A conformal active frequency selective absorbing system with broadband regulation characteristics and a design method

Abstract

The application discloses a conformal active frequency selective wave-absorbing system with broadband regulation characteristics and a design method, and the system comprises a multilayer flexible physical module, an active load regulation unit and a bias feed network. By establishing a generalized impedance matching theory framework based on a curvature factor, the impedance mismatch problem caused by local incident angle deviation of a traditional FSR in a bending state is solved. The system adopts a flexible fabric substrate, integrates PIN diodes to realize dynamic regulation of wave-absorbing rate, and utilizes a metal resonance pattern to construct a "bias-free line" direct current network. By establishing an equivalent circuit model to analyze the relationship between a curvature radius and an impedance trajectory, it is ensured that the system remains stable transmission below 2.8 GHz and realizes wideband wave-absorbing at 4.0-7.5 GHz in a conformal state. The application significantly improves the link stability of a conformal stealth device and is suitable for aerospace vehicle stealth skin and flexible wearable protection.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic metamaterials technology, and in particular to a conformal active frequency-selective absorbing system and its design method with broadband controllability. Background Technology

[0002] Frequency-selective absorbers (FSRs), as electromagnetic functional structures that combine spectrum filtering, broadband absorption, and low-loss transmission, play an irreplaceable role in modern aircraft stealth, electromagnetic compatibility, and electronic warfare. Their core value lies in ensuring the normal operation of friendly communication and radar systems while reducing the radar cross-section (RCS) through precise spectrum manipulation.

[0003] However, in practical engineering applications, existing FSR technologies face serious performance bottlenecks. The first is the conformal failure problem. Traditional FSR design theory is mainly based on a planar infinite array model and normal incidence conditions. However, in real-world scenarios, stealth devices often need to be fitted onto conformal surfaces with complex curvatures, such as aircraft skin, missile nose cones, or wearable devices. Due to surface curvature, plane waves will generate continuously varying local incident angles (θlocal) at different locations on the array. Based on the angle dependence of wave impedance and electrical length, this angular shift leads to severe impedance mismatch, causing a drastic reduction in absorption bandwidth, a significant shift in the transmission window, and a deterioration in absorption rate. Currently, the design of conformal FSRs largely relies on numerical simulations using massive amounts of data and trial-and-error methods, lacking an analytical design framework that can accurately map the relationship between "radius of curvature—local incident angle—impedance trajectory."

[0004] Secondly, there is a contradiction between dynamic control and structure. To adapt to the changing electromagnetic environment, researchers have introduced active components such as PIN diodes to achieve performance switching. However, the resulting complex bias feeding network not only increases the weight and thickness of the physical structure, but more seriously, these auxiliary leads generate strong parasitic scattering, which undermines the low polarization sensitivity and angular stability of the FSR itself. In addition, under extreme bending environments, traditional rigid or semi-rigid PCB substrates are prone to delamination or fracture, leading to the failure of active components. Summary of the Invention

[0005] The purpose of this invention is to provide a conformal active frequency-selective absorbing system and design method with broadband control characteristics, which solves the defects of existing frequency-selective absorbers when applied to conformal surfaces, such as severe impedance mismatch, deterioration of electromagnetic performance, and complex power supply network structure; and solves the problem of spatial heterogeneity of local incident angle caused by surface curvature.

[0006] This invention discloses a conformal active frequency-selective absorption system with broadband controllability, comprising: a multilayer flexible physical module, active load control units, and a bias feed network; wherein, the multilayer flexible physical module includes an active loss layer, a dielectric spacer layer, and a lossless frequency-selective transmission layer sequentially stacked along the electromagnetic wave incident direction; the active loss layer is provided with periodically arrayed active load control units, each of which integrates a variable impedance load element, the impedance of which is controlled by an external bias signal to regulate the system absorption rate; the bias feed network is constructed using the resonant metal pattern on the active loss layer itself. The metal pattern is divided into two electrically isolated polarity zones. The load element is connected across the different polarity zones to form a DC bias circuit. No additional bias leads are set in the system within or between units. The system's geometric topology and electromagnetic response are determined by the generalized impedance matching space model. The generalized impedance matching space model establishes the mapping relationship between the local incident angle and the surface geometry by calculating the spatial variation of the local incident angle caused by conformal bending. It also constructs an overlapping space in the complex impedance plane where the impedance trajectory converges within a preset bending radius. The system input impedance is constrained within the overlapping space to maintain the preset absorption bandwidth and transmission window in the conformal state.

[0007] Furthermore, the generalized impedance matching space model, based on the actual geometric configuration of the system under conformal bending, maps the ratio of spatial displacement to radius of curvature at different locations on the surface to corresponding local incident angle variables. According to transmission line theory, these local incident angle variables are introduced as dynamic compensation factors into the cascaded transmission matrix of the system to represent the free-space wave impedance shift and dielectric layer electrical length shift caused by conformal bending. The formula for the generalized impedance matching space model is as follows:

[0008] ;

[0009] Where A, B, C, and D are the components of the total transmission matrix of the cascaded system; δ = βt' = 2πtcosθ² / λ represents the equivalent electrical phase delay in the gap between the lossy and lossless layers, t is the distance between the two layers, and θ² is the refraction angle in the gap. The wavelength within the interstitial medium; Z0 TE,TM Z represents the characteristic impedance of free space under horizontal and vertical polarization. c TE,TM R represents the characteristic impedance of the gap medium under horizontal and vertical polarization. Y X represents the real part of the equivalent impedance of the lossy layer. Y β represents the imaginary part of the equivalent impedance of the lossy layer; β is the phase constant, t' is the projected length of the distance between the two layers in the direction of electromagnetic wave propagation, and λ is the wavelength; TE represents horizontal polarization, and TM represents vertical polarization.

[0010] Furthermore, the generalized impedance matching space model extracts the set of impedances that satisfy a preset reflection coefficient threshold under different local incident angles within the complex impedance plane, and defines the common intersection region of the impedance sets as the overlapping solution space, as shown in the following formula:

[0011] ;

[0012] Among them, P(R) Y ,X Y ) represents a candidate impedance point in the complex impedance plane; Θ represents the sampling sequence; Ω GIMS This represents the generalized impedance matching space.

[0013] Furthermore, the inherent input impedance trajectory of the active loss layer is confined within the overlapping solution space, ensuring that the impedance point remains within the boundary that satisfies the preset reflection coefficient threshold when the system experiences surface curvature or continuous changes in local incident angle, thus achieving conformal electromagnetic stability without the need for external dynamic compensation.

[0014] Furthermore, the resonant metal pattern employs a cross dipole array; wherein the cross dipole array is symmetrical; the horizontal and vertical metal arms of the cross dipole are defined as the two polarity partitions, respectively; the variable impedance load element is connected across the electrical isolation gap at the intersection of the horizontal and vertical metal arms; the DC bias current is transmitted along the surfaces of the horizontal and vertical metal arms to drive the load element without disrupting the resonant characteristics of the metal pattern at radio frequency.

[0015] Furthermore, in the multilayer flexible physical module, the active loss layer uses a flexible fabric substrate as the bearing base, and the dielectric spacer layer uses a lightweight closed-cell polymer foam material to provide mechanical buffer for the active loss layer and the lossless frequency selective transmission layer in a bending state.

[0016] Furthermore, the variable impedance load element is a PIN diode. When the PIN diode is operating in the first bias state, its equivalent resistance is located in the first impedance range, and the system exhibits a broadband absorption mode. When the PIN diode is operating in the second bias state, its equivalent resistance is located in the second impedance range, and the system switches to a high reflection mode, where the resistance value in the first impedance range is higher than the resistance value in the second impedance range.

[0017] The design method of a conformal active frequency-selective absorbing system with broadband control characteristics, as described in this invention, is implemented using the aforementioned conformal active frequency-selective absorbing system with broadband control characteristics, and includes the following steps:

[0018] Step 1: Based on the target conformal geometric boundary, establish a generalized mapping model between spatial coordinates and local incident angles;

[0019] Step 2: Construct the cascaded equivalent circuit equations and derive the mathematical expression for the generalized impedance matching space;

[0020] Step 3: Set the impedance matching domain in the complex impedance plane, and obtain the globally stable matching overlap domain within the target bending radius range through Boolean intersection operation;

[0021] Step 4: Optimize and constrain the array unit geometric topology parameters of the active loss layer according to the global stable matching overlap domain, and select the working bias curve of the variable impedance load element according to the preset absorption rate control requirements.

[0022] Compared with existing technologies, this invention has the following significant advantages: It utilizes an established analytical equivalent circuit model to define a robust overlapping impedance matching space, and combined with a bias-free integrated architecture, achieves dynamic adjustment of the absorption rate without introducing additional parasitic scattering. The ultimate goal is to provide an electromagnetic functional device that maintains broadband stable absorption, low-loss transmission, and a highly integrated physical structure even under extreme bending conditions (bending radius as small as 130mm), meeting the urgent environmental adaptability requirements of aerospace stealth skins and smart wearable electromagnetic protection. Attached Figure Description

[0023] Figure 1 This is a local spatial "curvature-incident angle" mapping diagram of the present invention; wherein, Figure 1 (a) in the diagram is a local incident model diagram; Figure 1 (b) in the diagram is a TE-polarized electromagnetic wave propagation model. Figure 1 (c) in the figure is a diagram of the propagation model of TM polarized electromagnetic waves; Figure 1 (d) in the diagram is a simplified model of electromagnetic wave propagation in the intermediate layer;

[0024] Figure 2 This is an equivalent circuit model diagram of the double-layer FSR of the present invention;

[0025] Figure 3 This is the generalized impedance matching space diagram calculated according to the present invention; wherein, Figure 3 (a) in the diagram is the real part range diagram under TE mode. Figure 3 (b) in the diagram is the imaginary part range diagram under TE mode. Figure 3 (c) in the diagram represents the real part range in TM mode. Figure 3 (d) in the diagram represents the imaginary part range in TM mode. Detailed Implementation

[0026] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0027] This invention provides a conformal active frequency-selective absorbing system with broadband control characteristics, comprising: a multi-layer flexible physical module, an active load control unit, and a bias feed network; wherein,

[0028] The multilayer flexible physical module includes an active loss layer, a dielectric spacer layer, and a lossless frequency-selective transmission layer stacked sequentially along the electromagnetic wave incident direction. The active loss layer has periodically arrayed active load control units, each integrating a variable impedance load element. The impedance of the load element is controlled by an external bias signal to regulate the system's absorption rate. The active loss layer uses a flexible fabric substrate as its bearing base, and the dielectric spacer layer uses lightweight closed-cell polymer foam material to provide mechanical buffering for the active loss layer and the lossless frequency-selective transmission layer in a bent state. The variable impedance load element is a PIN diode. When the PIN diode operates in a first bias state, its equivalent resistance is within the first impedance range, and the system exhibits a broadband absorption mode. When the PIN diode operates in a second bias state, its equivalent resistance is within the second impedance range, and the system switches to a high reflection mode, where the resistance value in the first impedance range is higher than that in the second impedance range.

[0029] Specifically, the flexible substrate material is Nomex 3A aramid fiber fabric, which serves as the structural carrier. This material possesses excellent flexibility, high-temperature resistance, and chemical stability. Its relative permittivity is between 1.90 and 2.00, preferably 1.94; its loss tangent is less than 0.03, preferably 0.025; and the substrate thickness h is set to 0.5 mm to 0.6 mm.

[0030] Conductive metallic materials: The array cells are fabricated using conductive fabrics with extremely low surface resistance (such as silver fibers or nickel-copper composite fabrics). Their surface resistance RS is between 0.01 Ω / sq and 0.1 Ω / sq, resulting in low DC power consumption in the feed network.

[0031] Air equivalent interlayer: A lightweight closed-cell polymer foam (such as PMI foam or polyethylene foam) is used. Its equivalent dielectric constant should be as close to 1.0 as possible (typically 1.05-1.15), and its thickness d is set to 9 mm to 11 mm, preferably 10 mm, based on the quarter-wavelength matching principle. This layer not only acts as an impedance transformer but also serves as a mechanical buffer layer during bending, protecting the active components from shear stress damage.

[0032] The dielectric layer thickness t = 9-11 mm (preferably 10 mm) is set based on the quarter-wavelength matching principle to achieve impedance transformation of the air equivalent transmission line between the active loss layer and the lossless bottom layer within the operating frequency band. The unit period P = 23-27 mm (preferably 25 mm) is determined based on the free space wavelength (approximately 40-75 mm) corresponding to the operating frequency band (4.0-7.5 GHz). The period is typically less than half the operating wavelength to avoid gate lobes. The PIN diode equivalent resistance range of 80-120 Ω (absorbing mode) and 10-30 Ω (reflection mode) is determined based on the bias current-resistance characteristic curve given in the SMP1307 series PIN diode device datasheet, and verified by ECM simulation that the system impedance point falls within the generalized matching space within this range.

[0033] A bias feeding network is constructed using the resonant metal pattern on the active loss layer. The metal pattern is divided into two electrically isolated polarity zones. Load elements are connected across the different polarity zones to form a DC bias loop. No additional bias leads are set within or between the units. The resonant metal pattern adopts a cross dipole array. The cross dipole array is symmetrical. The horizontal and vertical metal arms of the cross dipole are defined as the two polarity zones. Variable impedance load elements are connected across the electrically isolated gap at the intersection of the horizontal and vertical metal arms. The DC bias current is transmitted along the surfaces of the horizontal and vertical metal arms to drive the load elements without destroying the resonant characteristics of the metal pattern at radio frequency.

[0034] The choice of this structure is based on its excellent polarization insensitivity and the physical space advantage of easily integrating active loads.

[0035] Specifically, the period of each array unit on the flexible fabric substrate is set to P. The cross dipole consists of two orthogonally arranged metal resonant arms, each with a length of l and a width of w. To achieve dynamic impedance control, a finely spaced fracture is provided at the center point of the intersection of the two resonant arms for embedding and mounting the load element (such as an SMP1307 series PIN diode).

[0036] The period P of the array element, the arm length l of the cross dipole, and the width w satisfy a specific scaling ratio to ensure that the impedance mismatch in the absorbing band from 4.0 GHz to 7.5 GHz is less than 5% when the conformal bending radius r is reduced to 130 mm; and that the insertion loss is kept below 1.0 dB in the transmission window below 2.8 GHz.

[0037] The geometric dimensions of the element are optimized using the generalized impedance matching theory described in Part 1. In practical implementation, for the absorbing frequency band from 4.0 GHz to 7.5 GHz, the optimized combination of geometric parameters is as follows: the element period P ranges from 23 mm to 27 mm, preferably 25 mm; the total length l of the resonant arm ranges from 18 mm to 22 mm, preferably 20.5 mm; and the width w of the resonant arm ranges from 0.5 mm to 1.5 mm, preferably 1.0 mm. These parameter selections ensure that the local incident angle θ... local When the angle changes from 0° to 45°, the resonant point offset of the system is controlled within 3%, thereby reducing the input impedance trajectory Z. Y (f) Locked within the generalized matching overlap region of the complex impedance plane.

[0038] The system's geometric topology and electromagnetic response are determined by a generalized impedance matching space model. This model quantifies the spatial variation of the local incident angle caused by conformal curvature, establishes a mapping relationship between the local incident angle and the surface geometry, and constructs an overlapping solution space in the complex impedance plane where the impedance trajectory converges within a preset curvature radius. The system input impedance is constrained within this overlapping solution space to maintain the preset absorption bandwidth and transmission window under conformal conditions. The specific process is as follows:

[0039] To accurately describe the electromagnetic response in the conformal state, this invention constructs a generalized equivalent circuit model that maps "curvature-incident angle-wave impedance". Firstly, as... Figure 1 As shown in (a), the generalized impedance matching space model introduces a local incident angle variable. , The conformal bending radius r of the system and the spatial displacement x of the array element from the central axis satisfy the following geometric mapping relationship: ;

[0040] Figure 1 (b) and Figure 1 Section (c) presents the electromagnetic wave propagation models with incident angle θ under TE and TM polarizations, respectively. First, based on the definition of characteristic impedance, we obtain: ; ; in, For the angle of refraction, The intrinsic impedance of the intermediate layer dielectric: ;in, The intrinsic impedance in free space Let be the relative permittivity of the intermediate layer medium. Using the boundary continuity condition and according to Snell's theorem, we get: ; so: ; Ultimately, the cause was obtained Uneven spatial distribution leads to uneven wave impedance in the intermediate layer The offset pattern: ; ; Figure 1 (d) in the figure gives the angle of incidence as A simplified model of electromagnetic wave propagation in the intermediate layer is obtained based on transmission line theory: ; ; equivalent electrical length of dielectric layer Follow The offset pattern is as follows: ; in Let be the thickness of the intermediate layer. The electromagnetic response of the system is analytically defined using a cascaded ABCD matrix equation: ;

[0041] Based on transmission line theory (TL Theory), this invention simplifies the entire three-layer cascaded system into a two-port equivalent network, such as... Figure 2 As shown. The active loss layer is equivalent to a parallel complex impedance. Z Y = R Y + jX Y The lossless sublayer is equivalent to an inductive load Z in the target absorption frequency band. S = jX S The two layers are separated by a characteristic impedance of Equivalent thickness is The air equivalent transmission line connection.

[0042] Among them, Z Y Z is the equivalent surface impedance of the active loss layer. S Z is the equivalent surface impedance of the lossless frequency-selective transmission layer. c Z represents the characteristic impedance of the intermediate layer. c Both δ and θ are used as θ local The function is used for dynamic compensation calculation to obtain the complex reflection coefficient S under conformal state. 11 :

[0043] ;

[0044] Where A, B, C, and D are the components of the total transmission matrix of the cascaded system; δ = βt' = 2πtcosθ² / λ represents the equivalent electrical phase delay in the gap between the lossy and lossless layers, t is the distance between the two layers, and θ² is the refraction angle in the gap. The wavelength within the interstitial medium; Z0 TE,TM Z represents the characteristic impedance of free space under horizontal and vertical polarization. c TE,TM R represents the characteristic impedance of the gap medium under horizontal and vertical polarization. Y X represents the real part of the equivalent impedance of the lossy layer. Y β represents the imaginary part of the equivalent impedance of the lossy layer; β is the phase constant; t' is the projected length of the distance between the two layers in the direction of electromagnetic wave propagation; and λ is the wavelength.

[0045] Set performance threshold |S 11 | ≤ b (in this example, b = -10 dB), in the complex impedance plane (R Y , X Y The result is obtained by calculation within ) as θ local A series of continuously drifting elliptical trajectories. When θ local The elliptical trajectory of impedance matching at 0°. The local incident angle θ. local ∈[0°, 60°] are sampled at equal intervals to obtain the sampling sequence Θ={θ0, θ1, θ2, ..., θ n In this embodiment, the sampling step size is set to 15°. Numerical calculations are used to generate the solution space Ω(θ) for each sampling angle. i Perform Boolean intersection operation. Its logical criterion is: Let a point P(R) be an integer. Y ,X Y Let Ω be a candidate impedance point in the complex impedance plane. A point is considered to belong to the "generalized impedance matching space" if and only if it simultaneously satisfies the following logical conditions. GIMS :

[0046] ;

[0047] In terms of numerical implementation, a two-dimensional matrix mesh is constructed to pixelate the complex impedance plane. A logical AND operation is performed across angles on each mesh point to remove any point that deviates from the -10dB boundary at a specific angle, thereby extracting the common envelope region at all angles.

[0048] The -10 dB reflection coefficient threshold is a recognized "engineering pass / fail" standard in microwave engineering and antenna design. When the reflection coefficient is below -10 dB, it means that at least 90% of the incident power is absorbed or transmitted, and the reflected power is less than 10%. In the design of frequency selective absorbers (FSRs), -10 dB is widely used as the performance boundary for determining "effective absorption" or "effective transmission." A 15° sampling interval can effectively capture the impedance trajectory's trend with angle changes while ensuring computational efficiency. At this step size, the impedance offset between adjacent angles is small, and the continuous variation can be accurately restored through interpolation. This is a commonly used discretization strategy in electromagnetic simulation to balance accuracy and efficiency.

[0049] The final overlapping region boundary is obtained through the Boolean operations described above. This overlapping region is the "generalized impedance matching space," which characterizes the system's robustness limit to curvature variations. Finally, the Ro of this overlapping region within the target frequency band is extracted. Y and X Y The range of values ​​for this parameter serves as a hard constraint for subsequent optimization of the array element's geometric parameters. The calculated "generalized impedance matching space" is as follows: Figure 3 As shown ( Figure 3 (a) in the diagram is the real part range diagram in TE mode. Figure 3 (b) in the diagram is the imaginary part range diagram under TE mode. Figure 3 (c) in the diagram represents the real part range in TM mode. Figure 3 (d) in the diagram represents the imaginary part range in TM mode. This is achieved by adjusting the structural impedance point Z of the array element. Y (f) Constraints are placed within the intersection region to ensure that the system can withstand large-angle bending (i.e., θ). local Even with dramatic changes, its physical impedance point can still be maintained within the -10dB absorbing boundary, thus achieving conformal electromagnetic stability without the need for external dynamic compensation.

[0050] In implementation, this invention iterates over the aforementioned parameters using a gradient optimization algorithm (such as in an ADS or CST simulation environment). Unlike traditional designs, the objective function of this invention is not a single normal absorption rate, but rather a "conformal stability factor." Its expression is as follows:

[0051] ;

[0052] Among them, F obj The overall objective optimization function is defined by the function name, where a smaller value indicates that the performance is closer to the ideal objective and the stability is higher. w1 and w2 are weighting factors. w1 focuses on achieving the basic performance target, while w2 focuses on conformal stability. f is the operating frequency, ranging from the initial frequency f0. start to cutoff frequency f end A flat(f) is the absorption index of FSR in a flat state; A target This is the preset design target value. n represents the simulated typical bending condition (e.g., selecting two sets of conditions with bending radius R of 130mm and 200mm); A Ri (f) represents the antenna at the radius of curvature R. i Performance indices under conformal bending conditions. By calculating the mean square error of performance under different radii of curvature, a forced optimization algorithm is used to find structural parameters that are insensitive to geometric deformation.

[0053] In this optimization process, weighting factors w1 and w2 are used to balance the dual objectives: w1 prioritizes achieving the required absorption performance under flat conditions, while w2 prioritizes conformal stability under bending conditions. Prioritizing basic performance, by assigning an appropriate weight to w2, the optimization algorithm is forced to find a combination of structural parameters insensitive to geometric deformation. This multi-objective weighted optimization method is a common practice in electromagnetic structure design. The specific values ​​of the weighting factors can be fine-tuned according to actual engineering requirements (such as whether planar performance or bending stability is more important) without affecting the feasibility of the method.

[0054] Specifically, when the system is in the extreme state of a bending radius R = 130 mm, the phase delay caused by curvature is also taken into account in the algorithm. Parasitic capacitance is controlled by adjusting the gap size of the crossed dipole, and inductive reactance is compensated by adjusting the loading shape at the end of the resonant arm. This ensures stable electromagnetic characteristics in both planar and bending states.

[0055] To eliminate parasitic electromagnetic scattering and polarization stability interference caused by additional feed leads in traditional active frequency selective surfaces, this scheme designs and implements an integrated feed architecture based on the resonant pattern of the array unit itself.

[0056] The specific wiring logic and physical implementation methods are as follows:

[0057] Polarity Isolation and DC Path Construction: In the active loss layer, utilizing the geometric symmetry of the cross-dipole unit, the metal arms arranged horizontally in the array are defined as the first DC bias path, and the metal arms arranged vertically are defined as the second DC bias path. Since the cross-dipole has a slot at its physical center for mounting load elements, this solution uses metal vias to bridge the load elements in the vertical bias direction to the reverse side of the unit through inter-layer connections or by utilizing insulating bridging technology. This ensures that the horizontal and vertical paths maintain electromagnetic resonance characteristics in the RF state, but achieve electrical insulation in the DC state.

[0058] Interlayer interconnection and conductive embroidery process: To achieve uniform bias in large-scale arrays (such as 8×8 cell arrays), this solution employs a multilayer wiring scheme. Specifically, a pair of arms of the cross dipole are connected to a DC bus on the back of the substrate via conductive vias on the flexible fabric substrate or using conductive wire embroidery technology. The DC bus is distributed along the edge of the array, thereby forming a parallel / series hybrid power supply loop within the entire 225mm × 225mm effective aperture.

[0059] Parasitic effect elimination mechanism: Since the DC current passes directly through the unit metal itself, there is no need to introduce additional inductive or resistive bias lines outside the unit, thus effectively avoiding secondary reflection and scattering of incident electromagnetic waves by auxiliary lines, ensuring the system's low detection probability (stealth) and polarization purity under wide-angle incident conditions.

[0060] This invention achieves dynamic reconstruction of the overall electromagnetic response of the system by adjusting the bias current of the input feed network, thereby changing the equivalent physical model of the PIN diode. The physical mechanism is as follows:

[0061] Active component model: The PIN diode (preferably SMP1307-011LF) can be equivalent to a controlled real resistance R under DC bias. on With parasitic inductance L on The series model is used. By continuously changing the feed current (0mA to 10mA), the equivalent resistance R... on It can be continuously varied between 10Ω and 500Ω.

[0062] Absorption rate control logic:

[0063] High Absorptive State: When the feed current is adjusted to a preset optimal value (e.g., 1mA per branch, corresponding to R...), on When the impedance is approximately 100Ω, the complex impedance point of the loss layer is exactly close to the geometric center of the "generalized impedance matching space" described in the first part of this scheme. At this point, the incident wave energy undergoes strong ohmic loss in the loss layer, and the absorption rate of the system reaches over 90% in the 4.0 GHz to 7.5 GHz frequency band.

[0064] Reflective State Switching: When the DC current is cut off or adjusted to an extremely low value, the PIN diode enters a high-impedance state (OFF state), equivalent to a very small capacitor. At this time, the impedance of the loss layer shifts drastically, leaving the matching space. The incident wave energy is mainly reflected by the metal array of the loss layer, and the system switches from an "absorber" to a "reflector," realizing dynamic concealment and exposure control of the target's electromagnetic scattering characteristics.

[0065] The equivalent resistance R of a PIN diode on The bias current controls the continuous variation between 10Ω and 500Ω; when R on When the impedance is in the first range of 80Ω-120Ω, the system is in broadband absorption mode, with a peak absorption rate greater than 90%; when R on When the impedance is in the second range of 10Ω-30Ω, the system switches to high reflection mode.

[0066] To further demonstrate the superiority of the present invention and its stability under conformal bending conditions, a comparative experiment was conducted in this embodiment to test the performance of the present invention in planar and bending conditions, and to quantitatively compare it with existing public technologies in terms of conformal adaptability.

[0067] Experimental conditions settings:

[0068] a. Experimental Group A (Plane State): The system is placed flat on the microwave test platform with a bending radius r = ∞.

[0069] b. Experimental Group B (bending conformal state): The same system was tightly attached to a cylindrical air foam support frame with radii r = 200 mm and 130 mm.

[0070] c. Common parameters: In both states, the bias current of the PIN diode is adjusted through the feed network to ensure its equivalent resistance R. on Switching between 10Ω and 500Ω.

[0071] Comparative analysis of absorption frequency band stability:

[0072] The reflection coefficient (S) in the 3-8 GHz frequency band was measured using a vector network analyzer. 11 ):

[0073] a. In the absorbing control mode (R on =100Ω):

[0074] Experimental group A (plane): exhibits broadband absorption characteristics from 4.0 GHz to 7.5 GHz, with a peak absorption rate of 94% and a center frequency of 5.75 GHz.

[0075] Experimental group B (bent): Despite the significant surface curvature and local incident angle θ local Despite changes in location, its absorption frequency band remains between 4.1 GHz and 7.4 GHz, with a peak absorption rate of over 91%.

[0076] b. Comparative Conclusion: The relative frequency shift of the curved state compared to the planar state is only 2.6%, and the absorption rate drops by less than 3%. This proves that the generalized impedance matching theory described in this invention can effectively offset the impedance shift caused by curvature, realizing a "conformal performance-independent" design.

[0077] Comparative analysis of transmission window consistency:

[0078] Performance was tested in the low-frequency transmission band from 2.0 GHz to 3.0 GHz:

[0079] a. Experimental group A (plane): Transmission resonance is generated at 2.8 GHz with an insertion loss of 0.75 dB.

[0080] b. Experimental Group B (Bend): The insertion loss at 2.8 GHz increased only slightly to 0.88 dB, and the overlap of the 1 dB transmission bandwidth exceeded 95%.

[0081] c. Comparative Conclusion: Experimental data shows that the collaborative design between the active lossy layer and the lossless bottom layer of this invention ensures that the communication transparent window has extremely high physical insensitivity to bending deformation.

[0082] Table 1 lists quantitative comparison data between the embodiments of the present invention and the prior art in terms of conformal adaptability:

[0083] Table 1 Comparison of Flexible Conformal FSR Performance

[0084] Single-layer flexible dual-transmission absorber Non-reconfigurable \ 9.6, 13.4 6.4, 14.7;6.6, 11.1,14.7 8.4 Standard ECM Flexible frequency-selective absorber based on metal-graphene hybrid Non-reconfigurable \ 8.3 5.2-5.89;9.9-12.2 11.25 Standard ECM Graphene-based tunable absorber Switchable Additional bias network 12 6-8;17-18 13.33 Standard ECM Flexible transparent ultrawideband low-profile frequency selective absorber Non-reconfigurable \ 2.0-6.2 7.34-10.83 9 Standard ECM All-fabric flexible frequency selective absorber Non-reconfigurable \ 2.5 1.5-2;3-4 \ Standard ECM This invention Switchable No additional bias network 2.7-3.1 4-7.5 5.2 General theory

[0085] In Table 1, the normalized minimum curvature is defined as r / p, where r is the radius of curvature and p represents the period of the element. As shown in Table 1, this invention can support a smaller bending radius while achieving active dynamic control, which means that this invention has stronger surface conformal adaptation capabilities.

[0086] This invention also provides a design method for a conformal active frequency-selective absorbing system with broadband control characteristics, implemented using the aforementioned conformal active frequency-selective absorbing system with broadband control characteristics, comprising the following steps:

[0087] Step 1: Based on the target conformal geometric boundary, establish a generalized mapping model between spatial coordinates and local incident angles;

[0088] Step 2: Construct the cascaded equivalent circuit equations and derive the mathematical expression for the generalized impedance matching space;

[0089] Step 3: Set the impedance matching domain in the complex impedance plane, and obtain the globally stable matching overlap domain within the target bending radius range through Boolean intersection operation;

[0090] Step 4: Optimize and constrain the array unit geometric topology parameters of the active loss layer according to the global stable matching overlap domain, and select the working bias curve of the variable impedance load element according to the preset absorption rate control requirements.

Claims

1. A conformal active frequency-selective absorbing system with broadband modulation characteristics, characterized in that, include: Multi-layer flexible physical modules, active load control units, and bias power supply networks; among them, The multilayer flexible physical module includes an active loss layer, a dielectric spacer layer, and a lossless frequency selective transmission layer stacked sequentially along the electromagnetic wave incident direction. The active loss layer is provided with active load control units arranged in a periodic array. Each active load control unit integrates a variable impedance load element. The impedance of the load element is controlled by an external bias signal to regulate the absorption rate of the system. The bias feed network is constructed by utilizing the resonant metal pattern on the active loss layer. The metal pattern is divided into two electrically isolated polarity partitions. The load element is connected across the different polarity partitions to form a DC bias circuit. No additional bias leads are set in the system within or between units. The system's geometric topology and electromagnetic response are determined by the generalized impedance matching space model. The generalized impedance matching space model establishes the mapping relationship between the local incident angle and the surface geometry by calculating the spatial variation of the local incident angle caused by conformal bending. It also constructs an overlapping space in the complex impedance plane where the impedance trajectory converges within a preset bending radius. The system input impedance is constrained within the overlapping space to maintain the preset absorption bandwidth and transmission window under conformal conditions.

2. The conformal active frequency-selective absorbing system with broadband modulation characteristics according to claim 1, characterized in that, The generalized impedance matching space model is derived from the actual geometry of the system under conformal bending conditions. It maps the ratio of spatial displacement to radius of curvature at different locations on the surface to corresponding local incident angle variables. Based on transmission line theory, these local incident angle variables are introduced as dynamic compensation factors into the cascaded transmission matrix of the system to represent the free-space wave impedance shift and dielectric layer electrical length shift caused by conformal bending. The formula for the generalized impedance matching space model is as follows: ； Where A, B, C, and D are the components of the total transmission matrix of the cascaded system; δ = βt' = 2πtcosθ² / λ represents the equivalent electrical phase delay in the gap between the lossy and lossless layers, t is the distance between the two layers, and θ² is the refraction angle in the gap. The wavelength within the interstitial medium; Z0 TE,TM Z represents the characteristic impedance of free space under horizontal and vertical polarization. c TE,TM The characteristic impedance of the gap medium represents the characteristics of horizontally and vertically polarized dielectrics; R Y X represents the real part of the equivalent impedance of the lossy layer. Y β represents the imaginary part of the equivalent impedance of the lossy layer; β is the phase constant, t' is the projected length of the distance between the two layers in the direction of electromagnetic wave propagation, and λ is the wavelength; TE represents horizontal polarization, and TM represents vertical polarization.

3. A conformal active frequency-selective absorbing system with broadband modulation characteristics according to claim 2, characterized in that, The generalized impedance matching space model extracts the set of impedances that satisfy a preset reflection coefficient threshold under different local incident angles within the complex impedance plane, and defines the common intersection region of the impedance sets as the overlapping solution space, as shown in the following formula: ； Among them, P(R) Y ,X Y ) represents a candidate impedance point in the complex impedance plane; Θ represents the sampling sequence; Ω GIMS This represents the generalized impedance matching space.

4. A conformal active frequency-selective absorbing system with broadband modulation characteristics according to claim 3, characterized in that, The inherent input impedance trajectory of the active loss layer is confined within the overlapping solution space, ensuring that the impedance point remains within the boundary that satisfies the preset reflection coefficient threshold when the system experiences surface curvature or continuous changes in local incident angle.

5. A conformal active frequency-selective absorbing system with broadband controllability according to claim 1, characterized in that, The resonant metal pattern employs a cross dipole array; wherein the cross dipole array is symmetrical; the horizontal and vertical metal arms of the cross dipole are defined as the two polarity partitions, respectively; the variable impedance load element is connected across the electrical isolation gap at the intersection of the horizontal and vertical metal arms; the DC bias current is transmitted along the surfaces of the horizontal and vertical metal arms to drive the load element without disrupting the resonant characteristics of the metal pattern at radio frequency.

6. A conformal active frequency-selective absorbing system with broadband controllability according to claim 1, characterized in that, In the multilayer flexible physical module, the active loss layer uses a flexible fabric substrate as the bearing base, and the dielectric spacer layer uses a lightweight closed-cell polymer foam material to provide mechanical buffer for the active loss layer and the lossless frequency selective transmission layer in a bending state.

7. A conformal active frequency-selective absorbing system with broadband modulation characteristics according to claim 1, characterized in that, The variable impedance load element is a PIN diode. When the PIN diode is operating in the first bias state, its equivalent resistance is located in the first impedance range, and the system exhibits a broadband absorption mode. When the PIN diode is operating in the second bias state, its equivalent resistance is located in the second impedance range, and the system switches to a high reflection mode, where the resistance value in the first impedance range is higher than that in the second impedance range.

8. A design method for a conformal active frequency-selective absorbing system with broadband controllability, implemented using the conformal active frequency-selective absorbing system with broadband controllability as described in any one of claims 1-7, characterized in that, Includes the following steps: Step 1: Based on the target conformal geometric boundary, establish a generalized mapping model between spatial coordinates and local incident angles; Step 2: Construct the cascaded equivalent circuit equations and derive the mathematical expression for the generalized impedance matching space; Step 3: Set the impedance matching domain in the complex impedance plane, and obtain the globally stable matching overlap domain within the target bending radius range through Boolean intersection operation; Step 4: Optimize and constrain the array unit geometric topology parameters of the active loss layer according to the global stable matching overlap domain, and select the working bias curve of the variable impedance load element according to the preset absorption rate control requirements.

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