Vivaldi antenna model, applicable to the measurement of low-frequency antennas. Existing antenna measurements mostly employ conventional far-field measurements. When dealing with low-frequency antennas, this method requires excessively large test distances, making it difficult to construct an ideal test environment. Compacted-field far-field measurement methods based on optical reflectors and near-field measurement methods based on mathematical transformations cannot overcome the errors caused by edge warping due to the large size of low-frequency antennas. The nonlinear scaled-down model proposed in this embodiment can indirectly evaluate the low-frequency antenna to be tested by testing the performance of the scaled-down high-frequency antenna.

[0106] The technical solutions provided by the present invention have been described in further detail above with reference to the accompanying drawings in order to highlight their advantages and benefits, and are not intended to limit the present invention. Any modifications, combinations, improvements and equivalent substitutions of the present invention based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for designing a scaled-down model of a Vivaldi antenna with a constant dielectric substrate thickness, characterized in that, The method includes: Design three Vivaldi antennas for different frequency bands based on antenna principles; The Vivaldi antennas of the three different frequency bands were processed by curve fitting to obtain the scaling relationship between antenna size and frequency; Optimize the scaling relationship between the antenna size and frequency; A scaled-down model of the Vivaldi antenna is constructed based on the optimized scaling relationship between antenna size and frequency. The design of three Vivaldi antennas for different frequency bands based on antenna principles includes: designing the antenna's exponential slot width, antenna length, circular resonant cavity, and the diameter and angle of the sector terminal; The Vivaldi antennas of the three different frequency bands are processed by curve fitting to obtain the scaling relationship between antenna size and frequency, including: the scaling relationship of antenna exponential slot width, the scaling relationship of antenna length, the scaling relationship of circular resonant cavity, the scaling relationship of sector terminal diameter, and the scaling relationship of sector terminal angle. The scaling relationship of the antenna exponential slot linewidth is as follows: w= ， w1= ， w2= ， The antenna length scaling relationship is as follows: l= ， l1= ， l2= ， The scaling relationship of the circular resonant cavity is as follows: r1= ， The scaling relationship of the diameter of the sector-shaped terminal is as follows: r2= ， The scaling ratio of the fan-shaped terminal angle is as follows: you= , Where w is the width of the dielectric substrate, w1 is the maximum width of the slot opening, w2 is the minimum width of the slot opening, l is the length of the dielectric substrate, l1 is the length of the exponential curve slot, l2 is the distance from the center of the circular cavity to the edge of the antenna length, r1 is the circular resonant cavity, r2 is the diameter of the fan-shaped termination, and deg is the fan-shaped termination angle. , , All are undetermined coefficients. x The center frequency of the antenna; The optimization of the scaling relationship between the antenna size and frequency includes: filtering the various possible relationships obtained by using the sum of squared errors (SSE).

2. The method for designing a scaled-down model of a Vivaldi antenna with a constant dielectric substrate thickness according to claim 1, characterized in that, The relative bandwidth of the three different frequency bands of the Vivaldi antenna is 85.7%.

3. The method for designing a scaled-down model of a Vivaldi antenna with a constant dielectric substrate thickness according to claim 1, characterized in that, The dielectric substrate thickness of the three Vivaldi antennas in different frequency bands is 1.6 mm.

4. The method for designing a scaled-down model of a Vivaldi antenna with a constant dielectric substrate thickness according to claim 1, characterized in that, The method also includes verifying the rationality of the Vivaldi antenna scaling model, including: Simulation experiments were conducted on the scaled-down model of the constructed Vivaldi antenna using Vivaldi antennas with center frequencies of 2.1 GHz and 5.25 GHz, respectively, to obtain the bandwidth of the simulated 2.1 GHz and 5.25 GHz Vivaldi antennas. The simulated bandwidth was compared with the bandwidth of the scaled-down Vivaldi antenna model.

5. A measurement method for low-frequency antennas based on a scaled-down Vivaldi antenna model, characterized in that, The method includes: Extend the antenna frequency band to a higher frequency band and obtain a preset high-frequency antenna based on the basic principles of antenna design; The dimensional parameters of each part of the proposed low-frequency antenna are obtained by inversion using a nonlinear scaling model; the nonlinear scaling model is implemented based on the Vivaldi antenna scaling model design method described in claim 1. Construct a corresponding high-frequency antenna model based on the dimensional parameters and scaled-down model of each part of the low-frequency antenna; The performance of the high-frequency antenna model is used to indirectly evaluate the low-frequency antenna to be tested.

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